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Dr. Daniel B. Botkin objectively assesses the true prospects, limitations, costs, risks, dangers, and tradeoffs associated with every leading and emerging source of energy, including oil, natural gas, coal, hydroelectric, nuclear, wind, solar, ocean power, and biofuels. Next, Botkin addresses the energy distribution system, outlining how it currently works, identifying its inefficiencies, and reviewing options for improving it. Finally, Botkin turns to solutions, offering a realistic, scientifically and economically viable path to a sustainable, energy-independent future: one that can improve the quality of life for Americans and for people around the world. The Future of Fossil Fuels What can we realistically expect from oil, gas, and coal? Will Alternative Energy Sources Really Matter? Running the numbers on solar, wind, biofuels, and other renewables Must We All Wear Sweaters and Live in Caves? The right role for efficiency--and why energy minimalism isn't the solution Where We Can Start--and What Will Happen if We Don't No magic bullet, but there are sensible, realistic solutions Technology Technology eBook, Pearson Education


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GOP presidential front-runner Donald Trump Donald John TrumpObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE on Tuesday mocked Sen. Ted Cruz Rafael (Ted) Edward CruzSenate Republicans face tough decision on replacing Ginsburg Cruz: Trump should nominate a Supreme Court justice next week Renewed focus on Trump's Supreme Court list after Ginsburg's death MORE (R-Texas) for mistakenly calling Florida his home state.

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INTRODUCTION {#sec1-1}
============

Glycogenosis II \[Glycogen storage Disease type II (GSDII); Pompe disease\] is an autosomal recessive lysosomal storage disorder due to deﬁciency of acid alpha-glucosidase resulting in lysosomal accumulation of glycogen in skeletal, cardiac and smooth muscle, with progressive motor, cardiac and respiratory failure.\[[@ref1]\] Although the pathological process mainly affects muscles, several other tissues may be involved in the course of the disease; therefore GSD II should be regarded as a multisystem disorder also involving liver, spleen, salivary glands, kidney, bone and blood vessels.\[[@ref2][@ref3]\] Craniovertebral junction (CVJ) malformations have never been reported so far in GSDII patients.

We here report a GSDII patient who recurrently suffered from headache, neck pain and dizziness which were likely related to a very rare complex CVJ malformation.

CASE DESCRIPTION {#sec1-2}
================

We describe the case of a 43-year-old woman affected with GSDII who harbored the mutations IVS1-13T\>G and c.2237G\>A in the acid alpha-glucosidase gene. The onset of symptoms was at the age of 16 with difﬁculty in climbing stairs and standing up from the floor. Her neurological examination showed anserine gait, proximal muscle weakness especially of lower limbs, and mild eyelid ptosis.

Since several years she suffered from persistent neck pain, dizziness and headache that greatly affect her quality of life. In order to investigate these symptoms, she was submitted to brain MRI and cervical spine CT scan with selective study of skull occipital junction.

Neuroimaging showed a rare complex CVJ malformation composed of basilar invagination, basiocciput hypoplasia, partial C1 assimilation, C1 posterior arch hypoplasia, C1 lateral mass hypoplasia and offset \[[Figure 1](#F1){ref-type="fig"}\]. Measurement tools used to assess the diagnosis were Chamberlain line, Wackenheimclivus baseline and atlanto-occipital joint axis angle.\[[@ref4]\]

![Cervical spine CT scan: (a) Coronal view showing posterior C1 arch partial assimilation and hypoplasia, (b) Sagittal view showing basiocciput hypoplasia and basilar invagination, (c) Coronal view showing C1 right lateral mass hypoplasia and articular offset](JCVJS-5-137-g001){#F1}

DISCUSSION {#sec1-3}
==========

The bony CVJ is an articulation point capable of complex motions distinct from the remainder of the vertebral column. It can be conceptually divided into two components with respect to the governance of intersegmental movements.\[[@ref5]\] The first component mainly consists of a central pivot made up of the dens and the C2 vertebral body. However, the basiocciput, though anatomically part of the foramen magnum, is embryologically and functionally in vertical linearity with the dens and is thus part of the central pillar. The second component consists of two ringed structures surrounding the central pivot, albeit eccentrically. They are the foramen magnum ring (comprising the lateral portion of the basiocciput and the exocciput including the occipital condyles and the opisthion) and the atlantal ring with its anterior and posterior arches and lateral masses.

*Hox* and *Pax* genes are involved in the regulation of CVJ development.\[[@ref5]\] *Hox* genes control the body plan of the embryo along the anterior-posterior axis. Following primary segmentation, they determine the positional identity of the pre-vertebral segments and the vertebral phenotypes (types of vertebrae that will form on different segments). *Pax* gene family is important in early development for the specification of specific tissues and is implicated in sclerotomalresegmentation.

The malformation found in our patient involves both the components of CVJ, including basiocciput and atlantal ring, and it is likely to give rise to neck pain, dizziness and headache by altering the complex motion function of this region.

The correlation between CVJ malformation, *Hox* and *Pax* gene families and GSDII in this patient remains unknown and we cannot reasonably rule out the incidental co-occurrence of the two conditions. However, the rarity of this malformation as well as the well-known GSDII propensity to multisystem involvement (i.e. brain abnormalities, bone mineral density alterations, rigid spine, large vessel malformations, hemangiomas)\[[@ref6][@ref7][@ref8][@ref9][@ref10]\] makes intriguing the idea of a possible relationship, thus suggesting to study the CVJ in the diagnostic process of GSDII patients in order to assess the CVJ malformation frequency in GSDII population.

**Source of Support:** Nil

**Conflict of Interest:** None declared.


/*******************************************************************************
 * Copyright (c) 2013, 2017 Spring IDE Developers
 * All rights reserved. This program and the accompanying materials
 * are made available under the terms of the Eclipse Public License v1.0
 * which accompanies this distribution, and is available at
 * https://www.eclipse.org/legal/epl-v10.html
 *
 * Contributors:
 *     Spring IDE Developers - initial API and implementation
 *******************************************************************************/
package org.springframework.ide.eclipse.core.java.classreading;

import java.io.IOException;

import org.eclipse.core.resources.IFile;
import org.eclipse.core.runtime.IStatus;
import org.eclipse.core.runtime.Status;
import org.eclipse.jdt.core.IType;
import org.eclipse.jdt.core.JavaModelException;
import org.springframework.asm.ClassReader;
import org.springframework.core.io.Resource;
import org.springframework.core.type.AnnotationMetadata;
import org.springframework.core.type.ClassMetadata;
import org.springframework.core.type.classreading.MetadataReader;
import org.springframework.ide.eclipse.core.SpringCore;
import org.springframework.ide.eclipse.core.io.FileResource;
import org.springframework.ide.eclipse.core.type.asm.CachingClassReaderFactory;

/**
 * @author Martin Lippert
 * @since 3.3.0
 */
public class JdtConnectedMetadataReader implements MetadataReader {

	private final IType type;
	private final JdtConnectedAnnotationMetadataReadingVisitor visitor;

	public JdtConnectedMetadataReader(IType type, CachingClassReaderFactory classReaderFactory, ClassLoader classloader) throws IOException {
		this.type = type;

		this.visitor = new JdtConnectedAnnotationMetadataReadingVisitor(classloader, type);

		try {
			ClassReader classReader = classReaderFactory.getClassReader(type.getFullyQualifiedName());
			classReader.accept(this.visitor, 0);
		}
		catch (IOException e) {
			SpringCore.log(new Status(IStatus.WARNING, SpringCore.PLUGIN_ID, 0, e.getMessage(), e));
			throw e;
		}
	}

	public ClassMetadata getClassMetadata() {
		return this.visitor;
	}

	public AnnotationMetadata getAnnotationMetadata() {
		return this.visitor;
	}

	public Resource getResource() {
		try {
			return new FileResource((IFile) this.type.getUnderlyingResource());
		}
		catch (JavaModelException e) {
			return null;
		}
	}

}


1. Field of the Invention
The present invention relates to a vehicle body rear structure.
2. Description of Related Art
Conventionally, a vehicle body rear structure provided with approximately a Y-shaped stiffening structure in plane view has been known. This is disclosed in, for example, U.S. Pat. No. 6,834,910. FIG. 11A is a bottom plane view schematically showing a conventional vehicle body rear structure as seen from a bottom side of a vehicle body. FIG. 11B is a side view schematically showing a conventional vehicle body rear structure as seen from a side of the vehicle body.
As shown in FIG. 11A, the stiffening structure is formed in approximately the Y-shape by a support member 109 and a pair of tension-compression bars 101 (tank lower frames). The support member 109 is disposed at approximately a center of a vehicle body B in a vehicle width direction, and extends in a front-rear direction of the vehicle body B. A rear end of the support member 109 is jointed to a cross support member 106 (rear floor end cross member), and a front end of the support member 109 is jointed to a receiving bracket 110. It is noted that the cross support member 106 is jointed to each rear end portion of the rear frames 102.
Each rear end of the tension-compression bars 101 is jointed to the receiving bracket 110 at a position close to a center of the vehicle body B in the vehicle width direction, and each front end of the tension-compression bars 101 extending to each of side sills 105 in approximately a V-shape is jointed to the each of the side sills 105.
The vehicle body rear structure described above has a reinforced structure from the cross support member 106 disposed on a rear side of the vehicle body B to the side sills 105 disposed on right and left sides of the vehicle body B via the support member 109, receiving bracket 110, and tension-compression bars 101.
However, in the vehicle body rear structure, as shown in FIG. 11B, the support member 109 has been disposed to be inclined downward from the cross support member 106 to the receiving bracket 110. Therefore, when a load upon a rear-end collision is input to the cross support member 106, there has been a possibility that the load may not be sufficiently transmitted to the receiving bracket 110 from the cross support member 106 via the support member 109. As a result, in the conventional vehicle body rear structure described above, it has been difficult to effectively disperse the input load from the receiving bracket 110 to the tension-compression bars 101 and side sills 105 via the tension-compression bars 101.
Therefore, for solving the above issue, a vehicle body rear structure may be conceivable, in which the support member 109 is horizontally disposed and jointed between the cross support member 106 and receiving bracket 110. Therefore, in the vehicle body rear structure described above, a load input from the cross support member 106 upon a rear-end collision is transmitted to the tension-compression bars 101 via the support member 109, which is disposed horizontally.
However, in the vehicle body rear structure, when the tension-compression bars 101 are deformed by a large load upon a rear-end collision, a load-displacement characteristic of an ordinary tension-compression bars 101, which are formed by a hollow member (tubular member), shows a rapid decrease of the load after reaching a maximum of the load, which increases in response to the displacement. Therefore, the vehicle body rear structure described above can not sufficiently bear the large load input upon the rear-end collision.
In addition, in the conventional vehicle body rear structure, if front and rear portion structures of the stiffening members such as the support member 109, receiving bracket 110, and tension-compression bars 101, and strengths of the stiffening members are not balanced, it is difficult to deform the vehicle body rear structure by turns upon a rear-end collision from a rear portion of the structure. As a result, in the vehicle body rear structure, uncrushed portions are left in these stiffening members, thereby resulting in insufficient collision energy absorption upon the rear-end collision.
In addition, in the vehicle body rear structure, if the structures and strengths are not balanced as described above, an increase of a strength of each of the stiffening members is required for improving the strength of the vehicle body rear structure and collision energy absorption performance. Specifically, it is required to, for example, increase thicknesses of materials forming the stiffening members and cross sections of the stiffening members, or to apply a material having a higher strength to the stiffening members. As a result, in the vehicle body rear structure, a weight and manufacturing cost of the vehicle body rear structure are increased.
It is, therefore, an object of the present invention to provide a vehicle body rear structure which can bear a large load upon a rear-end collision and has an excellent collision energy absorption performance, in addition to enabling reductions in weight and manufacturing cost of the vehicle body rear structure.


Members of a Chinese honor guard wipe sweat off of their faces before a welcome ceremony for Palestinian President Mahmoud Abbas at the Great Hall of the People in Beijing, Tuesday, July 18, 2017. (Photo by Mark Schiefelbein/AP Photo)

This photo taken on August 5, 2017 shows visitors walking on stone piers crossing the Tuojiang River in the ancient town of Fenghuang in Xiangxi, in China' s central Hunan province. The old town district of Fenghuang nestles on the banks of a winding river in a picturesque, mountainous part of Hunan province, and boasts stunning Qing and Ming dynasty architecture dating back hundreds of years. (Photo by AFP Photo/Stringer)

A military band conductor rehearses ahead a ceremony to commemorate the 90th anniversary of the founding of the People's Liberation Army at the Great Hall of the People in Beijing, Tuesday, August 1, 2017. China's President Xi Jinping has issued a tough line on national sovereignty amid multiple disputes with his country’s neighbors, saying China will never permit any loss of territory. Xi’s declaration came during a nearly one-hour speech Tuesday in Beijing marking the 90th anniversary of the founding of the People’s Liberation Army. (Photo by Andy Wong/AP Photo)

A man wears a facekini mask in a seaside resort in Qingdao, China on July 22, 2017. (Photo by Reuters/China Stringer Network)

Train attendants take part in a parade training as they visit the national flag guard during a patriotic education event ahead of the 90th anniversary of the founding of the Chinese People's Liberation Army (PLA) in Beijing, China July 25, 2017. (Photo by Reuters/China Stringer Network)

Wang Zenan, the leading actor in “Jinsha River”, performs on the stage of the National Centre for the Performing Arts during opera's final dress rehearsal in Beijing, China July 27, 2017. “Jinsha River”, the opera adapted from a novel of the same name telling the story of the Red Army on the long march in Tibetan area in 1935, will have its premiere as the country marks the 90th anniversary of the founding of Chinese People's Liberation Army (PLA). (Photo by Damir Sagolj/Reuters)

A man tries Virtual Reality (VR) games at the China Digital Entertainment Expo and Conference (ChinaJoy) in Shanghai, China July 27, 2017. (Photo by Aly Song/Reuters)

Military soldiers and officers attend an opening ceremony of Memorial of the August 1 Nanchang Uprising after a renovation ahead of the 90th anniversary of the founding of the People's Liberation Army (PLA) in Nanchang, Jiangxi province, China July 28, 2017. (Photo by Reuters/China Stringer Network)

Tourists get on and off tour buses outside a hotel in Hong Kong, China July 30, 2017. (Photo by Bobby Yip/Reuters)

People play mahjong as they sit in water at a water park on a hot day in Chongqing, China August 2, 2017. (Photo by Reuters/China Stringer Network)

Fireworks explode over Juzi Island to mark the 90th anniversary of the founding of the China's People's Liberation Army in Changsha, Hunan province, China on August 2, 2017. (Photo by Reuters/China Stringer Network)

Yi ethnic minority girls wait to participate in a traditional performance to celebrate the Torch Festival in Butuo County, Sichuan province, China July 18, 2017. Picture taken July 18, 2017. (Photo by Natalie Thomas/Reuters)

People cool off at a water park on a hot day in Luzhou, Sichuan province, China, August 5, 2017. (Photo by Reuters/China Stringer Network)

Chinese visitors take selfies with their mobile phones on selfie sticks at the entrance of Gubeishui town at the bottom of the Simatai Great Wall in Miyun county, 120 kilometers northeast of Beijing, China, 23 July 2017. (Photo by How Hwee Young/EPA/EFE)

People visit a section of the Simatai Great Wall in Miyun county, 120 kilometers northeast of Beijing, China, 23 July 2017. Built during the Northern Qi dynasty (550-577) and rebuilt during the Ming dynasty, the Simatai Great Wall is 5.4 km long with 35 beacon towers and feature some of the less known parts of the Great Wall. It was closed in 2010 but has since opened to tourists in 2014. China's Great Wall was designated by UNESCO as a World Cultural Heritage site in 1987. (Photo by How Hwee Young/EPA/EFE)

Chinese tourists with swim rings enjoy swimming in the lake called “Dead sea of China” in a resort of Suining city, southwestern China's Sichuan province, 22 July 2017. More than 8,000 tourists gathered enjoy the water during hot weather. (Photo by Lola Levan/EPA/EFE)

Chinese tourists with swim rings enjoy swimming in the lake called 'Dead sea of China' in a resort of Suining city, southwestern China's Sichuan province, 22 July 2017. More than 8,000 tourists gathered enjoy the water during hot weather. (Photo by Lola Levan/EPA)

A child wears a pair of shoes embroidered with the map of China in the color of the national flag and the slogan “Those who invade my territory will be punished no matter how far away” as he lines up to visit an exhibition to mark the 90th anniversary of the founding of the People's Liberation Army at the military museum in Beijing, China, Tuesday, August 1, 2017. Chinese President Xi Jinping issued a tough line on national sovereignty Tuesday amid multiple territorial disputes with his country's neighbors, saying China will never permit the loss of “any piece” of its land to outsiders. (Photo by Ng Han Guan/AP Photo)

Two men practice martial arts techniques at a public park in Beijing, Wednesday, July 26, 2017. Beijing is dotted with urban parks that offer a quieter, greener respite from the crowded streets of China's capital. (Photo by Mark Schiefelbein/AP Photo)


On the first hospital visit of flu season

I’m not fighting with the registrar, exactly. We’re in A&E (of course we are – the start of flu season? We were bound to end up here eventually). It was a pretty typical lead up. Kai was working hard to just breathing and his chest was crackly. I’d been monitoring his o2 (92 – 95%, so slightly low), his heart rate (slightly fast), his respiratory rate (also fast) and his temp (37.9 – low grade fever).

Kai’s sick. Probably something like bronchiolitis.

I rang the nurses because I’d been oral suctioning after each cough. Not too often, because I didn’t want to increase his secretions. Just when he was having a tough time. What I wanted was a nurse to come do a nasal/trach suction (where they put a catheter down Kai’s nose and suction out the mucus he was having trouble shifting). I’d never done one and wasn’t about to do one maverick style now. Except that our nurses are a cautious bunch and instead of coming to do a suction, they were concerned with his o2 levels and suggested we take Kai to A&E.

While I’m always dubious of a ‘just in case’ hospital visit (dealing with the fear our team has and unnecessary escalation) I was keen at least to get swabs done to find out what was going on. So off we went. Kai rather magnificently timed a seizure which moved us from triage to majors (as always) and there we settled in.

Bloods, some suctioning, general monitoring – and yes, suspected broncolitis.

Now here’s where my polite but firm mama bear insistence comes in. They very politely told us that Kai’s white cell count is high and wanted to admit us, just for observation. We’d do repeat bloods and hopefully get discharged the next morning. It took a moment to absorb but when my brain finally kicked in here’s where it went:

We only did bloods because Kai’s regular blood work is due. Not because they regularly do bloods with bronciolitis or with Kai’s general presentation/breathing concerns.

White cell blood count could be high because of the elevated number of seizures (increased because: Kai is poorly) or because of bacterial infection.

If it’s seizures, the white cell count will not go down tomorrow. Meaning they just want to watch Kai, just in case and we’ll be in the same position 12 hours from now.

If it is a bacterial thing, the swabs will tell us. And the treatment is antibiotics, we have bottles at home for this very reason.

We also have suction, o2 tanks and a stat monitor to manage symptoms.

If we are admitted, Kai, as vulnerable as he is, is more likely to catch something else while we are here. Something worse, is my fear.

The risk of sending us home is if Kai deteriorates rapidly overnight. The peak of bronciolitis is day two/three. So tomorrow and the day after.

If Kai does deteriorate rapidly, we’re a short blue light ride from hospital but…

Kai has a terminal disorder. We decided early on not to put Kai through extreme or invasive procedures to extend his life unnecessarily. So if we’re being rushed to hospital… there’s not much more they would do there than we would at home. IV Fluids, maybe. But IV Fluids in the face of a severe deterioration…

So. There is nothing they can do in hospital we can’t do at home. If we have clear parameters, we can come back if we need to. If we need to come back, it will be because Kai is very very poorly. The benefits of home outweigh the risks of leaving. I’ve talked to two registrars. We’re waiting on the consultant. I feel like we’re in here for just in case. The fear of the worst, really. Not because we need to be here.

I’m hoping we can go home. I essentially bought him in for nasal suctioning and the swab. I’ve already asked for an o2 plan and nasal/trach suction training.

We’ll see. Settling in and waiting for someone else to tell us we can go home is nails-on-blackboard mind numbing.

Fingers crossed.

Update: Took two hours but we’ve been discharged out of A&E and are going home, NOT up to the ward. We have some very clear parameters for what do and when, and for when to call an ambulance and go back. Which is to say, we got an O2 plan, and I got a run down on how to do nasal/trach suctioning. YES!

Here is the plan:

If Kai’s o2 stats drop anywhere near 92% we start o2, starting at 0.2L and go up as needed.

If his stats don’t go up, or Kai changes colour, we call an ambulance and blue light in.

If Kai has a fever we try calpol, and escalate to ibuprofen if need be. If his temp doesn’t go down we try antibiotics and call the CCNs who no doubt will tell us to blue light it in.

If Kai is having a really rough time (increased heart rate or respiratory rate) and it doesn’t go down with the fever, we blue light in.

But you know what? While I absolutely would rush him back to hospital the merest hint of trouble, I’m pretty sure our little guy is going to be just fine at home!

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Team Mikaere is for those following the journey of Sam, Elly and Mikaere - a baby boy with Nonketotic Hyperglycinemia. We've partnered with Joseph's Goal to raise funds for the NKH Research done by Dr Nick Greene as part of UCL. He's currently the world leader in NKH research.

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“Once Upon a Time … in Hollywood” came out on top with three awards, including best musical or comedy. “1917” won best drama and director.

“Fleabag” and “Succession” each won two awards in the television categories.

Awkwafina, the star of “The Farewell,” became the first Asian-American to win the Golden Globe for best actress.

Kate McKinnon spoke candidly about being gay while presenting the Carol Burnett Award to Ellen DeGeneres. In her acceptance speech, DeGeneres said: “All I ever want to do is make people feel good and laugh.”

An emotional Tom Hanks offered actors advice while accepting the Cecil B. DeMille lifetime achievement award.

Ricky Gervais, who returned as host for the fifth time, was bleeped not once, but twice, during his monologue.


"The Kraken" tied a franchise record with 15 sacks in 2013 after generating 11 in a breakout 2012 season. Prior to racking up seven sacks in the final two games of the season, Hardy said he would be willing to accept "some cut" in his market value to stay with the Panthers.


*> \brief \b DTRMM
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
*       .. Scalar Arguments ..
*       DOUBLE PRECISION ALPHA
*       INTEGER LDA,LDB,M,N
*       CHARACTER DIAG,SIDE,TRANSA,UPLO
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION A(LDA,*),B(LDB,*)
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DTRMM  performs one of the matrix-matrix operations
*>
*>    B := alpha*op( A )*B,   or   B := alpha*B*op( A ),
*>
*> where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or
*> non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
*>
*>    op( A ) = A   or   op( A ) = A**T.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] SIDE
*> \verbatim
*>          SIDE is CHARACTER*1
*>           On entry,  SIDE specifies whether  op( A ) multiplies B from
*>           the left or right as follows:
*>
*>              SIDE = 'L' or 'l'   B := alpha*op( A )*B.
*>
*>              SIDE = 'R' or 'r'   B := alpha*B*op( A ).
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>           On entry, UPLO specifies whether the matrix A is an upper or
*>           lower triangular matrix as follows:
*>
*>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*>
*>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*> \endverbatim
*>
*> \param[in] TRANSA
*> \verbatim
*>          TRANSA is CHARACTER*1
*>           On entry, TRANSA specifies the form of op( A ) to be used in
*>           the matrix multiplication as follows:
*>
*>              TRANSA = 'N' or 'n'   op( A ) = A.
*>
*>              TRANSA = 'T' or 't'   op( A ) = A**T.
*>
*>              TRANSA = 'C' or 'c'   op( A ) = A**T.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*>          DIAG is CHARACTER*1
*>           On entry, DIAG specifies whether or not A is unit triangular
*>           as follows:
*>
*>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*>
*>              DIAG = 'N' or 'n'   A is not assumed to be unit
*>                                  triangular.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>           On entry, M specifies the number of rows of B. M must be at
*>           least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>           On entry, N specifies the number of columns of B.  N must be
*>           at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*>          ALPHA is DOUBLE PRECISION.
*>           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
*>           zero then  A is not referenced and  B need not be set before
*>           entry.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>           A is DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
*>           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
*>           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
*>           upper triangular part of the array  A must contain the upper
*>           triangular matrix  and the strictly lower triangular part of
*>           A is not referenced.
*>           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
*>           lower triangular part of the array  A must contain the lower
*>           triangular matrix  and the strictly upper triangular part of
*>           A is not referenced.
*>           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
*>           A  are not referenced either,  but are assumed to be  unity.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>           On entry, LDA specifies the first dimension of A as declared
*>           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
*>           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
*>           then LDA must be at least max( 1, n ).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is DOUBLE PRECISION array of DIMENSION ( LDB, n ).
*>           Before entry,  the leading  m by n part of the array  B must
*>           contain the matrix  B,  and  on exit  is overwritten  by the
*>           transformed matrix.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>           On entry, LDB specifies the first dimension of B as declared
*>           in  the  calling  (sub)  program.   LDB  must  be  at  least
*>           max( 1, m ).
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup double_blas_level3
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*>
*>  Level 3 Blas routine.
*>
*>  -- Written on 8-February-1989.
*>     Jack Dongarra, Argonne National Laboratory.
*>     Iain Duff, AERE Harwell.
*>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*>     Sven Hammarling, Numerical Algorithms Group Ltd.
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
*  -- Reference BLAS level3 routine (version 3.4.0) --
*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION ALPHA
      INTEGER LDA,LDB,M,N
      CHARACTER DIAG,SIDE,TRANSA,UPLO
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION A(LDA,*),B(LDB,*)
*     ..
*
*  =====================================================================
*
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC MAX
*     ..
*     .. Local Scalars ..
      DOUBLE PRECISION TEMP
      INTEGER I,INFO,J,K,NROWA
      LOGICAL LSIDE,NOUNIT,UPPER
*     ..
*     .. Parameters ..
      DOUBLE PRECISION ONE,ZERO
      PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
*     ..
*
*     Test the input parameters.
*
      LSIDE = LSAME(SIDE,'L')
      IF (LSIDE) THEN
          NROWA = M
      ELSE
          NROWA = N
      END IF
      NOUNIT = LSAME(DIAG,'N')
      UPPER = LSAME(UPLO,'U')
*
      INFO = 0
      IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
          INFO = 1
      ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
          INFO = 2
      ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
     +         (.NOT.LSAME(TRANSA,'T')) .AND.
     +         (.NOT.LSAME(TRANSA,'C'))) THEN
          INFO = 3
      ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
          INFO = 4
      ELSE IF (M.LT.0) THEN
          INFO = 5
      ELSE IF (N.LT.0) THEN
          INFO = 6
      ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
          INFO = 9
      ELSE IF (LDB.LT.MAX(1,M)) THEN
          INFO = 11
      END IF
      IF (INFO.NE.0) THEN
          CALL XERBLA('DTRMM ',INFO)
          RETURN
      END IF
*
*     Quick return if possible.
*
      IF (M.EQ.0 .OR. N.EQ.0) RETURN
*
*     And when  alpha.eq.zero.
*
      IF (ALPHA.EQ.ZERO) THEN
          DO 20 J = 1,N
              DO 10 I = 1,M
                  B(I,J) = ZERO
   10         CONTINUE
   20     CONTINUE
          RETURN
      END IF
*
*     Start the operations.
*
      IF (LSIDE) THEN
          IF (LSAME(TRANSA,'N')) THEN
*
*           Form  B := alpha*A*B.
*
              IF (UPPER) THEN
                  DO 50 J = 1,N
                      DO 40 K = 1,M
                          IF (B(K,J).NE.ZERO) THEN
                              TEMP = ALPHA*B(K,J)
                              DO 30 I = 1,K - 1
                                  B(I,J) = B(I,J) + TEMP*A(I,K)
   30                         CONTINUE
                              IF (NOUNIT) TEMP = TEMP*A(K,K)
                              B(K,J) = TEMP
                          END IF
   40                 CONTINUE
   50             CONTINUE
              ELSE
                  DO 80 J = 1,N
                      DO 70 K = M,1,-1
                          IF (B(K,J).NE.ZERO) THEN
                              TEMP = ALPHA*B(K,J)
                              B(K,J) = TEMP
                              IF (NOUNIT) B(K,J) = B(K,J)*A(K,K)
                              DO 60 I = K + 1,M
                                  B(I,J) = B(I,J) + TEMP*A(I,K)
   60                         CONTINUE
                          END IF
   70                 CONTINUE
   80             CONTINUE
              END IF
          ELSE
*
*           Form  B := alpha*A**T*B.
*
              IF (UPPER) THEN
                  DO 110 J = 1,N
                      DO 100 I = M,1,-1
                          TEMP = B(I,J)
                          IF (NOUNIT) TEMP = TEMP*A(I,I)
                          DO 90 K = 1,I - 1
                              TEMP = TEMP + A(K,I)*B(K,J)
   90                     CONTINUE
                          B(I,J) = ALPHA*TEMP
  100                 CONTINUE
  110             CONTINUE
              ELSE
                  DO 140 J = 1,N
                      DO 130 I = 1,M
                          TEMP = B(I,J)
                          IF (NOUNIT) TEMP = TEMP*A(I,I)
                          DO 120 K = I + 1,M
                              TEMP = TEMP + A(K,I)*B(K,J)
  120                     CONTINUE
                          B(I,J) = ALPHA*TEMP
  130                 CONTINUE
  140             CONTINUE
              END IF
          END IF
      ELSE
          IF (LSAME(TRANSA,'N')) THEN
*
*           Form  B := alpha*B*A.
*
              IF (UPPER) THEN
                  DO 180 J = N,1,-1
                      TEMP = ALPHA
                      IF (NOUNIT) TEMP = TEMP*A(J,J)
                      DO 150 I = 1,M
                          B(I,J) = TEMP*B(I,J)
  150                 CONTINUE
                      DO 170 K = 1,J - 1
                          IF (A(K,J).NE.ZERO) THEN
                              TEMP = ALPHA*A(K,J)
                              DO 160 I = 1,M
                                  B(I,J) = B(I,J) + TEMP*B(I,K)
  160                         CONTINUE
                          END IF
  170                 CONTINUE
  180             CONTINUE
              ELSE
                  DO 220 J = 1,N
                      TEMP = ALPHA
                      IF (NOUNIT) TEMP = TEMP*A(J,J)
                      DO 190 I = 1,M
                          B(I,J) = TEMP*B(I,J)
  190                 CONTINUE
                      DO 210 K = J + 1,N
                          IF (A(K,J).NE.ZERO) THEN
                              TEMP = ALPHA*A(K,J)
                              DO 200 I = 1,M
                                  B(I,J) = B(I,J) + TEMP*B(I,K)
  200                         CONTINUE
                          END IF
  210                 CONTINUE
  220             CONTINUE
              END IF
          ELSE
*
*           Form  B := alpha*B*A**T.
*
              IF (UPPER) THEN
                  DO 260 K = 1,N
                      DO 240 J = 1,K - 1
                          IF (A(J,K).NE.ZERO) THEN
                              TEMP = ALPHA*A(J,K)
                              DO 230 I = 1,M
                                  B(I,J) = B(I,J) + TEMP*B(I,K)
  230                         CONTINUE
                          END IF
  240                 CONTINUE
                      TEMP = ALPHA
                      IF (NOUNIT) TEMP = TEMP*A(K,K)
                      IF (TEMP.NE.ONE) THEN
                          DO 250 I = 1,M
                              B(I,K) = TEMP*B(I,K)
  250                     CONTINUE
                      END IF
  260             CONTINUE
              ELSE
                  DO 300 K = N,1,-1
                      DO 280 J = K + 1,N
                          IF (A(J,K).NE.ZERO) THEN
                              TEMP = ALPHA*A(J,K)
                              DO 270 I = 1,M
                                  B(I,J) = B(I,J) + TEMP*B(I,K)
  270                         CONTINUE
                          END IF
  280                 CONTINUE
                      TEMP = ALPHA
                      IF (NOUNIT) TEMP = TEMP*A(K,K)
                      IF (TEMP.NE.ONE) THEN
                          DO 290 I = 1,M
                              B(I,K) = TEMP*B(I,K)
  290                     CONTINUE
                      END IF
  300             CONTINUE
              END IF
          END IF
      END IF
*
      RETURN
*
*     End of DTRMM .
*
      END


The present invention pertains to seating apparatus, and more specifically, to inflatable, portable and storable seating apparatus, systems and methods of use.
The use of an inflatable mattress for camping and the like is known. People have used inflatable mattresses underneath sleeping bags to provide comfort on camping trips. Inflatable flotation devices also are known, for example for use by sunbathers at pools and lakes. For a number of reasons, however, inflatable seating apparatus have not been as well received.
To date, inflatable mattresses and inflatable furniture have experienced several difficulties. For example, inflatable devices to date typically provide insufficient stability to support seated adults who are more accustomed to wood or upholstered furniture. Difficulties in inflation, concern over punctures, and a lack of aesthetic appeal also are reasons why inflatable seating devices have not found widespread use in the American home.
It is desirable, therefore, to provide inflatable seating apparatus which are easily inflated and deflated in addition to being portable, storable and durable. It is further desirable to provide inflatable seating apparatus that are aesthetically pleasing and sufficiently stable for adult users without undue sagging or other instabilities.


 x(g) = g**5 + 3*g**4 + 2*g**3 - 2*g. Let u(k) = 6*k**5 + 16*k**4 + 10*k**3 - 11*k. Let s(p) = -2*u(p) + 11*x(p). Factor s(w).
-w**3*(w - 2)*(w + 1)
Let x(b) be the third derivative of -b**8/70560 + b**7/17640 + b**6/1260 - b**5/20 + 2*b**2. Let g(q) be the third derivative of x(q). Factor g(f).
-2*(f - 2)*(f + 1)/7
Let i be 20/25 - 4/6. Let b(p) be the second derivative of -i*p**5 - p + 1/9*p**3 + 0 - 1/6*p**4 + 0*p**2. Determine r, given that b(r) = 0.
-1, 0, 1/4
Let s = 1/56 + 221/168. Determine p so that s*p - 1/3 - p**2 = 0.
1/3, 1
Let h(l) be the third derivative of l**9/30240 + l**8/5040 + l**7/2520 + l**5/15 + 6*l**2. Let t(r) be the third derivative of h(r). Factor t(k).
2*k*(k + 1)**2
Suppose -2 = m - 2*m + j, 4 = 2*m + 5*j. Factor 0*r**2 + 5*r**m - 8 - 2*r**2 - r**2.
2*(r - 2)*(r + 2)
Let y(d) = d**3 + d**2 + d. Let g(u) = -8*u**3 - 5*u**2 - 2*u. Let p(t) = -g(t) - 5*y(t). Determine h so that p(h) = 0.
-1, 0, 1
What is f in -1/4*f + 0 + 1/4*f**2 = 0?
0, 1
Let -4*t + 60*t**2 + 5*t + t**3 - 62*t**2 = 0. Calculate t.
0, 1
Suppose 92*x**2 - 42*x**2 - 10 + 8*x - 48*x**2 = 0. Calculate x.
-5, 1
Factor -2/5*t**2 + 0 + 4/5*t - 2/5*t**3.
-2*t*(t - 1)*(t + 2)/5
What is t in 6/7*t**2 + 2/7*t**3 - 12/7*t - 16/7 = 0?
-4, -1, 2
Let x(o) be the second derivative of o**6/15 - 6*o**5/35 - 2*o**4/21 + 10*o. Factor x(z).
2*z**2*(z - 2)*(7*z + 2)/7
Let s(y) = -4*y + 35. Let j be s(8). Factor 1/5*t - 1/5*t**j - 1/5 + 1/5*t**2.
-(t - 1)**2*(t + 1)/5
Let b(s) be the third derivative of -s**7/105 + s**5/10 + s**4/6 + 30*s**2. Find q, given that b(q) = 0.
-1, 0, 2
Let h be 3*(0 + -1)*-1. Suppose -h*z + 12 = -3. Find c, given that 0*c - 1/3*c**z + 1/3*c**2 + 0 - 1/3*c**4 + 1/3*c**3 = 0.
-1, 0, 1
Let u(s) be the third derivative of -s**5/120 + s**4/72 + 33*s**2. Determine m, given that u(m) = 0.
0, 2/3
Solve -2/3*i**2 - 50/3 - 20/3*i = 0.
-5
Suppose -5*q + 11 = -54. Let u = q + -11. Factor -1/4*d + 0 - 1/4*d**u.
-d*(d + 1)/4
Let s = -4/7 - -26/21. Let g be 1/(9/6)*3. Factor 2/3*z**3 - 2*z**g - s + 2*z.
2*(z - 1)**3/3
Suppose i + 9 = 4*i. Suppose -7*c + i*c + 8 = 0. Solve -4*r - 2*r**c + 3*r - 2 + 5*r = 0.
1
Let r = -3 + 1. Let g be 2 - 4 - r - -2. Factor y**g + 4 + 0 - 5.
(y - 1)*(y + 1)
Let w(v) be the first derivative of 1/8*v**4 + 2/3*v**3 - 5 + v**2 + 0*v. Determine g so that w(g) = 0.
-2, 0
Let x(d) be the first derivative of -d**4 + 8*d**3 - 18*d**2 + 16*d + 21. Factor x(z).
-4*(z - 4)*(z - 1)**2
Suppose 94 - 4 = -5*u. Let m be ((-24)/154)/(u/63). Determine p so that -2/11*p + 8/11*p**3 + 0 + m*p**2 = 0.
-1, 0, 1/4
Let q be 1*(1 - (-2)/(-6)). Let -2/9*v - q*v**3 - 2/9*v**4 - 2/3*v**2 + 0 = 0. Calculate v.
-1, 0
Factor 1/7 - 1/7*w**2 + 0*w.
-(w - 1)*(w + 1)/7
Factor -3/2*c + 0 - 3/2*c**2 + 3/2*c**3 + 3/2*c**4.
3*c*(c - 1)*(c + 1)**2/2
Let -2/5*j**3 - 8/5 + 14/5*j - 4/5*j**2 = 0. What is j?
-4, 1
Factor m**4 - 2*m - 455*m**3 + 457*m**3 - 6 + 5.
(m - 1)*(m + 1)**3
Let o(n) be the second derivative of -7*n**6/480 - n**5/120 + n**2 + n. Let f(s) be the first derivative of o(s). Factor f(r).
-r**2*(7*r + 2)/4
Let y(n) be the first derivative of 0*n**3 - 3 + n + 0*n**4 + 0*n**2 + 1/10*n**5 + 1/21*n**7 + 2/15*n**6. Let v(f) be the first derivative of y(f). Factor v(z).
2*z**3*(z + 1)**2
Let v(x) be the second derivative of -x**6/60 + x**4/12 + 3*x**2/2 + 2*x. Let f(n) be the first derivative of v(n). What is c in f(c) = 0?
-1, 0, 1
Let q(a) be the third derivative of 3*a**2 + 0*a + 0 - 1/60*a**5 + 1/12*a**4 + 0*a**3. Factor q(t).
-t*(t - 2)
Let u(b) be the first derivative of -3/4*b**4 - 1/5*b**5 + 1/3*b**3 + 3 + 0*b + 1/6*b**6 + b**2. Factor u(k).
k*(k - 2)*(k - 1)*(k + 1)**2
Let a(j) be the second derivative of 1/3*j**2 + 3*j + 2/9*j**3 + 0 + 1/18*j**4. Factor a(w).
2*(w + 1)**2/3
Let w(t) be the second derivative of -1/9*t**4 - 5/18*t**3 - 1/60*t**5 + 0 - 1/3*t**2 - 2*t. Factor w(m).
-(m + 1)**2*(m + 2)/3
Let w(x) = -3*x**2 - 7*x + 5. Let g(z) be the second derivative of 11/6*z**3 + 5/12*z**4 + z + 0 - 4*z**2. Let d(o) = -5*g(o) - 8*w(o). Solve d(v) = 0 for v.
0, 1
Let a be 1 + -1 + -1 + 8. Suppose -3*f = -a + 1. Factor -1/2*v**3 + 0 - 2*v - f*v**2.
-v*(v + 2)**2/2
Let k(v) be the second derivative of -3/80*v**5 - 1/48*v**4 + 0 - 1/40*v**6 + v - 1/168*v**7 + 0*v**2 + 0*v**3. Factor k(i).
-i**2*(i + 1)**3/4
Let z(r) = r + 1. Let c be z(-1). Factor 5*y - 2*y + y**2 - 4*y + c*y**2.
y*(y - 1)
Let m(v) = 7*v**2 - v - 8. Let o(z) = z**2 - 1. Let h(w) = m(w) - 6*o(w). What is u in h(u) = 0?
-1, 2
Let y(b) be the first derivative of -b**6/12 - b**5/10 + b**4/8 + b**3/6 - 70. Solve y(h) = 0 for h.
-1, 0, 1
Let k(o) be the third derivative of -o**6/120 + o**5/10 - 3*o**4/8 - 8*o**2. Let k(n) = 0. What is n?
0, 3
Let b = 4 + -2. Suppose 5 = b*i - 7. Let j(d) = d**3 - d**2 + d + 3. Let n(l) = 4*l**3 - 3*l**2 + 4*l + 11. Let h(o) = i*n(o) - 22*j(o). Factor h(u).
2*u*(u + 1)**2
Determine j, given that -45*j**2 - 5*j**4 + 80*j**3 - 35*j + 48 - 22 - 45*j**3 + 24 = 0.
-1, 1, 2, 5
Let m(i) be the first derivative of -i**6/140 - i**5/30 + 4*i**3/21 - 9*i**2/2 + 4. Let n(t) be the second derivative of m(t). Solve n(q) = 0 for q.
-2, -1, 2/3
Let y = 40 - 34. Let v(a) be the second derivative of 0*a**2 + 0 - 2*a + 1/12*a**4 + 3/40*a**5 + 1/60*a**y + 0*a**3. What is n in v(n) = 0?
-2, -1, 0
Let i(k) be the first derivative of 2*k**3/21 + 3*k**2/7 + 4*k/7 + 33. What is x in i(x) = 0?
-2, -1
Suppose 3*p = 6, w = p + p - 2. Find i such that -3*i**w - 4*i**3 + i**3 + 6*i**3 = 0.
0, 1
Let y be 2 + (-3 - ((-24)/(-4))/(-3)). Let h(k) be the first derivative of -k**3 + 3/5*k**5 - 3/2*k**4 + 3*k**2 + y + 0*k. Factor h(b).
3*b*(b - 2)*(b - 1)*(b + 1)
Suppose -3*p + 13 + 83 = 0. Suppose p = -3*t + 7*t. What is o in -4*o**5 - 4*o + 2*o**4 - 4*o**2 + t*o**3 - 1 + 0*o**4 + 3 = 0?
-1, 1/2, 1
Let t = -77/2 + 39. Let i(f) be the second derivative of 0*f**2 + 0 - t*f**4 + 1/3*f**3 + 2*f. Find l, given that i(l) = 0.
0, 1/3
Let q = -5 - -8. Factor -2 - 2*t**3 + 0*t + 3*t + t**q.
-(t - 1)**2*(t + 2)
Let f be (-1 - 0)/((-7)/77). Let h = -9 + f. Suppose 2/9*c**h + 2/9 - 4/9*c = 0. Calculate c.
1
Let b(s) be the third derivative of s**5/40 - s**4/32 - 8*s**2. Suppose b(x) = 0. Calculate x.
0, 1/2
Let d be (6/(-7))/((-40)/140). Let n(h) be the first derivative of 0*h**2 + 1/4*h - 1 - 1/12*h**d. Factor n(a).
-(a - 1)*(a + 1)/4
Factor 1/6*f**3 - 1/3*f**2 - 1/6*f + 1/3.
(f - 2)*(f - 1)*(f + 1)/6
Let y(h) be the first derivative of -3*h**3 - 9*h**2/2 + 17*h - 3. Let l(k) = k**2 + k - 2. Let q(i) = -51*l(i) - 6*y(i). Let q(g) = 0. What is g?
-1, 0
Let q(p) be the third derivative of 189*p**6/80 - 3*p**5/4 - 11*p**4/12 + 2*p**3/3 + 2*p**2. Determine h, given that q(h) = 0.
-2/7, 2/9
Let i(n) = n**2 - n - 1. Let z(h) = -2*h**2 + h + 3. Let y(a) = i(a) + z(a). Let q(f) = -1. Let t(c) = 2*q(c) + y(c). Determine o, given that t(o) = 0.
0
Suppose 5*z - 24 = -9. Let f(w) be the third derivative of -3*w**2 + 0*w**z - 1/270*w**5 + 0 - 1/108*w**4 + 0*w. Determine y so that f(y) = 0.
-1, 0
Let n(b) be the second derivative of 0 - 1/28*b**4 - 6*b - 1/7*b**3 + 0*b**2. Determine f so that n(f) = 0.
-2, 0
Let y(x) be the third derivative of -x**7/560 - x**6/160 + x**4/32 + x**3/16 - 7*x**2. Find c such that y(c) = 0.
-1, 1
Let k(r) be the first derivative of -r**3 + 3*r + 12. Factor k(m).
-3*(m - 1)*(m + 1)
Let j(c) be the second derivative of 1/30*c**6 + 0*c**2 + 1/3*c**3 + 1/5*c**5 - 3*c + 5/12*c**4 + 0. Factor j(q).
q*(q + 1)**2*(q + 2)
Let f(v) = v + 15. Let m be f(-11). Suppose -3*i + 0*i**m + 3*i**4 - 3*i**4 - 3*i**5 + 6*i**3 = 0. What is i?
-1, 0, 1
Suppose 9 = -3*l - 5*v, -l + 4*v + 18 = 2*l. Let 0*s + 2/3*s**5 + 2/3*s**3 + 4/3*s**4 + 0 + 0*s**l = 0. Calculate s.
-1, 0
Suppose 2*b + 4*k + 6 = 0, 4*k = -k - 15. Suppose -3*h + 2*j = -4, -9*h - j = -4*h + 2. Factor -2*f**2 - 4*f + 1 + h*f - b.
-2*(f + 1)**2
Determine p so that 1/7*p**3 + 5/7*p - 2/7 - 4/7*p**2 = 0.
1, 2
Let c(f) be the third derivative of -f**7/1260 - f**6/540 + f**5/90 - f**3/6 + 3*f**2. Let j(u) be the first derivative of c(u). Factor j(d).
-2*d*(d - 1)*(d + 2)/3
Factor 28*s + 6 + 32*s**2 - 15*s + 9*s**3 + 14*s - 2*s**2.
3*(s + 1)*(s + 2)*(3*s + 1)
Let b(u) be the third derivative of -u**7/70 - 3*u**6/20 - 13*u**5/20 - 3*u**4/2 - 2*u**3 - 18*u**


Q:

rewrite rules for apache 2 to use with angular js

Obviously, there are a lot of mod rewrite discussions and answers all across the web. However, I am having a hard time grasping them. So I thought I would ask here.
I'm asking for rewrite rules to do what Andy Joslin explained in the comments here: https://stackoverflow.com/a/11100438
This is my current dir structure at the root of example.com

app/
app/index.html (the "root" of the angular js application)
api (This will be a symfony 2 app that is used for the 'api'. I'll be sending ajax requests to and from here from angular.)

I would like to redirect all requests to app/index.html except for requests to /api.
For example:
http://example.com/categories/electronics/ipod would actually be like going to http://example.com/app/index.html/categories/electronics/ipod
I would like for the app/index.html part to be hidden however.
Then, there would be an exception for requests to http://example.com/api because I will need to make ajax requests to those url paths.
Thanks for any and all help/guidance.

A:

The accepted answer to this question is outdated. You can now use the FallbackResource directive in your conf file with Apache 2.2.16+.
FallbackResource /app/index.html

If you want the FallbackResource directive to ignore the "/api" routes:
<Directory /api>
FallbackResource disabled
</Directory>

A:

Here's something to get you going (put this inside your /.htaccess file):
Options +FollowSymLinks
IndexIgnore */*
RewriteEngine on

# if a directory or a file exists, use it directly
RewriteCond %{REQUEST_FILENAME} -s [OR]
RewriteCond %{REQUEST_FILENAME} -l [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteCond %{REQUEST_URI} !/api

# otherwise forward it to index.html
RewriteRule ^.*$ - [NC,L]
RewriteRule ^app/. /app/index.html [NC,L]

NOTE: For newer Apache versions see also the next answer, which uses the much easier FallbackResource


Oscar Host Kevin Hart's History of Anti-Gay Tweets Creates New Problem for Academy

And facing a backlash over hundreds of homophobic jokes, Hart decided to step down as Oscar host.

The Motion Picture Academy faces a new public relations crisis over its choice of Kevin Hart as this year's Oscars host as old tweets, in which Hart expressed anti-gay sentiments and used homophobic terminology and slurs, have resurfaced.

In one 2011 tweet, the comedian and movie star wrote, "Yo if my son comes home & try's 2 play with my daughters doll house I'm going 2 break it over his head & say n my voice 'stop that's gay.'" In another from 2010, Hart says someone's profile pic looks "like a gay bill board for AIDS." And in another written in 2009, he calls someone a "fat faced fag."

Those tweets and many more like them were up as recently as Tuesday, the day Hart was announced as host of the 91st Academy Awards. But as word of them began to spread in the days following, they began to disappear.

The Academy did not respond to several requests from The Hollywood Reporter to comment on the controversy.

Nevertheless, the tweets drew condemnation from the likes of actor-comedian Billy Eichner, who tweeted, "You can tell its not just a joke — there's real truth, anger & fear behind these. I hope Kevin's thinking has evolved since 2011."

Journalist Mark Harris went even further, tweeting the choice of Hart as host was "out-of-sync for a year in which Rami Malek, Melissa McCarthy, Olivia Colman, Mahershala Ali, Richard E. Grant, Emma Stone, Rachel Weisz and Lucas Hedges could all get nominated for playing LBGTQ characters."

This is not the first time Hart's thoughts on LGBT people have caused controversy. A 2011 standup routine about his then 3-year-old son having a "gay moment" — "You've got to nip it in the bud!" he warned the audience — was criticized as promoting homophobic and dangerous parenting, according to The Guardian.

Hart told Rolling Stone in 2015 that he wouldn't tell the joke again, "because when I said it, the times weren't as sensitive as they are now."

The Academy has previously faced heat over anti-gay rhetoric in late 2011, when Brett Ratner resigned as producer of the 84th Academy Awards after saying "rehearsal is for fags" in a public Q&A for his film Tower Heist.

Ratner's exit led to the departure of Eddie Murphy, that year's announced host, who stepped down in solidarity. (Billy Crystal filled in.)

GLAAD has reached out to ABC, the Academy and Kevin Hart’s management to "discuss his rhetoric and record as well as opportunities for positive LGBTQ inclusion on the Oscars stage," said Rich Ferraro, chief communications officer for GLAAD. They have not yet responded.

And Pose star Indya Moore — whose groundbreaking trans series drew Golden Globe nominations for best drama and best actor (for Billy Porter) — penned a lengthy Twitter thread that laid into Hart for "sexualizing" his son in his 2011 routine, adding, "'Your choice to prevent' your child from being 'gay' is fear driven. You ARE homophobic Kevin."

"You @KevinHart4real are NOT FIT a model, or representative to Host for the @TheAcademy which CELEBRATES & WELCOMES talent of all genders, sexualities, & ethnicities," Moore continued. Pose executive producer Ryan Murphy retweeted several of the tweets.

Hart addressed the controversy in a defiant statement posted to Instagram on Thursday. In the black-and-white video, Hart, lying in bed shirtless, says, "I swear, man, our world is becoming beyond crazy. I'm not going to let the craziness frustrate me or anger me, especially when I worked hard to get to the mental space that I am at now."

Several hours later, Hart posted a second Instagram video in which he said he has refused a demand from the Academy to apologize. Speaking from Sydney, Australia, where he is currently on tour, Hart said he received a call from the Academy giving him an ultimatum: apologize for his old tweets or step down as Oscars host.

"I passed. The reason I passed is because I've addressed this several times. This is not the first time this has come up," he said.

"Regardless, to the Academy, I'm thankful for the opportunity, if it goes away, no harm, no foul," Hart added.

Just about two hours later, though, Hart, in a tweet, formally stepped down from the Oscar hosting gig. "I have made the choice to step down from hosting this year's Oscar's....this is because I do not want to be a distraction on a night that should be celebrated by so many amazing talented artists. I sincerely apologize to the LGBTQ community for my insensitive words from my past," Hart wrote.

He added seconds later, "I'm sorry that I hurt people. I am evolving and want to continue to do so. My goal is to bring people together not tear us apart. Much love & appreciation to the Academy. I hope we can meet again."

Ironically, in giving up the hosting spot, Hart actually offered the apology that earlier he had refused to provide.

Dec. 6, 3:28 p.m. Updated with GLAAD statement and Indya Moore tweets.

Dec. 6, 4:00 p.m. Updated with Hart's Instagram statement.

Dec. 6, 8:10 p.m. Updated with Hart's second Instagram statement.

Dec. 6, 9:30 p.m. Updated with Hart's tweet in which he stepped from hosting Oscars.


---
abstract: 'Dispersion curves to a oscillatory reaction-diffusion system with the self-consistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and characteristics of traveling waves. The point of inflection which separates the dispersion curves into two branches corresponding to trigger and phase waves, moves according to the value of the advection constant. The dynamics of phase wave in reaction-diffusion-advection equations has been studied by limit cycle perturbations. The dispersion relation obtained from the phase equation shows that the competition between diffusion and advection constants modulates the oscillation frequency from the bulk oscillation in the long-wave dynamics. Such a competition implies that phase waves with the flow have a wider variety of dynamics than waves without the flow.'
address: ' Bio-Mimetic Control Research Center, The Institute of Physical and Chemical Research (RIKEN) Shimoshidami, Moriyama, Nagoya, 463-0003, JAPAN '
author:
- Hiroyasu Yamada and Toshiyuki Nakagaki
title: ' Dispersion relations to oscillatory reaction-diffusion systems with the self-consistent flow '
---

Introduction {#sec: Introduction}
============

In biological systems of cell population, taxis induces cooperative movement of cells or the flow of cellular mass. Cells behave according to chemical and physiological signals given by themselves. Two well-known pattern formations for population dynamics of cells are the aggregation of cellular slime molds and the branching growth of bacterial colonies. Slime mould cells secrete signaling chemicals responding to extracellular chemicals, and move towards increasing some chemical concentration. They aggregate to centers of the wave pattern of chemicals with dendritic streaming lines and eventually form slugs[@Bonner94; @Devreotes89; @Tomchik81]. Morphology of bacterial colonies depends on agar concentration and nutrient level. Bacteria are swimming toward high concentration of nutrients, and form various colonial patterns as concentric rings and dendritic branchings[@Burdene; @BenJacob; @Matsushita]. Mechanisms of these pattern formations have been modeled by taxis equations or reaction-diffusion systems with the cellular flow.

For one of protozoan myxomycete, the [*Physarum*]{} plasmodium, which is a unicellular organism, a reaction-diffusion-flow model is presented in relation to control mechanism of amoeboid movements. The flow of endoplasm and chemicals induced by protoplasmic streaming in [*Physarum*]{} plays an important role in individual behavior under a large plasmodium state. It is not difficult to look for reaction, diffusion and flow couplings in various biological process, more and more. The self-consistent flow as above is realized by biological active process, and is a different character from physico-chemical ones. Effects of the self-consistent flow on simple reaction-diffusion systems are to be clarified in order to study a mechanism of functional self-organization of multicellular systems.

In the present article, we discuss basic effects of the flow on oscillatory phenomena in a reaction-diffusion system with the self-consistent flow. Although we dealt with a model for the [*Physarum*]{} plasmodium, it is expected that the results obtained here are applicable to other biological systems with the flow. We carry out numerical calculation of the dispersion relation in the system, and show effects of the flow on traveling plane waves. Then we derive the dynamics of phase waves from reaction-diffusion-advection equations in general form by means of limit cycle perturbations. In the coefficient of the gradients of the phase, the advection terms compete with diffusion terms.

Model equations for the plasmodium {#sec: Model equations}
==================================

The plasmodium of [*Physarum*]{} has a cytoplasmic cortex (ectoplasm) filled with endoplasm. The ectoplasm shows contractile oscillation everywhere within the organism [@Ueda78; @NaibMajani82; @Ishigami86], and the contraction causes intracellular streaming of the endoplasm [@Kamiya59]. The contraction-relaxation behavior is regulated by metabolic cycles of chemical oscillators [@Grebecki78; @Baranowski82]. Metabolic chemicals transported by endoplasmic streaming, affect chemical oscillators [@Yoshimoto78; @Miyake91; @Nakagaki96].

A model of contractile and motile dynamics of the [*Physarum*]{} plasmodium is represented by conservation of the cytoplasmic mass and reaction-diffusion system of metabolic elements with endoplasmic streaming[@Teplov; @Yamada99]. Under some assumptions, oscillatory dynamics in the plasmodium is governed by the following reaction-diffusion equations with advection terms: $$\frac{\partial {\bf u}}{\partial t}
  + M \vec{\nabla} {\bf u} \cdot \vec{\nabla} {\bf u}
  = {\bf f}({\bf u}) + D \vec{\nabla}^2 {\bf u},
  \label{eqn: rda}$$ where ${\bf u}$ is a $N$-component vector of reaction species which are separated into two types of metabolic elements, free chemicals and non-free ones. While the former is transported by the protoplasmic streaming, the latter is bound or stored at some cytoplasmic structure. Reaction kinetics ${\bf f}$ denotes the metabolic oscillation which emerges from the coupling of two types of reaction elements mentioned above, and the system is assumed to have a limit cycle orbit. The quantity $D$ is a diagonal matrix of diffusion constants. A tensor $M$ represents advection coefficients, here $M
\vec{\nabla} {\bf u}$ is a flow vector for each reaction component. This system has a generic form of reaction-diffusion equations with the self-consistent flow, and we derive the phase dynamics from eq. \[eqn: rda\] in section \[sec: Phase dynamics\].

In our numerical calculations, we use a more simple two-variable model[@Yamada99]: $$\begin{aligned}
  &&\frac{\partial u}{\partial t} + \vec{w} \cdot \vec{\nabla}
  = f(u, v) + D \vec{\nabla}^2 u,
  \nonumber\\
  &&\frac{\partial v}{\partial t} = g(u, v),
  \label{eqn: 2rda}\end{aligned}$$ where $u$ and $v$ are the concentrations of a free chemical substance and a bound/stored one, respectively. We adopt the Schnackenberg’s tri-molecular two species model for reaction kinetics of chemicals[@Schnackenberg79], $$f(u, v) = a - u + u^2 v,\quad g(u, v) = b - u^2 v,
  \label{eqn: tmts}$$ here $a$ and $b$ are positive constants. In the spatially homogeneous conditions ($D = 0$ and $\vec{w} = \vec{0}$), the system has a stable limit cycle as shown in Fig. \[fig: limit cycle\] for $b - a > (a + b)^3$. The quantity $D$ is the diffusion constant of the free chemical $u$. The velocity of the endoplasmic flow $\vec{w}$ is determined by the concentration of the metabolic chemical as $$\vec{w} = q \vec{\nabla} u,
  \label{eqn: flow}$$ and thus the flow is self-consistent. Here $q$ depends on the permeability and the mechanism of intracellular pressure. In the following calculation, $q$ is assumed to be constant.

Dispersion relation {#sec: Dispersion relation}
===================

The numerical calculations were carried out for eq. \[eqn: 2rda\] on a ring, that is a one-dimensional region with periodic boundary conditions. Using the limit cycle, we initiate a pulse traveling on the ring, and solve eq. \[eqn: 2rda\] until the solution becomes periodic in time. After we measured the rotating period of the traveling pulse on the ring, we repeat the calculation for rings of different lengths. As above, the dispersion relation has been obtained for periodic wave trains with the stable propagation.

In the measurements, parameters have been set as $a = 0.1$, $b = 0.5$, and $D = 1.0$. We have used the explicit Euler’s method for reaction terms, upwind differencing method for advection terms, and the implicit method for diffusion terms. The data have been recorded for waves in stationary propagation.

Dispersion curves in the reaction-diffusion-advection system \[eqn: 2rda\] are shown in Fig. \[fig: k-omega\] (wave number vs frequency) and Fig. \[fig: tau-v\] (period vs velocity) for various values of the advection constant $q$. Variations in the self-consistent flow make the propagation of plane waves quite changed. The inflection point which separates two branches corresponding to trigger waves and phase waves [@Aliev94; @Polezhaev95], moves according to the flow. It is the point that the variation of propagating behavior depends on the wave length. The other point is that the sign of $q$ gives different effects on waves in propagation features.

For the positive value of $q$, the oscillation frequency $\omega$ of phase waves gets slightly greater, while that of trigger waves becomes smaller. Hence, phase waves travel a longer way for the greater value of $q$ even if they have the same frequency. Such a case of positive $q$ corresponds to the phenomena of phase waves in the plasmodium, when we regard the reaction kinetics of eq. \[eqn: tmts\] as the oscillation of some metabolic element like Ca$^{2+}$. The flow make the plasmodium communicate local information to the wide area in the cell with phase waves.

When the advection constant $q$ is negative, the opposite situation to the case of positive $q$ arises. Furthermore, we find out the steep rise of the frequency in Fig. \[fig: k-omega\]. Such steepness denotes the sharp transition from phase waves to trigger waves with increasing dimensions of the propagating media.

Phase dynamics {#sec: Phase dynamics}
==============

In this section, we show that the effect of the flow comes out through the coefficient of the nonlinear term in phase dynamics for reaction-diffusion-advection systems. By means of limit cycle perturbations, the dynamics of phase waves in ordinary reaction-diffusion systems for oscillatory media are described by the Burgers equation[@Ortoleva; @Kuramoto]. We adopt the similar method to oscillatory reaction-diffusion equations with advection terms introduced in section \[sec: Model equations\].

We assume that the limit cycle of eq. \[eqn: rda\] has the frequency $\omega_0$. Then a solution of homogeneous oscillation is $$\begin{aligned}
  &&{\bf u} = {\bf u}_0(\tau),\quad
  \tau = \omega_0 t,\quad \mbox{where}
  \\
  &&\omega_0 {\bf u}_0' = {\bf f}({\bf u}_0),\quad \mbox{and} \quad
  {\bf u}_0(\tau + 2 \pi) = {\bf u}_0(\tau).\end{aligned}$$ Since the system \[eqn: rda\] is invariant under the time translation, ${\bf u}_0(\tau + \psi)$ ($\psi$ is an arbitrary constant) is also a solution of eq. \[eqn: rda\].

Let us consider the dynamics of phase waves in eq. \[eqn: rda\] when the advection and diffusion terms are small. We introduce multiple scales and asymptotic expansions, $$\begin{aligned}
  &&\vec{R} = \sqrt{\epsilon} \vec{r},\quad
  \tau = \omega_0 t,\quad
  T = \epsilon t,
  \nonumber\\
  &&{\bf u} = {\bf u}_0(\tau + \psi) + \epsilon {\bf u} + \cdots,
  \label{eqn: asymptotic expansions}\end{aligned}$$ where $\epsilon$ is a small parameter and $\psi = \psi(\vec{R}, T)$. Substitution of eq. \[eqn: asymptotic expansions\] into eq. \[eqn: rda\] yields perturbation equations for each order in $\epsilon$: $$\begin{aligned}
  &&\omega_0 \frac{\partial {\bf u}_0}{\partial \tau}
  = {\bf f}({\bf u}_0),
  \nonumber\\
  &&L {\bf u}_j = {\bf b}_j,\quad
  L = \omega_0 \frac{\partial}{\partial \tau}
  - \frac{\partial {\bf f}}{\partial {\bf u}}({\bf u}_0),
  \label{eqn: perturbation equations}\end{aligned}$$ here $j = 1, 2, \ldots$, and ${\bf b}_j$ denotes the inhomogeneous term of the $j$th order equation. For the first order equation in eq. \[eqn: perturbation equations\], the inhomogeneous term is $$\begin{aligned}
  {\bf b}_1
  &=& - \frac{\partial {\bf u}_0}{\partial T}
  - M \vec{\nabla}_R {\bf u}_0 \cdot \vec{\nabla}_R {\bf u}_0
  + D \vec{\nabla}_R^2 {\bf u}_0
  \\
  &=& - {\bf u}_0' \frac{\partial \psi}{\partial T}
  - M {\bf u}_0' {\bf u}_0' | \vec{\nabla}_R \psi |^2
  \\
  &&  + D {\bf u}_0'' | \vec{\nabla}_R \psi |^2
  + D {\bf u}_0' \vec{\nabla}_R^2 \psi,\end{aligned}$$ where $\vec{\nabla}_R$ is the nabla operator in respect to scaled coordinates $\vec{R}$. Thus the solvability condition for ${\bf u}_1$ gives the dynamics of phase waves: $$\frac{\partial \psi}{\partial T}
  = c_1 \vec{\nabla}_R^2 \psi + c_2 | \vec{\nabla}_R \psi |^2.
  \label{eqn: phase dynamics}$$ If we use a new dependent variable $\vec{V} \equiv \vec{\nabla}_R \psi$, then it satisfies the Burgers equation. The coefficients $c_1$ and $c_2$ are obtained from the relations, $$\begin{aligned}
  &&c_j = \langle {\bf v}^\dagger, {\bf v}_j \rangle
  / \langle {\bf v}^\dagger, {\bf u}_0 \rangle,
  \\
  &&{\bf v}_1 = D {\bf u}_0',\quad
  {\bf v}_2 = D {\bf u}_0'' - M {\bf u}_0' {\bf u}_0',\end{aligned}$$ here $\langle {\bf v}^\dagger, {\bf v} \rangle \equiv
\displaystyle\int_0^{2\pi} \!\!{\rm d}\psi ({\bf v}^\dagger, {\bf v})$ and ${\bf v}^\dagger$ is the nontrivial periodic solution to the adjoint differential equation of $L {\bf v} = {\bf 0}$. Equation \[eqn: phase dynamics\] describes slow and slight modulation of the homogeneous oscillation with the frequency $\omega_0$ by the phase $\psi$. We note that the coefficient of the nonlinear term, $c_2$, show competition between diffusion and advection.

When we use the quantity $\phi = \omega_0 t + \psi$, eq. \[eqn: phase dynamics\] becomes $$\frac{\partial \phi}{\partial t}
  = \omega_0 + c_1 \vec{\nabla}^2 \phi
  + c_2 | \vec{\nabla} \phi |^2.
  \label{eqn: phase}$$ The dispersion relation is thus estimated from the phase equation \[eqn: phase\] through the wave characteristics $\omega = \partial \phi / \partial t$ and $\vec{k} = \vec{\nabla} \phi$ as [@Aliev94] $$\omega = \omega_0 + c_2 k^2 + \cdots,\quad
  k = | \vec{k} |.
  \label{eqn: dispersion relation}$$ Since the scaling of coordinates in the perturbation expansions \[eqn: asymptotic expansions\] means spatially slight modulation, $k = O(\sqrt{\epsilon})$, eq. \[eqn: dispersion relation\] is the Taylor expansion for the dispersion curve, $\omega = \omega(k)$ in the vicinity of $k = 0$. Thus, the coefficient of nonlinear term in eq. \[eqn: phase\] is $c_2 = \omega''(0) / 2$. Here eq. \[eqn: dispersion relation\] has no linear term in $k$ because of the reflectional symmetry in space of eq. \[eqn: rda\]. As mentioned above, $c_2$ depends on advection constants as well as diffusion constants, and hence $c_2$ can take the value of a wide range.

We point out that the dispersion relation \[eqn: dispersion relation\] is only applicable to some of periodic waves with stationary traveling. It is not adopted to waves with non-uniform phase gradients [@Polezhaev95]. In such a case, we need to use the phase equation \[eqn: phase\], or analyze eq. \[eqn: rda\] directly.

Discussion {#sec: Discussion}
==========

By means of numerical calculations for eq. \[eqn: 2rda\], it has been shown that the flow make remarkable differences in the dispersion curves or propagation of phase waves. To elucidate such differences induced by the flow, we consider the spatial scale. The two-component system \[eqn: 2rda\] has the diffusion term only in the free element. Thus, without advection term, the variation of the diffusion constant is canceled by the scaling of spatial coordinates. In contrast, such a cancellation is impossible with the advection term because the advection coefficient is independent of the diffusion constant.

The deformation of the dispersion curves with the flow term has been shown for the branch of phase waves by the phase equation derived from eq. \[eqn: rda\]. Furthermore, we have found out another phenomenon of phase wave mentioned below.

Advection coefficients govern the coefficient $c_2$ of the quadratic term in the wave number $k$ to the dispersion relation \[eqn: dispersion relation\]. The coefficient $c_2$ is given by the addition of two parts which stem from the diffusion and advection terms, respectively. Thus, the competition between the diffusion and advection constants governs the value of $c_2$. The variation of $c_2$ gives a quadratic change in the frequency of long waves. This result elucidates the branch of phase waves ($k \sim 0$) for the dispersion curves obtained numerically in section \[sec: Dispersion relation\].

Varying the advection constants, we can take $c_2$ negative. Such a situation seems to be impossible for simple reaction-diffusion equations without the advection terms. The dispersion curve is convex for $c_2 < 0$, and hence $\omega = 0$ at some wave number. This means that the phase wave is frozen and stationary. It sounds strange, and we need to study these waves in detail. One of such a system is the $\lambda$-$\omega$ system with advection terms of phase gradients[@Yamada00].

When the coefficient $c_2$ becomes sufficiently small, it may be possible to derive other types of phase equations by introducing different scaling of independent variables from ones used in the present analysis. Furthermore we need to study waves with relaxation oscillations to know the characteristics of trigger waves with the flow, because the phase equation is satisfied only in the region of the phase-wave branch.

Acknowledgments {#acknowledgments .unnumbered}
===============

This study was supported by The Sumitomo Foundation (Grant No. 970628), and The Institute of Physical and Chemical Research (RIKEN) (T. N.).

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Precipitated Silica Market by End-Use Industry (Automobiles, Cosmetics, Electronics, Agriculture), by Application (Rubber, Personal Care, Food, Battery Separator, Coating & Inks, Adhesives & Sealants), & by Region - Global Forecast to 2021

http://www.marketsandmarkets.com/Market-Reports/precipitated-silica-market-248726425.html

Silica Fume Market by Application (Building Construction, Marine Structure Construction, Oil & Gas Well Grouting, Nuclear Power Plant Construction, Chemical Production Facilities Construction, by Geography (Middle East and Africa, North America, Asia-Pacific, South And Central America) - Global Analysis and Forecast to 2020

http://www.marketsandmarkets.com/Market-Reports/silica-fume-market-173625350.html

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Q:

Lest FPC and AW_BLog

We are having some problems with FPC and AW_BLOG ... the first blog page is being cached and after then clicking other links (in the blog) they always result in the samen page
Open this link
http://shirtsofcotton.com/blog/sinterklaas-cadeau-overhemd/
and then click a link in the blog section on rights hand; they dont seem to go to another page .... but again show the first open page
We have these set as cacheable actiosn: blog_index_list, blog_post_view
Is there something else we need to do?

A:

Under Configuration -> System -> Lesti FPC add the following
Add under cacheable actions

blog_index_list, blog_post_view

Under Uri params add

tag,identifier,cat,page

Thanks to Gordon Lesti
(works so far)


When and how are spatial perceptions scaled?
This research was designed to test the predictions of 2 approaches to perception. By most traditional accounts, people are thought to derive general-purpose spatial perceptions that are scaled in arbitrary, unspecified units. In contrast, action-specific approaches propose that the angular information inherent in optic flow and ocular-motor adjustments is rescaled and transformed into units related to intended actions. A number of studies have shown, for example, that the apparent distance to targets is scaled by the effort required to walk the extent. Such studies can be accommodated by the traditional account by asserting that the experimental manipulations of walking effort influenced not perception itself, but rather postperceptual response processes. The current studies were designed to assess when and how action-specific influences on distance perception have their effects. The results supported the action-specific account.


Teen Trade School Fair at Surrey Library: “Learn about a variety of careers and programs in the trades at the Teen Trade School Fair. For teens and young adults ages 13 to 25”

Employment Services for Newcomers at Libraries: “Drop in to get help with job searching, learn how to find a job in your field, and find out about skills training. For Permanent Residents.

Options Moving Ahead Program Community Welcoming Breakfast: Options Moving Ahead Program took part in a Community Welcoming Breakfast, organized/hosted by the Surrey Christian School as an ongoing initiative created in 2016 to promote a better understanding of WHY people become refugees, HOW refugees arrive in Canada as well as to highlight issues and challenges refugees face. At this Community Welcoming Breakfast, Options Moving Ahead Program brought our Spanish-speaking clients to meet with students from a Spanish Language Class. Students and newcomers were able to interact and share stories. The Spanish Language Instructor reported how well students appreciated learning from our newcomers despite language/communication challenges ... students try to use their Spanish language and appreciated the patience offered by newcomers. It was a great experience for our MAP clients as well. As our newcomers saw students struggle to keep a conversation and put sentences together, they realize/appreciate that language a new language is difficult for everyone. This experience was an encouragement for our newcomers to be less afraid to try to speak English with others.

A Yoga Instructor Visits the Youth Literacy Project: For the topic of Physical Wellness, the Youth Literacy Project had the pleasure of having a very special guest instructor. Elina Dolzhikov is a professional yoga instructor who showed our students how to do basic meditation, yoga techniques, and how yoga can be beneficial in everyday life! The students said the experience was “relaxing,” “restful,” and even a bit “painful” at times! The Youth Literacy Project continues to seek more engaging and entertaining ways to teach Youth not only English but also important life tips.

2nd Annual Refugee Claimant Resource Fair: Options organized its 2nd Annual Refugee Claimant Resource Fair, this time with MOSAIC as co-host. Over 55 attendees were able to gather information and resources from participating agencies: RCMP, BC211, Kinbrace, Fraser Health Services, Legal Services Society, Salvation Army, UNHCR, Surrey Libraries, and Hot Tubs & Spa Company. Fadi Yachoua from Embarkation Law Corporation offered a presentation on refugee appeals and answered questions related to refugee claims. We appreciate financial support from Vancity Credit Union and venue sponsorship from Surrey Libraries; this event was made possible through funding from the B.C. Ministry of Jobs, Trades and Technology.

RCMP Diversity Unit Visits the Current Events Discussion Class: Options Community Services is always seeking engaging and non-traditional ways for the newcomers to learn English! One of our activity-based literacy classes, Current Events Discussion Class, had two very special guest speakers for the topic of “Drugs and Crime in Surrey.” Sergeant Ray Stanford and Constable Yousef Nasimi are from Surrey RCMP Diversity Outreach Unit and were happy to have an open-dialogue with the students. No question was too small or too strange – the students had a golden opportunity to ask the officers about home safety, personal safety, and even how to dispute their speeding tickets! For more information on the Surrey RCMP Diversity Unit, visit their homepage: http://bc.rcmp-grc.gc.ca/ For more information on registering for Current Event Discussion class, please contact Brandon.Koo@options.bc.ca


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Q:

Computing the structure of the group completion of an abelian monoid, how hard can it be?

Cherry Kearton, Bayer-Fluckiger and others have results that say the monoid of isotopy classes of smooth oriented embeddings of $S^n$ in $S^{n+2}$ is not a free commutative monoid provided $n \geq 3$.   The monoid structure I'm referring to is the connect sum of knots.
Bayer-Fluckiger has a result in particular that says you can satisfy these equations $$a+b=a+c, \ \ \ \  b \neq c$$
where $a,b,c$ are isotopy classes of knots and $+$ is connect sum.
When $n=1$ it's an old result of Horst Schubert's that the monoid of knots is free commutative on countably-infinite many generators.
What I'm wondering is, does anyone have an idea of how difficult it might be to compute the structure of the group completion of the monoid of knots, say, for $n \geq 3$?  That's not really my question for the forum, though.
It's this: Do people have good examples where it's "easy" to compute the group-completion of a commutative monoid, but for which the monoid itself is still rather mysterious?  Meaning, one where rather minimal amounts of information are required to compute the group completion?  Presumably there are examples where it's painfully difficult to say anything about the group completion?  For example, can it be hard to say if there's torsion in the group completion?

A:

Do people have good examples where it's "easy" to compute the group-completion of a commutative monoid, but for which the monoid itself is still rather mysterious?

This happens all the time in K-theory $K^0(X)$, both algebraic and topological.  Perhaps it is even the reason that K-theory is a useful tool.
For a striking algebraic example, take $X = \mathbb{A}^n_k$ where $k$ is a field.  Then $K^0(X)$ is the group completion of the commutative monoid $M$ of isomorphism classes of finitely generated projective modules over $R = k[x_1, \ldots, x_n]$.  In 1955 Serre asked whether every such module was free, i.e., whether $M = \mathbb{N}$.  This question became known as Serre's conjecture.  Serre proved in 1957 that every finitely generated projective $R$-module is stably free, i.e., $K^0(X) = \mathbb{Z}$.  However, it was not until 1976 that Quillen and Suslin independently proved Serre's original conjecture.  So between 1957 and 1976, $M$ was an example of a commutative monoid whose group completion was known but which itself was not known.  This is only a historical example, because $M = \mathbb{N}$ turns out to be very simple; however, it illustrates the difficulty of the question in general.
A topological example where the commutative monoid is not so simple is given by $KO^0(S^n)$.  Let us take $n$ congruent to 3, 5, 6, or 7 modulo 8, so that $KO^0(S^n) = \mathbb{Z}$ by Bott periodicity (the generator being given by the trivial one-dimensional real vector bundle).  Let $T$ be the tangent bundle to $S^n$.  In $KO^0(S^n)$, of course, the class of $T$ is equal to its dimension $n$.  But if we let $M$ be the commutative monoid of isomorphism classes of finite-dimensional real vector bundles on $S^n$ (so that $KO^0(S^n)$ is the group completion of $M$) then the class of $T$ is not equal to the class of the trivial $n$-dimensional vector bundle unless $S^n$ is parallelizable, which only happens when $n$ is equal to (0 or 1 or) 3 or 7.  So for all other values of $n$, $M$ is not simply $\mathbb{N}$; there are extra vector bundles which get killed by the group completion process.  Understanding these monoids $M$ for all $n$ amounts to understanding the homotopy groups of all the groups $O(m)$, which I expect is not much easier than understanding unstable homotopy groups of spheres.
Finally, Pete's example of the monoid of cardinalities of at most countable sets and its absorbing element also makes an appearance in K-theory; here it is called the Eilenberg swindle and it explains why we restrict ourselves to finitely-generated projective modules.

A:

This example is similar to Reid's: If $G$ is a finite group, then $K^0(G-\mathrm{rep})$ is just the class functions on $G$. But the question of whether a specific class function is the character of a representation, or only of a virtual representation, can be very hard. In a sense, Mark Haiman got tenure at Berkeley for proving that certain class functions on $S_n$ were characters.

A:

An ultra-classical example: the failure of unique factorization in algebraic number fields. Here one looks at the multiplicative monoid of nonzero algebraic integers in a finite extension field of $\mathbb Q$. Factoring out units gives a quotient monoid $M$, and this is free (abelian) on the irreducible elements exactly when the unique factorization property holds. The monoid $M$ embeds in the ideal group, the free abelian group generated by the prime ideals, and the group completion of $M$ is the finite-index subgroup of the ideal group generated by the principal ideals. This subgroup is also free, but without a canonical basis. One can think of this subgroup as a somewhat skewed lattice in the ideal group, and $M$ is the intersection of this lattice with the positive "orthant" of the ideal group.
I'm not an expert on this stuff, so please correct any inaccuracies in what I said above. I gather that the structure of $M$ as a monoid can be rather complicated, even though it's a submonoid of a free monoid.  Perhaps this complexity is why the monoid structure seems rarely to be discussed explicitly. Does anyone know any references describing the monoid structure?