15 cm sFH 36, History
In 1935 the army drafted a requirement for a lightened version of the 15 cm schwere Feldhaubitze 18 which could be towed by a single horse team in one piece. After testing in 1938 a design from Rheinmetall was selected to meet the requirement. The new design consisted of a shortened sFH 18 barrel with a prominent muzzle brake with four rows of 13 baffles and a split trail carriage made largely of light alloys.


15 cm sFH 36, History
The carriage had two pressed steel wheels with solid rubber tires and for travel the barrel could be disconnected from the hydro-pneumatic recoil system and pulled back to lie on top of the closed trails for towing. A limber with a tow bar was provided for the horse team for towing. The sFH 36 used the same separate loading cased charges and projectile as the sFH 18 and it used the same sliding-block breech as the sFH 18.


15 cm sFH 36, History
However, the sFH 36 used up to 7 bagged charges to vary velocity and range, while the sFH 18 used up to 8. Production of the sFH 36 ceased in 1942 due to increased mechanization of the army, limited supplies of light alloys and the prioritization of their use for aircraft production.


15 cm sFH 93
The 15 cm sFH 93 was a German howitzer which served in a number of colonial conflicts, the Balkan Wars and World War I.


15 cm sFH 93, History
The 15 cm sFH 93 was designed and built by Krupp and entered service in 1893. The sFH 93 was designed with the lessons of the Franco-Prussian and Russo-Turkish war in mind where field guns with smaller shells and limited elevation had difficulty overcoming fortifications. What was needed was a howitzer capable of high-angle fire which could fire a large shell to drop inside the walls of enemy fortifications. The sFH 93 was fairly conventional for its time and most nations had similar guns. However, its lack of recoil mechanism made it dated and by the time the First World War broke out it had been largely replaced.


15 cm sFH 93, History
The majority of military planners before the First World War were wedded to the concept of fighting an offensive war of rapid maneuver which in a time before mechanization meant a focus on cavalry and light horse artillery firing shrapnel shells. Although the majority of combatants had heavy field artillery prior to the outbreak of the First World War, none had adequate numbers of heavy guns in service, nor had they foreseen the growing importance of heavy artillery once the Western Front stagnated and trench warfare set in.


15 cm sFH 93, History
The theorists hadn't foreseen that trenches, barbed wire, and machine guns had robbed them of the mobility they had been counting on and like in the Franco-Prussian and Russo-Turkish war the need for high-angle heavy artillery reasserted itself. Since aircraft of the period were not yet capable of carrying large diameter bombs the burden of delivering heavy firepower fell on the artillery. The combatants scrambled to find anything that could fire a heavy shell and that meant emptying the fortresses and scouring the depots for guns held in reserve. It also meant converting coastal artillery and naval guns to siege guns by either giving them simple field carriages or mounting the larger pieces on rail carriages.


15 cm sFH 93, History
Although largely replaced by the German Army before the First World War the sFH 93 was brought back into service because of a combination of higher than expected losses of field artillery and insufficient numbers of heavy guns which led to them being brought out of reserve and issued as replacements to field artillery regiments.


15 cm sFH 93, Design
The sFH 93 was a short barreled breech-loading cannon on a rigid two-wheeled box trail carriage. The barrel was a typical built-up gun of the period with all steel construction. The gun had an early form of horizontal sliding-block breech and it fired separate-loading, bagged charges and projectiles. The sFH 93 fired a wide variety of different projectiles which are listed . The advantage the sFH 93 had over its predecessors was that it was made from nickel-steel of much greater strength than previous guns of cast iron construction.


15 cm sFH 93, Design
This meant that the sFH 93 could be much smaller in diameter and lighter in weight than its predecessors which meant it was easier for it to keep pace with infantry divisions on the march. It also meant that unlike previous guns it could be transported in one piece and was light enough to be part of maneuvering forces to overcome local strong points rather than relegated to the slower siege train. However, the cavalry still felt the sFH 93 was too heavy for their use so they were assigned to heavy howitzer battalions of the infantry. For travel, the gun could be attached to a limber and towed by a six-horse team and each battery consisted of four guns with four batteries per battalion.


15 cm sFH 93, Design
Like many of its contemporaries, its carriage did not have a recoil mechanism. For prolonged use a spot of ground could be leveled and a wooden firing platform could be laid for the guns. The guns could then be connected to an external recoil mechanism which connected to a steel eye on the firing platform and a hook on the carriage between the wheels.


15 cm sFH 93, Design
A set of wooden ramps were then placed behind the wheels and when the gun fired the wheels rolled up the ramp and was returned to position by the combined effect of the recoil mechanism and gravity. In the field only ramps were used. There was also no traversing mechanism and the gun had to be levered into position to aim. A drawback of this system was the gun had to be re-aimed each time which lowered the rate of fire.


15 cm sFH 93, Photo Gallery
A Dutch sFH 93 during the Balinese Intervention of 1906.


15 cm sFH 93, Photo Gallery
A captured sFH 93 at the National World War I Museum in Kansas City, MO.


15 cm sIG 33
The 15 cm sIG 33 (schweres Infanterie Geschütz 33, lit. "Heavy Infantry Gun") was the standard German heavy infantry gun used in the Second World War. It was the largest weapon ever classified as an infantry gun by any nation.


15 cm sIG 33
Its weight made it difficult to use in the field, and the gun was increasingly adapted to various ad hoc mobile mountings. These were generically referred to as the SIG 33.


15 cm sIG 33, Development
Sources differ on the development history, but the gun itself was of conventional design. Early production models were horse-drawn, with wooden wheels. Later production models had pressed steel wheels, with solid rubber tires and air brakes for motor towing, albeit at a low speed (only carriages with pneumatic tires and suspension system could be towed at highway speeds). As with most German artillery carriages, the solid rubber tires and lack of springing meant that the gun could not safely be towed above 10 mph, and horse-drawing was still extensively employed.


15 cm sIG 33, Development
The sIG 33 was rather heavy for its mission, and it was redesigned in the late 1930s to incorporate light alloys. This saved about 150 kilograms (330 lb), but the outbreak of war forced the return to the original design before more than a few hundred were made, as the Luftwaffe had a higher priority for light alloys. A new carriage, made entirely of light alloys, was tested around 1939, but was not accepted for service.


15 cm sIG 33, Ammunition
Most of the shells used by the sIG 33 were unexceptional in design, but the Stielgranate 42 was different in fundamental ways from ordinary shells. The driving rod was loaded into the muzzle so that the finned projectile remained in front of, and outside, the barrel entirely. A special charge was loaded and would propel the projectile about 1,000 metres (1,100 yd). At about 150 metres (160 yd) distance, the driving rod would separate from the projectile. Unlike other Stielgranaten, this version was not intended for anti-tank use, but rather for the demolition of strongpoints and clearing barbed-wire obstacles and minefields by blast effect.


15 cm sIG 33 (Sf) auf Panzerkampfwagen I Ausf B
The 15 cm sIG 33 (Sf) auf Panzerkampfwagen I Ausf B, sometimes referred to (unofficially) as the Sturmpanzer I Bison  was a German self-propelled gun used during World War II.


15 cm sIG 33 (Sf) auf Panzerkampfwagen I Ausf B, Development and history
The Invasion of Poland had shown that the towed sIG 33 guns assigned to the infantry gun companies of the motorized infantry regiments had difficulties keeping up with the tanks during combat. The easiest solution was to modify a spare tank chassis to carry it into battle. A sIG 33 was mounted on the chassis of the Panzer I Ausf. B, complete with carriage and wheels, in place of the turret and superstructure. Plates 13 millimetres (0.51 in) thick were used to form a tall, open-topped fighting compartment on the forward part of the hull. This protected little more than the gun and the gunner himself from small arms fire and shell fragments, the loaders being completely exposed. The rearmost section of armor was hinged to ease reloading.


15 cm sIG 33 (Sf) auf Panzerkampfwagen I Ausf B, Development and history
There was no room to stow any ammunition, so it had to be carried by a separate vehicle. When mounted, the sIG 33 had a total traverse of 25° and could elevate from -4° to +75°. The gun used an Rblf36 sight. The chassis was overloaded and breakdowns were frequent. The vehicle's extreme height and lack of on-board ammunition were severe tactical drawbacks.


15 cm sIG 33 (Sf) auf Panzerkampfwagen I Ausf B, Combat use
Thirty-six vehicles were organized into independent schwere Infanteriegeschütz-Kompanie (mot.S.) ("self-propelled heavy infantry gun companies") numbers 701–706, assigned to Panzer divisions in the Battle of France as follows:


15 cm sIG 33 (Sf) auf Panzerkampfwagen I Ausf B, Combat use
As part of the 5th Panzer Division, assigned to the German XIVth Motorized Army Corps, the 704th company participated in Operation Marita, the invasion of the Balkans.


15 cm sIG 33 (Sf) auf Panzerkampfwagen I Ausf B, Combat use
Later in 1941, the same assignment was maintained for Operation Barbarossa, the invasion of the Soviet Union. The 705th and 706th belonging to the 7th and 10th Panzer Divisions respectively, were destroyed at this time. Of the remaining companies, only the 701st participated in the opening stages of the subsequent Case Blue in 1942, although it, and its parent 9th Panzer Division, were transferred to Army Group Center by the end of the summer of 1942.


15 cm sIG 33 (Sf) auf Panzerkampfwagen I Ausf B, Combat use
The last reference to these vehicles is with the 704th Company of the 5th Panzer Division during the middle of 1943.


15 cm sIG 33 auf Fahrgestell Panzerkampfwagen II (Sf)
The 15 cm sIG 33 auf Fahrgestell Panzerkampfwagen II (Sf), sometimes referred to as the Sturmpanzer II Bison, was a German assault gun used during World War II.


15 cm sIG 33 auf Fahrgestell Panzerkampfwagen II (Sf), Development
The 15 cm sIG 33 (Sf) auf Panzerkampfwagen I Ausf B that had participated in the Invasion of France in 1940 had proven to be too heavy for its chassis as well as being enormously tall.


15 cm sIG 33 auf Fahrgestell Panzerkampfwagen II (Sf), Development
The same gun was mated to the Panzerkampfwagen II chassis in an attempt to drastically lower its height while using a stronger chassis. The prototype used a standard Panzer II Ausf. B chassis when it was built in February 1941, but this was too cramped for use. The chassis was lengthened by 60 centimetres (24 in), which required adding a sixth roadwheel, and widened by 32 centimetres (13 in) to better accommodate the gun while preserving its low silhouette. 15-millimetre (0.59 in) plates formed the front and sides of the open-topped fighting compartment, which was also open at the rear. Its sides were notably lower than the front, which made the crew vulnerable to small arms fire and shell fragments. Large hatches were added to the rear deck to better cool the engine.


15 cm sIG 33 auf Fahrgestell Panzerkampfwagen II (Sf), Development
The 15-centimetre (5.9 in) sIG 33 gun was used to act as close support artillery and infantry support, for which 30 rounds were carried, could traverse a total of 5° left and right and used a Rblf36 sight.


15 cm sIG 33 auf Fahrgestell Panzerkampfwagen II (Sf), Combat use
Twelve were built at the end of 1941. In early 1942, they were shipped to North Africa, where they formed schwere Infanteriegeschütz-Kompanien (mot.S.) ("Heavy Self-propelled Infantry Gun Companies") 707 and 708. They were used as close support mobile artillery, with the former assigned to Schützen-Regiment 155 and the latter to Schützen-Regiment 200, both part of the 90. leichte Afrika-Division. Both companies fought until the Axis surrender in Tunisia in May 1943.


15 cm schwere Feldhaubitze M 14
The 15 cm schwere Feldhaubitze M 14 was a heavy howitzer which served with Austria-Hungary during World War I.


15 cm schwere Feldhaubitze M 14, Design
The Škoda 15 cm M 14 was developed and built at the Škoda works in Pilsen. Like other guns of the time it had two crew seats mounted on the Gun shield. It broke down into two loads for transport. The M 14 was modified to improve elevation and range as well as to strengthen the carriage as the M 14/16.


15 cm schwere Feldhaubitze M 14, Users
The successor states to the Austro-Hungarian Empire continued to use the M 14 and M 14/16 after the First World War. Postwar war modifications were common to make it suitable for motor traction and to address other issues. Former enemies such as Romania and Italy also operated this series of guns whether they were captured, bought or received as war reparations after the Treaty of Versailles.


15 cm schwere Feldhaubitze M 14, Users, Austria
The M 14 and M 14/16 were kept in service by Austria. Those captured by Germany after the Anschluss were given the designation 15 cm sFH M.14(ö).


15 cm schwere Feldhaubitze M 14, Users, Czechoslovakia
The M 14 and M 14/16 were kept in service by Czechoslovakia. Czechoslovak weapons were known as the 15 cm hrubá houfnice vz. 14 and 15 cm hrubá houfnice vz. 14/16. The German designation for captured Czech guns was 15 cm sFH M.14(t).


15 cm schwere Feldhaubitze M 14, Users, Hungary
The M 14 and M 14/16 was kept in service by Hungary. Hungarian weapons were upgraded in 1935 by MAVAG and designated as M.14/35. Later in 1939 another batch of guns were updated and designated as M.14/39.


15 cm schwere Feldhaubitze M 14, Users, Italy
M 14 and M 14/16 howitzers captured by Italy during the war or received as reparations, were put into service with the designation Obice da 149/13. Some 490 were on hand in 1939 and weapons captured by the Germans after the Italians changed sides in 1943 were used as the 15 cm sFH 400(i) and 15 cm sFH 401(i).


15 cm schwere Feldhaubitze M 94
The 15 cm schwere Feldhaubitze M 94 was a heavy howitzer used by Austria-Hungary in World War I. It had a bronze barrel and relied on wheel ramps to absorb its recoil. The barrel was modified in 1899 as the M 99 and can be identified by its octagonal shape. Both howitzers could be mounted on a wide variety of carriages to suit their mission, including a carriage only 1.13 metres (44 in) wide for mountain use. Around the start of the 20th century both the M 94 and M 99 were modified to increase their elevation up to 65°. The elevation arc had to be extended and the trunnion mounts and wheels had to be strengthened to withstand the greater recoil forces when firing at high elevation. They were known as the M 94/4 and the M 99/4 after modification.


15 cm schwere Feldhaubitze M. 15
The 15 cm schwere Feldhaubitze M. 15 was a heavy howitzer used by Austria-Hungary in World War I. Austrian and Czech guns were taken into Wehrmacht service after the Anschluss and the occupation of Czechoslovakia as the 15 cm schwere Feldhaubitze 15(t) or (ö).


15 cm schwere Feldhaubitze M. 15
The M. 15 was adapted from a fortress turret howitzer called the 15 cm Turmhaubitze M15 designed to throw the same ammunition as the schwere Feldhaubitze M.14 some 3.5 kilometres (3,800 yd) further. It didn't normally breakdown for transport, but could be disassembled into four loads for transport in mountainous areas.


15 cm schwere Feldhaubitze M. 15
The first five weapons were delivered in the first half of 1916. A total of 57 barrels and 56 carriages were completed by the end of the war.


15 cm schwere Feldhaubitze M. 15
The Finns purchased twenty weapons after the end of the Winter War. They arrived on the SS Widor on 9 October 1940. They were initially issued to Heavy Artillery Battalions 21, 22 and 28. They were unpopular with the field artillery as they were thought to be too heavy and were withdrawn from field duty during the Continuation War. Some went to equip the Maaselkä Fortification Artillery Battalions.


15 cm schwere Feldhaubitze M. 15, Notes
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15 cm/45 41st Year Type
The 15 cm/45 41st Year Type was a British naval gun designed by the Elswick Ordnance Company for export in the years before World War I that armed warships of the Imperial Japanese Navy. These guns served aboard Japanese ships during World War I and as coastal artillery during World War II.


15 cm/45 41st Year Type, History
The 15 cm/45 41st Year began life as a design produced by the parent company of Elswick, Armstrong Whitworth for export customers and called the Pattern GG. These guns did not serve aboard ships of the Royal Navy. On 5 October 1917 the Japanese designation system for artillery changed from inches 6 in/45 41st Year Type to centimeters 15 cm/45 41st Year Type. Whether the guns originated in Britain or were built in Japan they still shared the same 41st Year designation.


15 cm/45 41st Year Type, Construction
The 15 cm/45 41st Year was constructed of an A tube and wire wound with a protective outer jacket. Ships built in British shipyards for Japan were armed with Pattern GG guns and later Japan produced their own versions under license at the Kure Naval Arsenal. Four different models were produced at Kure which differed in the style of rifling used. Although sometimes referred to as QF guns, they were actually BL guns which used separate loading bagged charges and projectiles.


15 cm/45 41st Year Type, Naval Use
15 cm/45 41st Year guns equipped armored cruisers, predreadnought battleships and protected cruisers of the Imperial Japanese Navy.


15 cm/45 41st Year Type, Ammunition
Ammunition was of separate loading bagged charge and projectile. The bagged charges weighed 22 kg (49 lb), while the projectiles weighed 45.4 kg (100 lb).


15 cm/50 41st Year Type
The 15 cm/50 41st Year Type gun (50口径四十一式15cm砲, 50-kōkei yonjū-ichi shiki 15-senchi hō) was a naval gun used by the Imperial Japanese Navy before and during World War II. It had a 152 millimetres (6.0 in) bore with a length of 7.6 metres (25 ft) (50 calibre) and fired 45.4 kilograms (100 lb) shell for a distance of 18,000 metres (20,000 yd) (in single mount version) or 21,000 metres (23,000 yd) (in the later twin mounts). The gun was first used in single casemates on the Kongō-class battlecruisers and Fusō-class battleships and later in the Agano-class light cruisers in twin mountings.


15 cm/50 41st Year Type, History
The Type 41 was a Japanese version of the Vickers "Mark M", originally introduced by Vickers-Armstrong (Barrow) as the secondary battery for the Kongō-class. These original guns were designated by the Japanese Navy as the "Mark II", whereas the Japanese-designed copy (adopted from 1912) were designated as the "Mark III".


15 cm/50 41st Year Type, History
In the 1930s, the Kongō-class were modernized, at which time these guns were replaced by new 12.7 cm/40 DP guns. The old guns were placed in storage and were reused on the Agano-class. Some were taken to Guam and were used for coastal defense batteries.


15 cm/50 41st Year Type, History
In the Agano-class, the gun could elevate to 55° for anti-aircraft fire; however, its manual loading method allowed a rate of fire of only about 6 rounds per minute, which significantly limited its utility as an anti-aircraft weapon.


15 de Septiembre de Trujillo
15 de Septiembre was a Peru football club, located in the city of Trujillo, La Libertad. The club was founded with the name of Club 15 de Septiembre.


15 de Septiembre de Trujillo, History
The club have played at the highest level of Peruvian football on three occasions, in the 1988 Torneo Descentralizado until 1990 Torneo Descentralizado when was relegated.


15 equal temperament
In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is a tempered scale derived by dividing the octave into 15 equal steps (equal frequency ratios). Each step represents a frequency ratio of 15√2 (=2(1/15)), or 80 cents (Play (help·info)). Because 15 factors into 3 times 5, it can be seen as being made up of three scales of 5 equal divisions of the octave, each of which resembles the Slendro scale in Indonesian gamelan. 15 equal temperament is not a meantone system.


15 equal temperament, History and use
Guitars have been constructed for 15-ET tuning. The American musician Wendy Carlos used 15-ET as one of two scales in the track Afterlife from the album Tales of Heaven and Hell. Easley Blackwood, Jr. has written and recorded a suite for 15-ET guitar. Blackwood believes that 15 equal temperament, "is likely to bring about a considerable enrichment of both classical and popular repertoire in a variety of styles".


15 equal temperament, Notation
Easley Blackwood, Jr.'s notation of 15-EDO creates this chromatic scale:


15 equal temperament, Notation
B♯/C, C♯/D♭, D, D♯, E♭, E, E♯/F, F♯/G♭, G, G♯, A♭, A, A♯, B♭, B, B♯/C


15 equal temperament, Notation
An alternate form of notation, which is sometimes called "Porcupine Notation," can be used. It yields the following chromatic scale:


15 equal temperament, Notation
C, C♯/D♭, D, D♯/E♭, E, E♯/F♭, F, F♯/G♭, G, G♯, A♭, A, A♯/B♭, B, B♯, C


15 equal temperament, Notation
A notation that uses the numerals is also possible, in which each chain of fifths is notated either by the odd numbers, the even numbers, or with accidentals.


15 equal temperament, Notation
1, 1♯/2♭, 2, 3, 3♯/4♭, 4, 5, 5♯/6♭, 6, 7, 7♯/8♭, 8, 9, 9♯/0♭, 0, 1


15 equal temperament, Notation
In this article, unless specified otherwise, Blackwood's notation will be used.


15 equal temperament, Interval size
Here are the sizes of some common intervals in 15-ET:


15 equal temperament, Interval size
15-ET matches the 7th and 11th harmonics well, but only matches the 3rd and 5th harmonics roughly. The perfect fifth is more out of tune than in 12-ET, 19-ET, or 22-ET, and the major third in 15-ET is the same as the major third in 12-ET, but the other intervals matched are more in tune (except for the septimal tritones). 15-ET is the smallest tuning that matches the 11th harmonic at all and still has a usable perfect fifth, but its match to intervals utilizing the 11th harmonic is poorer than 22-ET, which also has more in-tune fifths and major thirds.


15 equal temperament, Interval size
Although it contains a perfect fifth as well as major and minor thirds, the remainder of the harmonic and melodic language of 15-ET is quite different from 12-ET, and thus 15-ET could be described as xenharmonic. Unlike 12-ET and 19-ET, 15-ET matches the 11:8 and 16:11 ratios. 15-ET also has a neutral second and septimal whole tone. To construct a major third in 15-ET, one must stack two intervals of different sizes, whereas one can divide both the minor third and perfect fourth into two equal intervals.


15 kV AC railway electrification
Railway electrification systems using alternating current (AC) at 15 kilovolts (kV) and 16.7 Hertz (Hz) are used on transport railways in Germany, Austria, Switzerland, Sweden, and Norway. The high voltage enables high power transmission with the lower frequency reducing the losses of the traction motors that were available at the beginning of the 20th century. Railway electrification in late 20th century tends to use 25 kV, 50 Hz AC systems which has become the preferred standard for new railway electrifications but extensions of the existing 15 kV networks are not completely unlikely. In particular, the Gotthard Base Tunnel (opened on 1 June 2016) still uses 15 kV, 16.7 Hz electrification.


15 kV AC railway electrification
Due to high conversion costs, it is unlikely that existing 15 kV, 16.7 Hz systems will be converted to  25 kV, 50 Hz despite the fact that this would reduce the weight of the on-board step-down transformers to one third that of the present devices.


15 kV AC railway electrification, History
The first electrified railways used series-wound DC motors, first at 600 V and then 1,500 V. Areas with 3 kV DC catenaries (primarily in Eastern Europe) used two 1,500 V DC motors in series. But even at 3 kV, the current needed to power a heavy train (particularly in rural and mountainous areas) can be excessive. Although increasing the transmission voltage decreases the current and associated resistive losses for a given power, insulation limits make higher voltage traction motors impractical. Transformers on each locomotive are thus required to step high transmission voltages down to practical motor operating voltages. Before the development of suitable ways to efficiently transform DC currents through power electronics, efficient transformers strictly required alternating current (AC); thus high voltage electrified railways adopted AC along with the electric power distribution system (see War of the currents).


15 kV AC railway electrification, History
The 50 Hz (60 Hz in North America) AC grid was already established at the beginning of the 20th century. Although series-wound motors can in principle run on AC as well as DC (the reason they are also known as universal motors) large series-wound traction motors had problems with such high frequencies. High inductive reactance of the motor windings caused commutator flashover problems and the non-laminated magnetic pole-pieces originally designed for DC exhibited excessive eddy current losses. Using a lower AC frequency alleviated both problems.


15 kV AC railway electrification, History
In the German-speaking countries, high-voltage electrification began at 16+2⁄3 hertz, exactly one third of the national power grid frequency of 50 Hz. This facilitated the operation of rotary converters from the grid frequency and allowed dedicated railway power generators to operate at the same shaft speed as a standard 50 Hz generator by reducing the number of pole pairs by a factor of three. For example, a generator turning at 1,000 rpm would be wound with two pole pairs rather than six.


15 kV AC railway electrification, History
Separate plants supply railway power in Austria, Switzerland and Germany, except for Mecklenburg-Western Pomerania and Saxony-Anhalt; converters powered by the grid supply railway power in those two German states plus Sweden and Norway. Norway also has two hydro-electric power plants dedicated for railway power with 16+2⁄3 hertz output.


15 kV AC railway electrification, History
The first generators were synchronous AC generators or synchronous transformers; however, with the introduction of modern double fed induction generators, the control current induced an undesired DC component, leading to pole overheating problems. This was solved by shifting the frequency slightly away from exactly ⅓ the grid frequency; 16.7 hertz was arbitrarily chosen to remain within the tolerance of existing traction motors. Austria, Switzerland and Southern Germany switched their power plants to 16.7 Hz on 16 October 1995 at 12:00 CET. Note that regional electrified sections run by synchronous generators keep their frequency of 16+2⁄3 Hz just as Sweden and Norway still run their railway networks at 16+2⁄3 Hz throughout.


15 kV AC railway electrification, History
One of the disadvantages of 16.7 Hz locomotives as compared to 50 Hz or 60 Hz locomotives is the heavier transformer required to reduce the overhead line voltage to that used by the motors and their speed control gear. Low frequency transformers need to have heavier magnetic cores and larger windings for the same level of power conversion. (See effect of frequency on the design of transformers.) The heavier transformers also lead to higher axle loads than for those of a higher frequency. This, in turn, leads to increased track wear and increases the need for more frequent track maintenance.


15 kV AC railway electrification, History
The Czech Railways encountered the problem of the reduced power handling of lower frequency transformers when they rebuilt some 25 kV AC, 50 Hz locomotives (series 340) to operate on 15 kV AC, 16.7 Hz lines. As a result of using the same transformer cores (originally designed for 50 Hz) at the lower frequency, the transformers had to be de-rated to one third of their original power handling capability, thereby reducing the available tractive effort by the same amount (to around 1,000 kW).


15 kV AC railway electrification, History
These drawbacks, plus the need for a separate supply infrastructure and the lack of any technical advantages with modern motors and controllers has limited the use of 16+2⁄3 Hz and 16.7 Hz beyond the original five countries. Most other countries electrified their railways at the utility frequency of 50/60 Hz. Newer European electrification is mostly 25 kV AC at 50 Hz (primarily in Eastern Europe). Conversion to this voltage/frequency requires higher voltage insulators and greater clearance between lines and bridges and other structures. This is now standard for new overhead lines as well as for modernizing old installations.


15 kV AC railway electrification, History
Simple European standardization with an alignment of voltage/frequency across Europe is not necessarily cost-effective since trans-border traction is more limited by the differing national standards in other areas. To equip an electric locomotive with a transformer for two or more input voltages is cheap compared to the cost of installing multiple train protection systems and to run them through the approval procedure to get access to the railway network in other countries. However, some new high-speed lines to neighbouring countries are already intended to be built to 25 kV (e.g. in Austria to Eastern Europe).


15 kV AC railway electrification, History
Newer locomotives are always built with asynchronous motor control systems that have no problem with a range of input frequencies including DC. However the Deutsche Bahn train operator does still use older models from the standard electric locomotive series - even though some are now as much as 50 years old. As soon as these obsolescent models are decommissioned, it will be easier to standardise, but this may take a few decades to happen. Meanwhile, the Deutsche Bahn tends to order train sets that are capable of running multiple electrification systems.


15 kV AC railway electrification, History, Distribution networks
In Germany (except Mecklenburg-Western Pomerania and Saxony-Anhalt), Austria and Switzerland, there is a separate single-phase power distribution grid for railway power at 16.7 Hz; the voltage is 110 kV in Germany and Austria and 132 kV in Switzerland. This system is called the centralized railway energy supply. A separate single-phase power distribution grid makes the recuperation of energy during braking extremely easy in comparison with 25 kV 50 Hz system tied to 3 phase distribution grid.


15 kV AC railway electrification, History, Distribution networks
In Sweden, Norway, Mecklenburg-Western Pomerania and Saxony-Anhalt, the power is taken directly from the three-phase grid (110 kV at 50 Hz), converted to low frequency single phase and fed into the overhead line. This system is called the decentralized (i.e. local) railway energy supply.


15 kV AC railway electrification, History, Generation and conversion
The centralized system is supplied by special power plants that generate 110 kV (or 132 kV in the Swiss system) AC at 16.7 Hz and by rotary converters or AC/AC converters that are supplied from the national power grid (e.g. 110 kV, 50 Hz), they convert it to 55-0-55 kV (or 66-0-66 kV) AC at 16.7 Hz. The 0 V point is connected to earth through an inductance so that each conductor of the single phase AC power line has a voltage of 55 kV (or 66 kV) with respect to earth potential.


15 kV AC railway electrification, History, Generation and conversion
This is similar to split-phase electric power systems and results in a balanced line transmission. The inductance through which the earthing is done is designed to limit earth currents in cases of faults on the line. At the transformer substations, the voltage is transformed from 110 kV (or 132 kV) AC to 15 kV AC and the energy is fed into the overhead line.


15 kV AC railway electrification, History, Generation and conversion, Asynchronous converters
The frequency of 16.7 Hz depends on the necessity to avoid synchronism in parts of the rotary machine, which consists principally of a three phase asynchronous motor and a single phase synchronous generator. Since synchronism sets in at a frequency of 16+2⁄3 Hz (according to the technical details) in the single phase system, the frequency of the centralized system was set to 16.7 Hz.


15 kV AC railway electrification, History, Generation and conversion, Asynchronous converters
Power plants providing 110 kV, 16.7 Hz, are either dedicated to generating this specific single phase AC or have special generators for the purpose, such as the Neckarwestheim nuclear power plant or the Walchensee hydroelectric power station.


15 kV AC railway electrification, History, Generation and conversion, Synchronous converters
The power for the decentralized system is taken directly from the national power grid and directly transformed and converted into 15 kV, 16+2⁄3 Hz by synchronous-synchronous-converters or static converters. Both systems need additional transformers. The converters consist of a three-phase synchronous motor and a single-phase synchronous generator. The decentralized system in the north-east of Germany was established by the Deutsche Reichsbahn in the 1980s, because there was no centralized system available in these areas.


15 kV AC railway electrification, Facilities for 15 kV AC railway electrification in Germany, Austria and Switzerland
Germany, Austria and Switzerland operate the largest interconnected 15 kV AC system with central generation, and central and local converter plants.


15 kV AC railway electrification, Germany, Substations
In these facilities, electricity is transformed down from 110 kV to the DB level of 15 kV. There is no conversion or generation of power.


15 kV AC railway electrification, Germany, Central converter plants
In these facilities the AC from the public grid is transformed and converted into the single phase AC and fed into the railway current distribution grid. At some facilities, power is also fed to the overhead line. Conversion is done by rotary converters or electronic inverters.


15 kV AC railway electrification, Germany, Local converter plants
In these facilities the AC from the public grid is transformed and converted into the single phase AC and fed to the overhead line. Conversion is done by rotary converters or electronic inverters.


15 kV AC railway electrification, Switzerland, Substations
In these facilities electricity is transformed down from 132 kV or 66 kV to 15 kV. There is no conversion or generation of power.


15 kV AC railway electrification, Switzerland, Central converter plants
In these facilities the AC from public grid is transformed and converted into the single phase AC and fed into the railway current distribution grid. At some facilities, power is also fed to the overhead line. Conversion is done by rotary converters or electronic inverters.


15 kV AC railway electrification, Austria, Substations
In these facilities electricity is transformed down from 110 kV to 15 kV. No conversion or generation of power takes place.


15 kV AC railway electrification, Austria, Central converter plants
In these facilities the AC from the public grid is transformed and converted into the single phase AC and fed into the railway current distribution grid. At some facilities, power is also fed to the overhead line. Conversion is done by rotary converters or electronic inverters.


15 kV AC railway electrification, Norway
In Norway all electric railways use 16 kV 162⁄3 Hz AC  (except the Thamshavnbanen museum railway which uses 6.6 kV 25 Hz AC). The Oslo T-bane and tramways use 750 V DC power.


15 kV AC railway electrification, Sweden
In Sweden most electric railways use 15 kV 162⁄3 Hz AC. Exceptions include: Saltsjöbanan and Roslagsbanan (1.5 kV DC), the Stockholm Metro (650 V and 750 V DC) and tramways (750 V DC). The Oresund Bridge linking Sweden and Denmark is electrified at 25 kV, Danish standard; the split is located on the Swedish side near the bridge. Only two-system trains (or diesel trains; rare) can pass the point.


15 km, Kemerovo Oblast
15 km (Russian: 15 км) is a rural locality (a settlement) in Topkinskoye Rural Settlement of Topkinsky District, Russia. The  population was 0 as of 2010.


15 let Kasakhstan
15 let Kasakhstan (Kazakh: Қазақстанға 15 жыл Russian: 15 лет Казахстана) is a village located in the Gabit Musirepov District of North Kazakhstan Region in northern Kazakhstan. Population: 243 (2009 Census results);.


15 mil dibujos
"15 mil dibujos" (15 thousand drawings) is a 1942 Chilean animated film of 35 millimeters made by the filmmakers Juan Carlos Trupp and Jaime Escudero Sanhueza, considered the third Chilean animated film, "15 mil dibujos" was filmed by Enrique Soto and musicalized by The Chilean band Los Huasos Quincheros. Other animated films of Chile that are currently lost are: "Transmisión del mando presidencial" and "Vida y milagros de Don Fausto".


15 mil dibujos, Plot
The story recounts the adventures from the condor anthropomorphous, Copuchita (whose name comes of the Chilean term "Copucha"), and of his friends, the Cougar dressed as mapuche Manihuel, the rooster dressed as huaso Ño Benhaiga, and a woman young named Clarita.


15 mil dibujos, Production
In 1930s Carlos Trupp met Jaime Escudero at the Arquitecture of Pontifical Catholic University of Chile in a workshop on the corner of Lira and Marcoleta, a street in the Santiago's center. And both began the realization of this short in an artisanal way, taking place in a workshop in the corner of the street "Lira con Marcoleta".


15 mil dibujos, Production
The film received financial help from friends and family of directors Trupp and Escudero, like Leopoldina, grandmother of Carlos Trupp, what made the music of the film, Escudero y Trupp wonning the support and financing of CORFO and the Corporación Chilena del Salitre ("Chilean Saltpeter Corporation"), where Escudero's father worked, who was a lawyer.


15 mil dibujos, Production
According to an interview with Escudero from the "Museo de la Historieta de Chile" (Chilean Cartoon Museum), the central idea of the film was born out of his interest in dignifying the Roto Chilean, and from this concept a large part of the characters were designed, Copuchita, the main character of the film, wears a typical hat of a Roto.


15 mil dibujos, Production
According Escudero: "I am already 87 years old, so I apologize for forgetting some things," says Escudero, however, Escudero was certain that it was a long-term film, since scenes filmed with actors to extend your footage, this sequences were filmed in Chilefilms, this was stated by Escudero, despite the great efforts of Escudero and Trupp, the movie went unfinished for a long time, which caused a drop in mood, especially from family members, since the monetary demand was very high.


15 mil dibujos, Production
In 1941 Walt Disney during your visit in Chile, visited Lira con Marcoleta, and watched the movie progress, Disney support and advice them to do their work more efficiently, since until then they used basic and handmade materials. After finishing his visit to Disney, seeing the effort put into production, he invited the filmmakers to work with him in United States, but this was never fulfilled due to the tense situation that the North American country during the World War II.


15 mil dibujos, Production
Although Escudero was the cartoonist, he recognizes that the presence of Carlos Trupp was what helped him to continue with the project, according to Escudero, Carlos Trupp was a fairly hyperkinetic young man. Escudero did not hesitate to consider that the film "was not good", against this Victor Uribe he pointed out that "Don Escudero detracts from his own work" and affirmed "but the value of this material as a historical document is invaluable".


15 mil dibujos, Reception
This film was premiered in a room from Santiago de Chile on December 24, 1942, after a week of its publication, the film was a box office flop, and the criticisms from the "Ecran" magazine on December 29, 1942 were mainly negative. in addition, the creators, unable to collect the money invested, were indebted to the cinemas that showed it.


15 mil dibujos, Reception
On November 5, 1947 Carlos Trupp directed the documentary "Santiago de Cuatro Siglos", a film on Black and white of 35 millimeters, that tells the Santiago de chile's story. The movie whose duration was 30 minutes, was scripted by Orlando Cabrera Leiva, filmed by Luis Bernal and sponsored by the Municipality of Las Condes. On the other hand Jaime Escudero later worked in other areas: either working in magazines like "El Cabrito" and "El Peneca", or creating the logos of the stations in the 1980s.


15 mil dibujos, Reception, Conservation status
About 2 years before 2001, Rodrigo Trupp, a Carlos Trupp's grandson, came across at their house located in Chicago, United States a chest what contained a old copy of the tape. Later he try to restore the tape "15 mil dibujos", thing that was never completed. Later, the Trupp's grandson along with Victor Uribe joined forces to go in search of lost pieces of the film and money to complete the project. Uribe asked for a total of $1 million, as Uribe explained: "My idea is to transfer this material from film to video and make a short film", however they did not continue with the project.


15 mil dibujos, Reception, Conservation status
Kylie Trupp, a Trupp's granddaughter and student at the University of the Americas, began a search to try to rediscover all the material that had been left over of the tape, in this way, he obtained a trunk containing rolls of the film "15 mil dibujos". According to the Chilean magazine El Mercurio, Kylie reported this discovery to the teachers of the university, who were in charge of the restoration and digitization of the work together with the Cineteca Nacional. While was not achieved to discover all the material of the tape, the little material that Kylie Trupp could find, her present it at the 2014 Noche de Monos Festival of  UDLA, and later uploaded to their YouTube account.


15 mil dibujos, In other media
In 1960 were used scenes from this film in the documentary "Recordando" by Edmundo Urrutia, in 2012, the Cineteca Nacional de Chile rediscovered a fragment of the film found in the aforementioned film but without its audio original. In 1962, during the production of the film "Condorito en el Circo" (film which was never released), the magazine "Ecran" published an article mentioning that Copuchita could be Condorito's father.


15 mil dibujos, In other media
In an interview with one of the film's directors together with "Ergocomics.cl" he pointed out that «the character "Copuchita" is from 1941 and Condorito appeared in "Okey" in 1949, so it must be one of the inspirations of Condorito, since Pepo met him and at some point talked about him, but nothing that can be proven, in any case it is an honor if it was so».


15 minutes of fame
15 minutes of fame is short-lived media publicity or celebrity of an individual or phenomenon. The expression was inspired by a quotation misattributed to Andy Warhol: "In the future, everyone will be world-famous for 15 minutes." Attributed to two other people, the first printed use was in the program for a 1968 exhibition of Warhol's work at the Moderna Museet in Stockholm, Sweden. The phenomenon is often used in reference to figures in the entertainment industry or other areas of popular culture, such as reality television and YouTube.


15 minutes of fame
An older version of the same concept in English is the expression "nine days' wonder." This phrase dates at least as far back as the Elizabethan era, referencing William Kempe.


15 minutes of fame, Origins
Warhol's alleged quotation first appeared in print in a program for his 1968 exhibit at the Moderna Museet in Stockholm, Sweden. In the autumn of 1967, Pontus Hultén (the director for the Moderna Museet) asked Olle Granath to help with the production of the exhibit, which was due to open in February 1968. Granath was tasked with writing a program for the exhibit, complete with Swedish translations. He was given a box of writings by and about Warhol to use for the program.


15 minutes of fame, Origins
Granath claims that submitting his manuscript, Hultén asked him to insert the quote: "In the future, everyone will be world-famous for 15 minutes." To which Granath replied that quote was not in the material he was given. Hultén replied, "if he didn’t say it, he could very well have said it. Let’s put it in."


15 minutes of fame, Origins
Photographer Nat Finkelstein claimed credit for the expression, stating that he was photographing Warhol in 1966 for a proposed book. A crowd gathered trying to get into the pictures and Warhol supposedly remarked that everyone wants to be famous, to which Finkelstein replied, "Yeah, for about fifteen minutes, Andy."


15 minutes of fame, Interpretation
German art historian Benjamin H. D. Buchloh suggests that the core tenet of Warhol's aesthetic, being "the systematic invalidation of the hierarchies of representational functions and techniques" of art, corresponds directly to the belief that the "hierarchy of subjects worthy to be represented will someday be abolished;" hence, anybody, and therefore "everybody," can be famous once that hierarchy dissipates, "in the future," and by logical extension of that, "in the future, everybody will be famous," and not merely those individuals worthy of fame.


15 minutes of fame, Interpretation
On the other hand, wide proliferation of the adapted idiom "my fifteen minutes" and its entrance into common parlance have led to a slightly different application, having to do with both the ephemerality of fame in the information age and, more recently, the democratization of media outlets brought about by the advent of the internet. In this formulation, Warhol's quote has been taken to mean: "At the present, because there are so many channels by which an individual might attain fame, albeit not enduring fame, virtually anyone can become famous for a brief period of time."


15 minutes of fame, Interpretation
There is a third and even more remote interpretation of the term, as used by an individual who has been legitimately famous or skirted celebrity for a brief period of time, that period of time being their "fifteen minutes."


15 minutes of fame, Interpretation
John Langer suggests that 15 minutes of fame is an enduring concept because it permits everyday activities to become "great effects." Tabloid journalism and the paparazzi have accelerated this trend, turning what may have before been isolated coverage into continuing media coverage even after the initial reason for media interest has passed.


15 minutes of fame, Derivative phrases
On their 1987 album Yoyo, Bourgeois Tagg have a song called "15 Minutes In The Sun" that is a direct reference to the Warhol statement.


15 minutes of fame, Derivative phrases
In the song "I Can't Read", released by David Bowie's Tin Machine in their 1989 debut album and re-released by Bowie in 1997 for the soundtrack of the movie The Ice Storm, the phrase is used in direct reference to Andy Warhol: "Andy, where's my 15 minutes?" The age of reality television has seen the comment wryly updated as: "In the future, everyone will be obscure for 15 minutes." The British artist Banksy has made a sculpture of a TV that has, written on its screen, "In the future, everyone will be anonymous for 15 minutes," which was later used in the lyrics of Robbie Williams' song "The Actor" from his 2006 album Rudebox.


15 minutes of fame, Derivative phrases
A more recent adaptation of Warhol's quip, possibly prompted by the rise of online social networking, blogging, and internet celebrity, is the claim that "In the future, everyone will be famous to fifteen people" or, in some renditions, "On the Web, everyone will be famous to fifteen people". This quote, though attributed to David Weinberger, was said to have originated with the Scottish artist Momus.


15 minutes of fame, Derivative phrases
The Marilyn Manson song "I Don't Like the Drugs (But the Drugs Like Me)", released on his 1998 album Mechanical Animals, alludes to the term in the line "We're rehabbed and we're ready for our fifteen minutes of shame", as part of the song's theme of unrepentant escapism through drugs.


15 minutes of fame, Derivative phrases
In 1993, the British techno/industrial music group Sheep on Drugs released a single "15 Minutes of Fame" which reached the lower reaches of the UK Singles Chart.


15 minutes of fame, Derivative phrases
Musician and actor Tim Minchin refers to the phrase (and to Warhol explicitly) in his song "15 minutes", wherein the phrase "15 minutes of shame" is sung repeatedly to describe the phenomenon of online shaming.


15 of the Best
15 of the Best is a compilation album by Canadian Country singer Anne Murray. It was released by Liberty Records in the spring of 1992. The album peaked at number 62 on the Billboard Top Country Albums chart.


15 point Programme for minorities
Prime Minister’s New 15 point Programme for minorities is a programme launched by Indian government for welfare of religious minorities in furtherance of  reports by committees such as the Sachar Committee Report that highlighted that minorities, especially Muslims, in the country were often in a worse socio-economic and political condition than communities such as the Scheduled Casts and Scheduled tribes communities that have  been oppressed over millennia through the caste system (also referred to as the varna system). It pegged the status of minorities on various indicators such as nutrition, health, education et al.


15 point Programme for minorities
of minorities and specially Muslims at an abysmally poor level. The 15 point program was the government's response to these finding by laying down guidelines to target minorities in schemes and entitlements that are already in place and designing and executing new schemes aimed at the empowerment of these groups. The programme advocated allocating 15% of plan outlays of welfare schemes identified under the 15 point programme.


15 point Programme for minorities, 15 Points
Three more schemes were introduced into the 15 point programme for minorities in 2009 namely:


15 point Programme for minorities, 15 Points
Certain state governments have opposed the allocation of resources  based on religion and called it communal budgeting and a ploy to divide society on religious lines.


15 puzzle
The 15 puzzle (also called Gem Puzzle, Boss Puzzle, Game of Fifteen, Mystic Square and many others) is a sliding puzzle having 15 square tiles numbered 1–15 in a frame that is 4 tiles high and 4 tiles wide, leaving one unoccupied tile position. Tiles in the same row or column of the open position can be moved by sliding them horizontally or vertically, respectively. The goal of the puzzle is to place the tiles in numerical order.


15 puzzle
Named for the number of tiles in the frame, the 15 puzzle may also be called a 16 puzzle, alluding to its total tile capacity. Similar names are used for different sized variants of the 15 puzzle, such as the 8 puzzle that has 8 tiles in a 3×3 frame.


15 puzzle
The n puzzle is a classical problem for modelling algorithms involving heuristics. Commonly used heuristics for this problem include counting the number of misplaced tiles and finding the sum of the taxicab distances between each block and its position in the goal configuration. Note that both are admissible, i.e. they never overestimate the number of moves left, which ensures optimality for certain search algorithms such as A*.


15 puzzle, Mathematics, Solvability
Johnson & Story (1879) used a parity argument to show that half of the starting positions for the n puzzle are impossible to resolve, no matter how many moves are made. This is done by considering a function of the tile configuration that is invariant under any valid move, and then using this to partition the space of all possible labeled states into two equivalence classes of reachable and unreachable states.


15 puzzle, Mathematics, Solvability
The invariant is the parity of the permutation of all 16 squares plus the parity of the taxicab distance (number of rows plus number of columns) of the empty square from the lower right corner. This is an invariant because each move changes both the parity of the permutation and the parity of the taxicab distance. In particular, if the empty square is in the lower right corner then the puzzle is solvable if and only if the permutation of the remaining pieces is even.


15 puzzle, Mathematics, Solvability
Johnson & Story (1879) also showed that the converse holds on boards of size m×n provided m and n are both at least 2: all even permutations are solvable. This is straightforward but a little messy to prove by induction on m and n starting with m=n=2. Archer (1999) gave another proof, based on defining equivalence classes via a hamiltonian path.


15 puzzle, Mathematics, Solvability
Wilson (1974) studied the generalization of the 15 puzzle to arbitrary finite graphs, the original problem being the case of a 4×4 grid graph. The problem has some degenerate cases where the answer is either trivial or a simple combination of the answers to the same problem on some subgraphs.


15 puzzle, Mathematics, Solvability
Namely, for paths and polygons, the puzzle has no freedom; if the graph is disconnected, only the connected component of the vertex with the "empty space" is relevant; and if there is an articulation vertex the problem reduces to the same puzzle on each of the biconnected components of that vertex. Excluding these cases, Wilson showed that other than one exceptional graph on 7 vertices, it is possible to obtain all permutations unless the graph is bipartite, in which case exactly the even permutations can be obtained. The exceptional graph is a regular hexagon with one diagonal and a vertex at the center added; only 1/6 of its permutations can be attained.


15 puzzle, Mathematics, Solvability
For larger versions of the n puzzle, finding a solution is easy, but the problem of finding the shortest solution is NP-hard. It is also NP-hard to approximate the fewest slides within an additive constant, but there is a polynomial-time constant-factor approximation. For the 15 puzzle, lengths of optimal solutions range from 0 to 80 single-tile moves (there are 17 configurations requiring 80 moves) or 43 multi-tile moves; the 8 puzzle always can be solved in no more than 31 single-tile moves or 24 multi-tile moves (integer sequence ). The multi-tile metric counts subsequent moves of the empty tile in the same direction as one.


15 puzzle, Mathematics, Solvability
The number of possible positions of the 24 puzzle is 25!/2 ≈ 7.76×1024 which is too many to calculate God's number. In 2011, lower bounds of 152 single-tile moves or 41 multi-tile moves had been established, as well as upper bounds of 208 single-tile moves or 109 multi-tile moves. In 2016, the upper bound was improved to 205 single-tile moves.


15 puzzle, Mathematics, Solvability
The transformations of the fifteen puzzle form a groupoid (not a group, as not all moves can be composed); this groupoid acts on configurations.


15 puzzle, Mathematics, Group Theory
Because the combinations of the 15 puzzle can be generated by 3-cycles, it can be proved that the 15 puzzle can be represented by the alternating group A15{\displaystyle A_{15}}. In fact, any 2k−1{\displaystyle 2k-1} sliding puzzle with square tiles of equal size can be represented by A2k−1{\displaystyle A_{2k-1}}.


15 puzzle, Alternate proof
In an alternate view of the problem, we can consider the invariant to be the sum of the parity of the number of inversions in the current order of the 15 numbered pieces and the parity of the difference in the row number of the empty square from the row number of the last row. (Let's call it row distance from the last row.)


15 puzzle, Alternate proof
This is an invariant because each column move, when we move a piece within the same column, changes both the parity of the number of inversions (by changing the number of inversions by ±1, ±3) and the parity of the row distance from the last row (changing row distance by ±1); and each row move, when we move a piece within the same row, does not change any of the two parities. Now if we look at the solved state of the puzzle, this sum is even.


15 puzzle, Alternate proof
Hence it is easy to prove by induction that any state of the puzzle for which the above sum is odd cannot be solvable. In particular, if the empty square is in the lower right corner (even anywhere in the last row) then the puzzle is solvable if and only if the number of inversions of the numbered pieces is even.


15 puzzle, History
The puzzle was "invented" by Noyes Palmer Chapman, a postmaster in Canastota, New York, who is said to have shown friends, as early as 1874, a precursor puzzle consisting of 16 numbered blocks that were to be put together in rows of four, each summing to 34.


15 puzzle, History
Copies of the improved Fifteen Puzzle made their way to Syracuse, New York, by way of Noyes' son, Frank, and from there, via sundry connections, to Watch Hill, Rhode Island, and finally to Hartford (Connecticut), where students in the American School for the Deaf started manufacturing the puzzle and, by December 1879, selling them both locally and in Boston, Massachusetts. Shown one of these, Matthias Rice, who ran a fancy woodworking business in Boston, started manufacturing the puzzle sometime in December 1879 and convinced a "Yankee Notions" fancy goods dealer to sell them under the name of "Gem Puzzle". In late January 1880, Dr. Charles Pevey, a dentist in Worcester, Massachusetts, garnered some attention by offering a cash reward for a solution to the Fifteen Puzzle.


15 puzzle, History
The game became a craze in the U.S. in 1880.


15 puzzle, History
Noyes Chapman had applied for a patent on his "Block Solitaire Puzzle" on February 21, 1880. However, that patent was rejected, likely because it was not sufficiently different from the August 20, 1878 "Puzzle-Blocks" patent (US 207124) granted to Ernest U. Kinsey.


15 puzzle, History, Sam Loyd
Sam Loyd claimed from 1891 until his death in 1911 that he invented the puzzle, for example writing in the Cyclopedia of Puzzles (published 1914): "The older inhabitants of Puzzleland will remember how in the early seventies I drove the entire world crazy over a little box of movable pieces which became known as the '14-15 Puzzle'." However, Loyd had nothing to do with the invention or initial popularity of the puzzle, and in any case, the craze was in 1880, not the early 1870s. Loyd's first article about the puzzle was published in 1886 and it was not until 1891 that he first claimed to have been the inventor.


15 puzzle, History, Sam Loyd
Some later interest was fuelled by Loyd offering a $1,000 prize for anyone who could provide a solution for achieving a particular combination specified by Loyd, namely reversing the 14 and 15, called by Loyd the 14-15 puzzle. This was impossible, as had been shown over a decade earlier by Johnson & Story (1879), as it required a transformation from an even to an odd permutation.


15 puzzle, Miscellaneous
The Minus Cube, manufactured in the USSR, is a 3D puzzle with similar operations to the 15 puzzle.


15 puzzle, Miscellaneous
Bobby Fischer was an expert at solving the 15-Puzzle. He had been timed to be able to solve it within 25 seconds; Fischer demonstrated this on November 8, 1972, on The Tonight Show Starring Johnny Carson.


15 till Midnight
15 till Midnight is a 2010 science fiction film directed by Wolfgang Meyer and written by Brandon Slagle, who also stars in the film. The film also stars Dee Martin and Devanny Pinn.


15 till Midnight, Plot
Lukas Reyes is trapped in a seemingly endless loop between parallel existences, one being occupied by his spouse, Sera, and another being occupied by a relation from another life, Nara. As worlds seem to begin colliding and further bleeding into one another, he finds himself pursued by a group of shadow-men known as "The Knowers". The common thread between everything being a significance with the time 11:45 - fifteen minutes until midnight.


15 Éxitos (Alejandra Guzmán album)
15 Éxitos is a compilation album by Mexican singer Alejandra Guzmán. It was released by her former record label Fonovisa and includes fifteen tracks recorded by her from 1988 to 1991.


15 Éxitos Vol. 2 (Los Caminantes album)
15 Éxitos Vol. 2 is a compilation album by Mexican group Los Caminantes, released in 1985 on Luna Records. It is the second of a three volume greatest hits collection from their Supe Perder, Especialmente Para Usted, and Numero Tres albums.


15 Éxitos Vol. 3 (Los Caminantes album)
15 Éxitos Vol. 3 is a compilation album by Mexican group Los Caminantes, released in 1987 on Luna Records. It is the third of a three volume greatest hits collection from their Corridos Al Estilo De Los Caminantes, Porque Tengo Tu Amor, Cada Dia Mejor, and De Guanajuato...Para America! albums.


15 Éxitos de Juan Gabriel
15 Éxitos de Juan Gabriel is a compilation album released by Juan Gabriel in 1981. Re -released on August 3, 2004.


15 éxitos (Flor Silvestre album)
15 éxitos (English: 15 Hits) is a greatest hits album by Mexican singer Flor Silvestre, released in 1984 by Musart Records. The 1989 CD reissue and most recent releases of this compilation include "Mi destino fue quererte" as the first track.


15 éxitos, vol. 2 (Flor Silvestre album)
15 éxitos, vol. 2 is a greatest hits album by Mexican singer Flor Silvestre, released in 1989 by Musart Records. It includes fifteen of Flor Silvestre's hits from the late 1950s to the late 1960s. Originally released as an LP record, it has been reissued several times on compact cassette, CD, and digital download.


15&
15& (Korean: 피프틴앤드, also known as Fifteen And) was a South Korean duo formed by JYP Entertainment in 2012. The duo consisted of Park Ji-min and Baek Ye-rin. The name means '15' being their age at debut and the ‘&’ in '15&' means that they can have success into the future. They debuted with and released their debut single "I Dream" on October 5, 2012. Following a four-year hiatus which began in February 2015, the group de facto disbanded upon the expiration of both member's contracts with JYP Entertainment in 2019.


15&, History, Formation
In 2012, Park Ji-min was the first-place winner of the South Korean reality TV competition, "K-pop Star". With the opportunity of signing with three major record labels (YG Entertainment, SM Entertainment and JYP Entertainment), she had chosen to sign with JYP Entertainment on May 21.


15&, History, Formation
When Baek Ye-rin was ten years old, she was introduced as a "R&B genius" on Star King. In 2008, she auditioned with Beyoncé’s "Listen" and was accepted as a trainee at the same time as 2PM's Wooyoung and Highlight's Doo-joon. Baek had been a JYP trainee for over four years before she officially debuted with Park.


15&, History, 2012–2013: Debut with I Dream and Somebody
15&'s debut single I Dream was released on October 5, 2012. The duo's debut officially began on October 7, 2012, performing on SBS Inkigayo. On October 12, 2012, 15& held their ‘school attack’ guerrilla concerts. The girls performed at the Chungdam Middle School, Eonnam Middle School, Sungil Information High School and Dankook University. For a total of eight hours, 15& held a surprise concert at each school, performing their debut song and their cover versions of Alicia Keys's "Put It in a Love Song", and Sistar19's "Ma Boy". The event attracted a total of 5,000 in attendance. Not only the students who attended the schools were there, but also the citizens living nearby who heard the news of the free concert.


15&, History, 2012–2013: Debut with I Dream and Somebody
15&'s second single Somebody was released on April 7, 2013. The music video showed the two parodying the "K-Pop Star" judge panel while reacting to staged auditions/cameos by Park Jin-young and some of Park Ji-min's fellow contestants from K-pop Star 1. On April 7, 2013, 15& made their comeback performance on K-pop Star 2 finale with "Somebody". Upon its release on the same day, the song rose to the summit of music charts on Olleh, Melon, Daum and others.


15&, History, 2014–2019: Can't Hide It, Sugar, Love is Madness, and unofficial disbandment
15&'s third single Can't Hide It was released on April 13. On the same day, they made their comeback performance on K-pop Star 3 finale with "Can't Hide It." It was also revealed that their first album is scheduled to be released in May 2014. 15&'s first album Sugar was released on May 26, 2014. They made their comeback on Mnet's M Countdown on May 29, 2014.


15&, History, 2014–2019: Can't Hide It, Sugar, Love is Madness, and unofficial disbandment
15& released the fourth single Love Is Madness, featuring Kanto of Troy on February 8, 2015. They performed the song for the first time along with other songs on February 14, 2015 for their Valentine's Day concert for singles.


15&, History, 2014–2019: Can't Hide It, Sugar, Love is Madness, and unofficial disbandment
Following four year of hiatus, the expiration and non-renewal of Park Ji-min's contract with JYP Entertainment in August 2019 led to the group's de facto disbanding.


15,000 BC in art, Events
Cave paintings were born during this time period. Historians now use these cave paintings as a guide to help them unravel our civilization's history.


15,000 Kids and Counting
15,000 Kids and Counting is a three-part British documentary on Channel 4, first shown in April 2014. It deals with children put up for adoption in the UK. The title is a reference to the American show 19 Kids and Counting.


15,000 Miles in a Ketch
15,000 Miles in a Ketch is a non-fiction book written by French explorer and sailor Captain Raymond Rallier du Baty, published by Thomas Nelson and Sons in 1922. The book describes Captain du Baty's experience on the voyage of the J.B. Charcot, a small French fishing ketch which weighed 48 tons. The aim of this voyage was to chart the subantarctic Kerguelen Islands, which they funded by hunting southern elephant seals in the local area and selling their oil. The crew set out from Boulogne in September 1907. and sailed across the South Atlantic, Antarctic and Indian seas to outside Melbourne Harbour in July 1909. The voyage totalled a distance of 15,000 miles, which is where the name of the novel originates.


15,000 Miles in a Ketch, Translations
Although du Baty's native language was French, 15,000 Miles in a Ketch was first published in English. It was later translated to and published in French in 1991 by Ed. maritimes et d'outre-mer under the title, Aventures aux Kerguelen.


15,000 Miles in a Ketch, Preface
Since Francis Drake went round the world in the Golden Hind there has perhaps been no voyage quite so venturesome as that in a little French fishing ketch, of forty-five tons, called the J.B. Charcot, which set out from Boulogne in September of the year 1907, and, sailing across the South Atlantic, and the Antarctic and Indian seas, lay to outside Melbourne Harbour in July 1909 - a distance of 15,000 miles.


15,000 Miles in a Ketch, Preface
She was commanded by two young French-men hardly more than boys in age, though captains in the French merchant service, named Raymond and Henri du Baty, and she carried a tiny crew of one seaman and three lads.


15,000 Miles in a Ketch, Preface
When a little while ago Captain Raymond Rallier du Baty was welcomed home by the French Geographical Society, Prince Roland Bonaparte, its president, summed up the voyage in the following words:


15,000 Miles in a Ketch, Preface
'You are sixteenth-century adventurers,' he said, 'who have been lost in the twentieth.'


15,000 Miles in a Ketch, Preface
The story of their remarkable trip in the little J. B. Charcot, named after the famous French explorer who has just returned from the Antarctic, as written by the leader of the expedition, is a true and vivid tale of romance and adventure which carries one back to the youth of the world, when men first began to venture out into unknown seas in frail craft. With high spirits, full of French gaiety, he tells of terrific storms encountered by his fishing boat, and of the many hardships which they faced with brave hearts.


15,16-Dihydroxy-alpha-eleostearic acid
15,16-Dihydroxy-α-eleostearic acid, or 15,16-Dihydroxy-(9Z,11E,13E)-9,11,13-octadecatrienoic acid, is an organic compound with formula C18H30O4, or H3C-CH2-(-CH(OH)-)2(-CH=CH-)3-(-CH2-)7-(C=O)OH. It can be seen as derived from α-eleostearic acid by the replacement of two hydrogen atoms by two hydroxyl (OH) groups.


15,16-Dihydroxy-alpha-eleostearic acid
The compound is found in the pulp and seeds of bitter melons (the fruits of Momordica charantia). It has been found to induce apoptosis in HL60 leukemia cells in vitro at a concentration of 160 μM, although it is less potent in this regard than the unsubstituted α-eleostearic acid (also found in the seed oil). While α-eleostearic acid has been found to prevent carcinogenesis in rats, this derivative does not seem to have that effect.


15,16-Dihydroxy-alpha-eleostearic acid
The compound can be extracted from the fruit with ethanol, and is soluble in ethyl acetate but not in water or acetone.


15,16-dihydrobiliverdin:ferredoxin oxidoreductase
15,16-dihydrobiliverdin:ferredoxin oxidoreductase (EC ) is an enzyme that catalyzes the following chemical reaction


15,16-dihydrobiliverdin:ferredoxin oxidoreductase
The two substrates of this enzyme are 15,16-dihydrobiliverdin and oxidized ferredoxin, whereas its two products are biliverdin IXalpha and reduced ferredoxin.


15,16-dihydrobiliverdin:ferredoxin oxidoreductase, Classification
15,16-dihydrobiliverdin:ferredoxin oxidoreductase belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with an iron-sulfur protein as acceptor. The systematic name of this enzyme class is 15,16-dihydrobiliverdin:ferredoxin oxidoreductase. This enzyme is also called PebA. This enzyme participates in porphyrin and chlorophyll metabolism.


15-25 Dalgety Road, Millers Point
15-25 Dalgety Road, Millers Point are heritage-listed terrace houses located at 15-25 Dalgety Terrace, in the inner city Sydney suburb of Millers Point in the City of Sydney local government area of New South Wales, Australia. The property is also called Dalgety Terraces and Dalgety Terrace. The property was added to the New South Wales State Heritage Register on 2 April 1999.


15-25 Dalgety Road, Millers Point, History
Millers Point is one of the earliest areas of European settlement in Australia, and a focus for maritime activities. These are a group of early twentieth century workman's terraces built c. 1911 as part of the post plague redevelopment by the Sydney Harbour Trust. First tenanted by the NSW Department of Housing in 1986.


15-25 Dalgety Road, Millers Point, Description
These large terraces feature elaborate timber verandahs with ornamental brackets in the Federation style. Also, they have teracotta Marsailles roofs. The terrace consists of a two bedroom units on both the ground floor and the first floor. The stairs leading to the upper units are generally shared by two units, with the entry to the lower units directly to the sides of them. Storeys: Two; Construction: Facebrick walls, tiled roof, timber verandah and balustrading. Style: Federation.


15-25 Dalgety Road, Millers Point, Heritage listing
As at 23 November 2000, this terrace is one of a group of early twentieth century workmen's terraces built as part of the post-bubonic plague redevelopment.


15-25 Dalgety Road, Millers Point, Heritage listing
It is part of the Millers Point Conservation Area, an intact residential and maritime precinct. It contains residential buildings and civic spaces dating from the 1830s and is an important example of 19th century adaptation of the landscape.


15-25 Dalgety Road, Millers Point, Heritage listing
Terraces was listed on the New South Wales State Heritage Register on 2 April 1999.


15-25 Dalgety Road, Millers Point, References, Attribution
This Wikipedia article was originally based on , entry number 925 in the New South Wales State Heritage Register published by the State of New South Wales and Office of Environment and Heritage 2018 under  , accessed on 13 October 2018.


15-Cis-phytoene desaturase
15-cis-phytoene desaturases (PDS, plant-type phytoene desaturases) (EC , 15-cis-phytoene:plastoquinone oxidoreductase), are enzymes involved in the carotenoid biosynthesis in plants and cyanobacteria. Phytoene desaturases are membrane-bound enzymes localized in plastids and introduce two double bonds into their colorless substrate phytoene by dehydrogenation and isomerize two additional double bonds. This reaction starts a biochemical pathway involving three further enzymes (zeta-carotene isomerase, zeta-carotene desaturase and carotene cis-trans isomerase) called the poly-cis pathway and leads to the red colored lycopene. The homologous phytoene desaturase found in bacteria and fungi (CrtI) converts phytoene directly to lycopene by an all-trans pathway.


15-Cis-phytoene desaturase, Biochemistry
PDS converts 15-cis-phytoene into 9,15,9'-tri-cis-ζ-carotene through reduction of the enzymes non-covalently bound FAD cofactor. This conversion introduces two additional double bonds at positions 11 and 11' of the carbon chain and isomerizes two adjacent already existing double bonds at positions 9 and 9' from trans to cis. The electrons involved in the reaction are subsequently transferred onto plastoquinone and to plastid terminal oxidase PTOX ultimately coupling the desaturation to oxygen reduction. Disruption of this biosynthesis step results in albinism and stunted plant growth.


15-Cis-phytoene desaturase, Applications
Disruption of PDS function can be achieved by bleaching herbicides such as norflurazon and fluridone. These inhibitors occupy the binding pocket of plastoquinone within the enzyme thus blocking it from its function. Due to the clear effect of PDS disruption in plants, the corresponding gene was targeted to showcase successful genome editing in fruit such as apples, grapes or bananas using CRISPR/Cas9 systems. In rice, the natural PDS was supplemented by its bacterial homolog to create Golden Rice and thus increase the β-carotene content of the rice endosperm.


15-Crown-5
15-Crown-5 is a crown ether with the formula (C2H4O)5. It is a cyclic pentamer of ethylene oxide that forms complex with various cations, including sodium (Na+) and potassium (K+), however, it is complementary to Na+ and thus has a higher selectivity for Na+ ions.


15-Crown-5, Synthesis
15-Crown-5 can be synthesized using a modified Williamson ether synthesis:


15-Crown-5, Synthesis
It also forms from the cyclic oligomerization of ethylene oxide in the presence of gaseous boron trifluoride.


15-Crown-5, Properties
Analogous to 18-crown-6, 15-crown-5 binds to sodium ions. Thus, when treated with this complexing agent, sodium salts often become soluble in organic solvents.


15-Crown-5, Properties
First-row transition metal dications fit snugly inside the cavity of 15-crown-5. They are too small to be included in 18-crown-6. The binding of transition metal cations results in multiple hydrogen-bonded interactions from both equatorial and axial aqua ligands, such that highly crystalline solid-state supramolecular polymers can be isolated. Metal salts isolated in this form include Co(ClO4)2, Ni(ClO4)2, Cu(ClO4)2, and Zn(ClO4)2. Seven coordinate species are most common for transition metal ions complexes of 15-crown-5, with the crown ether occupying the equatorial plane, along with 2 axial aqua ligands.


15-Crown-5, Properties
15-crown-5 has also been used to isolate salts of oxonium ions. For example, from a solution of tetrachloroauric acid, the oxonium ion [H7O3]+ has been isolated as the salt [(H7O3)(15-crown-5)2][AuCl4]. Neutron diffraction studies revealed a sandwich structure, which shows a chain of water with remarkably long O-H bond (1.12 Å) in the acidic proton, but with a very short OH•••O distance (1.32 Å).


15-Crown-5, Properties
A derivative of 15-crown-5, benzo-15-crown-5, has been used to produce anionic complexes of carbido ligands as their [K(benzo-15-crown-5)2]+ salts:


15-Hydroxyeicosatetraenoic acid
15-Hydroxyeicosatetraenoic acid (also termed 15-HETE, 15(S)-HETE, and 15S-HETE) is an eicosanoid, i.e. a metabolite of arachidonic acid. Various cell types metabolize arachidonic acid to 15(S)-hydroperoxyeicosatetraenoic acid (15(S)-HpETE). This initial hydroperoxide product is extremely short-lived in cells: if not otherwise metabolized, it is rapidly reduced to 15(S)-HETE. Both of these metabolites, depending on the cell type which forms them, can be further metabolized to 15-oxo-eicosatetraenoic acid (15-oxo-ETE), 5S,15S-dihydroxy-eicosatetraenoic acid (5(S),15(S)-diHETE), 5-oxo-15(S)-hydroxyeicosatetraenoic acid (5-oxo-15(S)-HETE, a subset of specialized pro-resolving mediators viz., the lipoxins, a class of pro-inflammatory mediators, the eoxins, and other products that have less well-defined activities and functions. Thus, 15(S)-HETE and 15(S)-HpETE, in addition to having intrinsic biological activities, are key precursors to numerous biologically active derivatives.


15-Hydroxyeicosatetraenoic acid
Some cell types (e.g. platelets) metabolize arachidonic acid to the stereoisomer of 15(S)-HpETE, 15(R)-HpETE. Both stereoisomers may also be formed as result of the metabolism of arachidonic acid by cellular microsomes or as a result of arachidonic acid auto-oxidation. Similar to 15(S")-HpETEs, 15(R)-HpETE may be rapidly reduced to 15(R)-HETE. These R,S stereoisomers differ only in having their hydroxy residue in opposite orientations. While the two R stereoisomers are sometimes referred to as 15-HpETE and 15-HETE, proper usage should identify them as R  stereoisomers. 15(R)-HpETE and 15(R)-HETE lack some of the activity attributed to their S stereoisomers but can be further to metabolized to bioactive products viz., the 15(R) class of lipoxins (also termed epi-lipoxins).


15-Hydroxyeicosatetraenoic acid
15(S)-HETE, 15(S)-HpETE, and many of their derivative metabolites are thought to have physiologically important functions. They appear to act as hormone-like autocrine and paracrine signalling agents that are involved in regulating inflammatory and perhaps other responses. Clinically, drugs that are stable analogs, and therefore mimic the anti-inflammatory actions of the lipoxins and drugs that block the production or actions of the pro-inflammatory eoxins may prove useful for treating acute and chronic inflammatory disorders.


15-Hydroxyeicosatetraenoic acid, Nomenclature and stereoisomers
15(S)-HETE is unambiguously designated by a shortened version of its IUPAC name viz., 15(S)-hydroxy-5Z,8Z,11Z,13E-eicosatetraenoic acid. In this terminology S refers to the absolute configuration of the chirality of the hydroxy functional group at carbon position 15. Its 15(R) enantiomer is designated 15(R)-hydroxy-5Z,8Z,11Z,13E-eicosatetraenoic acid. Z and E give the cis–trans isomerism about each double bond moiety at carbon positions 5, 8, 11, and 13 with Z indicating cis and E indicating trans isomerism. Both stereoisomers are produced from their corresponding S and R 15-HpETE stereoisomers, i.e. 15(S)-hydroperoxy-5Z,8Z,11Z,13E-eicosatetraenoic acid (15(S)-HpETE) and (15R)-hydroperoxy-5Z,8Z,11Z,13E-eicosatetraenoic acid (15(R)-HpETE).


15-Hydroxyeicosatetraenoic acid, Production
Human cells release arachidonic acid (i.e. 5Z,8Z,11Z,14Z-eicosatetraenoic acid) from its storage site in phospholipids by reactions that involve phospholipase C and/or lipase enzymes. This release is stimulated or enhanced by cell stimulation. The freed arachidonic acid is then converted to 15-hydroperoxy/hydroxy products by one or more of the following five pathways.


15-Hydroxyeicosatetraenoic acid, Production
15-Lipoxygenase-1: Cells metabolize arachidonic acid with 15-lipoxygenase-1 (i.e., 15-LO-1, ALOX15) to form 15(S)-HpETE as a major product and 12(S)-hydroperoxy-5Z,8Z,10E,15Z-eicosatetraenoic acid (12(S)-HpETE) and 14(S),15(S)-trans-oxido-5Z,8Z,11Z-14,15-leukotriene A4 as minor products; 15(S)-HpETE and 12(S)-HpETE are rapidly converted to 15(S)-HETE and 12(S)-hydroxy-5Z,8Z,10E,15Z-eicosatetraenoic acid (12(S)-hydroxyeicosatetraenoic acid), (i.e. 12(S)-HETE), respectively, or further metabolized through other enzyme pathways; 14(S),15(S)-trans-oxido-5Z,8Z,11Z-14,15-leukotriene A4 is metabolized by 15-LO-1 to various isomers of 8,15(S)-dihydroxy-5S,8S,11Z,13S-eicosatetraenoic acids, e.g. 8,15(S)-LTB4's.


15-Hydroxyeicosatetraenoic acid, Production
15-Lipoxygenase-2: Cells also used 15-lipoxygenase 2 (i.e. 15-LOX-2 or ALOX15B) to make 15(S)-HpETE and 15(S)-HETE. However this enzyme has a preference for metabolizing linoleic acid rather than  arachidonic acid. It therefore forms linoleic acid metabolites (e.g. 13-hydoxyperoxy/hydroxy-octadecadienoic and 9-hydroperoxy/hydroxyl-octadecadienoic acids) in greater amounts than 15(S)-HpETE and 15(S)-HETE. 15-LOX-2 also differs from 15-LOX-1 in that it does not make 12(S)-HpETE or the leukotriene A4 isomer cited above.


15-Hydroxyeicosatetraenoic acid, Production
Cycloxygenase: Cells can use prostaglandin-endoperoxide synthase 1 (i.e. cyclooxygenenase-1 or COX-1) and Prostaglandin-endoperoxide synthase 2 (COX-2) to metabolize arachidonic acid primarily to prostaglandins but also to small amounts of 11(R)-HETE and a racemic mixture of 15-HETEs composed of ~22% 15(R)-HETE and ~78% 15(S)-HETE. When pretreated with aspirin, however, COX-1 is inactive while COX-2 attacks arachidonic acid to produce almost exclusively 15(R)-HETE along with its presumed precursor 15(R)-HpETE.


15-Hydroxyeicosatetraenoic acid, Production
Microsome metabolism: Human and rat microsomal cytochrome P450s, e.g. CYP2C19, metabolize arachidonic acid to a racemic mixture of 15-HETEs, i.e., 15(R,S)-HETEs, >90% of which is the 15(R) stereoisomer.


15-Hydroxyeicosatetraenoic acid, Production
Autoxidation: The spontaneous and non-enzymatically-induced autoxidation of arachidonic acid yields 15(R,S)-hydroperoxy-5Z,8Z,11Z,13E-eicosatetraenoic acids. This non-enzymatic reaction is promoted in cells undergoing oxidative stress. Cells forming this racemic mixture of 15-hydroperoxy products may convert then to 15(R,S)-HETEs and other products. However, the uncontrolled overproduction of the 15-hydroperoxy products may react with other elements to produce cell injury.


15-Hydroxyeicosatetraenoic acid, Further metabolism
The newly formed products formed by the pathways cited in the previous section are bioactive but may also flow into down-stream pathways to form other metabolites with a different sets of bioactivity. The initially formed 15(S)-HpETE may be further metabolized by its parent cell or pass it to nearby cell by a process termed transcellular metabolism.


15-Hydroxyeicosatetraenoic acid, Activities, 15(S)-HpETE and 15(S)-HETE
Most studies have analyzed the action of 15(S)-HETE but not that of its less stable precursor 15(S)-HpETE. Since this precursor is rapidly converted to 15(S)-HETE in cells, it is likely that the two metabolites share similar activities. In many studies, however, is not clear that these activities reflect their intrinsic action or reflect their conversion to the metabolites sited above.


15-Hydroxyeicosatetraenoic acid, Activities, 15(S)-HpETE and 15(S)-HETE
15(S)-HpETE and 15(S)-HETE bind to and activate the G protein-coupled receptor, Leukotriene B4 receptor 2, i.e. BLT2. This receptor activation may mediate, at least in part, certain cell-stimulating activities of the two metabolites. BLT2 may be responsible in part or whole for mediating the growth-promoting and anti-apoptosis (i.e. anti-cell death) activities of 15(S)-HETE in cultured human breast cancer cells; human cancer colon cells, human hepatocellular HepG2 and SMMC7721 cancer cells;  mouse 3T3 cells (a fibroblast cell line); rat PA adventitia fibroblasts; Baby hamster kidney cells; and diverse types of vascular endothelial cells.


15-Hydroxyeicosatetraenoic acid, Activities, 15(S)-HpETE and 15(S)-HETE
These growth-stimulating effects could contribute to the progression of the cited cancer types in animal models or even humans and the excess fibrosis that causes the narrowing of pulmonary arteries in hypoxia-induced pulmonary hypertension or narrowing of portal arteries in the portal hypertension accompanying liver cirrhosis. 15(S)-HETE may also act through BLT2 to stimulate an immediate contractile response in rat pulmonary arteries and its angiogenic effect on human umbilical and dermal vascular endothelial cells.


15-Hydroxyeicosatetraenoic acid, Activities, 15(S)-HpETE and 15(S)-HETE
15(S)-HpETE and 15(S)-HETE also directly bind with and activate peroxisome proliferator-activated receptor gamma. This activation may contribute to the ability of 15(S)-HETE to inhibit the growth of cultured human prostate cancer PC-3, LNCaP, and DU145 cell lines and non-malignant human prostate cells; lung adenocarcinoma A549 cells; human colorectal cancer cells; corneal epithelial cells; and Jurkat T-cell leukemia cells.


15-Hydroxyeicosatetraenoic acid, Activities, 15(S)-HpETE and 15(S)-HETE
The decline in the level of 15(S)-HpETE-forming enzymes and consequential fall in cellular 15-HETE production that occurs in human prostate cancer cells may be one mechanism by which this and perhaps other human cancer cells (e.g. those of the colon, rectum, and lung) avoid the apoptosis-inducing actions of 15(S)-HpETE and/or 15(S)-HETE and thereby proliferate and spread. In this scenario,  15(S)-HETE and one of its formaing enzymes, particularly 15-LOX-2, appear to act as tumor suppressors.


15-Hydroxyeicosatetraenoic acid, Activities, 15(S)-HpETE and 15(S)-HETE
Some of the inhibitory effects of 15(S)-HpETE and 15(S)-HETE, particularly when induced by high concentrations (e.g. >1-10 micromolar), may be due to a less specific mechanism: 15(S)-HpETE and to a lesser extent 15(S)-HETE induce the generation of Reactive oxygen species. These species trigger cells to activate their death programs, i.e. apoptosis, and/or are openly toxic to the cells. 15(S)-HpETE and 15(S)-HETE inhibit angiogenesis and the growth of cultured human chronic myelogenous leukemia K-562 cells by a mechanism that is associated with the production of reactive oxygen species.


15-Hydroxyeicosatetraenoic acid, Activities, 15(S)-HpETE and 15(S)-HETE
Several bifunctional electrophilic breakdown products of 15(S)-HpETE, e.g. 4-hydroxy-2(E)-nonenal, 4-hydroperoxy-2(E)-nonenal, 4-oxo-2(E)-nonenal, and cis-4,5-epoxy-2(E)-decanal, are mutagens in mammalian cells and thereby may contripute to the development and/or progression of human cancers.


15-Hydroxyeicosatetraenoic acid, Activities, 15(R)-HETE
Similar to 15(S)-HpETE and 15(S)-HETE and with similar potency, 15(R)-HETE binds with and activates peroxisome proliferator-activated receptor gamma. The precursor of 15(R)-HETE, 15(R)-HpETE may, similar to 15(S)-HpETE, break down to the mutagenic products 4-hydroxy-2(E)-nonenal, 4-hydroperoxy-2(E)-nonenal, 4-oxo-2(E)-nonenal, and cis-4,5-epoxy-2(E)-decanal and therefore be involved in cancer development and/or progression.


15-Hydroxyeicosatetraenoic acid, Activities, 15-oxo-ETE
In cultured human monocytes of the THP1 cell line, 15-oxo-ETE inactivates IKKβ (also known as IKK2) thereby blocking this cell's NF-κB-mediated pro-inflammatory responses (e.g.,. Lipopolysaccharide-induced production of TNFα, Interleukin 6, and IL1B) while concurrently activating anti-oxidant responses upregulated through the anti-oxidant response element (ARE) by forcing cytosolic KEAP1 to release NFE2L2 which then moves to the nucleus, binds ARE, and induces production of, e.g. hemoxygenase-1, NADPH-quinone oxidoreductase, and possibly glutamate-cysteine ligase modifier. By these actions, 15-oxo-ETE may dampen inflammatory and/or Oxidative stress responses.


15-Hydroxyeicosatetraenoic acid, Activities, 15-oxo-ETE
In a cell-free system, 15-oxo-ETE is a moderately potent (IC50=1 μM) inhibitor of 12-lipoxygenase but not other human lipoxygenases. This effect could also have anti-inflammatory and anti-oxidative effects by blocking the formation of 12-HETE and Hepoxilins. 15-Oxo-ETE is an example of an  α,β unsaturated ketone Electrophile. These ketones are highly reactive with nucleophiles, adducting to, for example, the cysteines in transcription and transcription-related regulatory factors and enzymes to form their alkylated and thereby often inactivated products. It is presumed that the preceding activities of 15-oxo-ETE reflect its adduction to the indicated elements.


15-Hydroxyeicosatetraenoic acid, Activities, 15-oxo-ETE
15-Oxo-ETE, at 2-10 μM, also inhibits the proliferation of cultured Human umbilical vein endothelial cells and LoVo human colorectal cancer cells  and at the extremely high concentration of 100 μM inhibits the proliferation of cultured MBA-MD-231 and MCF7 breast cancer cells as well as SKOV3 ovarian cancer cells. They may use a similar "protein-adduction" mechanism; if so the target protein(s) for these effects have not been defined or even suggested. This 15-oxo-ETE action may prove to inhibit the remodeling of blood vessels and reduce the growth of the cited cell types and cancers. At sub-micromolar concentrations, 15-oxo-ETE has weak Chemotaxis activity for human monocytes and could serve to recruit this White blood cell into inflammatory responses.


15-Hydroxyeicosatetraenoic acid, Activities, 5-Oxo-15(S)-hydroxy-ETE
5-Oxo-15(S)-hydroxy-ETE is properly a member of the 5-HETE family of agonists which binds to the Oxoeicosanoid receptor 1, a G protein-coupled receptor, to activate its various target cells. As such, it is a potent stimulator of leukocytes, particularly eosinophils, as well as other OXE1-bearing cells including MDA-MB-231, MCF7, and SKOV3 cancer cells (see 5-Hydroxyicosatetraenoic acid and 5-oxo-eicosatetraenoic acid). It also binds with and activates PPARγ and thereby can stimulate or inhibit cells independently of OXE1.


15-Hydroxyeicosatetraenoic acid, Activities, Lipoxins
LXA4, LXB4, AT-LXA4, and AT-LXB4 are specialized proresolving mediators, i.e. they potently inhibit the progression and contribute to the resolution of diverse inflammatory and allergic reactions (see specialized proresolving mediators#lipoxins and Lipoxins).


15-Hydroxyeicosatetraenoic acid, Activities, Eoxins
Eoxin A4, Eoxin C4, Eoxin D4, and Eoxin E4 and analogs of leukotriene A4, C4, leukotriene D4, and E4. Formation of the leukotrienes is initiated by 5-lipoxygenase metabolism of arachidonic acid to form a 5,6-epoxide viz, leukotriene A4; the latter metabolite is then converted to C4, D4, and E4 in succession. Formation of the eoxins is initiated by a 15-lipoxyenase-mediated metabolism of arachiconic acid to a 14,15-epoxide, eoxin A4 followed by its serial conversion to epoxins C4, D4, and E4 using the same pathways and enzymes that metabolize leukotriene A4 to its down-stream products.


15-Hydroxyeicosatetraenoic acid, Activities, Eoxins
Preliminary studies have found that the eoxins have pro-inflammatory actions, suggest that they are involved in severe asthma, aspirin-induced asthma attacks, and perhaps other allergic reactions. The production of eoxins by Reed-Sternburg cells has also led to suggestion that they are involve in the lymphoma of Hodgkins disease. Drugs blocking the 15-lipoxygenases may be useful for inhibiting inflammation by reducing the production of the eoxins.


15-Minute Hamlet
15-Minute Hamlet is a 1976 comedic abridgement of William Shakespeare's Hamlet, written by Tom Stoppard.


15-Minute Hamlet
The play, an excerpt from Dogg's Hamlet, condenses the original Hamlet, including all the best-known scenes, into approximately 13 minutes of on-stage action. This is followed by another even more drastically reduced performance of the play from beginning to end, lasting 2 minutes, bringing the total running time up to 15 minutes.


15-hydroxyicosatetraenoate dehydrogenase
In enzymology, a 15-hydroxyicosatetraenoate dehydrogenase (EC ) is an enzyme that catalyzes the chemical reaction


15-hydroxyicosatetraenoate dehydrogenase
The 3 substrates of this enzyme are 15-Hydroxyicosatetraenoic acid (i.e. 15(S)-15-hydroxy-5,8,11-cis-13-trans-icosatetraenoate), NAD+, and NADP+, whereas its 4 products are 15-oxo-5,8,11-cis-13-trans-icosatetraenoate, NADH, NADPH, and H+.


15-hydroxyicosatetraenoate dehydrogenase
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (15S)-15-hydroxy-5,8,11-cis-13-trans-icosatetraenoate:NAD(P)+ 15-oxidoreductase. This enzyme is also called 15-hydroxyeicosatetraenoate dehydrogenase. This enzyme participates in arachidonic acid metabolism.


15-hydroxyprostaglandin dehydrogenase (NAD+)
Hydroxyprostaglandin dehydrogenase 15-(NAD) (the HUGO-approved symbol = HPGD; HGNC ID, HGNC:5154), also called 15-hydroxyprostaglandin dehydrogenase (NAD+), (EC ), is an enzyme that catalyzes the following chemical reaction:


15-hydroxyprostaglandin dehydrogenase (NAD+)
Thus, the two substrates of this enzyme are (5Z,13E)-(15S)-11alpha,15-dihydroxy-9-oxoprost-13-enoate and NAD+, whereas its 3 products are (5Z,13E)-11alpha-hydroxy-9,15-dioxoprost-13-enoate, NADH, and H+.


15-hydroxyprostaglandin dehydrogenase (NAD+)
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (5Z,13E)-(15S)-11alpha,15-dihydroxy-9-oxoprost-13-enoate:NAD+ 15-oxidoreductase. Other names in common use include NAD+-dependent 15-hydroxyprostaglandin dehydrogenase (type I), PGDH, 11alpha,15-dihydroxy-9-oxoprost-13-enoate:NAD+ 15-oxidoreductase, 15-OH-PGDH, 15-hydroxyprostaglandin dehydrogenase, 15-hydroxyprostanoic dehydrogenase, NAD+-specific 15-hydroxyprostaglandin dehydrogenase, prostaglandin dehydrogenase, and 15-hydroxyprostaglandin dehydrogenase (NAD+).


15-hydroxyprostaglandin dehydrogenase (NAD+), Structural studies
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code .


15-hydroxyprostaglandin dehydrogenase (NADP+)
In enzymology, a 15-hydroxyprostaglandin dehydrogenase (NADP+) (EC ) is an enzyme that catalyzes the chemical reaction


15-hydroxyprostaglandin dehydrogenase (NADP+)
Thus, the two substrates of this enzyme are (13E)-(15S)-11alpha,15-dihydroxy-9-oxoprost-13-enoate and NADP+, whereas its 3 products are (13E)-11alpha-hydroxy-9,15-dioxoprost-13-enoate, NADPH, and H+.


15-hydroxyprostaglandin dehydrogenase (NADP+)
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (13E)-(15S)-11alpha,15-dihydroxy-9-oxoprost-13-enoate:NADP+ 15-oxidoreductase. Other names in common use include NADP+-dependent 15-hydroxyprostaglandin dehydrogenase, NADP+-linked 15-hydroxyprostaglandin dehydrogenase, NADP+-specific 15-hydroxyprostaglandin dehydrogenase, type II 15-hydroxyprostaglandin dehydrogenase, and 15-hydroxyprostaglandin dehydrogenase (NADP+).


15-hydroxyprostaglandin dehydrogenase (NADP+), Structural studies
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code .


15-hydroxyprostaglandin-D dehydrogenase (NADP+)
In enzymology, a 15-hydroxyprostaglandin-D dehydrogenase (NADP+) (EC ) is an enzyme that catalyzes the chemical reaction


15-hydroxyprostaglandin-D dehydrogenase (NADP+)
Thus, the two substrates of this enzyme are (5Z,13E)-(15S)-9alpha,15-dihydroxy-11-oxoprosta-5,13-dienoate and NADP+, whereas its 3 products are (5Z,13E)-9alpha-hydroxy-11,15-dioxoprosta-5,13-dienoate, NADPH, and H+.


15-hydroxyprostaglandin-D dehydrogenase (NADP+)
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (5Z,13E)-(15S)-9alpha,15-dihydroxy-11-oxoprosta-5,13-dienoate:NADP+ 15-oxidoreductase. Other names in common use include prostaglandin-D 15-dehydrogenase (NADP+), dehydrogenase, prostaglandin D2, NADP+-PGD2 dehydrogenase, dehydrogenase, 15-hydroxyprostaglandin (nicotinamide adenine, dinucleotide phosphate), 15-hydroxy PGD2 dehydrogenase, 15-hydroxyprostaglandin dehydrogenase (NADP+), NADP+-dependent 15-hydroxyprostaglandin dehydrogenase, prostaglandin D2 dehydrogenase, NADP+-linked 15-hydroxyprostaglandin dehydrogenase, NADP+-specific 15-hydroxyprostaglandin dehydrogenase, NADP+-linked prostaglandin D2 dehydrogenase, and 15-hydroxyprostaglandin-D dehydrogenase (NADP+). This enzyme participates in arachidonic acid metabolism.


15-hydroxyprostaglandin-I dehydrogenase (NADP+)
In enzymology, a 15-hydroxyprostaglandin-I dehydrogenase (NADP+) (EC ) is an enzyme that catalyzes the chemical reaction


15-hydroxyprostaglandin-I dehydrogenase (NADP+)
The 3 substrates of this enzyme are (5Z,13E)-(15S)-6,9alpha-epoxy-11alpha,15-dihydroxyprosta-5,13-, dienoate, and NADP+, whereas its 3 products are (5Z,13E)-6,9alpha-epoxy-11alpha-hydroxy-15-oxoprosta-5,13-dienoate, NADPH, and H+.


15-hydroxyprostaglandin-I dehydrogenase (NADP+)
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (5Z,13E)-(15S)-6,9alpha-epoxy-11alpha,15-dihydroxyprosta-5,13-dienoa te:NADP+ 15-oxidoreductase. Other names in common use include prostacyclin dehydrogenase, PG I2 dehydrogenase, prostacyclin dehydrogenase, NADP+-linked 15-hydroxyprostaglandin (prostacyclin) dehydrogenase, NADP+-dependent PGI2-specific 15-hydroxyprostaglandin dehydrogenase, and 15-hydroxyprostaglandin-I dehydrogenase (NADP+).