16.6B: Petroleum Biodegradation
- Show how microbes biodegrade petroleum waste
Biodegradation is the process in which living organisms, most often microorganisms, break down material into simpler components. Such material is usually organic matter that could be dissolved into chemical elements by organisms that possess the metabolic pathways to perform the reactions. Some microorganisms produce enzymes that can degrade a variety of chemical compounds, including hydrocarbons like oil.
Petroleum (crude oil) is a liquid fossil fuel. It is a product of decaying organic matter, such as algae and zooplankton. It is one of the major energy sources in the world, and is also used by the chemical industry to manufacture a large number of consumer products. However, oil drilling or transportation can cause accidents that lead to contamination of the environment. Oil spills in marine environments are especially damaging because they cannot be contained and can spread over huge areas. The aromatic compounds in oil are toxic to living organisms and such spills can render havoc in an ecosystem. Natural seepages from unexplored oil sources is another source of contamination.
In the environment, such spills are naturally cleaned by microorganisms that can break down the oil. The dominant group of such bacteria are the hydrocarbonoclastic bacteria (HCB). The concentration of these bacteria increases significantly in areas of oil spill. One of the best studied representative of this group is Alcanivorax borkumensis; it’s also the only one to have its genome sequenced. This species contains individual genes responsible for breaking down certain alkanes into harmless products. It also possesses genes to direct the production of a layer of biosurfactant around the cell to enhance the oil emulsification. The addition of nitrogen and phosphorus to the Alcanivorax environment increases its growth rate. However, the addition of these nutrients in natural environments to improve the cleanup of oil spills is not desirable, since it can have an overall negative impact on the ecosystem.
Aside from hydrocarbons, crude oil contains additional toxic compounds, such as pyridine. These are degraded by representatives of other genera such as Micrococcus and Rhodococcus. Oil tarballs are biodegraded slowly by species from the genera Chromobacterium, Micrococcus, Bacillus, Pseudomonas, Candida, Saccharomyces and others. In the clean up of the Deepwater Horizon oil spill, genetically modified microorganisms were used, but some scientists suspect they might have caused health issues for people in the affected areas.
Key Points
- Biodegradation is the process of breaking down material in simpler components by living organisms, most often microorganisms.
- Oil spills occur due to accidents in the industry as a result of extraction or transportation. Since such spills spread over great areas and have deleterious effects on living organisms. It is important to use environmentally friendly mechanisms for their cleanup.
- There are many microorganisms that can break down petroleum, the most prominent being hydrocarbonoclastic bacteria. A representative of this group is Alcanivorax borkumensis, and its genome contains genes that code for the degradation of alkanes.
Key Terms
- hydrocarbons : Organic compounds made only of carbon and hydrogen. Examples include alkanes, alkenes, and aromatic hydrocarbons.
- emulsification : The process of forming a mixture of substances that are nonmixable under normal conditions.
- tarball : A blob of petroleum oil.


3.9: Foot Protection
Footwear
Employees who face possible foot or leg injuries from falling or rolling objects or from crushing or penetrating materials should wear protective footwear. Also, employees whose work involves exposure to hot substances or corrosive or poisonous materials must have protective gear to cover exposed body parts, including legs and feet. If an employee’s feet may be exposed to electrical hazards, non-conductive footwear should be worn. On the other hand, workplace exposure to static electricity may necessitate the use of conductive footwear.
An interactive or media element has been excluded from this version of the text. You can view it online here:
Examples of situations in which an employee should wear foot and/or leg protection include:
- When heavy objects such as barrels or tools might roll onto or fall on the employee’s feet;
- Working with sharp objects such as nails or spikes that could pierce the soles or uppers of ordinary shoes;
- Exposure to molten metal that might splash on feet or legs;
- Working on or around hot, wet or slippery surfaces; and
- Working when electrical hazards are present.
Safety footwear must meet ANSI minimum compression and impact performance standards in ANSI Z41-1991 (American National Standard for Personal Protection-Protective Footwear) or provide equivalent protection. Footwear purchased before July 5, 1994, must meet or provide equivalent protection to the earlier ANSI Standard (ANSI Z41.1-1967). All ANSI approved footwear has a protective toe and offers impact and compression protection. But the type and amount of protection is not always the same. Different footwear protects in different ways. Check the product’s labeling or consult the manufacturer to make sure the footwear will protect the user from the hazards they face.
Foot and leg protection choices include the following:
- Leggings protect the lower legs and feet from heat hazards such as molten metal or welding sparks. Safety snaps allow leggings to be removed quickly.
- Metatarsal guards protect the instep area from impact and compression. Made of aluminum, steel, fiber or plastic, these guards may be strapped to the outside of shoes.
- Toe guards fit over the toes of regular shoes to protect the toes from impact and compression hazards. They may be made of steel, aluminum or plastic.
- Combination foot and shin guards protect the lower legs and feet, and may be used in combination with toe guards when greater protection is needed.
- Safety shoes have impact-resistant toes and heat-resistant soles that protect the feet against hot work surfaces common in roofing, paving and hot metal industries. The metal insoles of some safety shoes protect against puncture wounds. Safety shoes may also be designed to be electrically conductive to prevent the buildup of static electricity in areas with the potential for explosive atmospheres or nonconductive to protect employees from workplace electrical hazards.
Special Purpose Shoes
Electrically conductive shoes provide protection against the buildup of static electricity. Employees working in explosive and hazardous locations such as explosives manufacturing facilities or grain elevators must wear conductive shoes to reduce the risk of static electricity buildup on the body that could produce a spark and cause an explosion or fire. Foot powder should not be used in conjunction with protective conductive footwear because it provides insulation, reducing the conductive ability of the shoes. Silk, wool and nylon socks can produce static electricity and should not be worn with conductive footwear. Conductive shoes must be removed when the task requiring their use is completed.
Note: Employees exposed to electrical hazards must never wear conductive shoes.
Electrical hazard, safety-toe shoes are nonconductive and will prevent the wearers’ feet from completing an electrical circuit to the ground. These shoes can protect against open circuits of up to 600 volts in dry conditions and should be used in conjunction with other insulating equipment and additional precautions to reduce the risk of an employee becoming a path for hazardous electrical energy. The insulating protection of electrical hazard, safety-toe shoes may be compromised if the shoes become wet, the soles are worn through, metal particles become embedded in the sole or heel, or employees touch conductive, grounded items.
Note: Nonconductive footwear must not be used in explosive or hazardous locations.
Care of Protective Footwear
As with all protective equipment, safety footwear should be inspected prior to each use. Shoes and leggings should be checked for wear and tear at reasonable intervals. This includes looking for cracks or holes, separation of materials, broken buckles or laces. The soles of shoes should be checked for pieces of metal or other embedded items that could present electrical or tripping hazards. Employees should follow the manufacturers’ recommendations for cleaning and maintenance of protective footwear.


11.6: Thoughts on Neglected Taxa
Most of today’s species-centric conservation initiatives are biased towards species that are showy, charismatic, or economically important. Consequently, conservation efforts for the vast majority of taxa are neglected, particularly in Africa where conservation funding is often more limited than elsewhere. One well-known example is known as plant blindness, the perception that animals take precedence above plants in conservation efforts. This isn’t just a case of hurt feelings among botanists: there are likely significantly more plant than animal species that should be considered as threatened (see Table 2.1); however, thorough threat assessments are hampered because, as a group, plants receive significantly less funding compared to animals (Negron-Ortiz, 2014). One explanation for this disparity is that plants are often seen as the backdrop of the environment rather than the critical foundation (as primary producers) of every food web on Earth. While showy plant species may indeed have highly visible roles in maintaining the environment and regional economies, neglected species may play an equally—sometimes even more—important role in maintaining ecosystems and ecosystem services (Schleuning et al., 2016).
Fortunately, the number of professional and amateur societies interested in protecting neglected taxa, such as reptiles, amphibians, invertebrates, fungi, and plants are rising. Some groups of experts are also organised into Specialist Groups ( https://www.iucn.org/ssc-groups ) by the IUCN. These societies and expert groups highlight the plight of neglected taxa and are willing to provide in-house expertise on best practices for protecting those species.


13.2: How to Publish to Lulu xPress
Use the LibreTexts Online Bookstore
To get a printed copy of a LibreTexts books, requires that it has been compiled as described in Section 4.8 . The print copy of any book or chapter reflects the book/chapter at the time of compilation, either as done by an administrator or by the weekly automatic batch compilation process. Thus if you have made changes and want to print that version of the book you should request recompilation by sending email to<EMAIL_ADDRESS>.
The simplest way of getting a printed copy of a book is to use the LibreTexts Online Bookstore. This is accessed either through the Download dropdown button using the Buy Print Copy selection
or through LibreTexts Commons which lists all of the books that have been compiled in each library.
Find the LibreText you want, either by using the search bar or by scrolling through the collection to select it,
and then select the Buy Print Copy button in the blue menu at the bottom left. This brings up the LibreTexts Bookstore
Books with more than 800 pages (there are several) cannot be printed in this way. Contact<EMAIL_ADDRESS>and we can help. You can select color/greyscale, paperback/hardcover and there are several delivery choices. Although Lulu is reliable, they do get backed up at the start of semesters and you should allow more time then, but you will always be able to read on line, or print pages out locally.
LibreTexts has an 8% processing fee. Payment is through Stripe and there is a quick check before leaving the LibreTexts site.  LibreTexts does its best, but with 2000+ books it is hard to be perfect. It pays to check the full pdf. If you find problems send Email to<EMAIL_ADDRESS>and we will endeavor to correct them quickly.
Getting the Publication zip file
Sometimes you may want to use another printer. Sometimes you may want your own covers, or to split books up into smaller volumes. LibreTexts openly provides the files you need.
- Click on Print Book Files in order to download Publication.zip.
- This will download the Publication zip file you will need for Lulu! or other printers. Feel free to rename this zip file, especially if you are preparing books for multiple courses.
Working with Lulu xPress at https://xpress.lulu.com/
- Make a Lulu xPress account at https://xpress.lulu.com/
- Once logged in, click Get Started or Your Account > Projects > Start New Project to begin!
- On your computer, unzip the Publication zip file that you have previously downloaded.
- It is highly recommended to skim through all of the PDFs within the Publication zip file for any errors. These files are automatically generated, so please contact us at<EMAIL_ADDRESS>if you encounter any problems!
- Enter a book title.
- For the Upload Interior file section, upload the Contents.pdf file within the unzipped Publication folder. This should take a while depending on the size of the textbook.
- Pick your Interior Color and Paper type. This can be easily changed later since these options affect the cost.
- Select a Binding type. Perfect Bound is softcover/paperback while Casewrap is hardcover.
- Choose a cover finish.
- At this point, the cost estimator will activate. Feel free to try different combinations of these options to balance the cost.
-
The next step is to upload the cover. Make sure to pick the cover that corresponds to the Binding type such as casewrap or perfect bound!
- If you go back and change the binding type, you will need to reupload the matching cover!
-
Lastly, a preview will load at the bottom for you to take a look at. This will take a few minutes, so maybe this is a good time to refill your coffee!
- Please ensure that all of the contents are correct! Once the book has been ordered, its contents cannot be modified. If you find any content problems, please contact us at<EMAIL_ADDRESS>so we can fix it!
- Third Party Statement: "Lulu accepts no responsibility for the quality of the content (including misspelled words, grammatical errors, etc.), formatting, design or overall appearance and will not provide refunds for those reasons."
 If multiple people you know want the same book, you may want to combine your orders to take advantage of Lulu's bulk discount.


6.5: Non-uniform circular motion
-
- Last updated
- Save as PDF
In non-uniform circular motion, an object’s motion is along a circle, but the object’s speed is not constant. In particular, the following will be true
- The object’s velocity vector is always tangent to the circle.
- The speed and angular speed of the object are not constant.
- The angular acceleration of the object is not zero.
- The acceleration vector will not point towards the center of the circle.
Since the acceleration vector does not point towards the center of the circle, it is usually convenient to break up the acceleration vector into two components: \(a_R\) , a component that is radial (towards the center of the circle), and \(a_T\) , a component that is tangent to the circle (and perpendicular to to the radial component). The radial component is “responsible” for the change in direction of the velocity such that the object goes in a circle. the magnitude of the radial acceleration is the same as it is for uniform circular motion:
\[\begin{aligned} a_R=\frac{v^2}{r}\end{aligned}\]
where the speed is no longer constant in time. The tangential component of the acceleration is responsible for changing the magnitude of the velocity of the object:
\[\begin{aligned} a_T = \frac{dv}{dt}\end{aligned}\]
Example \(\PageIndex{1}\)
A small ant is sleeping on a turntable just as the turntable starts to spin from rest, with an angular acceleration \(\alpha=1\text{rad/s}^{2}\) that is small enough so that, initially, the ant remains on the turntable. The ant is a distance \(R=0.1\text{m}\) from the center of the turntable, as shown in Figure \(\PageIndex{1}\) and the coefficient of static friction between the ant’s “feet” and the turntable is \(\mu_s=0.5\) . After how much time will the ant slide off from the turntable?
Solution
As the turntable accelerates, the force of static friction between the turntable and the ant will keep the ant moving with the turntable. Once the turntable is going fast enough, the force of friction will no longer be large enough to provide the total acceleration that is required to keep the ant moving with the turntable (with a constant tangential component of the acceleration and an increasing radial component of the acceleration).
The forces on the ant are:
- \(\vec F_g\) , its weight, with magnitude \(mg\) .
- \(\vec N\) , a normal force exerted by the turntable on the ant.
- \(\vec f_s\) , a force of static friction exerted by the turntable on the ant. The force of friction will be such that it has both radial and tangential components.
A free-body diagram for the forces on the ant is shown in Figure 6.4.2, as seen from above and from the side, for some point in time. We have chosen the point in time to be just when the ant is about to slide off of the turntable, when the force of static friction makes an unknown angle \(\theta\) with the \(x\) axis. We have placed the origin of the coordinate system at the center of the turntable and chosen the \(x\) axis such that the ant is located on the positive \(x\) axis with its velocity in the positive \(y\) direction. We used a three dimensional coordinate system where the weight and normal force are exerted in the \(z\) (vertical) direction since the acceleration vector of the ant will have both radial ( \(x\) ) and tangential ( \(y\) ) components.
Newton’s Second Law has to be written out in three components. The \(z\) component relates the weight and normal force:
\[\begin{aligned} \sum F_z &= N - F_g = 0\\[4pt] \therefore N&=mg\end{aligned}\]
The \(x\) component of Newton’s Second Law is such that the \(x\) component of the acceleration is its radial component:
\[\begin{aligned} \sum F_x &= -f_s\cos\theta = -ma_R = -m\frac{v^2}{R}\\[4pt] \therefore f_s\cos\theta &= m\frac{v^2}{R}\end{aligned}\]
The \(y\) component of Newton’s Second relates the tangential component of the force of static friction to the tangential component of the acceleration:
\[\begin{aligned} \sum F_y &= f_s\sin\theta = ma_T \\[4pt] \therefore f_s\sin\theta &= m\alpha R\end{aligned}\]
where we used the fact that the (linear) tangential acceleration, \(a_T\) , is related to the angular acceleration, \(\alpha\) , by:
\[\begin{aligned} a_T = \alpha R\end{aligned}\]
Summarizing the three equations that we obtained from the three components of Newton’s Second Law:
\[\begin{aligned} f_s\cos\theta &= m\frac{v^2}{R}\\[4pt] f_s\sin\theta &= m\alpha R\\[4pt] N&=mg\end{aligned}\]
Also, note that the speed, \(v(t)\) at some time \(t\) is given by simple kinematics:
\[\begin{aligned} v(t)=v_0+a_Tt=(0)+\alpha R t\end{aligned}\]
The ant will start to slip when the force of friction reaches its maximal amplitude, \(f_s=\mu_sN=\mu_Smg\) . The \(x\) of Newton’s Second Law can be used to find an expression for the time at which force of friction reaches its maximal value (in terms of the unknown angle \(\theta\) ):
\[\begin{aligned} f_s\cos\theta &= m\frac{v^2}{R}\\[4pt] \mu_sg\cos\theta &= R\alpha^2t^2\\[4pt] \therefore t &= \sqrt{\frac{\mu_sg\cos\theta}{R\alpha^2}}\end{aligned}\]
We can use the \(y\) component to determine the angle
\(\theta\) :
\[\begin{aligned} f_s\sin\theta &= m\alpha R\\[4pt] \mu_sg\sin\theta &= \alpha R\\[4pt] \therefore \sin\theta &= \frac{\alpha R}{\mu_s g}\\[4pt] \therefore \theta &= \sin^{-1}\left( \frac{\alpha R}{\mu_s g} \right)=\sin^{-1}\left( \frac{(1\text{rad/s}^{2})(0.1\text{m})}{(0.5)(9.8\text{N/kg})} \right)\\[4pt] &=1.17^{\cdot}\end{aligned}\]
The angle is very small, and we see that the force of friction is mostly directed towards the center of the circle. The radial acceleration is thus much larger than the tangential acceleration. We can then use the angle to find the time using the expression we derived above:
\[\begin{aligned} t &= \sqrt{\frac{\mu_sg\cos\theta}{R\alpha^2}}= \sqrt{\frac{(0.5)(9.8\text{N/kg})\cos(1.17^{\cdot})}{(0.1\text{m})(1\text{rad/s}^{2})^2}}\\[4pt] &=7.0\text{s}\end{aligned}\]


14.2: DNA Sequencing
-
- Last updated
- Save as PDF
- Ying Liu
- City College of San Francisco
DNA sequencing determines the order of nucleotide bases within a given fragment of DNA. This information can be used to infer the RNA or protein sequence encoded by the gene, from which further inferences may be made about the gene’s function and its relationship to other genes and gene products. DNA sequence information is also useful in studying the regulation of gene expression. If DNA sequencing is applied to the study of many genes, or even a whole genome, it is considered an example of genomics.
Dideoxy sequencing
Recall that DNA polymerases incorporate nucleotides (dNTPs) into a growing strand of DNA, based on the sequence of a template strand. DNA polymerases add a new base only to the 3’-OH group of an existing strand of DNA; this is why primers are required in natural DNA synthesis and in techniques such as PCR. Most of the currently used DNA sequencing techniques rely on the random incorporation of modified nucleotides called terminators. Examples of terminators are the dideoxy nucleotides ( ddNTPs ), which lack a 3’-OH group and therefore cannot serve as an attachment site for the addition of new bases to a growing strand of DNA (Figure \(\PageIndex{1}\)). After a ddNTP is incorporated into a strand of DNA, no further elongation can occur. Terminators are labeled with one of four fluorescent dyes, each specific for one the four nucleotide bases.
To sequence a DNA fragment, you need many copies of that fragment (Figure \(\PageIndex{2}\)). Unlike PCR, DNA sequencing does not amplify the target sequence and only one primer is used. This primer is hybridized to the denatured template DNA, and determines where on the template strand the sequencing reaction will begin. A mixture of dNTPs, fluorescently labeled terminators, and DNA polymerase is added to a tube containing the primer-template hybrid. The DNA polymerase will then synthesize a new strand of DNA until a fluorescently labeled nucleotide is incorporated, at which point extension is terminated. Because the reaction contains millions of template molecules, a corresponding number of shorter molecules is synthesized, each ending in a fluorescent label that corresponds to the last base incorporated.
The newly synthesized strands can be denatured from the template, and then separated electrophoretically based on their length (Figure \(\PageIndex{3}\)). Since each band differs in length by one nucleotide, and the identity of that nucleotide is known from its fluorescence, the DNA sequence can be read simply from the order of the colors in successive bands. In practice, the maximum length of sequence that can be read from a single sequencing reaction is about 700 bp.
A particularly sensitive electrophoresis method used in the analysis of DNA sequencing reactions is called capillary electrophoresis (Figure \(\PageIndex{6}\)). In this method, a current pulls the sequencing products through a gel-like matrix that is encased in a fine tube of clear plastic. As in conventional electrophoresis, the smallest fragments move through the capillary the fastest. As they pass through a point near the end of the capillary, the fluorescent intensity of each dye is read. This produces a graph called a chromatogram. The sequence is determined by identifying the highest peak (i.e. the dye with the most intense fluorescent signal) at each position.
Next-generation sequencing
Advances in technology over the past two decades have increased the speed and quality of sequencing, while decreasing the cost. This has become especially true with the most recently developed methods called next-generation sequencing. Not all of these new methods rely on terminators, but one that does is a method used in instruments sold by a company called Illumina . Illumina sequencers use a special variant of PCR called bridge PCR to make many thousands of copies of a short (45bp) template fragment. Each of these short template fragments is attached in a cluster in a small spot on a reaction surface. Millions of other clusters, each made by different template fragment, are located at other positions on the reaction surface. DNA synthesis at each template strand then proceeds using dye-labeled terminators that are used are reversible. Synthesis is therefore terminated (temporarily) after the incorporation of each nucleotide. Thus, after the first nucleotide is incorporated in each strand, a camera records the color of fluorescence emitted from each cluster. The terminators are then modified, and a second nucleotide is incorporated in each strand, and again the reaction surface is photographed. This cycle is repeated a total of 45 times. Because millions of 45 bp templates are sequenced in parallel in a single process, Illumina sequencing is very efficient compared to other sequencing techniques. However, the short length of the templates currently limits the application of this technology.


1.9: Medication Types
Prescription Medications, OTCs, Herbals, and Supplements
There are a variety of drug types and substances patients may utilize for symptom management or to enhance wellness. Having an accurate record and knowledge of the different types of substances a patient is taking is important to the patient’s medical and nursing plan of care. It is also important to note any substances that are prescribed, over-the-counter, or herbal that have been taken in the past month, as some medications have a long half-life and still be in the body with the potential to interact with new medications.
A variety of substances available to the public include (but are not limited to) prescription medications (including brand name and generic drugs), over-the-counter medications, and herbals and supplements.
Prescription Medications
Drugs are prescribed by a licensed prescriber for a specific person’s use and regulated through the United States Food and Drug Administration (FDA). More information about FDA approval of medications is described in the “Legal/Ethical” chapter. Prescription medications include brand-name medications and generic medications. [1]
Generic Medications
Generic medications can be safe and effective alternatives to their brand-name counterparts and often at a reduced cost. By FDA law, generic medications must have the same chemically active ingredient in the same dose (i.e., they must be “bio-equivalent”). However, the excipients (the base substance that holds the active chemical ingredient into a pill form (such as talc) or the flavoring can be different. Some patients do not tolerate these differences in excipients very well. When prescribing a medication, the provider must indicate that a generic substitution is acceptable. Nurses are often pivotal in completing insurance paperwork on the patient’s behalf if the brand-name medication is more effective or better tolerated by that particular patient. When studying medications in nursing school, it is important to know medications by their generic name, since the NCLEX exam does not currently include brand-name medications in their question format. [2]
Over-the-Counter Medications
Over-the-counter (OTC) medications do not require a prescription. They can be bought at a store and may be used by multiple individuals. OTC medications are also regulated through the FDA. Some prescription medications are available for purchase as OTC in smaller doses. For example, diphenhydramine (Benadryl) is commonly prescribed as 50 mg every 6 hours, and the prescription strength is 50 mg. However, it can also be purchased OTC in 25 mg doses (or less for children.) [3]
Herbals & Supplements
Herbs and supplements may include a wide variety of substances including vitamins, minerals, enzymes, and botanicals. Supplements such as “protein powders” are marketed to build muscle mass and can contain a variety of substances that may not be appropriate for all individuals. These herbal and supplement substances are not regulated by the FDA and most have not undergone rigorous scientific testing for safety for the public. While patients may be tempted to try these herbals and supplements, there is no guarantee that they contain the ingredients listed on the label. It is also important to remember that there is a potential for adverse effects or even overdose if the herbal or supplement contains some of the same drug that was also prescribed to a patient. [4]
-
U.S. Food & Drug Administration. (2017, Nov. 13).
Prescription drug and over the counter drugs: Questions and answers.
https://www.fda.gov/drugs/questions-answers/prescription-drugs-and-over-counter-otc-drugs-questions-and-answers
↵
-
U.S. Food & Drug Administration. (2018, Jun. 19).
Patient education
.
https://www.fda.gov/drugs/generic-drugs/patient-education
↵
-
U.S. Food & Drug Administration. (2017, Nov. 13).
Prescription drug and over the counter drugs: Questions and answers.
https://www.fda.gov/drugs/questions-answers/prescription-drugs-and-over-counter-otc-drugs-questions-and-answers
↵
-
U.S. Food & Drug Administration. (2017, Nov. 13).
What are dietary supplements?
https://www.fda.gov/food/information-consumers-using-dietary-supplements/tips-older-dietary-supplement-users#what
↵


2.3: The US and Iran
-
- Last updated
- Save as PDF
Following the end of the Second World War, Iran found itself placed in a geostrategic hotspot. It shared a long border to its north with the Soviet Union and as a result acted as a geographical buffer to any Soviet moves into the Middle East. Iran’s wider location, known as the Persian Gulf, was a region that contained the world’s largest-known pool of oil – the steady supply of which was vital for the fuelling of Western-orientated economies. So, a coincidence of time, place, politics and economics judged Iran – in most ways a weak and underdeveloped state – important. When Iran’s king, known as the Shah, found himself side-lined by a powerful left-leaning government, the United States, in league with the British, conspired to restore him to power via a covert coup in 1953. During the Cold War the United States feared that leftward political developments in nations would result in a domestic communist revolution and/or an alliance with the communist Soviet Union. In certain cases, therefore, the United States took interventionist action to contain communism from spreading. The coup was a watermark in US-Iranian history. It set up a pattern of close relations that would last 25 years, as the Shah became a loyal ally of the United States in a volatile region. This volatility was not just due to Cold War geostrategic rivalry between the United States and Soviet Union. The wider region was embroiled in a series of crises caused by decolonisation and the resulting phenomenon of Arab nationalism, regional opposition to the creation of Israel, and a major ongoing conflict between India and Pakistan. Then, as now, this was a highly unstable area of the world to live in.
Iran has always been a nation that, despite different manifestations of its internal shape and character, has aspired to greater stature internationally, or at the very least regional predominance. For example, the Shah, whose autocratic rule was brought to an end by the 1979 revolution that erased his regime and created the Islamic Republic of Iran, harboured grand designs for Iran as the premier nation of the Middle East. This vision was shared by the United States, which armed Iran with advanced weaponry, of the non-nuclear kind, during the Shah’s rule. The United States hoped its support of the Shah would allow him to widen and deepen Iranian power in order to help stabilise the region. Iran today is not much different to the Shah’s Iran in the sense that it exists within the same borders and is a nation of the same peoples. However, a significant caveat is that the regional and global role Iran was to play under the Shah was largely in line with American desires, while the role envisioned by the Islamic Republic of Iran is deeply antagonistic to just about every facet of American politics. Hence, US-Iran relations are packed with insight and intrigue due to the history and divergent paths both nations have experienced.
The Iran hostage crisis
To connect our US-Iran case study to the issue of diplomacy, we do not need to look far beyond the birth of the Islamic Republic of Iran to an episode known as the Iran hostage crisis. In November 1979 a gang of Iranian students invaded the US Embassy in Tehran, Iran’s capital city, and captured the personnel they found there. This occurred after the Shah, who was in exile, had taken residence in New York for cancer treatment. The protesters demanded his return to stand trial for various crimes committed by his regime, such as torturing political dissidents. So the prisoners, most of them US diplomatic personnel, were taken hostage as a bargaining chip, their freedom offered in exchange for the return of the Shah. The United States and Iran found themselves in uncharted waters when Iran’s new government, led by the once-exiled anti-Shah cleric Ruhollah Khomeini, officially sanctioned the hostage-taking.
Due to established diplomatic customs, an embassy – although hosted on foreign soil – is forbidden from being entered by the host state unless permission is given. So, when the Iranian protesters invaded the US Embassy in Tehran they violated a key feature of diplomacy developed over centuries to allow diplomats the freedom to do their work. This is why, to use a more contemporary example, WikiLeaks founder Julian Assange was able to avoid arrest by British police by taking up residence in an innocuous-looking terraced house in London – the house is the Embassy of Ecuador and police were refused entry. Strange as it may sound, police officers were then stationed outside the door waiting to arrest Assange should he decide to leave – an operation that has cost the British taxpayer millions of pounds. It is evident from the Assange example how highly such diplomatic customs are regarded by nations and how little this changes over time – even when those nations are in conflict.
In Iran’s case, its disregard for established diplomatic principles was both shocking and extreme. Not only did it violate established diplomatic principles, but hostage-taking by a state is defined as a war crime under the Geneva Conventions. Predictably, the United States rejected Iran’s demands and the hostage crisis became a tense diplomatic stand-off lasting 444 days. It turned Iran into an international pariah: there was worldwide outrage at its disregard not only for the rules of the international system but also for human decency as it paraded the hostages – bound and gagged – in front of news cameras. It also marked a new anti-Western political path for Iran, one in stark opposition to its pro-US stance during the time of the Shah. Despite the eventual freeing of the hostages in January 1981, the once-friendly nations had become foes. Following the crisis, all direct diplomatic links between the United States and Iran were severed until an issue of nuclear proliferation brought them to the same table over thirty years later.
Nuclear Iran
The idea of Iran possessing nuclear weapons is understandably controversial. Iran’s known disregard for international laws and customs, as evidenced by the hostage crisis and reinforced by the regular accusation that it supports terrorist and radical groups, creates an atmosphere of mistrust in the international community. News of Iran’s nuclear ambitions has been a point of major international diplomatic focus since 2002, when news leaked out that Iran had begun the development of a modern nuclear programme that showed signs of weaponisation (see Sinha and Beachy 2015 and Patrikarakos 2012). This was in spite of the fact that Iran is a signatory of the Non-Proliferation Treaty and therefore bound to neither receive nor develop nuclear arms. Iran protested that its programme was for civilian and peaceful purposes only. However, due to Iran’s international profile, few believed this. Given that the United States had just declared its ‘Global War on Terrorism’ following the 9/11 terrorist attacks, it was a tense period.
In 2002 the United States had no appetite for diplomacy with Iran over the nuclear issue. The US had already invaded Afghanistan in late 2001 and was preparing to invade Iraq in early 2003 as part of its campaign to rid the Middle East of regimes which might provide safe harbour to transnational terrorist groups such as Al Qaeda – the perpetrators of the 9/11 attacks. The United States also had a larger goal: to secure regime change in Iran, which it considered the world’s leading state-sponsor of terrorism. Seen through that logic, a war on terror was meaningless if it did not target the world’s chief terrorist. This would be done by demonstrating the might of the United States through its invasion of Iran’s neighbours – note that Afghanistan borders Iran to the east and Iraq borders Iran to the west. This would then create internal pressure on Iran’s leadership to reform of its own accord; it might even incite another revolution. If that failed, the United States was prepared to engage with Iran in some fashion in order to destroy its nuclear research facilities and possibly engineer regime change via military means, as it did in Iraq and Afghanistan. This is best encapsulated by president George W. Bush’s oftrepeated phrase that ‘all options are on the table’ regarding dealing with Iran – outlined in more complete terms by the following passage from an official government document:
The Iranian regime sponsors terrorism; threatens Israel; seeks to thwart Middle East peace; disrupts democracy in Iraq; and denies the aspirations of its people for freedom. The nuclear issue and our other concerns can ultimately be resolved only if the Iranian regime makes the strategic decision to change these policies, open up its political system, and afford freedom to its people. This is the ultimate goal of U.S. policy. In the interim, we will continue to take all necessary measures to protect our national and economic security against the adverse effects of their bad conduct. (The National Security Strategy of the United States of America 2006, 20)
In that climate, diplomacy seemed a non-starter. However, an unlikely candidate entered the fray – the European Union (EU). In 2003, three EU nations, the UK, Germany and France, initiated high-level diplomacy with Iran in an attempt to prevent a war and introduce mediation to the situation. The talks were rejected by the United States, which refused to take part, given its above-mentioned objectives. For the European nations, diplomacy was worth pursuing. Despite the UK, France and Germany being traditional allies of the United States, there was no appetite in Europe for more war in the Middle East. The war in Iraq was controversial, as many – including the United Nations, which refused to mandate the war – did not accept its rationale. The 2003 invasion of Iraq also divided Europe politically and caused mass popular protests. In this context, engaging Iran was a bold move of diplomacy – effectively stepping in the way of the world’s sole superpower when it was at its most belligerent. The talks were initially inconclusive, but they at least succeeded in engaging Iran in diplomacy, stalling its nuclear programme and offering a path to resolution other than confrontation.
In the years that followed invasion, military operations in Iraq and Afghanistan became deeply troubled as both nations (for different reasons) descended into instability. This required a longer-term, and more substantial, military presence by the United States than had been planned. As a result, the US became bogged down and was not in a position to realistically pursue a military strategy against Iran. Thus, it joined the EU-Iran talks, albeit reluctantly, in 2006. China and Russia also joined, making it a truly international diplomatic affair. It took almost a decade, but the parties finally reached agreement in July 2015. That agreement is a marvel of diplomacy. What were once mutually opposing positions characterised by decades of mistrust between the United States and Iran were painstakingly worked on by diplomats at all levels over many rounds of diplomacy until compromises acceptable to both sides were found.
Personal relationships between the diplomats were also built during the years of the negotiations, and these helped transcend state rivalries. Wendy Sherman, the US lead negotiator, recalled how she and her Iranian counterpart, Abbas Araghchi, both became grandparents during their negotiations and shared videos of their grandchildren with each other. Personal relationships like this do not dissolve or change pre-set national interests on either side, but they were instrumental in both sides developing the resolve to work tirelessly and not give up until they were able to agree on key parameters. Similar personal relations were developed between officials at the highest level when they spent 17 days locked in intense discussions in Vienna during the concluding phase of the negotiations. Sherman later described the scene on the final day, with all the diplomatic personnel gathered together, as US Secretary of State John Kerry addressed the parties:
Secretary Kerry was the last person to speak. He recounted that when he was 21 he went off to war in Vietnam. He made a commitment that he would do whatever he could in his life to make sure that there was never war, ever again. The room was absolutely still. There was quiet. And then everyone, including the Iranians, applauded. Because, I think for all of us we understood that what we had done was to try to ensure peace, not war. (Sherman 2016)
Much like the resolution of the Cuban Missile Crisis, the key to the success of the diplomatic strategy underlining the agreement was to focus on verification rather than the seemingly impossible goal of establishing trust. The diplomats laboured in the one area where a resolution was possible and found a way to make it acceptable for both sides. For Iran this overtly involved the phased removal of punitive economic sanctions that had been sponsored by the United States and also the tacit removal of any direct military threat. For the Americans, the deal placed Iran under a strict regime of verification to ensure that it cannot easily develop nuclear weapons, and if they appeared to be doing so there would be time for the international community to react before those weapons became useable. This is known as a ‘breakout’ period (see Broad and Peçanha 2015). Such a thing is only possible via an unprecedented system of strict international inspection of Iran’s facilities, which Iran agreed to.
The resolution of the US-Iran nuclear standoff would not have been possible without the bold move of three European Union nations to start a diplomatic process during the tense year of 2003. Not only was a serious confrontation between Iran and the United States avoided, but the important nonproliferation principle that has become central to international relations was upheld by securing Iran’s commitment to the Non-Proliferation Treaty. The Iran nuclear deal, although a clear example of a diplomatic success in the face of tall odds, is contentious and fragile. It will need to weather multiple political shifts in the United States and Iran that might unseat it in years to come – and it does not remove the enmity between the states, which continue to mistrust each other. However, it may be seen in retrospect as the opening act on a path of rapprochement between the two nations that may gradually replace the toxic pattern of relations begun in 1979 with the hostage crisis. Even if the United States and Iran resume a path of confrontation, it does not take away from the triumph of diplomacy in this case, with nuclear weapons in the Middle East prevented from proliferating during a critical period and an alternative offered to what might have been a major war.


4.7: Exponential Relationships (5 of 6)
Learning Objectives
- Use an exponential model (when appropriate) to describe the relationship between two quantitative variables. Interpret the model in context.
The exponential model used in the Chinook salmon example showed a decline over the years and a negative association between the variables; we call such a model an exponential decay model . (Compare this model to the exponential growth model we investigated earlier with the eagle pairing data.)
Now we investigate the meaning of the numbers in the exponential decay model.
Example
Understanding the Numbers in the Exponential Decay Model
Our goal in this example is to understand the meaning of the numbers 49,304 and 0.854 in the exponential model for predicting the Chinook population.
Predicted Chinook population = 49,304 (0.854) t
As before, the 49,304 is the initial value for the exponential model. It is the predicted value for y when t = 0.
-
To see this, plug
t
= 0 into the exponential model:
Predicted Chinook population = 49,304 (0.854) t
- Interpretation in context: When t = 0, the year is 1970. In 1970, the predicted number of Chinook is 49,304.
- It is also the y -intercept where the exponential model crosses the y-axis.
Now let’s investigate the meaning of 0.854 in the context of Chinook population.
For 1971, when t = 1, the model predicts y = 49,304 (0.854) 1 = 42,106 Chinook salmon in the Sacramento River.
For 1972, when t = 2, the model predicts y = 49,304 (0.854) 2 = 35,958 Chinook.
We can also view the calculation for t = 2 as repeated multiplication by 0.854:
Note: From this viewpoint, we find the Chinook population for 1972 by multiplying the 42,106 Chinook from the previous year by 0.854.
Here is another example: For 1973, when t = 3, we can rewrite (0.854) 3 as repeated multiplication: (0.854)(0.854)(0.854). The exponent 3 tells us to multiply the initial value 49,304 by 0.854 three times.
Note: We can also view this process as multiplying the estimated 35,985 Chinook from the previous year by 0.854.
In general, to find the estimated number of Chinook for the next year, we multiply the previous year’s estimated population by 0.854. We call this the decay factor .
We view the decay factor as containing information about the percentage decrease in the population over the previous year. To see how this works, let’s start with a hypothetical situation in which there is no change in the number of Chinook from one year to the next. Then we look at different percentages of decay for the first year to build to an understanding of the meaning of 0.854. This is the same type of thinking we performed to analyze the exponential growth model previously.
No change in the number of Chinook: If there is no change in a year, we have 100% of the fish from the previous year, so the decay factor is 1.00, which is 100% written in decimal form. As before, this is important to understand. A decay factor of 1.00 means no decline in the population. This makes sense because 49,304 (1.00) = 49,304; there is no change when we multiply by 1.00.
5% decay in the first year:
- 100% of the Chinook – 5% decrease in the Chinook = 95% remaining.
- Convert to decimal form to find the decay factor: 95% = 0.95.
- Now multiply the decay factor by 49,304 to find the number of Chinook for the next year: 49,304(0.95) = 46,839
- So, if we multiply by 0.95, this is a 5% decrease .
6.8% decay in the first year:
- 100% of the Chinook – 6.8% decrease in the Chinook = 93.2% remaining.
- Convert to decimal form to find the decay factor: 93.2% = 0.932.
- Now multiply the decay factor by 49,304 to find the number of Chinook for the next year: 49,304 (0.932) = 45,951
- So, if we multiply by 0.932, this is a 6.8% decrease .
What is the meaning of 0.854 in the model Predicted Chinook population = 49,304 (0.854) t ?
Answer: The 0.854 is the decay factor; as a percentage, it is 85.4%. This tells us that 85.4% of the previous year’s Chinook population are here this year. To determine the percent decrease, calculate 100% – 85.4% = 14.6%. There is an estimated 14.6% decrease in the number of Chinook each year. (Remember the 100% represents no change in the population.)
Contributors and Attributions
- Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution


2: Rock Forming Minerals
Identify processes of the rock cycle and the different rock types associated with each step.
- Identify igneous rocks and the steps of the rock cycle related to their formation.
- Identify sedimentary rocks and the steps of the rock cycle related to their formation.
- Identify metamorphic rocks and the steps of the rock cycle related to their formation.
One of the related fields of geology is mineralogy: the study of minerals. Geologists rely on minerals for many reasons. Not only are some minerals considered resources we use, such as gypsum, but they are the basis for the formation of rocks. Minerals are classified in different ways based on the elements that they contain. Matter (elements) makes up the minerals and minerals make up rocks. We can’t understand rocks and rock forming process or some of the other areas of geology until we have a basic knowledge of minerals.
Thumbnail: Close-up (1×1 cm) of sand from the Gobi Desert, Mongolia. (CC BY-SA 3.0;
).Contributors and Attributions
-
Original content from Kimberly Schulte (Columbia Basin College) and supplemented by Lumen Learning . The content on this page is copyrighted under a Creative Commons Attribution 4.0 International license.


1.1: Scattering Experiments on Quantum Particles
Quantum particles exhibit a feature known as wave-particle duality , which can be summarized in the quantum double-slit thought experiment . As shown in the figure below, a source emits electrons with energy \(E\) , which travel towards a screen with a pair of slits. A detector is positioned on the other side of the screen. By moving the detector around, we can measure the rate at which electrons are detected at different positions.
According to quantum theory, the experiment reveals the following: (i) the electrons arrive in discrete units—one at a time, like classical particles; (ii) when we move the detector around to measure how the detection events are statistically distributed in space, the resulting distribution matches an interference pattern formed by a classical wave diffracted by the slits. The wavelength \(\lambda\) is related to the electron energy \(E\) by
\[\lambda = \frac{2\pi}{k}, \;\;\; E = \frac{\hbar^2k^2}{2m},\]
where \(\hbar = h/2\pi\) is Dirac’s constant, and \(m\) is the electron mass. (This also implies that we can deduce the spacing of the slits from the diffraction pattern, if \(E\) is known.)
Wave-particle duality arises from quantum theory’s distinction between a particle’s state and the outcomes of measurements performed on it. The state is described by a wavefunction \(\psi(\mathbf{r})\) , which can undergo diffraction like a classical wave. Measurement outcomes, however, depend probabilistically on the wavefunction. In a position measurement, the probability of locating a particle in a volume \(dV\) around position \(\mathbf{r}\) is \(|\psi(\mathbf{r})|^2 \,dV\) .
In this chapter, we will study a generalization of the double-slit experiment called a scattering experiment . The idea is to take an object called a scatterer , shoot quantum particles at it, and measure the resulting particle distribution. Just as the double-slit interference pattern can be used to deduce the slit spacing, a scattering experiment can be used to deduce various facts about the scatterer. Scattering experiments constitute a large proportion of the methods used to probe the quantum world—from electron- and photon-based laboratory experiments for measuring the properties of materials, to huge accelerator experiments that study high-energy phenomena like the Higgs boson.
We will focus on a simple scenario with a single non-relativistic quantum particle and a classical scatterer. Consider a continuous and unbounded \(d\) -dimensional space, describable by coordinates \(\mathbf{r}\) . Somewhere around the origin, \(\mathbf{r} = 0\) , is a finite-sized scatterer. An incoming quantum particle, with energy \(E\) , is governed by the Hamiltonian
\[\hat{H} = \hat{H}_0 + V(\hat{\mathbf{r}}), \;\;\; \hat{H}_0 = \frac{\hat{\mathbf{p}}^2}{2m}.\]
Here, \(\hat{H}_0\) describes the particle’s kinetic energy, \(m\) is the particle’s mass, \(\hat{\mathbf{r}}\) and \(\hat{\mathbf{p}}\) are position and momentum operators, and \(V\) is a scattering potential describing how the scatterer affects the quantum particle. We assume that \(V(\mathbf{r}) \rightarrow 0\) as \(|\mathbf{r}| \rightarrow \infty\) , i.e., the scattering potential becomes negligible far from the origin.
We prepare an incoming particle state with energy \(E\) , and want to see how the particle is scattered by the potential. However, converting these words into a well-defined mathematical problem is a bit tricky! We will give the formulation first, before discussing its meaning:
-
The particle state
\(|\psi\rangle\)
obeys the time-independent Schrödinger equation
\[\hat{H} |\psi\rangle = E |\psi\rangle,\]
where \(E\) is the incoming particle energy.
-
This state can be decomposed into two terms,
\[|\psi\rangle \,=\, |\psi_i\rangle \,+\, |\psi_s\rangle,\]
where \(|\psi_i\rangle\) is called the incident state and \(|\psi_s\rangle\) is called the scattered state .
-
The incident state is described by a plane wave—a simultaneous eigenstate of
\(\hat{H}_0\)
(with energy
\(E\)
) and
\(\hat{\mathbf{p}}\)
(with momentum
\(\mathbf{p}_i\)
):
\[\hat{H}_0 |\psi_i\rangle = E |\psi_i\rangle \;\; \mathrm{and}\;\; \hat{\mathbf{p}} |\psi_i\rangle = \mathbf{p}_i |\psi_i\rangle, \;\; \mathrm{where}\;\; E = \frac{|\mathbf{p}_i|^2}{2m}.\]
- We require the scattered state to be an “outgoing” state. This is the most subtle of the conditions, and we will describe what it means later.
The first condition says that the scattering process is elastic. Since the scatterer takes the form of a potential \(V(\mathbf{r})\) , its interaction with the particle is conservative (i.e., the total energy \(E\) is fixed). The second condition says that the particle’s wavefunction, \(\psi(\mathbf{r}) = \langle \mathbf{r} |\psi\rangle\) , consists of a superposition of an incoming wave and a scattered wave. The third condition defines the incoming wave as a plane wave whose wavelength is determined by the chosen energy \(E\) . The final condition says that the scattered wave moves out toward infinity.
Note that this is not an eigenproblem ! Usually, when we use the time-independent Schrödinger equation, we treat it as an eigenproblem and solve for the energy eigenvalues and eigenstates. But in this case, \(E\) is an input to the calculation, describing the energy assigned to the incoming quantum particle. Given \(|\psi_i\rangle\) , \(E\) , and \(V(\mathbf{r})\) , we want to find \(|\psi_s\rangle\) .


1.1: What is Argument?
What is argument?
An argument can be a disagreement: often, we think of an argument as a kind of verbal fight that occurs between friends, relatives, or even strangers.
An argument can also be a position: You might argue strongly for something (free parking, cheaper tuition, better coffee) or against something. The facts and evidence you put together in favor of your side are your argument.
In academics, an argument is a composition, usually written, that takes a position and supports it using appropriate evidence. The word “evidence” might make you think of a courtroom, but in reality, anything you present that supports your case is evidence. Data and statistics can be evidence; experience — either yours or someone else’s — can be evidence. Evidence should be true, but it doesn’t necessarily need to be a fact, to support an academic argument.
If that sounds confusing, it’s in part because some of the terms we use to talk about academic argument are used a little differently than how we use them in our everyday life. This chapter will introduce the key terms that we’ll use to talk about argument and explain why we use them. Along the way, we’ll start getting into what argument is, how you can use it, and why you should.


2.7: II Glossary
Active listening: Communicating both verbally and nonverbally that we are interested in what the other person is saying while also actively verifying our understanding with them.
Motivational interviewing (MI): A communication skill used to elicit and emphasize a client’s personal motivation for modifying behavior to promote health.
Nurse-client relationship: A relationship that establishes trust and rapport with a specific purpose of facilitating therapeutic communication and engaging the client in decision-making regarding their plan of care.
SOLER: A mnemonic for effective nonverbal communication that stands for the following [1] :
- S: Sit and squarely face the client
- O: Open posture
- L: Lean towards the client to indicate interest in listening
- E: Eye contact
- R: Relax
Telehealth: The use of digital technologies to deliver medical care, health education, and public health services by remotely connecting multiple users in separate locations.
Teletherapy: Mental health counseling over the phone or online with videoconferencing tools.
Therapeutic communication: A type of professional communication defined as the purposeful, interpersonal, information-transmitting process that leads to client understanding and participation. [2]
- Stickley, T. (2011). From SOLER to SURETY for effective non-verbal communication. Nurse Education in Practice, 11 (6), 395–398. https://doi.org/10.1016/j.nepr.2011.03.021 ↵
- Abdolrahimi, M., Ghiyasvandian, S., Zakerimoghadam, M., & Ebadi, A. (2017). Therapeutic communication in nursing students: A Walker & Avant concept analysis. Electronic Physician, 9( 8), 4968–4977. https://doi.org/10.19082/4968 ↵


3.2: Definitions and Examples
The integers mod \(n\) and the symmetries of a triangle or a rectangle are examples of groups. A binary operation or law of composition on a set \(G\) is a function \(G \times G \rightarrow G\) that assigns to each pair \((a,b) \in G \times G\) a unique element \(a \circ b\text{,}\) or \(ab\) in \(G\text{,}\) called the composition of \(a\) and \(b\text{.}\) A group \((G, \circ )\) is a set \(G\) together with a law of composition \((a,b) \mapsto a \circ b\) that satisfies the following axioms.
-
The law of composition is
associative
. That is,
\[ (a \circ b) \circ c = a \circ (b \circ c) \nonumber \]
for \(a, b, c \in G\text{.}\)
-
There exists an element \(e \in G\text{,}\) called the
identity element
, such that for any element \(a \in G\)
\[ e \circ a = a \circ e = a\text{.} \nonumber \]
-
For each element \(a \in G\text{,}\) there exists an
inverse element
in G, denoted by \(a^{-1}\text{,}\) such that
\[ a \circ a^{-1} = a^{-1} \circ a = e\text{.} \nonumber \]
A group \(G\) with the property that \(a \circ b = b \circ a\) for all \(a, b \in G\) is called abelian or commutative . Groups not satisfying this property are said to be nonabelian or noncommutative .
The integers \({\mathbb Z } = \{ \ldots , -1, 0, 1, 2, \ldots \}\) form a group under the operation of addition.
Solution
The binary operation on two integers \(m, n \in {\mathbb Z}\) is just their sum. Since the integers under addition already have a well-established notation, we will use the operator \(+\) instead of \(\circ\text{;}\) that is, we shall write \(m + n\) instead of \(m \circ n\text{.}\) The identity is \(0\text{,}\) and the inverse of \(n \in {\mathbb Z}\) is written as \(-n\) instead of \(n^{-1}\text{.}\) Notice that the set of integers under addition have the additional property that \(m + n = n + m\) and therefore form an abelian group.
Most of the time we will write \(ab\) instead of \(a \circ b\text{;}\) however, if the group already has a natural operation such as addition in the integers, we will use that operation. That is, if we are adding two integers, we still write \(m + n\text{,}\) \(-n\) for the inverse, and 0 for the identity as usual. We also write \(m - n\) instead of \(m + (-n)\text{.}\)
It is often convenient to describe a group in terms of an addition or multiplication table. Such a table is called a Cayley table .
The integers mod \(n\) form a group under addition modulo \(n\text{.}\) Consider \({\mathbb Z}_5\text{,}\) consisting of the equivalence classes of the integers \(0\text{,}\) \(1\text{,}\) \(2\text{,}\) \(3\text{,}\) and \(4\text{.}\)
Solution
We define the group operation on \({\mathbb Z}_5\) by modular addition. We write the binary operation on the group additively; that is, we write \(m + n\text{.}\) The element 0 is the identity of the group and each element in \({\mathbb Z}_5\) has an inverse. For instance, \(2 + 3 = 3 + 2 = 0\text{.}\) Figure 3.10 is a Cayley table for \({\mathbb Z}_5\text{.}\) By Proposition 3.4, \({\mathbb Z}_n = \{0, 1, \ldots, n-1 \}\) is a group under the binary operation of addition mod \(n\text{.}\)
\(Figure \text { } 3.10 .\) Cayley table for \(({\mathbb Z_5}, +)\)
Not every set with a binary operation is a group.
Solution
For example, if we let modular multiplication be the binary operation on \({\mathbb Z}_n\text{,}\) then \({\mathbb Z}_n\) fails to be a group. The element 1 acts as a group identity since \(1 \cdot k = k \cdot 1 = k\) for any \(k \in {\mathbb Z}_n\text{;}\) however, a multiplicative inverse for \(0\) does not exist since \(0 \cdot k = k \cdot 0 = 0\) for every \(k\) in \({\mathbb Z}_n\text{.}\) Even if we consider the set \({\mathbb Z}_n \setminus \{0 \}\text{,}\) we still may not have a group. For instance, let \(2 \in {\mathbb Z}_6\text{.}\) Then 2 has no multiplicative inverse since
\begin{align*} 0 \cdot 2 & = 0 \qquad 1 \cdot 2 = 2\\ 2 \cdot 2 & = 4 \qquad 3 \cdot 2 = 0\\ 4 \cdot 2 & = 2 \qquad 5 \cdot 2 = 4\text{.} \end{align*}
By Proposition 3.4, every nonzero \(k\) does have an inverse in \({\mathbb Z}_n\) if \(k\) is relatively prime to \(n\text{.}\) Denote the set of all such nonzero elements in \({\mathbb Z}_n\) by \(U(n)\text{.}\) Then \(U(n)\) is a group called the group of units of \({\mathbb Z}_n\text{.}\) Figure 3.12 is a Cayley table for the group \(U(8)\text{.}\)
\(Figure \text { } 3.12 .\) Multiplication table for \(U(8)\)
The symmetries of an equilateral triangle described in Section 3.1 form a nonabelian group.
Solution
As we observed, it is not necessarily true that \(\alpha \beta = \beta \alpha\) for two symmetries \(\alpha\) and \(\beta\text{.}\) Using Figure 3.7, which is a Cayley table for this group, we can easily check that the symmetries of an equilateral triangle are indeed a group. We will denote this group by either \(S_3\) or \(D_3\text{,}\) for reasons that will be explained later.
We use \({\mathbb M}_2 ( {\mathbb R})\) to denote the set of all \(2 \times 2\) matrices. Let \(GL_2({\mathbb R})\) be the subset of \({\mathbb M}_2 ( {\mathbb R})\) consisting of invertible matrices; that is, a matrix
\[ A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \nonumber \]
is in \(GL_2( {\mathbb R})\) if there exists a matrix \(A^{-1}\) such that \(A A^{-1} = A^{-1} A = I\text{,}\) where \(I\) is the \(2 \times 2\) identity matrix.
Solution
For \(A\) to have an inverse is equivalent to requiring that the determinant of \(A\) be nonzero; that is, \(\det A = ad - bc \neq 0\text{.}\) The set of invertible matrices forms a group called the general linear group . The identity of the group is the identity matrix
\[ I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\text{.} \nonumber \]
The inverse of \(A \in GL_2( {\mathbb R})\) is
\[ A^{-1} = \frac{1}{ad-bc} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}\text{.} \nonumber \]
The product of two invertible matrices is again invertible. Matrix multiplication is associative, satisfying the other group axiom. For matrices it is not true in general that \(AB = BA\text{;}\) hence, \(GL_2({\mathbb R})\) is another example of a nonabelian group.
Let
\begin{align*} 1 & = \begin{pmatrix} 1 & 0\\ 0 & 1 \end{pmatrix} \qquad I = \begin{pmatrix} 0 & 1\\ -1 & 0 \end{pmatrix}\\ J & = \begin{pmatrix} 0 & i\\ i & 0 \end{pmatrix} \qquad K = \begin{pmatrix} i & 0\\ 0 & -i \end{pmatrix}\text{,} \end{align*}
where \(i^2 = -1\text{.}\)
Solution
Then the relations \(I^2 = J^2 = K^2 = -1\text{,}\) \(IJ=K\text{,}\) \(JK = I\text{,}\) \(KI = J\text{,}\) \(JI = -K\text{,}\) \(KJ = -I\text{,}\) and \(IK = -J\) hold. The set \(Q_8 = \{\pm 1, \pm I, \pm J, \pm K \}\) is a group called the quaternion group . Notice that \(Q_8\) is noncommutative.
Let \({\mathbb C}^\ast\) be the set of nonzero complex numbers. Under the operation of multiplication \({\mathbb C}^\ast\) forms a group. The identity is \(1\text{.}\) If \(z = a+bi\) is a nonzero complex number,
Solution
then
\[ z^{-1} = \frac{a -bi}{a^2 +b^2} \nonumber \]
is the inverse of \(z\text{.}\) It is easy to see that the remaining group axioms hold.
A group is finite , or has finite order , if it contains a finite number of elements; otherwise, the group is said to be infinite or to have infinite order . The order of a finite group is the number of elements that it contains. If \(G\) is a group containing \(n\) elements, we write \(|G| = n\text{.}\) The group \({\mathbb Z}_5\) is a finite group of order \(5\text{;}\) the integers \({\mathbb Z}\) form an infinite group under addition, and we sometimes write \(|{\mathbb Z}| = \infty\text{.}\)
Basic Properties of Groups
The identity element in a group \(G\) is unique; that is, there exists only one element \(e \in G\) such that \(eg = ge = g\) for all \(g \in G\text{.}\)
- Proof
-
Suppose that \(e\) and \(e'\) are both identities in \(G\text{.}\) Then \(eg = ge = g\) and \(e'g = ge' = g\) for all \(g \in G\text{.}\) We need to show that \(e = e'\text{.}\) If we think of \(e\) as the identity, then \(ee' = e'\text{;}\) but if \(e'\) is the identity, then \(ee' = e\text{.}\) Combining these two equations, we have \(e = ee' = e'\text{.}\)
Inverses in a group are also unique. If \(g'\) and \(g''\) are both inverses of an element \(g\) in a group \(G\text{,}\) then \(gg' = g'g = e\) and \(gg'' = g''g = e\text{.}\) We want to show that \(g' = g''\text{,}\) but \(g' = g'e = g'(gg'') = (g'g)g'' = eg'' = g''\text{.}\) We summarize this fact in the following proposition.
If \(g\) is any element in a group \(G\text{,}\) then the inverse of \(g\text{,}\) denoted by \(g^{-1}\text{,}\) is unique
Let \(G\) be a group. If \(a, b \in G\text{,}\) then \((ab)^{-1} = b^{-1}a^{-1}\text{.}\)
- Proof
-
Let \(a, b \in G\text{.}\) Then \(abb^{-1}a^{-1} = aea^{-1} = aa^{-1} = e\text{.}\) Similarly, \(b^{-1}a^{-1}ab = e\text{.}\) But by the previous proposition, inverses are unique; hence, \((ab)^{-1} = b^{-1}a^{-1}\text{.}\)
Let \(G\) be a group. For any \(a \in G\text{,}\) \((a^{-1})^{-1} = a\text{.}\)
- Proof
-
Observe that \(a^{-1} (a^{-1})^{-1} = e\text{.}\) Consequently, multiplying both sides of this equation by \(a\text{,}\) we have
\[ (a^{-1})^{-1} = e (a^{-1})^{-1} = a a^{-1} (a^{-1})^{-1} = ae = a\text{.} \nonumber \]
It makes sense to write equations with group elements and group operations. If \(a\) and \(b\) are two elements in a group \(G\text{,}\) does there exist an element \(x \in G\) such that \(ax = b\text{?}\) If such an \(x\) does exist, is it unique? The following proposition answers both of these questions positively.
Let \(G\) be a group and \(a\) and \(b\) be any two elements in \(G\text{.}\) Then the equations \(ax = b\) and \(xa = b\) have unique solutions in \(G\text{.}\)
- Proof
-
Suppose that \(ax = b\text{.}\) We must show that such an \(x\) exists. We can multiply both sides of \(ax = b\) by \(a^{-1}\) to find \(x = ex = a^{-1}ax = a^{-1}b\text{.}\)
To show uniqueness, suppose that \(x_1\) and \(x_2\) are both solutions of \(ax = b\text{;}\) then \(ax_1 = b = ax_2\text{.}\) So \(x_1 = a^{-1}ax_1 = a^{-1}ax_2 = x_2\text{.}\) The proof for the existence and uniqueness of the solution of \(xa = b\) is similar.
If \(G\) is a group and \(a, b, c \in G\text{,}\) then \(ba = ca\) implies \(b = c\) and \(ab = ac\) implies \(b = c\text{.}\
This proposition tells us that the right and left cancellation laws are true in groups. We leave the proof as an exercise.
We can use exponential notation for groups just as we do in ordinary algebra. If \(G\) is a group and \(g \in G\text{,}\) then we define \(g^0 = e\text{.}\) For \(n \in {\mathbb N}\text{,}\) we define
\[ g^n = \underbrace{g \cdot g \cdots g}_{n \; \text{times}} \nonumber \]
and
\[ g^{-n} = \underbrace{g^{-1} \cdot g^{-1} \cdots g^{-1}}_{n \; \text{times}}\text{.} \nonumber \]
In a group, the usual laws of exponents hold; that is, for all \(g, h \in G\text{,}\)
- \(g^mg^n = g^{m+n}\) for all \(m, n \in {\mathbb Z}\text{;}\)
- \((g^m)^n = g^{mn}\) for all \(m, n \in {\mathbb Z}\text{;}\)
- \((gh)^n = (h^{-1}g^{-1})^{-n}\) for all \(n \in {\mathbb Z}\text{.}\) Furthermore, if \(G\) is abelian, then \((gh)^n = g^nh^n\text{.}\)
We will leave the proof of this theorem as an exercise. Notice that \((gh)^n \neq g^nh^n\) in general, since the group may not be abelian. If the group is \({\mathbb Z}\) or \({\mathbb Z}_n\text{,}\) we write the group operation additively and the exponential operation multiplicatively; that is, we write \(ng\) instead of \(g^n\text{.}\) The laws of exponents now become
- \(mg + ng = (m+n)g\) for all \(m, n \in {\mathbb Z}\text{;}\)
- \(m(ng) = (mn)g\) for all \(m, n \in {\mathbb Z}\text{;}\)
- \(m(g + h) = mg + mh\) for all \(n \in {\mathbb Z}\text{.}\)
It is important to realize that the last statement can be made only because \({\mathbb Z}\) and \({\mathbb Z}_n\) are commutative groups.
Historical Note
Although the first clear axiomatic definition of a group was not given until the late 1800s, group-theoretic methods had been employed before this time in the development of many areas of mathematics, including geometry and the theory of algebraic equations.
Joseph-Louis Lagrange used group-theoretic methods in a 1770–1771 memoir to study methods of solving polynomial equations. Later, Évariste Galois (1811–1832) succeeded in developing the mathematics necessary to determine exactly which polynomial equations could be solved in terms of the coefficients of the polynomial. Galois' primary tool was group theory.
The study of geometry was revolutionized in 1872 when Felix Klein proposed that geometric spaces should be studied by examining those properties that are invariant under a transformation of the space. Sophus Lie, a contemporary of Klein, used group theory to study solutions of partial differential equations. One of the first modern treatments of group theory appeared in William Burnside's The Theory of Groups of Finite Order [1], first published in 1897.


1.21.3: Thermodynamic Energy: Potential Function
The Master Equation states that the change in thermodynamic energy of a closed system is given by equation (a).
\[\mathrm{dU}=\mathrm{T} \, \mathrm{dS}-\mathrm{p} \, \mathrm{dV}-\mathrm{A} \, \mathrm{d} \xi ; \quad \mathrm{A} \, \mathrm{d} \xi \geq 0 \nonumber \]
At constant entropy (i.e. \(\mathrm{dS} = 0\)) and constant volume (i.e. \(\mathrm{dV} = 0\)), equation (a) leads to equation (b).
\[\mathrm{dU}=-\mathrm{A} \, \mathrm{d} \xi \nonumber \]
But
\[A \, d \xi \geq 0 \nonumber \]
Therefore all spontaneous processes at constant \(\mathrm{S}\) and constant \(\mathrm{V}\) take place in a direction for which the thermodynamic energy decreases.
The latter statement shows the power of thermodynamics in that it is quite general; we have not stated the nature of the spontaneous process. Of course chemists are interested in those cases where the spontaneous process is chemical reaction. Thus we have a signal of what happens to the energy of the system; the key word here is spontaneous.
In the context of most chemists interests, equation (b) is not terribly helpful. Chemists do not normally run their experiments at constant \(\mathrm{S}\) and constant \(\mathrm{V}\). In fact it is not obvious how one might do this. Nevertheless equation (b) is important finding its application when we turn to other thermodynamic variables which can be used as thermodynamic potentials; e.g. Gibbs energy.


15.21F: Lyme Disease
- Discuss the mode of transmission and symptoms for lyme disease
Lyme disease (aka Lyme borreliosis) is caused by bacteria from the Borrelia genus, and is the most common tick-borne disease in the Northern Hemisphere. Borrelia burgdorferi sensu stricto is the main cause of Lyme disease in North America, whereas Borrelia afzelii and Borrelia garinii cause most European cases. Borrelia is transmitted to humans through the bite of infected ticks belonging to a few species of the genus Ixodes (“hard ticks” ). The disease is named after the towns of Lyme and Old Lyme, Connecticut, where a number of cases were identified in 1975. Although it was realized that Lyme disease was a tick-borne disease in 1978, the cause of the disease remained a mystery until 1981, when B. burgdorferi was identified.
Lyme disease can affect multiple body systems and produce a range of symptoms, though not all patients with Lyme disease will have all symptoms, and many of the symptoms are not specific to Lyme disease. The incubation period from infection to the onset of symptoms is usually one to two weeks, but can be much shorter (days), or much longer (months to years). Most infections are caused by ticks in the nymphal stage, as they are very small and may feed undetected for long periods of time, with symptoms occurring most often from May through September because of this life cycle. An infected tick must be attached for at least a day for transmission to occur, and only about 1% of recognized tick bites result in Lyme disease.
Lyme disease begins with a localized infection, affecting the area at the site of the tick bite with a circular, outwardly expanding rash called erythema chronicum migrans (EM), which gives the appearance of a bullseye. Patients may also experience flu-like symptoms, such as headache, muscle soreness, fever, malaise, fatigue, and depression. In most cases, the infection and its symptoms are eliminated by antibiotics, especially if the illness is treated early. Delayed or inadequate treatment can lead to more serious symptoms, which can be disabling and difficult to treat. Asymptomatic infections may occur, though this is the case in less than 7% of infected individuals in the United States. Asymptomatic infection may be more common in Europe.
Left untreated, Borrelia bacteria begins to spread through the bloodstream within days to weeks after the onset of local infection, progressing symptoms to the joints, heart, and central nervous system. These symptoms include migrating pain in muscles, joints, and tendons; neck stiffness; sensitivity to light; and heart palpitations and dizziness caused by changes in heartbeat. Acute neurological problems, termed “neuroborreliosis”, appear in 10–15% of untreated patients. EM may even develop at sites across the body that bear no relation to the original tick bite. Radiculoneuritis causes shooting pains that may interfere with sleep, as well as abnormal skin sensations. Mild encephalitis may lead to memory loss, sleep disturbances, or mood changes.
After several months, untreated or inadequately treated patients may go on to develop severe and chronic symptoms, including permanent paraplegia in the most extreme cases. Patients may develop Lyme arthritis, usually affecting the knees; nerve pain radiating out of the spine (Bannwarth syndrome); and shooting pains, numbness, and tingling in the hands or feet. A neurologic syndrome called Lyme encephalopathy is associated with subtle cognitive problems, such as difficulties with concentration and short-term memory. These patients may experience profound fatigue. Chronic encephalomyelitis can involve cognitive impairment, weakness in the legs, awkward gait, facial palsy, bladder problems, vertigo, and back pain. In rare cases, untreated Lyme disease may cause frank psychosis, which has been mis-diagnosed as schizophrenia or bipolar disorder. Panic attacks and anxiety can occur; as well as delusional behavior and detachment from themselves and reality.
Key Points
- Borrelia is transmitted to humans through the bite of infected ticks belonging to a few species of the genus Ixodes (“hard ticks”).
- Lyme disease can affect multiple body systems and produce a range of symptoms.
- Lyme disease begins with a characterized bullseye rash called erythema chronicum migrans.
Key Terms
- nymphal : In some invertebrates, of or pertaining to the immature form.
- asymptomatic : not exhibiting any symptoms of disease.
- paraplegia : A condition where the lower half of a patient’s body is paralyzed and cannot move.


7.13: Interactions
-
- Last updated
- Save as PDF
- Cindy Stephens, Gina Peterson, Sharon Eyrich, & Jennifer Paris
- College of the Canyons via College of the Canyons
It cannot be repeated enough that human beings are social creatures that thrive on relationships. In order to maximize a child’s interests, willingness to take risks, try again when initial attempts have not gone as planned, and learn to their fullest, we must establish and maintain relationships with children that foster trust and encourage autonomy and initiative.
Interactions should be as much of what we plan for as the materials and experiences themselves. Built into every curriculum plan should be thoughts about how the teacher will:
- Create a sense of safety and trust
- Acknowledge children’s autonomy
- Foster a growth mindset
- Extend learning through open-ended statements and conversations
Reflect back on Chapter 3 - The Teacher’s Role and the importance of establishing and maintaining relationships to foster brain development. The concept of a “Neuro-Relational approach” will be present in the curriculum that we plan for young children.
Quality interactions will include:
- Valuing each child for who they are
- Finding something special and positive about each child
- Maintaining a positive attitude
- Finding time each day to interact and make a connection with every child
- Respecting children’s opinions and ideas
- Being present for children
- Reflecting back what they say and do
- Listening to listen hear rather than respond
- Creating a warm and welcoming environment
- Being consistent as a means of establishing trust
- Focusing on the process
- Focusing on what children CAN do rather than what they can’t do YET
- Including families as valuable team members (for more information refer to Chapter 8 – Relating to Families)
- Understanding and respecting each child’s individual and group culture
Pause to Reflect
Do these make sense to you? Are there others? Which will be easiest for you? Most difficult? Why?
Communication goes hand in hand with interaction. Being aware of what we are saying and how we are saying it is crucial in establishing and maintaining relationships. Positive communication includes:
Nonverbal
- Get down to children’s level
- Observe
- Be present
- Listen
- Understand
- Use positive facial expressions
- Look interested
- Smile
Verbal
- Be aware of the tone and volume of your voice
- Speak slowly and clearly
- Use facial expressions and body movements that match your words
- Give choices and share control
- Focus on the positive
- Describe what you are doing as children are watching
- Model appropriate language
- Reflect back what children are saying
- Have conversations with multiple exchanges
- Consider close vs. open-ended questions and statements
The type of questions you ask will elicit different responses. Sometimes we want a direct answer while most of the time we want to generate deeper thinking to promote learning. Consider each of the questions below regarding the color blue:
- “Are you wearing blue today”?
- “What color are your pants”?
- “Tell me all the things you see that are blue”
Each will point out that the child’s pants are blue, but in very different ways.
Considering what type of thinking we want to promote enables us to create questions and statements that spark that knowledge. Thinking is often broken down into two types:
- Convergent thinking – emphasizes coming up with one correct response; “converging” on the “right” answer.
- Divergent thinking – emphasized generating multiple responses, brainstorming and “thinking outside the box”; “diverging” into different ways of thinking and answering.
Both can be valuable as children develop and learn. Often starting with divergent questions and then following up with convergent questions allows for broad thinking that can then be narrowed down.
Pause to Reflect
How might you use these communication strategies in your planning, implementing, and reviewing/assessing curriculum for children?
Vignette
Teacher Odom sets up a play dough table with ingredients to make dough and materials to use after it is made. He lets the children know that he will be there if anyone wants to join him. Three children hurry over and he greets each of them and says, “I’m so happy you decided to join. Let’s get started”. He shows them the recipe and encourages them to decide how to proceed. They take turns adding the ingredients and he shows patience and interest as they take the lead, asking open-ended questions along the way, “What will we do next?” “What do you think will happen?” and facilitating conversations. He points out each of their contributions along the way and focuses on the processes they are using rather than the finished product. He encourages them to interact with each other, “Wow, look at how B did that” and “Isn’t it interesting how you both added flour but you did it so differently”. Other children come to join and he encourages the original three to find ways to include them. When the dough is complete, the children use a variety of rolling pins, cookie cutters, and dull plastic knives to play with it. He continues expressing his interest, by commenting on how each child is using the materials and asks open-ended questions to foster deeper learning.
Pause to Reflect
What are some ways the teacher fostered interactions with children to enhance their trust, encourage their autonomy and initiative, and foster thinking and learning?
Pause to Reflect
Going back to Table 6.1 on Development and Learning, can you find skills from each of the categories that the children would be enhancing? How do interactions help foster these skills?
In Chapter 4 (Observation and Assessment) we discussed the importance of using our observational skills to get to know the individual children we are planning for. We introduced the Cycle of Reflection, which begins with observing, documenting, and interpreting so that you can plan, implement and evaluate appropriate interactions and experiences that make sense and meet the needs of the particular children we are working with. Below we will take a deeper look at the ways we use our observational data and interpretations.