text:
Grands Échezeaux is an Appellation d'origine contrôlée (AOC) and Grand Cru vineyard for red wine in the Côte de Nuits subregion of Burgundy, with Pinot noir as the main grape variety. Grands Échezeaux is located within the commune of Flagey-Echézeaux, on a strip of land between the territory of the communes Vosne-Romanée, Vougeot and Chambolle-Musigny. Grands Échezeaux borders on Clos de Vougeot and its wall in the east and north, and on Échezeaux in the west and south. The AOC was created in 1936.

Wine style
In general, Grands Échezeaux is considered a better appellation than its larger and more variable neighbour Échezeaux. In the early 2000s, there were 21 vineyard owners in Grands Échezeaux, but 80 in Échezeaux. The most well-known owner in Grands Échezeaux is Domaine de la Romanée-Conti.

Production
In 2008,  of vineyard surface was in production within the AOC, and 240 Hectolitres of wine was produced, corresponding to 32,000 bottles.

AOC regulations
The main grape variety for Grands Échezeaux is Pinot noir. The AOC regulations also allow up to 15 per cent total of Chardonnay, Pinot blanc and Pinot gris as accessory grapes, but this is practically never used for any Burgundy Grand Cru vineyard. The allowed base yield is 35 Hectolitres per hectare, a minimum planting density of 9,000 vines per hectare and a minimum grape maturity of 11.5 per cent potential alcohol is required.

See also
List of Burgundy Grand Crus
Échezeaux

References

Burgundy (historical region) AOCs

redpajama_set_name: RedPajamaWikipedia


Wednesday, January 16th at 12:30pm Iowa Learning Farms will kick off our 15th anniversary by hosting a webinar with Iowa Secretary of Agriculture Mike Naig.
The webinar will feature ILF program manager Dr. Jacqueline Comito and Secretary Naig discussing conservation, water quality and the Secretary's vision for Iowa. They will also discuss the Iowa Nutrient Reduction Strategy and how Iowans are working to meet the nitrogen and phosphorus loss reductions outlined in the Strategy. Webinar participants will be able to submit questions for Secretary Naig during the webinar through the Zoom Webinar software.


text:
Do all rabbits have white tails?
The classic image of a bunny rabbit is only complete with a fluffy cotton-white tail bobbing about as it frolics across a field. But, does every rabbit have a white tail, and if so why?
Read on for the intriguing answer and insights about this key rabbit adaptation that makes rabbits excellent survivors.
So, do all rabbits have white tails?
Pet rabbits are bred for variety, tails included
Why are rabbit tails mainly white?
Let's put this all in context. Rabbits are a prey species.
Rabbits use their white tails to signal too
Other survival strategies that rabbits have to hand.
In short no. There is significant variation in tail color, particularly in domesticated pet rabbit breeds where color variations have actively been bred into them.
However, among wild rabbits, a white flashing tail is a predominant and necessary characteristic.
Wild rabbits that tend to have rural grassland, woodland, wilderness, or cliffside habitats have a brown coat that is flecked with grey, white and black to blend in with their surroundings.
The tail and underside being bright white couldn't be more different.
Domestic rabbits are descended from white rabbits but have been bred in such a way that they no longer have a selective advantage for life in the wild.
One of the results of this breeding is the sheer variety of fur colors and patterns in domesticated rabbits including under-tails that are orange, slate, or cream.
Let's look at why a white tail is advantageous to rabbits and how they are used.
The classic brilliant white cotton tufty tail of a rabbit stands out when compared to the drab, brown coat that is common in wild rabbits.
The contrast is remarkable enough to have invited the investigation of biologists who have studied rabbit tails and how they have used them over time.
Initially, it was thought that the flashing of the white tail was associated with the mating rituals that are common amongst these animals.
But German researchers from the University of Göttingen
have definitively answered the question by finding out that the tail's primary function is to distract and confuse a potential predator.
By recreating the movements of a rabbit in a computer model, these evolutionary biologists were able to demonstrate that the presence of a bobbing whitetail can distract a would-be predator from targeting the main body of the rabbit.
The bright rump of the rabbit proves an obvious target for both airborne and land predators, but when combined with an evasive Zig-zag sprint, the predator has to constantly readjust its focus, buying its would-be dinner vital seconds to make its escape.
The findings of the 2013 German study were consistent with the survival of white rabbits being known to be higher where their tails are white.
In the wild, rabbits live their lives with the constant threat of predation by other animals. Prey species like rabbits are essentially food for a wide range of other species.
This means that they have to use physical characteristics and abilities that enable them to escape predators and survive long enough to mate and bring forth another generation.
The whitetail is one such adaptation and makes an excellent survival strategy. Domestic bunnies that live a life of luxury don't need this feature to remain safe. A whitetail is also seen in deer too where the tail is similarly used to evade predators.
It is likely that the whitetail also serves the purpose of communicating a threat or danger to other nearby rabbits. The tail flashing may be associated with the thumping of the hind legs as a strong warning.
Even if the signaling rabbit does not survive the flashing white signal will warn their neighbors to get away quickly.
Rabbits use their tails to communicate in other ways too, including wagging the tail which is thought to indicate displeasure, or in association with mating.
With predators lurking around every corner, the life expectancy of a wild rabbit is very short.
Rabbits can only expect 1 to 2 years at most so to prolong their days they need to use every physical advantage available to them to escape predation.
Apart from the whitetail other protective characteristics include:
Running: When a rabbit gets in gear it can hit speeds of up to 35 miles per hour (55 kilometers per hour) to shake off even the most determined of predators. They are also experts of their terrain which provides an added advantage in giving claws or teeth the slip.
Kicking: Strong hind legs can land a powerful blow on anything that tries to approach a rabbit from behind, buying vital time for a hasty escape.
Wide visual field: Amazingly rabbits have an almost 360-degree field of vision, meaning that they can spot a predator approaching in almost any direction, including above. Their vision is poorest directly in front of them, but this is compensated by their whiskers. You can learn more about this in the article "Do rabbits have whiskers?".
Outstanding hearing: Rabbits have incredible hearing that can detect high-[itched sounds up to two miles away. Their long ears can also be directed to pick up sounds in a specific direction meaning that they can remain continually primed for flight.
It's clear to see that that cute white tail is the difference between life and death for many rabbits.
White tails are an advantage in the wild and over time have been passed on by successive generations of rabbits that have been able to survive long enough to breed.
The instinctive use of a bright white tail is also needed for signaling and other social behaviors of wild rabbits, but for domesticated rabbits, this characteristic has reduced in prevalence in favor of other distinctive characteristics.
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redpajama_set_name: RedPajamaCommonCrawl


There has been a lot of talk regarding Real Madrid and the upcoming summer transfer market due to the poor season Los Blancos have had. And while several big-name players have been linked with a move to the Santiago Bernabeu outfit, two are the names that have gotten repeated the most.
Coincidentally, both play for Chelsea since we're talking about Eden Hazard and N'Golo Kante. While the Belgium international has been a target for Madrid since the first tenure of Zinedine Zidane, now the French defensive specialist has also gotten attention from Madrid's officials.
However, it does not look as if Kante would end up completing the switch to the Liga giants any time soo. According to a report from the London Evening Standard, Kante was quote as saying: "I am at Chelsea, and I still have aims here — what is said elsewhere is not important." So we can esentially pull the plug on any potential rumour that would bring the French star to Spain's capitol city.
Things could be different with Hazard, though. The Belgian is yet to sign a contract extension with The Blues and while losing him could represent a huge hit, they already sealed a move to sign Christian Pulisic next summer and still have other decent alternatives for the wing roles such as Willian and Pedro.
The upcoming summer will undoubtedly be big for Los Blancos. Especially if they want to return to the place they were until last season.


If you find it challenging to achieve a flat stomach and tight abs, you're not alone. Even when you eat a healthy diet, workout all the time and do countless hours of crunches, it's common for these efforts to fall short of your desired outcome. Often, factors such as genetics, aging, prior pregnancies and weight fluctuations limit the effectiveness of your efforts. If you feel like your workouts are starting to reach a point of diminishing margin of returns, a tummy tuck can help you deliver the toned, flat stomach you desire.
A tummy tuck, also called an abdominoplasty, is one of the most popular body contouring procedures performed at Farris Plastic Surgery. Dr. Farris will remove excess fat and skin while tightening loose abdominal muscles in order to help you restore a more fit appearance in your stomach region. Many of our patients comment that their tummy tuck provides increased self-confidence that translates into every aspect of their life.
You can learn more about your tummy tuck options and receive individualized treatment recommendations by speaking with Dr. Zachary Farris in person. Please call 214-363-1073 today to schedule a consultation. We serve patients in the Dallas, Texas area.
As part of the aging process, it's common for your metabolism to slow down. As a result, it becomes increasingly difficult to burn off fat in certain areas of the body, including the abdominal region. This, combined with weakened muscle tissue and a loss of skin elasticity, often causes your midsection to expand with age. In many instances, diet and exercise can only do so much to combat these effects of aging, and a tummy tuck may be your best option to put the finishing touches on your workout efforts.
Weight loss – Significant weight loss often results in stretched abdominal muscles and loose, hanging skin in your midsection. As a result, you may be unable to achieve a fit stomach in spite of all the hard work you put in to lose the excess weight.
Pregnancy – Your abdominal muscles become stretched and often separate during pregnancy. It's also common to experience stretch marks following childbirth. As a result, it can become challenging to regain a tight midsection after having children.
Genetics – Your genetics play a major role in your body type. Some people are simply predisposed to store fat in their midsection, and even the most rigorous workout regimen is often unable to override your genetic makeup.
If you are experiencing any of these issues, a tummy tuck can provide the most effective option to help you achieve your desired abdominal appearance.
There are also several psychological benefits associated with a tummy tuck. It's common to experience a boost in self-confidence and an improved self-image after your procedure. You may also find that you have a new-found motivation to live a healthy lifestyle in order to make sure your beautiful results last for many years to come.
If you are planning on having children in the future, you should discuss these plans with Dr. Farris during your consultation. While future pregnancies won't prevent you from undergoing a tummy tuck, it is generally best to wait until you are finished with this phase of your life since pregnancy and childbirth can undo many of the results achieved by your procedure.
If you're a smoker, you will need to quit prior to surgery and throughout the recovery period. Cigarettes contain nicotine, which constricts small blood vessels and diminishes the blood supply to tissue. If nicotine is in your system, it would increase the risks of developing an infection or other complications. Dr. Farris recommends that you stop smoking about 2-3 months before surgery. The longer nicotine is out of your system, the better your chances are to heal without complications.
A tummy tuck is highly effective at addressing many of the changes to your abdominal region commonly caused by pregnancy and childbirth. By tightening loose or stretched muscles and removing excess skin and fat, you are more easily able to regain the toned stomach you enjoyed prior to having children. For this reason, Dr. Farris often includes a tummy tuck as part of a mommy makeover.
Similarly, a tummy tuck is a great way to put the finishing touches on your weight loss efforts. After massive weight loss, you may be left with loose, hanging skin in the abdominal region. A tummy tuck can help eliminate this excess skin in order to provide you with the toned appearance you've worked so hard to achieve. As a result, Dr. Farris often recommends abdominoplasty as part of post-bariatric body contouring surgery.
Your tummy tuck will be performed on an outpatient basis under general anesthesia. Depending on the specifics of your procedure and whether you undergo a full or mini tummy tuck, it may take anywhere between 2-5 hours to complete the surgery.
Dr. Farris will make an incision from hip to hip (for a full tummy tuck) in addition to an incision that releases your belly button. The skin and fat layer is then lifted off the underlying abdominal wall, up to the level of the ribs. Any loose or stretched abdominal muscles will be tightened, and excess skin and fat will be removed. The incision is closed using sutures.
During your procedure, stretchmarks located below the level of the belly button will be eliminated. The stretch marks that are located higher up are improved, but often not entirely eliminated.
The full tummy tuck will address issues with the entire abdominal area. A longer incision is required, resulting in a longer recovery and a larger scar. However, you will achieve more dramatic results with this option.
A mini tummy tuck only addresses the region underneath the belly button. It is an excellent option when there are minimal amounts of excess skin and fat that need to be removed. There will be a smaller incision, smaller scar and shorter recovery time. However, your results won't be as dramatic as what can be accomplished with a full tummy tuck.
Dr. Farris will provide you with detailed aftercare instructions. It's crucial that you follow these carefully to ensure proper healing and the best possible results.
You should plan on having someone drive you home after surgery due to the lingering effects of the anesthesia. It's also a good idea to make sure someone is home to assist you for the remainder of the day.
You'll experience some mild bruising and swelling which will gradually subside as you heal. Dr. Farris will prescribe medication to help you manage any discomfort you experience. We recommend only taking this medication when you have pain.
Dr. Farris will provide instructions on drain care, and you will be wearing a compression garment for 4 weeks. For the first 5 days, you should walk slightly stooped over (bent at the hips). Sleep with your hips bent and your head elevated with several pillows. Stitches are placed underneath the skin during surgery so there is nothing to remove in the office.
Avoid prolonged exposure of the scars to sunlight for 4-6 months and use sunscreen as necessary. You may use vitamin E cream and scar products beginning 3 weeks after surgery to optimize healing of your scars. Scars change in appearance and improve over time up to 12 months.
Begin light walking as soon as you feel up to it in order to facilitate blood flow and prevent the formation of blood clots. You may resume most light activities after 1 week and you should generally be able to return to work after 2 weeks, especially if your job doesn't involve any strenuous activity or heavy lifting.
Regular or strenuous activity can usually be resumed after 4 weeks. It is imperative that you avoid any strenuous activity including heavy lifting, straining, or climbing of multiple stairs immediately after surgery as this may increase your risk for bleeding.
Preliminary results will begin to appear as bruising and swelling subsides. However, it may take several months before you see your final results. It's crucial that you live a healthy lifestyle that includes a balanced diet and regular exercise in order to maintain your results for years to come.
Please contact Farris Plastic Surgery using the form on this page or call 214-363-1073 today to schedule your tummy tuck consultation. We serve patients in the Dallas, Texas area.


He was nothing short of predatory as he made his way through the jungle that called itself the home of the Volary Flights. There was nothing friendly about the smooth, stone-like muscle that rippled beneath his golden pelt, nothing welcoming about his cold copper gaze. And it wasn't hard to see from a glance that he wasn't there to join. Rather, the large hybrid was far past the clans border, prowling about rather close to the camp. He was a handsome and capable looking young thing, covered in scars with the look of a well toned warrior about him. Whoever found him wouldn't find themselves in a plesant situation though, because Damian Dimera wasn't there to play nice.
god, he felt horrible. his body going through both withdrawals, and lack of feeding had driven his body down. he couldnt even die, he couldnt leave this weak vessel that was his body, and so he just walked around. as much as he wanted to feed, needed to feed on blood, the vampire was too weak. his feral side was dead, gone, never to return to the light of day or even the shine of the moon, yet the hyena seemed to have been better off. the gold orbs sunken in as he moved along, his heightened senses picking up the new scent. any scent caused his mouth to water, stomach growling, snarling even, just wanting a deop of blood. just a drop. he was so thirst, that his throat burned. maybe he could convince whoever this person was. maybe.
It took Damian little effort to spot the other, mainly because neither seemed to be making any attempt to hide themselves from the other. Damian didn't put too much stock into this, because logically they were either coming to try and greet him or to drive him off, and he could meet either extreme with one of his own. Bloodlust and desperation weren't things that crossed the handsome youths mind, and so the encounter would likely turn into an interesting one, even if he had no way of knowing that yet. Instead he strode toward the other with swift, purposeful steps, the approach far from casual or friendly. It was stiff and formal, golden eyes cold and calculating. "You there, what's your name?" he asked, as if the other were the intruder and he were in the right to go asking the questions.


text:
The Life of Bill Baggs – Book Signing Event
« STUDIO SPACES OPENING SOON!
November First Friday Art Walk »
The Marion Cultural Alliance, together with Craig and Mary Baggs, cordially invite you to a book signing to celebrate the release of "A Nervous Man Shouldn't Be Here: The Life of Bill Baggs," Nov. 5, 5-7 p.m., at the Brick City Center for the Arts.
Festivities Include:
•Celebrity Bartenders: Beth McCall & Jessica McCune serving Baggs's signature drink.
•Author Talks: Amy Paige Condon & Craig Baggs 5:20 & 6:20pm.
•Tour Open Gallery: Private Collection of Bill Baggs memorabilia, famous correspondence, etc.
•Enjoy refreshments and mid century music.
•Books available for purchase or signing throughout the celebration.
•Masks and social distancing requested.
In this first biography of one of the 20th century's most influential editors, author Amy Paige Condon traces how an orphaned boy from Colquitt, Georgia, traveled the world, fought for freedom, landed in Miami, and led the Miami News to three Pulitzer Prizes – all while leading on civil rights, Latin American diplomacy, the Cuban Missile Crisis, environmental and historic preservation, and peace in Vietnam. Along the way, he befriended everyone from an elderly man born into slavery to a farmer in Panama to U.S. presidents from Harry S Truman to John F. Kennedy.
It's an extraordinary, yet intimate story of one man's impact on the world we still live in. As Bill's son Craig Baggs can attest, Bill's brief life offers lessons that resonate today and reminds us of the necessity of an independent local press to democracy.
About the Presenters:
CRAIG BAGGS
Craig Baggs—the son of two Georgia peaches, Bill and Frec Baggs—grew up in the strange alchemy of journalism and politics that swirled in midcentury Miami. He attended his first national political conventions at age six, and by the age of eleven, found himself standing in the Oval Office with his father, the editor of the Miami News, being introduced to Supreme Court Justice Earl Warren.
Craig studied the great books at St. John's College in Santa Fe, New Mexico, and later received his B.A. in international affairs at Florida State University in Tallahassee, where he also worked on a master's degree in communications. Baggs and his wife Mary, have raised their three children in Ocala and have both just recently retired from careers in sales and marketing in the newspaper, healthcare and insurance industries.
Baggs is a member of the Marion Cultural Alliance, a reading pal for the United Way of Marion County, a member of the Friends of Silver Springs State Park, board member at Interfaith Emergency Services and member of Grace Episcopal Church. He enjoys time at the family getaway on coastal Georgia, gardening at his beloved home "Kingfish Corner," and growing up once again with his six grandchildren and grand dog Mack, who like Craig, is a southern gentleman.
AMY PAIGE CONDON
Born to a whisk-wielding cake baker and a tequila-swilling gentleman, Amy Paige Condon was reared in Fort Worth, Texas. She traveled to Miami, Florida, for what she thought would be a one-year internship in the Miami-Dade County manager's office, and ended up staying for 16 years, finding an accidental career as a park planner – a profession she fell in love with until her first love, writing, kept calling her back.
She and her husband sold everything and moved to Savannah, Georgia, where Amy earned a master's degree in writing. While still a graduate student, she co-authored the New York Times bestselling The Back in the Day Bakery Cookbook (2012, Artisan) with baker-owners Cheryl and Griffith Day. Her master's thesis became the basis for the Wiley's Championship BBQ Cookbook (Gibbs Smith 2014), which was named the best cookbook of the year by the National Barbecue News.
She was editor of the award-winning Savannah magazine, and in 2017 opened the Refinery Writing Studio, where she teaches creative writing classes. She lives in Savannah, Georgia, with her husband, three mutts, and a talkative pig named Gus.
Social distancing enforced with 45 max capacity and masks required while inside the gallery.
Community Art Events, MCA Events
art, exhibit opening
https://www.facebook.com/events/673155873625144/?acontext=%7B%22action_history%22%3A[%7B%22surface%22%3A%22page%22%2C%22mechanism%22%3A%22page_admin_bar%22%2C%22extra_data%22%3A%22%7B%5C%22page_id%5C%22%3A337626562928103%7D%22%7D%2C%7B%22surface%22%3A%22events_admin_tool%22%2C%22mechanism%22%3A%22events_admin_tool%22%2C%22extra_data%22%3A%22[]%22%7D]%2C%22has_source%22%3Atrue%7D
Marion Cultural Alliance
Brick City Center for the Arts @ Ocala, FL
23 SW Broadway St.
Ocala, FL 34471 United States + Google Map


555 EATS - GRILLED CAJUN CHICKEN FAJITAS — FORK AND HOSE CO.
WE LOVE SHARING HEALTHY FIREHOUSE RECIPES WITH OUR FRIENDS AT 555 FITNESS ! TO LEARN MORE ABOUT 555 FITNESS, CLICK HERE AND DON'T FORGET TO HASHTAG YOUR HEALTHY MEALS #FORKANDHOSECO #55EATS !
IF I AM EVER LOOKING FOR A QUICK, HEALTHY LUNCH THAT DOESN'T NEED MUCH PREP....I GO WITH FAJITAS. THEY ARE GREAT BECAUSE OF THE ENDLESS WAYS YOU CAN PREPARE THEM. THIS RECIPE IS SO EASY AND DELICIOUS, IT IS SURE TO PLEASE THE CREW AND THE FAMILY AT HOME!
Fajitas are also a great way to incorporate veggies into a meal. Besides peppers and onions, mushrooms and squash are also great additions. Get creative with what is in season!
Place chicken in a large bowl, season with Cajun spices. Cover and place in the refrigerator while you prep the vegetables.
Set a grill on medium-high heat. In a large cast iron pan over medium heat, add a glug of olive oil.
When oil is just starting to smoke, add peppers and onions. While they are cooking, place the chicken on the grill and cook for 8-10 minutes or until done. Meanwhile, sprinkle some Cajun seasoning on the peppers and onions and add the can of tomatoes. When the peppers are just starting to soften, remove from heat and sprinkle in some cilantro. Place the chicken on the wrap, top with the pepper and onion mixture and finish with avocado and more cilantro.
Posted on November 19, 2015 by Arthur Fusco.


Grilled nuggets are gluten free and really flavorful. You also can't go wrong with their waffle fries!
Great. Good food and great have policies in place to avoid cross contamination. Fries are also fried in a separate fryer from the chicken!


text:
using Aspose.Tasks.Visualization;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

/*
This project uses Automatic Package Restore feature of NuGet to resolve Aspose.Tasks for .NET API reference
when the project is build. Please check https:// Docs.nuget.org/consume/nuget-faq for more information.
If you do not wish to use NuGet, you can manually download Aspose.Tasks for .NET API from https://www.nuget.org/packages/Aspose.Tasks/,
install it and then add its reference to this project. For any issues, questions or suggestions
please feel free to contact us using https://forum.aspose.com/c/tasks
*/

namespace Aspose.Tasks.Examples.CSharp.Miscellaneous
{
    class SaveCostOverviewReport
    {
        public static void Run()
        {
            string dataDir = RunExamples.GetDataDir(System.Reflection.MethodBase.GetCurrentMethod().DeclaringType.FullName);

            // ExStart:SaveCostOverviewReport
            Project project1 = new Project(dataDir + "OzBuild 16 Orig.mpp");
            project1.SaveReport(dataDir + "CostOverview_out.pdf", ReportType.CostOverview);
            // ExEnd:SaveCostOverviewReport
        }
    }
}

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}

The theory of special relativity is usually said to derive from two assumptions. First, the principle of relativity, which denies privileged status to any inertial frame; second, the postulate of the constancy of the speed of light, which stipulates that this velocity is independent of the velocity of the emitter and of the receiver.

Several works have tried to test the validity of these assumptions by creating alternative theories in which they are violated to some degree or other. These test theories of special relativity were naturally centered on possible violations of either the principle of the constancy of light \cite{edwards} or the principle of relativity \cite{robertson,mansouri}.

It has long been known that the special theory of relativity is not actually based on these two assumptions alone, however \cite{levy}. One must also add space homogeneity and isotropy. These symmetries had long been held to be so fundamental as to be almost beyond need of verification. Indeed, Einstein did not even mention them as separate assumptions in his original paper \cite{einstein}, though he later admitted they were necessary.

The discovery of parity violation \cite{parity1,parity2} significantly altered this attitude. The idea that even apparently fundamental symmetries of the universe can be broken has found many uses and has gained wide acceptance. Most of these symmetries are highly formal, however, and the fundamental symmetries of space-time, homogeneity and isotropy,  remain unexamined to a large extent.

Because the theory of special relativity itself is based on a rethinking of basic concepts of space and time, it represents the natural seeting in which to explore possible violations of these fundamental symmetries. It is also a theory that remains fundamental to our description of the universe. It is therefore natural to explore whether giving up on the exactness of these symmetries appears has any measurable effect in this theory.

This step markedly differs from other attempts at changing the basic assumptions of special relativity (SR). Initially, the principle of relativity seemed to be more obvious, because of its long history in classical mechanics, and verification of SR concentrated on the postulate of the constancy of the speed of light. It soon became clear that while the constancy of the two-way speed of light (measured along a closed path) is directly testable empirically, the one-way speed of light is another matter entirely. Measurements of this speed require a clock synchronization procedure, and the conventional character of such a procedure has given rise to an extensive literature \cite{reichenbach,grunbaum1,grunbaum2}.

Edwards formulated a theory in which the one-way speed of light could be anisotropic, with values that depended on direction \cite{edwards}. The interpretation of such theories is delicate, however, because the time parameter that appears in the equation may not be directly related to the time experimentally measured by clocks. This happens because experimentally, one needs to synchronize clocks at different locations and the choice of synchronization method determines the relation between measured time and the time that appears in the transformations. It turns out that when this is done, Edwards's theory is empirically equivalent to standard special relativity \cite{zhang,zhang2}. In this sense, Edwards's theory is not a true test theory of special relativity.

A true test theory was formulated by Robertson \cite{robertson} and generalized by Mansouri and Sexl into the currently best known test theory of SR \cite{mansouri}. Mansouri and Sexl point out that the principle of relativity is less obvious than was previously thought because cosmological consideration seem to single out a special frame of reference, i.e., the frame in which the cosmic background radiation is isotropic. They then explore the consequences of violating the principle of relativity by assuming the existence of a single system in which synchronization by infinitesimally slow transport of clocks coincides with synchronization by light signals. That chosen frame is the only one in which the speed of light turns out to be isotropic. In all other frames, it depends on the direction of propagation. Unlike in Edwards's theory, this effect cannot be eliminated by some appropriate choice of synchronization procedure and represents a true physical difference between the preferred frame of reference and all the others.

Thus, in the Mansouri-Sexl theory, anisotropy always means anisotropy of the speed of light in some frames of reference. It has become usual to identify this effect with the very notion of spatial anisotropy in SR. The present paper takes a different view, one that is in some sense the opposite (or the complementary) of the Mansouri-Sexl one.

In all previous modification of SR, one assumes that space-time homogeneity and isotropy hold, and tests for the influence of variations in the speed of light on the theory. This paper proceeds in the exact opposite manner. I hold on to Einstein's postulates, viz, the relativity principle and the constancy of the speed of light in all reference frames, but give up spatial homogeneity and isotropy. It must be noted that accordingly, the speed of light is assumed to be isotropic in all frames. Acording to the normal usage of the term "spatial anisotropy" in the context of special relativity, this would appear to be begging the question, since only the speed of light is ever assumed to be anisotropic in standard test theories.

There is no logical reason why it must be so, however. Standard relativity theory endows the speed of light with unique properties. Obviously, that its value is frame-invariant does not mean that all other velocities or physical quantities are also frame-invariant, quite the reverse. The same will be shown to be the case here. The speed of light has unique properties. While its value is assumed not to depend on orientation, we will see that other properties do. Thus, I will show that the two postulates of special relativity allow for a more general form of Lorentz transformations that make length contraction and time dilation direction-dependent, even though the speed of light is not. In this sense, we are truly testing for the possible anisotropy of space, not for the anisotropy of light propagation.

The structure of the paper is as follows. Section \ref{sec:constantc} starts with the most general coordinate transformations that are compatible with the principle of relativity, assuming neither space-time homogeneity, isotropy nor the principle of constancy of the speed of light. The technical details of this somewhat lengthy but straightforward derivation appear in the appendix. These transformations are then combined with the requirement that the speed of light be identical in all reference frames. This yields automatically linear and hence homogeneous equations, which shows that adding space homogeneity to the Einstein postulates is redundant. Section \ref{sec:group} completes the derivation of the one-dimensional transformations by requiring that they form a group. Section \ref{sec:final} extends the result to three dimensional space and contains the final transformations. These turn out to differ from the Lorentz equations by a velocity dependent factor. The dependence on spatial orientation is expressed by an anisotropy exponent $\kappa$ that vanishes if space is isotropic. Its basic properties and implications are explored in section \ref{sec:kappa}. Section \ref{sec:doppler} then examines the doppler effect within such a theory in order to suggest a possible method of measuring the exponent $\kappa$. The paper concludes with a summary.

\section{Constancy of the speed of light}
\label{sec:constantc}

We seek the most general coordinate transformations from one inertial frame S to another, S', which verify Einstein's two postulates, namely the principle of relativity and the principle of the constancy of the speed of light.

The first requirement is that inertial (uniform) motions in a frame of reference S be transformed into inertial motions in another frame S'. The most general inertiality-preserving coordinate transformations are the Fock-Lorentz transformations. The appendix contains a new derivation of this result, which makes use of more elementary mathematics than the one provided by Fock \cite{fock}. The transformations are:
\begin{eqnarray}
\label{eq:inert-trans}
x' = \dfrac{p_1x + p_2t}{q_0 + q_1t + q_2 x} \nonumber \\
t' = \dfrac{t + Bx}{q_0 + q_1t + q_2 x}
\end{eqnarray}
where $p_1, p_2, B, q_0, q_1, q_2$ are all arbitrary constants that must now be determined from additional assumptions.

The result Eq.(\ref{eq:inert-trans}) is completely general, in that it does \textit{not} assume either homogeneity or isotropy of space. The usual procedure is to impose these two additional conditions and then add the requirement that the velocity of light be invariant in all frames. This yields the Lorentz transformations.

I ignore space homogeneity and isotropy, and instead impose only the condition that the velocity of light be identical in all frames, independently of any properties of the light source or of the observer. Thus, in the frame S, any light signal propagating along the x-axis will be described as
\begin{equation}
\label{eq:Ssignal}
x = \pm ct + x_0
\end{equation}
where the $\pm$ sign follows from the requirement that \textit{any} light signal travel at the speed $c$, irrespective of its direction.

By inserting Eq.(\ref{eq:Ssignal}) into the general transformations, Eqs.(\ref{eq:inert-trans}), we obtain:
\begin{eqnarray}
\label{eq:translight}
x' = \dfrac{p_1x_0 + \left(p_2 \pm c p_1 \right) t}
{q_0 + \left(q_1 \pm c q_2 \right)t + q_2x_0} \nonumber \\
t' = \dfrac{Bx_0 + \left(1 \pm c B \right) t}
{q_0 + \left(q_1 \pm c q_2 \right)t + q_2x_0}
\end{eqnarray}

The principle of the constancy of the speed of light requires that the same light signal be described, in the $S'$-frame, as
\begin{equation}
\label{eq:Spsignal}
x' = \pm ct' + b_{\pm}
\end{equation}
where the constants $b_{\pm}$ may differ for each direction of propagation.

Substituting the transformations Eqs.(\ref{eq:translight}) into Eq.(\ref{eq:Spsignal}) yields the relation:
\begin{equation}
p_1x_0 + \left(p_2 \pm c p_1 \right) t = \left(c^2 B \pm c \right) t \pm c Bx_0 +  b_{\pm}\left[q_0 + q_2x_0 + \left(q_1 \pm c q_2 \right)t \right]
\end{equation}
Comparing the time dependent and time-independent terms on both sides, we find that:
\begin{eqnarray}
\label{bpm}
b_{\pm}(q_0 + q_2x_0) = x_0 \left(p_1  \mp c B \right) \\
\label{prule}
p_2 \pm c p_1 = c^2 B + b_{\pm} \left( q_1 \pm cq_2 \right) \pm c
\end{eqnarray}

Eq.(\ref{bpm}) shows that if $x_0 = 0$, $b_{\pm}$ also vanishes. Substituting this into Eq.(\ref{prule}), we find
\begin{equation}
p_2 - c^2 B = \pm c(1 - p_1)  \Longrightarrow \; p_2 = c^2 B \; \; ; \; \;  p_1 = 1
\end{equation}
The right hand side follows from the equations obtained by taking separately the plus and minus signs.

Returning to Eq.(\ref{prule}) and substituting the values of $p_1$ and $p_2$, we find immediately that for any $b_{\pm}$,
\begin{equation}
b_{\pm}\left( q_1 \pm c q_2 \right) = 0  \Longrightarrow  q_1 = q_2 = 0
\end{equation}
Again, the relations follow from a comparison of the plus and minus signs in the terms.

The coordinate transformations now become
\begin{eqnarray}
\label{eq:constc}
x' = \dfrac{x +p_2 t}{q_0} \nonumber \\
t' = \dfrac{t + \left(\dfrac{p_2}{c^2}\right)x}{q_0}
\end{eqnarray}
Finally, by definition, the origin of the S'-frame, $x' = 0$, moves with respect to the S-frame at a speed $v$, which immediately implies that
\begin{equation}
p_2 = -v  \Longrightarrow B = -\dfrac{v}{c^2}
\end{equation}
and thus,
\begin{eqnarray}
\label{eq:trans1}
x' = \dfrac{x - vt}{q_0(v)} \nonumber \\
t' = \dfrac{t - \dfrac{v}{c^2}x}{q_0(v)}
\end{eqnarray}

Note that these transformations are linear, and that this was obtained without assuming spatial homogeneity. In the standard derivation of the Lorentz equations, it is the homogeneity of space that guarantees the linearity of the equations \cite{levy}. Thus, homogeneity turns out to be redundant, and the linearity is actually guaranteed by the principle of the constancy of the speed of light on its own.

The form of the remaining parameter $q_0(v)$, which clearly may depend on $v$, is fixed by the requirement that these transformations should form a group.

\section{Group property}
\label{sec:group}
Let us introduce a third frame, S'', which moves with velocity $u'$ with respect to the S'-frame. The transformation from S' to S'' now reads
\begin{eqnarray}
\label{eq:trans2}
x'' = \dfrac{x' - u't'}{q_0(u')} \nonumber \\
t'' = \dfrac{t' - \dfrac{u'}{c^2}x'}{q_0(u')}
\end{eqnarray}

Combining these transformations with the transformations from S to S', Eqs.(\ref{eq:trans1}), we obtain the relations
\begin{eqnarray}
\label{eq:combo}
x'' = \dfrac{x - \left( \dfrac{u' + v}{1 + \dfrac{u'v}{c^2}}\right)t}{\left[ \dfrac{q_0(u')q_0(v)}{1 + \dfrac{u'v}{c^2}}\right]} \nonumber \\
t'' = \dfrac{t - \left( \dfrac{u' + v}{1 + \dfrac{u'v}{c^2}}\right)\dfrac{x}{c^2}}{\left[ \dfrac{q_0(u')q_0(v)}{1 + \dfrac{u'v}{c^2}}\right]}
\end{eqnarray}
The group property requires that this should be identical with the direct transformation from S to S'',
\begin{eqnarray}
\label{eq:direct}
x'' = \dfrac{x - ut}{q_0(u)} \nonumber \\
t'' = \dfrac{t - \dfrac{u}{c^2}x}{q_0(u)}
\end{eqnarray}
where $u$ is the velocity of the S''-frame with respect to the S frame. Comparison of this expression with the combined transformation, Eq.(\ref{eq:combo}), shows immediately that we must have
\begin{equation}
\label{eq:veloadd}
u = \dfrac{u'+ v}{1 + \dfrac{u'v}{c^2}}
\end{equation}
and the relation
\begin{equation}
\label{eq:q}
q_0 (u) = q_0\left(\dfrac{u'+ v}{1 + \dfrac{u'v}{c^2}}\right) = \dfrac{q_0(u')q_0(v)}{1 + \dfrac{u'v}{c^2}}
\end{equation}

Eq.(\ref{eq:veloadd}) is the standard relativistic velocity addition formula. Thus, this formula does \textit{not} require either spatial homogeneity or isotropy. It follows from only two assumptions, the principle of relativity and the principle of the constancy of the speed of light. No additional spatial symmetries are required.

On the other hand, $q_0$ differs from the Lorentz form. Note first that if we choose $u' = 0$ in Eq.(\ref{eq:q}), we find that
\begin{equation}
q_0\left(v \right) = q_0(0)q_0(v) \Longrightarrow q_0(0) = 1
\end{equation}

Keeping the velocity $v$ as a constant parameter, let us define a new variable, $\epsilon$, as
\begin{equation}
\label{eq:defepsilon}
\epsilon = u - v = u' \dfrac{1 - \dfrac{v^2}{c^2}}{1 + \dfrac{u' \cdot v}{c^2}}
\end{equation}
where the rightmost side is obtained from Eq.(\ref{eq:veloadd}).

Let us define a new function $\eta(v)$ by
\begin{equation}
\label{eq:defeta}
\eta(v) = \ln{q_0(v)}
\end{equation}

Eq.(\ref{eq:q}) now becomes
\begin{equation}
\eta(v+\epsilon) = \eta(v) + \eta\left(\dfrac{\epsilon c^2}{c^2 - \epsilon v - v^2}\right) - \ln{\left[ 1 + \dfrac{\epsilon \cdot v}{c^2 - \epsilon v - v^2}\right]}
\end{equation}
Finally, we can form the derivative of $\eta(v)$ by taking
\begin{equation}
\lim_{\epsilon \rightarrow 0} \dfrac{\eta(v + \epsilon)- \eta(v)}{\epsilon} = \lim_{\epsilon \rightarrow 0} \dfrac{\eta\left(\dfrac{\epsilon c^2}{c^2 - \epsilon v - v^2}\right)}{\epsilon} - \lim_{\epsilon \rightarrow 0} \dfrac{\ln\left(1 + \dfrac{\epsilon v}{c^2 - \epsilon v - v^2}\right)}{\epsilon}
\end{equation}
Using the fact that $\eta(0) = 0$, we obtain immediately:
\begin{equation}
\label{eq:deriveta}
\dfrac{d \eta(v)}{dv} = \dfrac{1}{1 - \dfrac{v^2}{c^2}}\left[ \dfrac{d \eta}{dv}(0) - \dfrac{v}{c^2}\right]
\end{equation}
The derivative of $\eta (v)$ at $v = 0$ is a constant that we can denote as
\begin{equation}
\dfrac{d \eta }{d v}(0) = \dfrac{2}{c} \kappa
\end{equation}
where $\kappa$ is some constant. It is important to note that $\kappa$ does not depend on $v$ and is therefore frame-invariant.

Eq.(\ref{eq:deriveta}) is immediately integrable and yields:
\begin{equation}
\eta(v) = \dfrac{1}{2}\ln{\left(1 - \dfrac{v^2}{c^2}\right)} + \kappa \ln{\left( \dfrac{c + v}{c - v}\right)}
\end{equation}
From the definition of $\eta(v)$, Eq.(\ref{eq:defeta}), we finally obtain the form of $q_0$:
\begin{equation}
\label{q0}
q_0(v) = \sqrt{1 - \dfrac{v^2}{c^2}}\left( \dfrac{c + v}{c - v}\right)^{\kappa}
\end{equation}

\section{Final transformations}
\label{sec:final}
Next consider the transverse axes. Let a light signal be emitted in a diagonal direction in the x-y plane from the origin of the frame S at a time $t_0 = 0$. The position of a point on the wavefront is $(ct, x, y, 0)$ when observed in the S frame, and $(ct', x', y', 0)$ when observed in the S' frame. Since the speed of light is invariant, we must have that

\begin{eqnarray}
\label{wavefront}
x^2 + y^2 = c^2t^2 \nonumber \\
x'^2 + y'^2 = c^2t'^2
\end{eqnarray}

Substituting the transformations for $x'$ and $t'$ from Eq.(\ref{eq:trans1}) and comparing with the first of Eqs.(\ref{wavefront}), we obtain

\begin{equation}
y'^2 = c^2t'^2 - x'^2 = \left(1 - \dfrac{v^2}{c^2}\right) \dfrac{y^2}{q_0^2(v)}
\end{equation}

Using Eq.(\ref{q0}) for $q_0(v)$, we obtain the final form of the transformations:
\begin{eqnarray}
\label{finalx}
x' = \left( \dfrac{1 - \beta}{1 + \beta} \right)^{\kappa} \dfrac{x - \beta c t}{\sqrt{1 - \beta^2}}  \\
\label{finaly}
y' = \left( \dfrac{1 - \beta}{1 + \beta} \right)^{\kappa} y \\
\label{finalz}
z' = \left( \dfrac{1 - \beta}{1 + \beta} \right)^{\kappa} z \\
\label{finalt}
ct' = \left( \dfrac{1 - \beta}{1 + \beta} \right)^{\kappa} \dfrac{ct - \beta x}{\sqrt{1 - \beta^2}}
\end{eqnarray}
where $\beta = \dfrac{v}{c}$, as usual. The transformation for $z'$ is obtained in the same way we obtained the transformation for $y'$.

These transformations differ from the Lorentz transformations, but one may wonder whether the difference is not merely conventional. As mentioned above, this is what happens in the Edwards theory, where a different synchronization procedure leads to apparently different transformations, but these involve a non-observable time parameter \cite{edwards}. This time parameter must then be related to observable time via the definition of a proper synchronization procedure. Once this is done, the Edwards theory turns out to be empirically equivalent to SR \cite{zhang,zhang2}.

This is not the case here, however. The standard synchronization method is the Einstein convention, which uses light signals. Since test theories of SR alter the postulate of constancy of speed of light, this method is no longer directly usable in the new theories. This is why care must be taken to relate the time parameter that appears in the transformations to the experimental time measured by synchronized clocks. Here, on the other hand, the postulate of constancy of the speed of light remains untouched. Thus, the one-way speed of light is isotropic by definition, and the Einstein clock synchronization procedure is applicable. This means that the time obtained in the transformations is directly measurable. In Eqs.(\ref{finalx})-(\ref{finalt}), all relevant parameters  represent true physical quantities. The difference with the Lorentz transformation represents an actual physical effect, therefore, and cannot be eliminated merely by a change of conventions.

\section{Properties of $\kappa$}
\label{sec:kappa}

The Lorentz transformations are recovered if we set $\kappa = 0$. If $\kappa$ does not vanish, however, its value will in general depend on the choice of the x-axis.

Let S' be a frame moving at a velocity $v$ in the positive x direction with respect to the frame S. The x-axis and x'-axis are parallel. Consider an event E happening at a space-time point $\left( ct, x \right)$ in the S-frame. In the S'-frame, the position of the event is given by Eq.(\ref{finalx}).

Now let us rotate the frames by $\pi$ radians. Denote the rotated S-frame by $S_R$ and the rotated S'-frame by $S'_R$. We do not reverse the direction of motion of the frame S', and consequently,  $\beta_R = - \beta$. The event E now takes place on the negative x-axis, so that $x_R = -x$ and $x'_R = - x'$. Clearly we have that

\begin{equation}
\label{xR1}
x'_R = \left( \dfrac{1 - \beta_R}{1 + \beta_R}\right)^{\kappa_R} \dfrac{x_R - \beta_R c t}{\sqrt{1 - \beta_R^2}}
\end{equation}

Substituting the values of $x_R$ and $\beta_R$ into Eq.(\ref{xR1}) yields now

\begin{equation}
\label{xR2}
-x'= x'_R = \left( \dfrac{1 + \beta}{1 - \beta}\right)^{\kappa_R} \dfrac{-x + \beta c t}{\sqrt{1 - \beta^2}}
\end{equation}

Comparison with Eq.(\ref{finalx}) shows immediately that

\begin{equation}
\label{kr}
\kappa_R = - \kappa
\end{equation}

Thus, we see that if the exponent $\kappa$ does not vanish, its value depends on the orientation of the $x$-axis. This means that the exponent $\kappa$ represents a measure of the anisotropy of space.

Since $\kappa$ changes sign under a rotation of $\pi$, there must be at least one specific direction in space for which $\kappa = 0$. Along this axis, standard special relativity is valid without any alterations. Let us then denote by $\theta$ the angle of any other direction with respect to this preferred axis. Eq.(\ref{kr}) can now be rewritten as

\begin{equation}
\label{kappatheta}
\kappa(\theta + \pi) = - \kappa (\theta)
\end{equation}
which is necessarily a symmetry of the anisotropy exponent.

As one motivation for their work, Mansouri and Sexl mention that cosmological considerations hint at the special status of a specific reference frame, namely that frame in which the background cosmic radiation is isotropic. It is tempting to think of the present work in similar terms, i.e., the idea that there might be a preferred frame in which physics is isotropic, with other frames exhibiting anisotropy via the scaling factor $\left( \dfrac{1 - \beta}{1 + \beta} \right)^{\kappa}$. Such an interpretation would be incorrect, however.

First, contrary to the Mansouri-Sexl theory, the present work assumes the validity of the principle of relativity, and hence the equal status of all reference frames. If the anisotropy of physical effects were frame-dependent, this would violate the relativity principle. Second, the anisotropy exponent, $\kappa$, was found to be independent of the velocity of the frames. Thus, it is a frame-invariant quantity. If space is anisotropic, therefore, this is not an effect that can be eliminated by transferring to some proper frame of reference. The effect will show up identically in all inertial frames.

One may think that this is an unlikely state of affairs. It would seem at first sight far more likely that there exists a cosmologically preferred frame of reference in which all directions are equivalent, with other frames exhibiting anisotropy with respect to the preferred frame, depending, e.g., on the direction of motion of the frames.

The present analysis does not forbid such a state of affairs. Instead, it proves that if anisotropy is frame-dependent, the speed of light cannot remain frame-independent. In other words, if there exists a frame-dependent anisotropy, the speed of light will exhibit a similar frame-dependence dependency. This is basically the situation covered in standard test theories such as the Mansouri-Sexl theory. The present work seeks to investigate the more radical possibility that there exists a physical difference between directions in space, that cannot be erased by selecting an appropriate frame. However unlikely one may think this is, it is worth verifying, and Eqs.(\ref{finalx})-(\ref{finalt}) offer a numerical assessment of whether and to what extent such a preferred direction might exist.

Clearly we expect $\kappa$ to be small, otherwise we would likely have noticed its effects already. Any non-zero value of $\kappa$ will only appear in high-precision experiments, therefore. Note again that according to Eq.(\ref{eq:veloadd}), effects depending on velocity addition are isotropic, and thus cannot serve to measure $\kappa$. Since some optical measurements can be made to a very high precision, however, it would appear that this is a convenient field in which to search for the effects of spatial anisotropy.

There is unfortunately no reliable way to extract bounds on the value of $\kappa$ from present measurements, however precise. The reason is Eq.(\ref{kappatheta}), which implies that there is at least one direction in space along which $\kappa = 0$. Thus, a single experiment will never provide reliable bounds on $\kappa$ because one cannot discard the possibility that the experiment was performed, by chance, in the direction of vanishing anisotropy exponent. For the same reason, one cannot extract a bound on $\kappa$ from existing data, since the direction in which the experiments were set up is not typically recorded. A proper measurement of $\kappa$ requires a setup in which the direction of measurement can be varied, and the results compared for different orientations. it is the variation of the value of $\kappa$ in space that would provide the signal test for the existence of spatial anisotropy.

\section{Measuring $\kappa$ through the Doppler shift}
\label{sec:doppler}

One convenient possibility of measuring $\kappa$ is through the Doppler shift. Consider a light source that emits a signal with frequency $f_0$ in its rest frame S'. Let this rest frame be moving at velocity $v$ with respect to the lab frame S and the light be emitted towards the S observer. The transformation Eq.(\ref{finalt}) implies that in the S-frame, the emitted period, $T$, differs from the rest period $T_0$ by

\begin{equation}
\label{t0}
T_0 = \left( \dfrac{1 - \beta}{1 + \beta} \right)^{\kappa} \dfrac{T - \dfrac{\beta}{c}x}{\sqrt{1 - \beta^2}}
\end{equation}

The emitter can be chosen as the origin of the frame S', so that its position in the S frame is $x = \beta c T$. Substituting this into Eq.(\ref{t0}) yields

\begin{equation}
\label{tmove}
T = \left( \dfrac{1 + \beta}{1 - \beta} \right)^{\kappa} \dfrac{T_0}{\sqrt{1 - \beta^2}}
\end{equation}

In the S frame, the emitted wavelength is $\lambda_{emit} = c/T$, but S observes a different wavelength because the distance between two successive crests is shortened by the emitter's motion. The received wavelength $\lambda_{rec}$ is given by the standard relation

\begin{equation}
\lambda_{obs} = \lambda_{emit} - vT
\end{equation}

Substituting the value of $T$ from Eq.(\ref{tmove}) into this relation yields

\begin{equation}
\lambda_{obs} = \left( \dfrac{1 + \beta}{1 - \beta} \right)^{\kappa - 0.5} \lambda_0
\end{equation}
where $\lambda_0 = cT_0$ is the wavelength emitted in the rest frame. Finally, the frequency that S measures is

\begin{equation}
\label{doppler}
\dfrac{c}{\lambda_{obs}} = f_{obs} = \left( \dfrac{1 + \beta}{1 - \beta} \right)^{0.5 - \kappa} f_0
\end{equation}

Thus, a precise measurement of the Doppler shift along various directions can provide a determination of the isotropy of space. Any deviation of the exponent in Eq.(\ref{doppler}) from $0.5$ would be a confirmation that space is anisotropic.

As mentioned in the previous section, much more significant would be a scan of the Doppler shift in various directions, while keeping the speed of the emitter, $v$, constant. A non-vanishing value of $\kappa$ would reveal itself as a systematic variation of the exponent in Eq.(\ref{doppler}), which must verify the symmetry relation Eq.(\ref{kappatheta}). Thus, the exponent should rise slightly as the direction of the motion of the emitter is rotated from the preferred direction along which $\kappa = 0$, then dip after completing a half-turn, finally to return to its original value once the circle is complete. A measurement of this (or a similar) effect would provide us with a quantitative estimate of the degree of anisotropy of our universe.

The transverse Doppler shift arises, as in standard relativity, from the changes in frequency only. Thus, if a source S' moves in the x-direction and emits a light signal in the y-direction, the observer in the S-frame will observe a different frequency only because of the time dilation effect, Eq.(\ref{tmove}). Hence, the transverse frequency will be observed to be
\begin{equation}
\label{transdoppler}
f_{trans} = \left( \dfrac{1 - \beta}{1 + \beta} \right)^{\kappa}\sqrt{1 - \beta^2} f_0
\end{equation}

Because $\kappa$ depends on the orientation, identical emitters sending pulses of light transversally but along different lines should exhibit a different doppler shift, if the anisotropy exponent does not vanish.

\section{Conclusions}

In this paper, I have examined whether a possible violation of spatial isotropy and homegeneity would be detectable. Because these symmetries play a special role in the theory of special relativity, it is natural to examine the implications of their violations in this theory.

I have shown that homogeneity is recovered automatically from the postulate of the constancy of the speed of light and therefore any violation of this symmetry will not show up in the Lorentz transformations or its consequences.

Second, the relativistic rule of addition of velocities is also independent of the assumptions of homogeneity and isotropy, and derives solely from Einstein's two original assumptions. Thus, any effect that derives from this rule will also be impervious to any violation of isotropy or homogeneity.

The coordinate transformations themselves are altered, however, if isotropy is violated. The violation appears as an additional factor that is direction dependent. The standard Lorentz transformations are now multiplied by the term $\left( \dfrac{1 - \beta}{1 + \beta}\right)^\kappa$. The exponent $\kappa$ depends on the direction of the velocity of the frame S', which is chosen to be the x-direction. The exponent changes sign upon a rotation by $\pi$ radians of the direction of the x-axis.

The exponent is frame-independent, however, so the anisotropy under discussion here differs fundamentally from what is expected at present from cosmological considerations. The cosmological frame in which the cosmic background radiation is isotropic holds no particular position here. A non-vanishing $\kappa$ would show up experimentally even in that frame.

If such an effect does exist, I suggest that a good place to seek it is by checking the doppler shift of emitters moving in  various directions. Present data is insufficient to analyse the value of $\kappa$ because the direction in which the measurement is performed is not recorded. Since there exists at least one direction in space in which $\kappa$ vanishes, there is no way to assess whether past experiments should exhibit a measurable effect. A proper measurement of $\kappa$ requires a rotation of the apparatus along a full circle to check for possible variations in the value of the measured quantities.

Should such an effect be discovered, its implications could be profound for the description of our universe. Besides the import of the added terms in the Lorentz transformations, which would extend to every theory based on special relativity, a non-zero value of the anisotropy exponent further implies that there is a preferred direction in our universe along which the exponent vanishes, as noted above. This direction ought then to present further peculiarities of interest, which might open new fields of research in cosmology among others.

redpajama_set_name: RedPajamaArXiv


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If the HTC One M9 didn't excite you with its FHD display and you could do away with less metal, the Taiwanese phone maker has a new flagship-ish smartphone up its sleeve. The company today announced the HTC One ME, one of the most exciting smartphones it has ever made.
Instead of the full metal body, the HTC One ME comes wrapped in a polycarbonate shell with metal frame. It's pretty much like the One M9+ the company had launched earlier this year, but there are a few noticeable differences such as the dual-SIM capability among others.
As for the specifications, the One ME sports a 5.2-inch display with QHD (2560 x 1400 pixels) screen resolution flaunting an impressive 565 ppi pixel density — evidently the sharpest display HTC has placed in a phone. Other hardware specs don't disappoint either. The One ME is powered by Helio X10 eight-core chipset (the Mediatek made processor competes with Qualcomm's Snapdragon 810) clocked at 2.2GHz. On the connectivity front, the One ME supports 4G LTE (FDD: band 1,3,5,7,8,28; TDD: band 38,39,40,41), 3G, and is dual-SIM capable — which makes us believe that the phone is targeted at Asian countries.
The device also comes with a fingerprint scanner which could store information of up to 5 fingers. With Android M offering native support for fingerprint readers, the phone could make use of many new features. On the software side, the company hasn't mentioned the exact version of Android and HTC Sense the phone runs, but it's likely 5.0 Lollipop.
Other features include 3GB RAM, and 32GB of internal storage, which as the company notes, could be expanded up to 2TB via microSDXC. On the camera front, the device — unlike the One M9+ — doesn't equip the duo-setup. Instead, it is shipping with a 20-megapixel sensor, which is capable of recording videos at 4K resolution, with LED flash in the rear end and a 4-megapixel UltraPixel selfie shooter upfront. The phone retains the company's signature Dolby Audio featuring dual HTC BoomSound speakers placed on the front side. There's a 2,840mAh battery which the company says will run for 13.5 h on 3G mode.
The One ME will ship in — whenever that happens — in rose gold, gold sepia, and meteor grey color options. That's because the company doesn't have the pricing and availability information ready to share with us just yet, but it's likely to be sold only across Asian regions.


text:
Q: How can I programmatically find out current Azure Storage Account count and limit? I'm writing some code that will automatically provision new ARM storage accounts, and as part of it, I need to check how close I am to the max number of storage accounts.  I can't find anything concrete by searching (only this, which is a bit of a dead-end).  I'm operating entirely with HTTP calls (no .NET Azure library dependencies).
Effectively, I'm trying to find the ARM way to get the MaxStorageAccounts and CurrentStorageAccounts properties of this classic endpoint: https://msdn.microsoft.com/en-us/library/azure/hh403995.aspx

A: Found the right URL to hit by taking the Get-AzureRmStorageUsage cmdlet and running it through ILSpy to decompile:
http://management.azure.com/subscriptions/{subscription ID}/providers/Microsoft.Storage/usages?api-version=2016-01-01

Not sure why I couldn't find any references to it online.

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Attaches quickly to any MOLLE-compatible system keep your radio accessible and secure. Made of 1000D nylon with an adjustable elastic cord and locking clasp this pouch is extremely durable and practical. The Radio Pouch can be easily removed and relocated to other molle compatible systems using our Slickstick MOLLE attachment system.


text:
Q: Simplest way to keep a NSInteger in an iPhone? I am coding my first iPhone game with cocos2D. And I want to save the best score of the player (just an NSInteger) in the app. What is the best and simplest way to keep this information ?
Thanks !

A: Just 1 integer?
// write
[[NSUserDefaults standardUserDefaults] setInteger:theInteger forKey:@"bestScore"];

...

// read
theInteger = [[NSUserDefaults standardUserDefaults] integerForKey:@"bestScore"];

(Usually games support top-10, and you'd want to box the NSInteger into an NSNumber, insert all 10 of them into an NSArray, and save the array.)

A: You could save name/value pairs to a plist via NSDictionary. Here's a tutorial:
http://www.dbuggr.com/leothenerd/cocos-saving-data-file-nsdictionary/

A: Yes, use NSInteger and store it in your preferences or a private file.
Store in user defaults with:
    [[NSUserDefaults standardUserDefaults] setObject:[NSArchiver archivedDataWithRootObject:highScore] forKey:@"HighScore"];
Retrieve With:
NSNumber * highScore = [defaults objectForKey:@"HighScore"];


By crikey it's parky this morning! Really thick frost which has made the field opposite look as though it's covered in snow, but the sheep don't care – they're chewing away on the frozen grass!
I hope that wherever you are it's thawing out a little, and that the snowfall we had didn't cause too much distress!
My nephew lives in New York and was luckily unhurt but unable to work for a couple of days because of the flooding in the subways there.
Aside from snowfall and rainfall, what about Skyfall?!! Have you seen the new Bond movie yet? What did you think? Personally, I loved it! I do think Daniel Craig is completely convincing, and it was good to see more of M in this one!
The new Q was well cast too, and Colin and I recognised him from a brilliant BBC Drama – the third series of which begins again this week! Adele's rendition of the theme song (which incidentally she wrote as well) is particularly catchy and reminds me of Shirley Bassey and Diamonds are Forever, and the special effects in this film are exceptional!
I'm wondering though if you can help me place Javier Bardem – who plays the baddie – naturally dark haired, I can't think of anything else he might have appeared in? Do let me know if you can!
Infact, looking back over the last week or more, we've done a fair bit of partying and socialising with our family and friends. The weekend before last was Colin's daughter Vicky's birthday, so we went out for supper and then on to his son, Dan's Halloween party.
We all had to dress up, and Sam joined us for the evening, so we had a great time, although felt a little dusty the next day!!
On Tuesday, directly after my Percy and Reed show I met Colin and we headed off to the Albert Hall to see Diana Krall perform. Such a talent, and an incredible voice – most of the songs were from her new album Rag Doll, which I don't have, but will now buy. I really enjoy her music, but particularly when she sings the classics, but with her own twist.
Talking of music, Colin would like me to thank you so very much for watching his video and listening to the songs from his album – he's had over 3,000 plays! I have been given a list with e mail addresses of all those of you who wish to buy the album, and will be mailing you asap – Bless You!!
This Saturday saw Colin and I travelling to Surrey to spend the evening with old school friends of mine – including Ros and Chris – for a very enjoyable catch up.
The food, wine and company were exemplary, and Ros and Chris saved the night by bringing their aero bed for us, as I'd remembered the quilt – complete with Northern Nights flannel covers – but forgotten the bed to sleep on!
Of course, November 5th rolled round again, and as it's tradition with our family, I got the children together, bought the hot dogs, and set up the fireworks. The weather was perfect – cold but dry – and Sam and Jack took up the igniting duties 🙂 We always have Catherine Wheels in memory of my dad, because he insisted on them, and inspite of his best efforts they NEVER worked!
This year, the first one fell off the tree after a rather pathetic attempt to sparkle, and although the second one started well, a section of it came adrift, and it was more like a flame thrower than a Catherine Wheel!
Still, a good time was had by all, and the sparklers never disappoint 🙂 It will be my last Fireworks night in the cottage, as hopefully we should exchange on the new house soon, and be moving by the end of the month… It was 1st December 2010 when I actually moved in here – I can't believe it's been almost two years!
Let's hope the weather is kinder this time when we come to load the lorry – a foot of snow and frozen conditions didn't help at all last time!
Keep in touch, and as always, I'll look forward to hearing how your week has been.
What a busy and exciting time you are having at the moment. It is great to see you moving forward, such an inspiration.
I had a birthday last week, but postponed the celebrations as it coincided with feeling very tired a week post Chemo. But we celebrated yesterday instead, just a quite meal with my OH, but it was a great evening out.
Next week I have the last of my EC Chemo, which will be good to get through, then I start on Taxol and can look forward to this coming to an end. I can then start looking forward to reconstruction and moving into a more normal life again. Happily the cold cap is still managing to keep most of my hair attached to my head, I am just hoping that will continue when I change drugs.
I saw my Consultant earlier in the week and he is very pleased with how the 'football' is looking. I had been quite concerned as I have quite a lot of arm pain, but he confirmed that this is the nerves coming back to life, so whilst uncomfortable, it was good to know that it was nothing to worry about; it comes and goes anyway and there are more days when there is only pins and needles, and only a few when it is on the pain scale. At least I now know that it is just part of the healing process.
I have started to do some work from home this week, which is great, getting some degree of normality and using my brain again is so good.
Our three cats, Mustard, Salt and Pepper, known collectively as The Condiments, are keeping me amused and as the weather is getting colder they are spending more and more time with me, although I think the fire may be the main attraction, but I like to think that it is me really!
Thank you for being such an inspiration to us and the best possible luck with the upcoming move.
Javier B was in No Country for Old Man – a brilliant film and he was AMAZING!
Hi Alison, yet another event packed week for you and I hope the girlie break is thoroughly enjoyable. Unfortunately, I am unable to assist you in yout Skyfall question as I have not yet seen it. I will be totally honest, James Bond or Daniel Craig doesn't float my boat (give me Gethin Jones or John Barrowman any day) but my son and husband are going to see it at the weekend. I do love the song though but my daughter points out that I have 'pitching issues' when I sing it in the car..how very rude!!
I did not get snowed in in Cumbria over the half term and returned to school on Monday..no kids just a staff training day to ease us in but even so, I can't believe this time last week we were 'Up North'.
As you may remember, we stayed in a mobile home in a park in Silloth, my twin, me and my two children in one and my sister and her two in another. As far as caraveans go they were lovely but I was naive enough to think that the single beds would be singles and not the width of a sun lounger! Chloe slept like a baby each night but I could hear Jack banging his nead, legs, arms and indeed hear every bodily movement from his bedroom which was next to mine and the partitioning wall resembled a paprered piece of cardboard. He didnt cope well so on the second night |I joined my sister and dog Phoebe on the L shaped sofa and Jack had my room which had a small double bed. His room became the laundry room as it was like a steaming hot house and as it rained most days all day and night (plus conker sized hail stones and winds like I have never experienced)we needed a place to dry our clothes. That said, my sister and I coped well on the sofas but had a little dog trouble on a couple of nights..phoebe insisted on sharing my pillow on many occasions and decided to then lodge herself in the foot flap of my sister's luxury animal print slanket! Hilarious!! I am amazed that at times we didnt take off at night as the wind was so strong, the whole caravan literally rocking and rolling, and had the tv on full volume to mask the noise of the rain however, luckily, we had QVC on our freeview tele so we watched QVC into the early hours; my sister ordered the Ninja TSV and it got delivered before we got home. Amazing service!
We went to Scotland on one day and did a 10km walk up and down hills, went to Lake Windermere – a little dissapointing purely because we were given the wrong instructions from a local. We were advised to walk along the white water stream to get to the main lake only to find that after an hour, the woodland path we were following dissappeared as the water levels were so high. We found ourselves climbing over a double thickness dry stone wall onto a dual carriageway which was very bazaar and a little scary. Phoebe the dog was chucked over the wall and clearly not impressed! We visited Keswick on a particularly rainy day to visit a 'Stars and their Cars' Museum as we thought the kids would like it. It was lashing down and we walked through the town to the museum only to find that it had been shut for over a year! We were soggy and very fed up but found a beautiful chocolate shop which cheered us all up. We also climbed a 1612ft hill ( I think it was a mountain really) which needed the skills and fitness of a mountain goat to climb. It was one hell of a climb and my poor lungs had had it by the time I got to the top and my inhalers for my COPD and asthma were working overtime but the views were spectacular for about two minutes….. The cloud suddenly enveloped us and it started to snow! We made it down safely and enjoyed a well deserved cream scone in the tea shop at the bottom.
Back to normality now but it was lovely to spend quality time with both my sisters and get some wonderful photos as memories.
My annual Xmas shopping weekend to MIlton Keynes is in three weeks so can't wait for that.
Oh and my Clarisonic TSV arrived today and I removed my makeup with it when I got in from work with my Gatineau cleansing cream..it was fab. It certainly wont be going back. Hubby has looked at my Christmas list….still hoping for a Lulu bag!!!
lovely to have your catch up and see what you have been up to. I loved the grey dress you had on yesterday (I think it was) – you looked just fantastic. I have been asked by my daughter to say thank you for recommending the Ohh Arr bra – (she had the major surgery and reconstruction in October) I think that is what you called it some time ago when you had your last surgery. The two I had ordered came today and my daughter has said how wonderful it feels – no rubbing on her scars and the difference in wearing this bra to a normal one is amazing. She is doing really well and we are all delighted with her progress. So once again thank you so much for sharing all your treatment etc it has helped more women that you can ever imagine.
Dear Ali, glad to hear you had a fun bonfire night. We went to a organised one in our village, which was an hour late and we were all freezing, but it was worth the wait! We rushed home to get a warm in front of our log burner which was very cosy.(will you still have a log burner in your new home?)We saw Michael McIntyre last weekend he was sooo funny my cheeks were aching from laughing, highly recommended.
We also went to see Skyfall, I think Daniel Craig is the best Bond ever!! I thoroughly enjoyed the film and have to admit it's the first one I have really enjoyed and understood!!!
Well I've read your blog! You it soo much in! It's just great! Love the photos and shame you lost the headpiece…you'll have to get a new one for next year! I noticed that M didn't pick up her bag either by the way lol. Thought when she turned round she was going abck to get it lol! Sounds like you've hada lovely few nights out again this last while. And so lovely your village girls take a cottage once a year. How lovely. Will look forward to that. Hope the move goes ahead and with less snow. Re NY and the NorthEast yes dreadful. My friends were also affected but unhurt. Awful the new storm has hit with snow too now.
I just wanted to say you really made me laugh there when I read your comment to Ali…your lovely cats are called The Condiments!! Wonderful! Thank you. And I wish you all the luck in the world for your transition with the drugs and the best of health for the future.
I hope you'll have a great time with your friends.
Hope your house move will go smoothly. I'm sure you will be really happy in your new home Ali – lots of exciting and happy times ahead.
Thank you so much for your reply Ali – I will certainly pass this on to my daughter. I feel that it would be much easier for me if I was going through this rather than her but she is very strong and just wants to get on with it and move forward and get it over with then put all this behind her (or as much as she can for the moment). How good to know your hair started to grow back after two weeks of the chemo stopping- I shall also mention that to my daughter – you see I have to say once again how much help your blog has been – not just for me but all the other women reading it. I will update you when we have some more progress reports.
Please don't give your comments about the cold cap another thought – I am just grateful to have you there – I am like you and would prefer not to have the cold cap – there are some wonderful wigs around and you looked stunning in yours. Tomorrow when my daughter comes here we will check some out and then she can decide what she wants to do – she is not a fussy hair person so that will help -but grateful thanks and also from my daughter. I will if you don't mind perhaps ask some questions nearer the time of when the chemo starts. It is such a help looking at your earlier blogs to see how you went along and to see how very great you look now.
It was so nice to read your reply and thankyou for that.
Well the nightmare I was dreading is over, I had my Mastectomy on Monday afternoon at 15:30 and was discharged at 10:00 on Tuesday. I must admit the operation part was okay, shame about the hospital stay although very brief afterwards. I am home now back in my own bed and with my cat's Ollie and Solo. I am going back to the hospital next Wednesday for the results of my op and to see if they are going to give me anymore treatment. I have been in contact with BCC and they are wonderful and I have a wonderful Breast Cancer Nurse at the hospital who comes to all my appointments with me as I am on my own. The nurses from Hospice at Home are also very nice, they are coming in everyday for the next couple of weeks so that pleases me. My drain should come out on Saturday which I am looking forward to because it is quite uncomfortable and little Ollie loves trying to get a hold of the pipe bless him. All in all I feel okay at the moment I remembered everything you had written to me beforehand whilst in hospital and that seemed to keep my moral up so thankyou so much for that.
I hope that you are having a good week and look forward to your next blog. I will let you know how I get on next week and thanks once again for writing to me.
Enjoyed reading your blog as usual, I hope you had a great weekend with your girlfriends.
I have had a wonderful day today as my son returned home after 8 months working in America. It is wonderful to have him back but he enjoyed himself so much he is going back in March. I thought hurricane Sandy might put him off but unfortunately not.
Not going to think about that yet, tomorrow we are having a welcome home party for him at my daughters which should be great as my brothers, sister and families will be there and we always have a wonderful time when we get together.
Just read your blog to Ali – I would just like to say I'm so glad you are now back home after your operation and you were so well looked after by BCC. It must be so tough facing this on your own. I really hope your operation was a success. Seeing how Ali has coped must be giving you lots of strength as she is such an inspiration!


Question - Explain the role of advertising in marketing communications. Also describe the steps in the process of advertising.
The finest products, the most attractive price tags, and the best marketing channels are of no mean if the target customers don't know the product; and the chances of product success is low. Effective marketing communication is crucial for the success of a product or a business. In marketing communications advertising plays an important role.
Marketing communications are the means by which organisations attempt to inform, persuade, and remind consumers about products, services, or brands. Marketing communications inform and make consumers aware about the availability of the product or service, about its usage, price and special offers. Marketing Communications attempt to persuade potential consumers to purchase and try the product. Marketing communications can also be used to reinforce experiences, or to remind consumers about their needs and their past experiences related to the product with a view to convince them for repurchases. Marketing communication also differentiate products in markets where there is little to separate competing products and brands.
Advertising is a paid form of a non-personal message communicated through the various media by industry, business firms, nonprofit organisations, or individuals. Advertising is persuasive and informational and is designed to influence the purchasing behavior and/or thought patterns of the audience.
Briefing - Advertising process starts with briefing - a document confirming understanding between client and advertising agency on - what product to advertise, objective of advertising, time-frame of ad campaign, strategies to reach the audience, and total estimated cost.
Market Research - After briefing market research will done. Research include - comparison of advertiser's product or service with competitor's product or service, consumers' perception of their brand in comparison to their competitors, study of competitors' advertising, and response of consumers to competitors' advertising.
Identify Target Audience - Next step is to identify target audience. Using the market research, the advertising agency will identify the target audience.
Media Selection - Using the research, the advertising agency or the media agency will select the media that should be used to reach the target audience in the most cost effective way.
Ad Designing & Ad Creation - At this step the creative people of advertising agency will convert the advertising communication into words and pictures. The copywriter will write the copy of advertising and the art director will visually implement the copywriter's message.The advertising agency may get the filming or taping done by outside production companies.
Decide Place & Time - This step is to decide where and when the advertisement will be shown. Traffic department within the advertising agency will ensure that the commercials are ready on time and all required legal approvals have been granted.
Execution - Finally the advertisement will be executed.
Performance Check - Once the advertisement is executed, the media agency will check its performance.
Following the above steps the client or marketer can effectively communicate its marketing messages with its target audience.


Making the move from road races to having fun on the trails..
I sort of grew a beard for this one and I don't really know why. My wife hated it and I certainly found it an annoyance. However once race day was looming I was damned if I would shave it off. I think it must be a mid life facial hair crisis. From a distance it looked like I had been eating coal.... badly. Needless to say I have toned it down since although it only got a trim rather than a full shave. I have now formed an attachment to it like an ugly puppy.
I think when you have run a few ultramarathons before you start to "normalise" distances which any other human being would think totally stupid to try to run. This was to be my 7th ultra and was my longest to date. I wasn't particularly worried. No siree bob, not me. However, rather than think of it as "a jolly day out in the hills" I should have seen it as it really was - a tough double marathon (53 miles) over some crazy terrain in the highlands. That sounds hard and was a little more accurate with hindsight. At least this time I didn't get drunk the night before.
The start at Milngavie was a low key relaxed affair and we were off before I had the chance to reflect or worry. I had worn my heart rate monitor so I could keep the effort down in the first half of the race and keep the effort up whilst walking the hilly sections. However it gave an inaccurate HR/Pace reading (adrenaline?) until it was too late anyway. I felt fast but comfortable for the first half however this section was fairly easy underfoot. After this the terrain was much more difficult and I should have kept more back in reserve. I had been warned this THE DAY BEFORE by Karen! Stupid mistake and muppetry of the highest order.
The second half (or second marathon in reality!) was either very tough underfoot or involved lots of hilly sections. Silly boy for running too strong in the first half. My frequency of walking increased the further I got however I was aware that I was more and more ahead of schedule at each checkpoint. I left the final checkpoint Bein Glas (40.5miles) in absolute pieces. I still had 12.5 hilly miles ahead of me and I just wanted it over. Not a nice feeling at all. It was at this point I spoke briefly to John Kynaston who said I'd be able to get under 11 hours if I cracked on a bit. This proved to be a real shot in the arm. John is an experienced ultramarathoner so I reckoned he knew his apples. I made an effort for the next 6 miles of the final 12. Then I *really* gave up the ghost and just tried to get one foot in front of the other. I was even walking down some hills. Oh yeah, look at Mister Experienced Ultramarathoner - he runs everything* (*except uphill, downhill or flat sections).
Who ate all the coal?
It was going to end eventually and right enough I heard the pipers in the woods by Tyndrum. It was a brilliantly supported finish and very emotional. I don't think I've ever been as happy to cross the line in my life and the beer that George Reid gave me was the finest I've ever drunk.
I came in at 11:08. I had planned for 11:45 so in all not bad for a race which I felt could have went better. It is an odd feeling though - I'd much rather have ran a 12hr or 12:30hr Fling and enjoyed it all (ie been more consistent) rather than get an OK time but only enjoyed 2/3rds of it.
In terms of food I learned a few lessons. Sweet stuff every 15 minutes until about 7 hours and then switch to savoury every 15 mins or whatever you can stomach. Muller rice early on but switch to orange juice/lucozade later. Fizzy coke at each checkpoint is brilliant!
The bits of the race I enjoyed the most were the bits most folk warn you about. Coming down Conic Hill was slippy but it was an absolute blast. The technical section at Lochside was also brilliant fun although I almost fell on my face 2 or 3 times which could have been nasty. Some of the course was stunningly beautiful but I prefered the barren mountainous scenery of the northern part of the West Highland Way. It feels like running through Mordor.
Overall then I had a mixed result. I learned a lot about pacing during bigger ultras (ie slow the hell down) and that my food strategy needs a little tweaking. I would also do it all again which is a good sign. "Luckily" I have another bigger run in a few weeks time to try to put these lessons into effect! Also, this was the first time I have felt achievement at finishing an ultra. Normally I'm just glad it is over but don't have any "well done me" pat myself on the back feelings. I think it was the double marathon distance on tough terrain that did it.
The only photo I took all day!
It was great to see so many friendly familiar faces on Saturday. I felt lucky and privileged to be part of such a friendly well organised run. It is great to see mates who you only meet at these mental days out. EVERY runner that passed me said "well done" and I said it to every runner that I passed. How many running events does that happen in, eh?
Great perspective Dave and good learning experience for the Cateran. Have a blast and well done!
Great run Dave. It was good to meet you on the way up the loch. Hope you have a great run at the Cateran.
Well done Dave. You were looking good when you went past us. Hope I didn't set your bar too high! I must admit I was having fun trying to work out what time various folk who went past us would finish in!
Recover well and I look forward to seeing what you do next!
Are you really the same Davy Morrow who I went to school with?! He couldn't run the length of himself!
Aye Al, its a long way from trying to do as little as possible on the Rugby pitches at Friends! Hope you are well sir?


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Everything changes, and that's just the way life is. Especially in high school. People get taller, voices get deeper, and cliques are formed and destroyed.
Some of us have adjusted by now, some of us aren't sure how, and some of us don't know any other way because our lives change so often. In high school, change is inevitable.
Change is uncomfortable and upsetting, but sometimes, it's for the better.
But it has to happen, and we have to learn that not everything is our choice. It's how we deal with it that matters.
This year, several things changed. As a student body we were introduced to several new teachers and staff members.
At the beginning of the year, we felt the change right away. An example is the infamous parking lot policy: we're now accustomed to it and it has proven to be more efficient.
While not all students resist change, it's safe to say not all change is done willingly. But more changes are rapidly approaching: underclassmen are going to be switching to the eight-period day, one of the biggest transitions during their high school careers, and seniors are heading off into the real world. Some goodbyes are temporary, but for some students who enlisted in the military, leave is as early as June 3.
So, while we're here and while things are changing, we might as well cope the best we can.
Students should be taking change as an opportunity to learn what the real world is going to be like.
"Change is always hard in the beginning, and people always aren't open to it, but they will eventually get accustomed to it and become more optimistic," Carissa Miller, sophomore, said.
As a staff, we are losing our adviser of four years, Cheryl Borrowdale. Borrowdale is a guru when it comes to anything. And we mean anything. She's a wizard with InDesign and an insanely wise mentor.
Between the shorter periods and the change in advisers, there will be major changes on Krier. Most of what we do as a staff involves deadlines, intense debates and brainstorming; doing it on a shorter schedule and with a new adviser will be an adjustment.
Yet we can approach it as a learning opportunity instead of as a doom-and-gloom scenario. It's the exact kind of opportunity that should take place during high school.
This change will prompt students to take control and provide guidance, something that otherwise wouldn't happen.
It's constantly a shuffle, but we can never get too comfortable. That's what makes change harder to accept and adjust to.
"Change is a normal part of life that at times can bring us challenges. Challenges make us stronger," Melissa Maloney, government teacher, said.
The four years students' experience may be the best or may be a nightmare, but it's nowhere near the end.
The content of these halls teach the adolescent mind more than just algebraic equations. More than about a covalent bond, more than about just past participles.
"Teens have a strong attachment to certain identities, what you know is a part of your identity. Who you are without this is a big reason people stay in something unhealthy," Patrick Trapp, social worker, said.
Right now, while our lives are as simple as they're going to get, we need to familiarize ourselves with what change is like.
Switching classes is a refreshing feeling after the months we spent with the same people. As much as we want to imagine that life is unicorns and rainbows, it's not going to get easier.
We're all adjusting to the changes that were made this year, and we'll learn to adjust when the 8-period day is fully implemented.
But we have a tremendous amount of people at our disposal to help.
Although the counselors are supposed to only deal with our schedules, they do much, much more than that. They have the ability to alter our classes and offer priceless advice. The counselors offer a tremendous amount of guidance and are an amazing resource for students to use.
"For teens it's helpful to have an older wiser mentor, to normalize change, or have a friend who can relate. Don't internalize what you're feeling about change, talk about it," Trapp said.
Change is just a part of growing up. Whether it's good or bad, we'll get through it.