I haven't purchased a toy or figure in ages. But that all changed when I visited Deal Extreme and encountered these two items.
Believe it or not, this Android figure was licensed from Google — well that's what the box said. I'm disappointed by quality of it. I don't know if it's that noticeable, but there's a white paint around its neck/mouth is chipped and that black speck on its body (I can't get rid of it).
On the bright side, its arms move and so does the head. And it looks neat.
I'm not even an Android owner nor will I pick up an Android product at this point in time. I do love the idea of Android and its logo though.
How Many Games Did I Pre-order Again?
BestBuy.ca held an online only sale Saturday and Sunday night. Games and game accessories were 15% off.
All seven titles total up to $403.34 or $57.62 each. Plus, some of them even offer an additional 800 Reward Zone points (that's a $10 value). I'll be able to collect more RZ points as soon as my BestBuy VISA card gets here.
I could have pre-ordered more, but these are the titles I believe won't be receiving timely price drops or promotions, so I chose them. Since these were all individual orders, if I run into cheaper offers, I'll be able to cancel my order without much fuss.
My PlayStation 3's 19 blade fan arrived today and I installed without any trouble. I started up the system and it sounds noticeably quieter during idle. I tried running [email protected] for 30 minutes or so and it remained quiet. I'll put it through its paces when I get my hands on Castlevania: Lords of Shadow which my bro is currently playing through. Or maybe I'll play some Bad Company 2 multiplayer.
Who am I kidding? I'll be playing Civilization V.
Which is one reason why I haven't been playing around with the Windows Home Server v2 Vail beta I installed on the Shuttle ST20G5 finally! So far it's been a cinch to connect and administer, but I have yet to try any backups or media streaming. Perhaps I'll have more time during this upcoming long weekend.
Apparently, Bluehost is having some server performance issues which is causing PHP calls to slowdown. As a result, QSF5.com is a tad slower to load. I've installed WP-SuperCache plugin to alleviate some of the load, but I don't know how much that'll help.
I've also taken the opportunity to sort through some plugins. I've changed the sidebar login into a link located on the bottom right sidebar and I've removed the GameDealsCanada Twitter feed — it seemed redundant with the daily round-ups anyways.
I'm also looking into optimizing images for web consumption. They're not the smallest images, but I'll see what I can do.
On the plus side, this gives me a great opportunity to learn about website tweaking.


Is it safe to pay online? What is the guaranty period when shopping in e-shop seated in another EU country? How long is the cooling-off period when I want to withdraw from the contract without giving any reason and sanction? Who covers delivery costs in case of withdrawal or claim? Is it enough to send claimed goods by mail? What are my rights when shopping on auction websites?


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Miami's Commercial Real Estate is on Fire
Jan 17 No Comments
As we entered into this new year the Miami Commercial Real Estate market as continued to see a lot of growth. Investors from the northeast U.S. and Latin America continue to spend their money in Miami. One firm in particular can attest to this growth.
Please read this amazing article by Rebecca San Juan.
"BGI Capital "closed on $90 million in commercial bridge loans in the last 90 days of 2019, the firm said. Some 90% of the closings — valued at $80 million — occurred in Miami, with the rest in New York City, said co-managing partner Robert Barthelmess. Investors from the northeast, Colombia, Mexico and Venezuela helped the firm exceed its' lending goal of $80 million, he said."
"It is a market that we feel comfortable about. Because of the situation in Latin America and tax changes, investors are coming to Miami from elsewhere," Barthelmess said.
Deals in Edgewater and Coral Gables topped the list for the firm's biggest investments. Among its deals were a $27.5 million construction loan for a Holiday Inn at 414 NE 36th St. and a $12 million refinance and re-purpose loan at 299 Alhambra Circle, a Class C office building.
BGI Capital has yet to determine a lending goal for the first quarter of 2020. But, Barthelmess said, the firm will prioritize investing in high-density areas in Miami-Dade County, Broward and West Palm Beach. Coral Gables, Wynwood, Edgewater and Hialeah are of particular interest, he said.
"We like high density areas because population can cure a lot of ills," Barthelmess said. "It drives demand.
Read more here: https://www.miamiherald.com/news/business/real-estate-news/article239363598.html

redpajama_set_name: RedPajamaCommonCrawl


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EA CEO: We're 'pushing forward' with loot boxes despite regulation
Jeff Grubb@jeffgrubb	 May 8, 2018 4:37 PM
Open another card pack, maybe you'll get Ronaldo.
Image Credit: EA Sports
Belgium and the Netherlands have ruled that many loot boxes in games like FIFA Ultimate Team are equivalent to gambling and in violation of their laws, but FIFA publisher Electronic Arts says it plans to continue its loot-box Ultimate Team mode.
"We're going to continue pushing forward [with FIFA Ultimate Team]," EA chief executive officer Andrew Wilson said during a conference call with industry analysts. "We're always thinking about our players. We're always thinking about how to deliver these types of experiences in a transparent, fun, fair, and balanced way for our players — and we'll continue to work with regulators on that."
EA also confirmed that its Ultimate Team modes in FIFA, Madden NFL, NHL, and NBA Live on PC, consoles, and mobile are its biggest live-service moneymakers. These modes bring in more than the Sims games or Battlefield, and they lean on the sale of card packs that act like loot boxes. These card packs include random soccer players that can improve your team and your chances of winning against friends and others online. And some people, policymakers, and regulators — including the gaming authorities in Belgium and Netherlands — that those card packs have are gambling.
Wilson explained to investors that it is working to protect this valuable revenue source, which has helped the company grow year-over-year to $1.25 billion during its last quarter even without releasing a major new game.
"We're working with all of the industry associations globally and with regulators in certain regions and territories," said Wilson. "Many of [the regulators] we've been working with for a long time, and they have evaluated and established that programs like FIFA Ultimate Team are not gambling."
EA, of course, says it doesn't think FIFA Ultimate Team and other video game loot boxes are equivalent to slot machines. Wilson explained why.
"First, players always receive a specified number of items in every FUT pack," the executive explained. "Second, we don't provide or authorize any way to cash out digital items or virtual currency for real-world money. And there's no real-world value assigned to in-game items."
But on the internet, where there's a will (and money) there's a way. You can find a number of sites that will exchange your virtual currency and items for real-world cash that will work at the grocery store. EA says that it is aware of this as well.
"While we forbid the transfer of items and in-game currency outside of the games, we also actively seek to eliminate that where it's going on in an illegal environment," said Wilson. "We work with various regulators on that."
EA will have to convince policymakers around the world that it is doing enough and that its mechanics are not the same as the kinds of games you'd find in a casino. For now, however, it is telling investors that the FIFA Ultimate Team factory is still printing money.
AMD CTO: How making the right bets years ago is paying off now


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Strictly speaking, gluten is a protein component in wheat, but the term is collectively applied to disease-activating proteins in wheat, rye and barley.
Celiac disease is characterised by chronic inflammation of the small intestinal mucosa that may result in atrophy of intestinal villi. The progressive destruction of the small intestinal mucosa causes malabsorption, and a variety of clinical manifestations, including diarrhoea, abdominal pain, vitamin and mineral deficiencies, iron-deficiency anaemia, osteoporosis, Procalamine (Amino Acid and Glycerin)- FDA delay, skin lesions, neurological disorders, etc.
Diagnosis of the disease requires examination of biopsies of small intestinal mucosa(Reference Mulder and Cellier11). The Marsh classification(Reference Marsh12) has been adopted to describe the progression of the abnormalities in the mucosa, from early stages with normal architecture and a lymphocytic infiltration of the villus epithelial layer up to total atrophy of the villi caused by chronic inflammation.
A number of serologic tests are available commercially for identifying individuals who require an intestinal biopsy examination to diagnose celiac disease(Reference Rostom, Dube and Cranney13).
The best markers are the detection in serum of anti-tissue transglutaminase IgA by ELISA, or anti-endomysial IgA by immuno-fluorescence. Both tests appear to have equivalent diagnostic accuracy as the tissue transglutaminase is the specific protein that is recognised by the IgA-endomysial antibody. Procalamine (Amino Acid and Glycerin)- FDA antibody tests are no longer routinely recommended because of their lower sensitivity and specificity(Reference Rostom, Dube and Cranney13).
The increasing Procalamine (Amino Acid and Glycerin)- FDA of serologic screening is leading to diagnosis in milder cases. It is eli lilly recognised that, at certain points in time, the disease is not associated with obvious clinical signs and symptoms.
In latent celiac disease, small bowel biopsy shows only minimal changes (increased intraepithelial lymphocyte infiltration) and anti-tissue transglutaminase or endomysial antibodies may be detected, but the characteristic feature is that the subjects develop symptoms and positive serologic and histological markers, while on a gluten-containing diet.
Procalamine (Amino Acid and Glycerin)- FDA celiac disease precedes diagnosis of celiac disease or follows successful treatment of active disease with a gluten-free diet. Population-based estimates of the incidence of confirmed celiac disease vary from two to thirteen new cases per 100 000 person-years. These rates have to be interpreted with caution because many patients diagnosed as adults are likely to have had several years of untreated celiac 750 cipro, and thus do not represent true new cases.
The recent increase in the incidence rates has likely been due to increasing use of serologic screening leading Procalamine (Amino Acid and Glycerin)- FDA diagnosis in milder cases(Reference Rewers14). However, celiac disease is virtually unknown in East Asian and African populations, whereas rates close to those in Europe have been reported from the Middle East and India(Reference Rewers14).
Genetic background appears to be a major risk factor for celiac disease. It is unequivocal that celiac disease is strongly associated with specific HLA class II genes that map to the DQ locus of the MHC used for cell-to-cell interaction during the process of antigen presentation(Reference Liu, Rewers and Eisenbarth16).
The presence of specific alleles at the HLA-DQ locus appears to be necessary, although not sufficient, for the phenotypic expression of disease. Environmental factors also play a major role. It is well established that celiac disease is strictly dependent on exposure to wheat gluten and related proteins in rye and barley.
Thus, these cereal proteins are necessary causal factors both to initiate and to maintain the disease process. On the other hand, epidemiological studies have shown that breast-feeding is a protective factor. Introduction of gluten-containing foods while the infant is still breast-feeding reduces the risk for celiac disease(Reference Ivarsson17). The age of the infant at introduction of gluten-containing mucoclear does not seem to be an independent risk factor, but it is well established scared to death introduction of gluten-containing foods in large amounts, as compared with small or medium amounts, increases the risk for celiac disease.
Infectious episodes affecting the gut mucosal barrier could potentially contribute to the development of celiac disease in genetically susceptible individuals(Reference Ivarsson17). Of note, such gluten-activated Th1 cells were isolated from the small intestinal mucosa of patients with celiac disease, but they are i feel my heart beating found in the intestinal mucosa of individuals without celiac disease, who also have temperature normal body relevant disease-associated DQ2 or DQ8 HLA class II molecules(Reference Kagnoff18).
These cytokines increase epithelial permeability and proinflammatory cytokine production, which in turn will increase the passage of gluten peptides and peptide binding to DQ2 and DQ8 molecules on antigen-presenting cells, leading to a chronic feedback of the 3017 process as long as gluten peptides are present in the intestinal lumen.
A strict gluten-free diet for life is the only accepted treatment for celiac disease(Reference Procalamine (Amino Acid and Glycerin)- FDA and Khosla19). Successful outcomes are highly dependent on compliance to such a diet.
Advanced celiac disease may not respond to a gluten-free diet, and these refractory cases are being treated with immunosuppressant drugs, including azathioprine and anti-TNF therapies with variable Procalamine (Amino Acid and Glycerin)- FDA (Fig. Ulcerative colitis (UC) and Crohn's disease (CD) are the two main forms of inflammatory bowel disease (IBD). UC and CD are both acute and chronic disabling inflammatory illnesses, whose aetiologies are unknown.
IBD is incurable, but typical maintenance treatments involve the use of immunosuppressant and anti-inflammatory drugs, antibiotics and surgery. An important factor differentiating CD from UC is that it Procalamine (Amino Acid and Glycerin)- FDA affect any part of the gastrointestinal tract, not just the large bowel as in UC. Whereas CD is characterised by patchy, transmural inflammation with inflammatory processes occurring deep in the tissues, the inflammatory response in UC is primarily located in the colonic mucosa and submucosa resulting in severe tissue damage, ulceration and haemorrhage(Reference Carter, Lobo and Procalamine (Amino Acid and Glycerin)- FDA. In both forms of IBD, large infiltrates of neutrophils can be seen in the inflamed tissues, together with the presence of microabscesses in the lamina propria.
Both CD and UC are associated with a 5-fold increased risk of developing colon cancer. Up to two million people are affected by IBD globally, with the disease being mainly associated with industrialised countries in the subfilms hemisphere.
Overall, the incidence and prevalence of UC is approximately twice that of CD. Although a genetic component is Procalamine (Amino Acid and Glycerin)- FDA to be involved in IBD, with both CD and UC sharing some susceptibility genes, there is stronger evidence for a genetic link in CD(Reference Farrell and Peppercorn21, Reference Shanahan22).
NOD2 is a cytoplasmic receptor for muramyl peptide found in bacterial cell walls, which may result in CD patients with this mutation having a reduced ability to clear invasive bacteria. A higher incidence of UC has been found in Jewish than Zemaira (Alpha-Proteinase Inhibitor (Human))- Multum non-Jewish families, and Ashkenazi Jews born in the West have been found to have a higher incidence of CD than those born in Israel or non-Ashkenazi Jews.
Largely uncategorised environmental factors are thought to predispose towards IBD. However, the change to a playing sports helps to reduce stress Western-style diet has been suggested as a link in IBD development. Smokers are more likely to develop CD and have more aggressive disease, with more severe relapses than non-smoking CD patients, although smoking has been shown to be protective in UC.
Physiological stress, particularly long-term stress, may also be Omtryg (Omega-3-Acid Ethyl Esters A Capsules)- FDA precipitating factor in IBD.
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Click here for a link to the Bereavement Authority of Ontario's Consumer Information Guide.
Note for Catholics:
Two items included in the Consumer Information Guide are not in keeping with the teachings of the Catholic Church. They are alkaline hydrolysis and the scattering of cremated remains.
Alkaline hydrolysis
The Canadian Conference of Catholic Bishops discourages the practice of alkaline hydrolysis, as it "does not manifest adequate respect for the dignity of the human body as proclaimed by the faith of the Church."
Scattering of cremated remains
According to Church teachings, scattering cremated remains on the sea, in the air, on the ground, or keeping them in the homes of relatives does not display appropriate reverence for the remains of the body, which was the temple of the Holy Spirit (cf. Ad resurgendum cum Christo). When for legitimate reasons, cremation has been chosen, the cremated remains of the faithful must be laid to rest in a sacred place, that is, in a cemetery or, in certain cases, in a church or an area set aside for this purpose, and so dedicated by a bishop.


Aventura Vantage Raptor Series is surveillance software whichsupport live video stream, video record and playback, video remoteplayback,snapshots and PTZ control, etc.
Aventura CCTV Fiber Optic CalculatorFiber Optic Calculator LossEstimation. Estimate the total dB loss of fiber optic transmissionbased upon the light source, cable type, cable length, slices andconnectors. The resulting information provides the bandwidth in hzand the total dB loss.
Aventura CCTV VantageConnect to your Aventura Video ManagementSystem from anywhere using your Android device.Aventura Vantageallows you to view cameras and use PTZ functionality.
Aventura CCTV Voltage CalculatorEstimate voltage drop by inputtingthe wire material and gauge, voltage and phase and the ampere load.The resulting information provides the voltage drop as well as theload at the end of the circuit . Additionally, the percentage ofvoltage drop and the CMA of the conductor are also represented.
pharaoh adventure questPlay and take the challenge! Pharaohadventure questIt's an addictive game for everyone with Pharaohadventure. Over 780+ Levels is waiting for you.!Just swap and matchthree or more same gems jewels to eliminate them, try to make morecombos. Your target is to line up same kind of gems jewels!Enjoyvarious animation & effect with special items !.How to play-Touch and slide the jewels with finger to change its position.Youcan erase 3 or more jewels by putting them on the same line!- Getpoint by erasing them.- Make longer chain of jewels to get morepoints!
Play beautiful Music both ONLINE and OFFLINE It's time foradventure with cute characters. ♬ ★ Music Various classical (likeCanon, Kankan, Black key, etc) and original music (over 100) ♬ ★Various modes 1. [Level] - Compete with other people with yoursummoned heroes and heal the planet. 2. [Music] - Play variouspatterns of 3, 4, 5, 6 and 9 keys. Offline support. 3. [Arena] -Check the strength of my heroes. 4. [Event] - There are variouscontents that can summon Heroes. ♬ ★ Hero 1. Beethoven, Mozart,Chopin, Schubert, and dozens of other classical musicians turnedinto heroes! 2. Collect heroes of various personalities. 3. Raiseyourself to the strongest hero and win the battle. ♬ ★ Box 1. Playthe game and win various boxes. 2. The box contains items to helpyou play the game. ♬ ★ Story A distant future, devastated by theinvasion of Dust! There you are the last hope. Playing beautifulMusic with cool Heroes Please return the universe to its formerappearance! ◆ User Community ◆ Official Facebook:https://www.facebook.com/rhythmstar.official Official Twitter:https://www.twitter.com/anb_rhythmstar Official fan cafe:https://www.plug.game/rhythmstarglobal *** Rhythm Star isrequesting the following permission. *** * READ_EXTERNAL_STORAGE :To upload images or videos to the community.
Super Sboy game that started it all is now free-to-play andoptimized for mobile devices! And more gifts for Chrismas time.After sucess of Sboy World Adventure, IMO Games make new for allaround the world with new adventures: new character, new boss, newgameplay and more nice arts, effects. Sboy World Adventure 2 iss anew classic platform game with a journey off super boy (Sboy) thatbrings your childhood back. Great Features Of Games - Begin with 20levels - Up to 80 levels soon. - Attractive art and effects. - 5Leaderboards and 14 archievements How to play more easy? - Left andright arrows to move left or right - Arrow down to go inside thepipe to the bonus level where you can find lots of coins - Buttonto run faster or firing - Button to skip character . - Buttonbuying power switch to superhero and shooting fire . Now, let'splay and win!
Message Quest is a tiny stained-glass point-and-click adventureabout laziness and its herald. The atmosphere and story wereinspired y a well-known Japanese animation studio. This is thestory of a lazy herald called Feste. You may know heralds, the guyswho show up at the beginning of every story, looking for a hero todeliver that "call to adventure" thing to. You know, right beforethe interesting stuff starts to happen. That's exactly our Feste'sjob: find a hero, give them their call to adventure, and be donewith it. No exploits, no saving the world. But all he wants to dois sleep and eat candy. You must become his conscience and lead himthrough the struggles and strange encounters of the Road BetweenWorlds. A cute fantastic journey for one evening—the game lastsabout an hour and a half, so you'll get the full story in onesession. The adventure will be fun for children and adults alike.Message Quest is an RPG for anyone who loves unusual tales offantasy. Features: - Unusual stained-glass graphics that makeeverything look like a fairy tale; - Charming characters withunpredictable reactions who share their stories; - Puzzles withtraditional mechanics that allow you to fully enjoy the storywithout losing game immersion; "- Funny boss fights in true JRPGstyle with zany attacks and bonuses; - A new dialogue system thatallows you to control multiple characters in a conversation;" -Jokes and easter eggs that will surprise you when you least expectit; - A magical soundtrack written especially for Message Questthat will immerse you in the bizarre fantasy universe of the RoadBetween Worlds.
Adventure Doreamon Running is the best platform adventure for yourkids Everything has been carefully designed for you to have a lotof fun.Doraemon game goals are to crush all the difficulties anddefeat all the enemies on his way to save the princess and hisfriends Noby and Shizuka from the evil black doramon monsterhand.Download the application AND BECOME A PART OF THE FAMILLYThereare many obstacles that must Dorae through, like Fellows, Eagle andMonster stones etc. Finish the mission and collect as many pointsas its fate.The anime favored by different age categories, and wehope that this game is also a favorite game. Download AdventureDoreamon Running Shop fast.Great Features of Doreamon RunningAdventure:- Great graphics and music:- 100 free levels with 5worlds and 9 bosses to fight and more soon.- More than 20 enemies,monsters and obstacles.- Underground and aquatic world, swimming,super jump and super race.- Doremon Running can transform its sizeand become super blue cat agent by taking the mushroom.-Displaceable bricks, blocks and platforms.For more information,contact us .
Help Ben capture the strength of his watch to become new aliens.★Protect the planet from running to defeat the invaders.★ Go insearch of new powers and capture strength for transformations!★Have super speed!★ Move only by sliding your fingers.★ 16-bit PixelGraphics!Enter this adventure with Ben and save the Planet!


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Théodore-Augustin Forcade MEP (ur. 2 marca 1816 w Wersalu, zm. 12 września 1885 w Aix-en-Provence) – francuski duchowny rzymskokatolicki, biskup, misjonarz w Japonii, Chinach i na Gwadelupie, arcybiskup Aix.

Biografia
Théodore-Augustin Forcade urodził się 2 marca 1816 w Wersalu we Francji. 16 marca 1839 otrzymał święcenia prezbiteriatu i został kapłanem diecezji wersalskiej. Początkowo pracował jako wikariusz, a następnie był wykładowcą filozofii w Wyższym Seminarium Duchownym w Wersalu. 2 października 1842 wstąpił do Towarzystwa Misji Zagranicznych w Paryżu. W tym samym roku wyjechał na Daleki Wschód. Początkowo służył w Makau, a następnie na Riukiu.

27 marca 1846 papież Grzegorz XVI mianował go wikariuszem apostolskim Japonii i biskupem in partibus infidelium Samosu. Był on pierwszym biskupem mianowanym dla Japonii. 21 lutego 1847 w Hongkongu przyjął sakrę biskupią z rąk wikariusza apostolskiego Hubei i Hunanu Giovanniego Domenico Rizzolatiego OFMRef. Asystował mu prefekt apostolski Hongkongu o. Antonio Feliciani OFM.

Jako że w Japonii wciąż obowiązywała izolacjonistyczna polityka sakoku powrócił do Francji, gdzie bezskutecznie próbował zainteresować rząd ewangelizacją Japonii. 5 października 1847 podczas pobytu w Rzymie otrzymał nominację na proprefekta apostolskiego Hongkongu, pozostając wikariuszem apostolskim Japonii. Założył pierwszy sierociniec w Hongkongu. W 1850 zrezygnował z urzędu proprefekta apostolskiego Hongkongu.

Zawarł porozumienie z jezuitami, powierzając im misje w Japonii. W 1852, gdy Kongregacja Rozkrzewiania Wiary uznała, że przekroczył tym swoje uprawnienia, złożył rezygnację z urzędu wikariusza apostolskiego Japonii.

12 września 1853 został biskupem Gwadelupy i Basse-Terre na Antylach. 18 marca 1861 biskupem Nevers we Francji. 25 lipca 1873 przeniesiony na arcybiskupstwo Aix, gdzie pozostał do śmierci 12 września 1885 spowodowanej cholerą, którą zaraził się przy łóżku chorego.

Jako ojciec soborowy wziął udział w soborze watykańskim I.

Bibliografia
 Catholic-hierarchy
 GCatholic
 Archiwum MEP

Francuscy biskupi katoliccy
Towarzystwo Misji Zagranicznych w Paryżu
Uczestnicy soboru watykańskiego I
Ludzie urodzeni w Wersalu
Urodzeni w 1816
Zmarli w 1885

redpajama_set_name: RedPajamaWikipedia


Students enrolled in the Saybrook University's School of Mind Body Medicine often tell stories of how they found their way to Saybrook. Many describe their path as a calling, or as an answer to their quest for finding a new way of working with people, one that addresses the many dimensions of human experience. Helen's story is about meeting a fellow Saybrook student, Beth Haggett, who is also the first student to receive a PhD from Saybrook University School of Mind Body Medicine. While attending a conference facilitated by the Berkana Institute, Helen met Beth, and was moved by Beth's inspiration to make a difference in the world via her experiences and knowledge gained at Saybrook. During the three days they spent together, Beth generously guided some of the conference participants in Qi gong and a shaking exercise. Experiencing these new methods to bring greater mind-body connection as well as hearing about the degree-program at Saybrook planted a seed in Helen's head, which held fast even as Helen returned home to work and her personal and community commitments.
Helen's professional background is in corporate consulting, working for Gagen McDonald, a consulting firm focused on strategic communications, leadership development, and culture change. Helen is fascinated by organizational change and human development, and has realized over the years of working on large-scale transformations that no matter how broad the change is, it must always begin at the individual level. Helen describes her work in corporate consulting as rewarding, yet stressful. Her personal experience with the impact of stress on her physically led her to explore mind-body techniques such as acupuncture, massage therapy, and energy medicine. The personal relief she experienced through mind-body techniques coupled with her interaction with Beth fueled her curiosity.
A few months after meeting Beth, during a sabbatical from work, Helen had the time to reflect upon her personal and career goals and research the programs offered in the field of mind-body medicine. She couldn't ignore her intuition, which told her that Saybrook was the perfect fit, so she applied. In January of 2013 Helen began working toward a PhD in Mind-Body Medicine in the doctoral Practice Specialization.
Helen has recently switched from a full time position to a freelance employee status in order to balance school and work, and to make time for her new marriage. Helen has always been interested in coaching, and therefore found that beginning her journey with the MBM Coaching for Health and Wellness course provided a seamless introduction for her developing career. Helen's goal is to make life coaching a bigger part of her work as it will allow her to focus on one person at a time, providing the right environment to make a mind, body, and soul connection – one that enables true transformation at the personal, community, and organizational levels.
Helen and her husband live in Chicago and have been enjoying their first year of marriage doing the things they love – cooking, volunteering in the community, traveling to visit friends and family, and training for triathlons.


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In American English, the word "truck" has historically been preceded by a word describing the type of vehicle, such as a "tanker truck". In British English, preference would lie with "tanker" or "petrol tanker".
A trailer is not very difficult to categorize. In general, it is an unpowered vehicle towed by a powered vehicle. Trailers are most commonly used for the transport of goods and materials. Although some do enjoy recreational usage of trailers as well.
With the partial deregulation of the trucking industry in 1980 by the Motor Carrier Act, trucking companies increased. The workforce was drastically de-unionized. As a result, drivers received a lower pay overall. Losing its spotlight in the popular culture, trucking had become less intimate as some unspoken competition broke out. However, the deregulation only increased the competition and productivity with the trucking industry as a whole. This was beneficial to the America consumer by reducing costs. In 1982 the Surface Transportation Assistance Act established a federal minimum truck weight limits. Thus, trucks were finally standardized truck size and weight limits across the country. This was also put in to place so that across country traffic on the Interstate Highways resolved the issue of the 'barrier states'.
"Country music scholar Bill Malone has gone so far as to say that trucking songs account for the largest component of work songs in the country music catalog. For a style of music that has, since its commercial inception in the 1920s, drawn attention to the coal man, the steel drivin' man, the railroad worker, and the cowboy, this certainly speaks volumes about the cultural attraction of the trucker in the American popular consciousness." — Shane Hamilton
According to the U.S. Census Bureau, 40 million United States citizens have moved annually over the last decade. Of those people who have moved in the United States, 84.5% of them have moved within their own state, 12.5% have moved to another state, and 2.3% have moved to another country.
The American Association of State Highway and Transportation Officials (AASHTO) is an influential association as an advocate for transportation. Setting important standards, they are responsible for publishing specifications, test protocols, and guidelines. All which are used in highway design and construction throughout the United States. Despite its name, the association represents more than solely highways. Alongside highways, they focus on air, rail, water, and public transportation as well.
In 1938, the now-eliminated Interstate Commerce Commission (ICC) enforced the first Hours of Service (HOS) rules. Drivers became limited to 12 hours of work within a 15-hour period. At this time, work included loading, unloading, driving, handling freight, preparing reports, preparing vehicles for service, or performing any other duty in relation to the transportation of passengers or property. The ICC intended for the 3-hour difference between 12 hours of work and 15 hours on-duty to be used for meals and rest breaks. This meant that the weekly max was limited to 60 hours over 7 days (non-daily drivers), or 70 hours over 8 days (daily drivers). With these rules in place, it allowed 12 hours of work within a 15-hour period, 9 hours of rest, with 3 hours for breaks within a 24-hour day.
Implemented in 2014, the National Registry, requires all Medical Examiners (ME) who conduct physical examinations and issue medical certifications for interstate CMV drivers to complete training on FMCSA's physical qualification standards, must pass a certification test. This is to demonstrate competence through periodic training and testing. CMV drivers whose medical certifications expire must use MEs on the National Registry for their examinations. FMCSA has reached its goal of at least 40,000 certified MEs signing onto the registry. All this means is that drivers or movers can now find certified medical examiners throughout the country who can perform their medical exam. FMCSA is preparing to issue a follow-on "National Registry 2" rule stating new requirements. In this case, MEs are to submit medical certificate information on a daily basis. These daily updates are sent to the FMCSA, which will then be sent to the states electronically. This process will dramatically decrease the chance of drivers falsifying medical cards.
The basics of all trucks are not difficult, as they share common construction. They are generally made of chassis, a cab, an area for placing cargo or equipment, axles, suspension, road wheels, and engine and a drive train. Pneumatic, hydraulic, water, and electrical systems may also be present. Many also tow one or more trailers or semi-trailers, which also vary in multiple ways but are similar as well.
The 1980s were full of happening things, but in 1982 a Southern California truck driver gained short-lived fame. His name was Larry Walters, also known as "Lawn Chair Larry", for pulling a crazy stunt. He ascended to a height of 16,000 feet (4,900 m) by attaching helium balloons to a lawn chair, hence the name. Walters claims he only intended to remain floating near the ground and was shocked when his chair shot up at a rate of 1,000 feet (300 m) per minute. The inspiration for such a stunt Walters claims his poor eyesight for ruining his dreams to become an Air Force pilot.
With the onset of trucking culture, truck drivers often became portrayed as protagonists in popular media. Author Shane Hamilton, who wrote "Trucking Country: The Road to America's Wal-Mart Economy", focuses on truck driving. He explores the history of trucking and while connecting it development in the trucking industry. It is important to note, as Hamilton discusses the trucking industry and how it helps the so-called big-box stores dominate the U.S. marketplace. Hamilton certainly takes an interesting perspective historically speaking.
The term 'trailer' is commonly used interchangeably with that of a travel trailer or mobile home. There are varieties of trailers and manufactures housing designed for human habitation. Such origins can be found historically with utility trailers built in a similar fashion to horse-drawn wagons. A trailer park is an area where mobile homes are designated for people to live in. In the United States, trailers ranging in size from single-axle dollies to 6-axle, 13 ft 6 in (4,115 mm) high, 53 ft (16,154 mm) in long semi-trailers is common. Although, when towed as part of a tractor-trailer or "18-wheeler", carries a large percentage of the freight. Specifically, the freight that travels over land in North America.
With the ending of World War I, several developments were made to enhance trucks. Such an example would be by putting pneumatic tires replaced the previously common full rubber versions. These advancements continued, including electric starters, power brakes, 4, 6, and 8 cylinder engines. Closed cabs and electric lighting followed. The modern semi-trailer truck also debuted. Additionally, touring car builders such as Ford and Renault entered the heavy truck market.


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text:
The public's reaction to Rihanna's River Island debut during London Fashion Week might have been less than stellar, but the singer isn't about to stop her train anytime soon. She's just announced a new partnership with MAC cosmetics that will result in multiple releases later on this year. WWD reports that the first product to launch will be a RiRi Woo lipstick inspired by Rihanna's favorite red shade, MAC's Ruby Woo. The lipstick is described as blue-red and retro matte with a moisturizer finish that works on every skin tone.
"When you think of makeup, the brand that pops into your mind — for something legit — is MAC," Rihanna said. "Whatever color you want, it's like 'Let's go to MAC.' I've been using MAC on tour for such a long time it was a natural fit for me. I have always loved makeup, and I always said that if I do it, I want to do it with a credible brand."
This is the first time the cosmetics brand is teaming up with a celeb for an ongoing collaboration, calling the singer a "creative partner." Rihanna said the deal is "a no-brainer."
"I really got to play," Rihanna said. "There's so much to choose from, and you can mix different textures with different colors and different greens in different eye shadows. I learned so much about the detail of makeup and what makes things look different. What makes it apply different is really important. Every little detail is important."
RiRi Woo will be released during Rihanna's Diamonds Tour concerts at the Barclays Center in Brooklyn, NY, on May 4 and 5. MAC will open a pop-up shop on location to promote the release.
Get ready for the BET Experience, featuring Beyoncé, Snoop Lion, Erykah Badu, Kendrick Lamar and many more. Go here for more details and info on how to buy tickets.
(Photo: PacificCoastNews.com)


Check out the official video to the track 'Gabru Bigad Gaya' by Twin Beats featuring the vocal talents of Billa Ferozepuri. The track is taken from the second studio album by by Twin Beats entitled 'Lektronik Zamana' which is out now on VIP Records.
Gabru Bigad Gaya from the album Lektronik Zamana is available for download via iTunes, Google Play & Amazon MP3.


text:
Derby Gdańska – derby piłkarskie z udziałem najwyżej notowanych klubów piłkarskich Gdańska: Lechii, Gedanii i Polonii.

Starsze są derby Lechii i Gedanii, sięgające 1945 roku, jednakże więcej rozegrano pojedynków Lechii i Polonii – 31. Część pojedynków rozegrano na szczeblu centralnym: w II lidze oraz w Pucharze Polski.

Od sezonu 1999/2000 najczęściej rozgrywane są mecze Gedanii i Polonii – 20 pojedynków w IV lidze i klasie okręgowej.

Derbami Gdańska bywają nazywane także mecze z udziałem zespołu rezerw Lechii Gdańsk.

Kluby
Lechia jest najbardziej utytułowanym gdańskim klubem piłkarskim i jedynym, który odnotował występy w Ekstraklasie. Gedania jest najstarszym polskim klubem piłkarskim Gdańska i całego Trójmiasta, pierwszym gdańskim uczestnikiem mistrzostw Polski (1946) oraz jedynym gdańskim klubem zgłoszonym do polskich rozgrywek przedwojennych (Klasa A 1939/1940). Lechia, Gedania i Polonia są jedynymi klubami z Gdańska, które występowały w II lidze.

Bilans
 Lechia – Gedania (13 meczów):
 10 zwycięstw Lechii
 3 zwycięstwa Gedanii
 Lechia – Polonia (31 meczów):
 12 zwycięstw Lechii
 12 remisów
 7 zwycięstw Polonii
 Gedania – Polonia (2 mecze):
 1 zwycięstwo Gedanii
 1 zwycięstwo Polonii

Pozycje ligowe

Uwagi

Przypisy

Gdańsk
Gedania Gdańsk
Lechia Gdańsk
Zawody sportowe w Gdańsku


Sonic returns in another flash game Grab the golden rings and don't die. The levels may look familiar, they look like levels from the Super Nintendo hit Super Mario World. Let's show these mario goons just what Sonic The Hedgehog is made of. Spin bash these baddies till there begging for you to stop. Enjoy this free sonic game.


text:
Children-focused footwear brand Plaeto forays into the UAE market
The Bengaluru-based company recently raised Rs 40 crore in Series A funding round led by Florintree Advisors, a Mumbai based financial institution and other marquee investors in the D2C space.
Updated: August 18, 2022, 17:27 IST
New Delhi: Plaeto, a children-focused footwear brand, has announced its global foray with its entry into the UAE market, said a media release.
For this, the Bengaluru-based company has partnered with Threads, UAE's premier and largest retailer for school uniforms, shoes, and accessories.
Recently, it raised Rs 40 crore in Series A funding round led by Florintree Advisors, a Mumbai based financial institution and other marquee investors in the D2C space.
Ravi Kallayil, cofounder and CEO, Plaeto, said, "We will be catering to all the key regions across the Emirates through the Threads stores as well as their online store."
Further, the company plans to explore retail and distribution partnerships in UAE and other Middle East markets for its range of shoes for children aged 5-15 years.
Launched in 2021, the brand's founding team consists of erstwhile top executives from Nike, Adidas, and Apple. Last year, Plaeto announced Rahul Dravid, Team India cricket coach, as their brand ambassador and strategic advisor.
plaeto
rahul dravid
kallayil
florintree advisors


text:
You are here: Home1 / About Us2 / News & Events3 / Bulletins4 / Maintenance issue forces police helicopter to land near Long Beach sho...
Maintenance issue forces police helicopter to land near Long Beach shoreline
Bulletins, misc
A Long Beach police helicopter made an unplanned landing in a grassy area along Shoreline Drive because the aircraft was having a maintenance issue Sunday night, according to the department.
The helicopter set down around 11:10 p.m., witnesses said. It was landed as a precaution, police spokeswoman Arantxa Chavarria said, and was grounded for no more than about 90 minutes.
Maintenance issues are not uncommon and the helicopter was safely flown back to the department's heliport, Chavarria said.
This was before a thunderstorm hit Long Beach, with lightning, sheets of rain and howling wind. Chavarria said the helicopter being grounded was not related to the storm.
https://www.lbfdcalendar.org/wp-content/uploads/2020/10/logo.png 512 425 Henry Haley https://www.lbfdcalendar.org/wp-content/uploads/2020/10/logo.png Henry Haley2020-12-27 15:55:402020-12-28 15:56:20Maintenance issue forces police helicopter to land near Long Beach shoreline


text:
Quantum Mechanics Beginners
*******************************

Fundamental Concepts
==================================

What're the most important tricks in QM calculations?
---------------------------------------------------------

* **Remember what basis we are working in**
* **Identity**

First Three Postulates
-------------------------

* Physical state is described by kets in a Hilbert space. We need to specify a complete basis {:math:`\ket{i}`} to do calculations.

  .. math:: \ket{\psi} = \sum_i \ket{i}\bra{i}\ket{\psi} = \sum_i C_i \ket{i}

* Operators are given by Hermitian operators; A measurement of the variable :math:`\hat \Omega` will yield one of the eigenvalues :math:`\omega` with the probability

  .. math:: \left|\braket{\omega}{\psi}\right|^2 .

  And the state of the system will change to :math:`\ket{\omega}`.
* The state vector obeys the Schrödinger equation,

  .. math:: i\hbar \frac{\d}{\d t}\ket{\psi(t)} = \hat H \ket{\psi(t)} ,

  where :math:`\hat H` is the Hamiltonian operator.

  .. admonition:: Comments
     :class: note

     The logic here is that we first find the way to describe a system, then think about how to find out the information we need from the state vector and also find the evolution of the state vector. Then we need the operator and Schrodinger equation. Finally, we would like to relate the theory to experiments, and it comes the measurement postulate.

     Later we will need the relation between position and momentum, which becomes the fourth postulate.

* How to solve the evolution of a system?
  We just define a magical operator, propagator

  .. math::
     \hat U \ket{\psi(t_0)} = \ket{\psi(t)} .

  This operator just gives us the evolution of state vector! Wait, can we write down the explicit expression of it?

  Let's find out. The only thing we know about the evolution of a state vector is the third postulate up there.

  .. math::
     i\hbar \frac{\d }{\d t}\ket{\psi(t)} & =  \hat H \ket{\psi(t)} \\
     i\hbar \frac{\d }{\d t}\hat U \ket{\psi(t_0)} & =  \hat H \hat U \ket{\psi(t_0)} \\
     i\hbar \frac{\d }{\d t}\hat U & =  \hat H \hat U

  Looks familiar? This just gives us a exponential result, **if the Hamiltonian is time independent**.

  .. math:: \hat U = e^{- i \hat H (t-t_0)/\hbar}

  **We can prove that this operator is Unitary because** :math:`\hat H` **is Hermitian.**

  This is just the abstract representation, we work in some basis, and the most convenient basis is the eigenstates of Hamiltonian, { :math:`\ket{\epsilon_i}` },

  .. math::
 	   \hat U \ket{\phi} & =  e^{- i \hat H (t-t_0)/\hbar} \ket{\psi}   \\
     \hat U \ket{\phi} & =  \sum_i e^{- i \hat H (t-t_0)/\hbar} \ket{\epsilon_i}\bra{\epsilon_i}  \ket{\psi}  \\
	   \hat U \ket{\phi} & =  \sum_i e^{- i \epsilon_i (t-t_0)/\hbar} \ket{\epsilon_i}\bra{\epsilon_i}  \ket{\psi}

  And we are going to use

  .. math:: \hat U = \sum_i e^{- i \epsilon_i (t-t_0)/\hbar} \ket{\epsilon_i}\bra{\epsilon_i}

  from now on. (Well, only on discrete eigenvalues ones.)

  **(See that? Identity does the work again.)**

Position and Momentum Space
-----------------------------

.. admonition:: Summary
   :class: note

   * Position
       1. Define {:math:`\ket{x}`} basis.
       2. Define :math:`\hat x` operator.
       3. Find wave function in this basis.
       4. Find measurement.
   * Evolution
   	1. Need propagator :math:`\hat U`.
   	2. Propagator needs the solution of Hamiltonian eigensystem.
   	3. (Free particles) Hamiltonian needs the solution of momentum eigensystem.
   * Momentum
   	1. Before we define some arbitrary momentum space, we should check the relation between momentum and position. And it turns out to be related by a commutator.(Postulate IV)
   	2. Use the postulate to momentum operator.
   	3. Find eigenstates.
   	4. (Calculate the propagator.)

Position Space
""""""""""""""""

1. Define :math:`\ket{x}` basis.

   **Orthonormal condition is**

   .. math::
      \braket{x}{x'}=\delta(x-x').

   **Completeness condition is**

   .. math::
      \int \braket{x'}{x'} \d x' = \mathbb{I}

2. Define position operator.

   The position operator is defined as

   .. math::
      \hat x \ket{x} = x \ket{x}

   And in :math:`\{\ket{x}\}` basis, this operator becomes a function, which is

   .. math::
      &\bra{x}\hat x \ket{x'}  \\
      =& \left(\bra{x}\hat x \right)\ket{x'} \\
      =& x \braket{x}{x'} \\
      =& x \delta(x-x')

3. Find state vector in :math:`\{\ket{x}\}` basis.

   .. math::
      \psi(t,x) = \braket{x}{\psi(t)}

   **Normalized**

   .. math::
      \int \left| \psi(t,x) \right|^2 \d x = 1.

   And we are interpreting :math:`\left| \psi(t, x)\right|^2` as probability density.
4. Calculate probability of a measurement. Taking :math:`\hat x` as an example.

   .. math::
      &\bra{\psi} \hat x \ket{\psi} \\
      &= \iint \braket{\psi}{x}\bra{x} \hat x \ket{x'} \braket{x'}{\psi}  \d x \d x' \\
      &= \iint  \psi^ * (t,x) x\delta(x-x') \psi(t,x')  \d x \d x'  \\
      &= \int \left| \psi(t,x) \right|^2 x \d x

Momentum Space
"""""""""""""""

To find the momentum operator, we need to check the relation between momentum and position before we just randomly define one. Truth is, we have a fourth postulate states the relation between them.

Postulate IV
^^^^^^^^^^^^^^

The commutator of :math:`\hat x`, :math:`\hat p` is

.. math::

   \left[ \hat x, \hat p \right] = i \hbar

Two comments:
  * Why i ? Eigenvalue of Anti-Hermitian operator.
  * Why :math:`\hbar`? Because people define the dimensions of position and momentum differently before they know this commutator. We would like to assign them the same dimension if we already know this relation.

Momentum Space
^^^^^^^^^^^^^^^^

1. Find momentum operator in position basis {:math:`\ket{x}`}.

   .. math:: \bra{x} \left[ \hat x, \hat p\right] \ket{x'} = i\hbar \delta(x-x')

   And write out the commutator and use the relation of delta function :math:`x\delta'(x) = -\delta(x)`, we find out the momentum operator in {:math:`\ket{x}`} basis,

   .. math:: \bra{x}\hat p \ket{x'} = -i\hbar \frac{\d }{\d t} \delta(x-x')

   **Let's talk physics.** What does that operator mean? We need to see what the result is when momentum operator is applied to a state. And remember we would work in {:math:`\ket{x}`} basis.

   .. math::
      &\bra{x} \hat p \ket{\psi} \\
      & =  \iint \braket{x}{x'} \bra{x'} \hat p \ket{x''}\braket{x''}{\psi} \d x' \d x''  \\
      & =  \int \bra{x}\hat p \ket{x''}\psi(t,x'') \d x'' \\
      & =  \int \left( -i\hbar \frac{\d}{\d x} \delta(x-x') \psi(t,x') \right) \d x' \\
      & =  \int \left( -i\hbar \frac{\d}{\d x'} \delta(x'-x) \psi(t,x') \right) \d x'

   **Integrate by parts, we will find the expression.** (I am having a problem finding the right answer.)

   .. math:: \bra{x} \hat p \ket{\psi} = - i\hbar \frac{\d }{\d x}\psi(x) .

2. Eigenfunction for momentum.

   .. math::

      \hat p \ket{p} = p \ket{p} .

   Again, we are going to project it on the {:math:`\ket{x}`} basis,

   .. math:: \bra{x}\hat p\ket{p} = \bra{x} p \ket{p} ,

   where :math:`\braket{x}{p}` is the eigenstates in {:math:`\ket{x}`} basis, we call it :math:`\phi_p(x)`.

   .. math::
      \bra{x}\hat p\ket{p} & =  p \phi_p(x)    \\
      \int \bra{x}\hat p \ket{x'}\braket{x'}{p}\d x' & =  p \phi_p(x)    \\
      -i\hbar \frac{\d }{\d x} \phi_p(x) & =  p \phi_p(x)

   The solution is

   .. math:: \phi_p(x) = \mathrm{C} e^{i p x/\hbar}

   This constant C is found by the normalization condition,

   .. math:: \braket{p}{p'}=\int \phi_p^*(x)\phi_{p'}(x)\d x = \delta(p-p')

   **The final results should be**

   .. math:: \phi_p(x)=\frac{1}{\sqrt{2\pi \hbar}} \exp{(i p x/\hbar)}

3. Find the dynamics of free particles in quantum mechanics.
   **Find the propagator and everything solves.**
   The hamiltonian for a free particle is

   .. math:: \hat H = \frac{\hat p^2}{2m} .

   We argue here that the eigenvectors of momentum are also the eigenvectors of this hamiltonian. And we can easily guess the eigenvalues are :math:`p^2/2m`. So the propagator is

   .. math:: \hat U = \int e^{-i p^2 t/2m\hbar} \ket{p}\bra{p} \d p

   But that is too abstract to use, we can find the expression in {:math:`\ket{x}`} basis.

   .. math::
      \bra{x}\hat U\ket{x} & =  \int e^{-i p^2 t/2 m \hbar} \braket{x}{p}\braket{p}{x} \d p    \\
      & =  \int e^{-i p^2 t/2 m \hbar} \left| \phi_p \right|^2 \d p

Quantum in 1D
==============

General
----------

Always start with the propagator for time independent Hamiltonian.

.. math:: \ket{\psi(t)} = \hat U \ket{\psi(0)}

For cases that Hamiltonian with discrete eigenvalues,

.. math:: \ket{\psi(t)} = \sum _ n e^{-i \epsilon _ n t/ \hbar } \ket{n}\braket{n}{\psi(0)}

If the initial state is just one of the eigenstates of Hamiltonian, say the mth one (normalized),

.. math:: \ket{\psi(t)} = e^{- i \epsilon _ m t/\hbar} \ket{ m }

Well, that phase factor doesn't have any effect for the topic we discuss. So our time evolution will stay on the same state forever.

The same thing happens for continuous cases.

So our task is simplified to solve the eigensystem of Hamiltonian, which is

.. math:: \hat H \ket{\epsilon} = \epsilon \ket{\epsilon}

Infinite Barriers
""""""""""""""""""

Math
^^^^^

Setup
~~~~~~

* Potential in a box

  .. math::
     V(x) = & 0,  0< x <L \\
      & \infty, \text{Other}

Solve the Problem
~~~~~~~~~~~~~~~~~~~

* Hamiltonian

  .. math:: \hat H = \frac{\hat p ^2}{2 m } + V(x)

* Dynamic equation

  .. math:: \hat H \ket{\psi(t)} = \epsilon \ket{\psi(t)}

  We are happy to work in {:math:`\ket{x})`} basis,

  .. math:: \bra{x} \hat H \ket{\psi(t)} = \bra{x} \epsilon \ket{\psi(t)} .

  Put the Hamiltonian in, and remember that in position basis

  .. math:: \bra{x} \hat p \ket{\psi} = - i \hbar\frac{\d}{\d x} \psi ,

  the equation of motion becomes

  .. math:: - \frac{\hbar ^2}{2 m} \frac{\d^2}{\d x^2} \psi(x,t) + V(x) \psi(x,t) = \epsilon \psi(x,t)

* Boundary conditions

  .. math::

     \psi _ I(0,t) = \psi _ {II}(0,t)

     \psi _ {II}(L, t) = \psi _ {III}(L, t)

* Guess the Solutions

  .. math:: \psi_{II} = \psi = C \sin (k x) + D \cos(kx)

* Find the wavenumber k, by putting the assumed solutions into equation of motion

  .. math:: k = \pm \sqrt{\frac{2m \epsilon}{\hbar^2} }

  Since we can always merge the negative into the constants, it is fine to use

  .. math:: k = \sqrt{\frac{2m \epsilon}{\hbar^2} }

* Use Boundary Condition
  1. At x=0,

     .. math:: \psi(0,t)=0 .

     This gives us :math:`D = 0` .

  2. At :math:`x=L`,

     .. math:: \psi(L,t)=0 .

     This leads to

     .. math:: k L = n \pi .

     Since :math:`n=0` gives us a 0 wave function, we would just drop :math:`n=0`. For the same reason why we drop the negative values of k, we would drop all the negative values of n.
     This BC gives us the possible values of energy because wavenumber k is related to energy,

     .. math:: \epsilon = \frac{\hbar^2}{2m L^2 } (n\pi)^2 ,

     with

     .. math:: n=1,2,3, \cdots

* Normalization as the last constraint for the last undetermined parameter,

  .. math:: C=\sqrt{\frac{2}{L}}

Physics
^^^^^^^^^^

1. Estimation

	 * Find the expression for energy using dimensional analysis.
	 * Using uncertainty relation to estimate the expression for energy.

2. Comments

	 * Why is the solution quantized?
  	   1. Too many constraints. BCs + normalization.

    * Why do the n in the solution goes into the expression for energy?
  	   1. Have a look at the kinetic energy term, the derivative does it.

    * What's so weird?
  	   1. For :math:`n=2`, no particles found at :math:`x=L/2`. And so on.

Some General Properties
~~~~~~~~~~~~~~~~~~~~~~~~

1. 1D bound states have no degeneracy. Prove it by assume that there is a degeneracy state.

2. 1D bound states' wave function can be chosen to be real. (if potential V is real.)

Parity
================

Passive and Active Transformations
---------------------------------------

Generally, there are two ways of interpreting a transformation.

.. image:: qmimg/transformations.png
   :alt: Transformations

Here in QM, passive means transform the operator :math:`\hat \Omega`, while active means change the state :math:`\ket{\psi}`. Suppose we have a system :math:`\ket{\psi}`, an operator :math:`\hat \Omega`, a transformation :math:`\hat U`.

Transformation :math:`\hat U \ket{\psi}` is identical to :math:`\hat U^\dagger \hat \Omega \hat U` because they give the same observation results. The first one is called active, while the second one is called passive.

Parity
------------

Definition
""""""""""""""

.. math:: \hat \Pi \ket{x}= \ket{-x}

Properties
""""""""""""""

1. Act on momentum eigenvectors,

   .. math::
      \hat \Pi \ket{p} = \ket{-p} .

  * Physics: Parity changes the coordinate, so the direction of momentum is also changed.
  * Math:

    .. math:: \hat \Pi \ket{p} = \int \hat \Pi \ket{x}\braket{x}{p}\d x= \int \ket{-x}\braket{x}{p}\d x

    Change coordinate from x to -x,

    .. math:: \hat \Pi \ket{p} = \int \ket{x}\braket{-x}{p}\d x = \int \ket{x}\braket{x}{-p}\d x  = \ket{-p}

2. Hermitian,

   .. math::
      \bra{x}\hat \Pi \ket{x'} = \delta(x+x')
      (\bra{x'}\hat \Pi \ket{x})^\dagger = \bra{x}\hat \Pi^\dagger \ket{x'} =\delta(x+x')

3. Unitary

   .. math:: \bra{x}\hat \Pi^\dagger \hat \Pi \ket{x'}= \braket{-x}{-x'}=\delta(-x+x')=\delta(x-x')=\braket{x}{x'}

4. Inverse of parity

   .. math:: \hat \Pi \hat \Pi = \hat \Pi \hat \Pi^\dagger = \hat I

5. Eigensystem of parity.

   .. math:: \hat \Pi \ket{\pi}=\pi\ket{\pi}

   Apply another operator

   .. math:: \hat \Pi^2 \ket{\pi} = \pi^2 \ket{\pi}

   So,
   * Eigenvalues: 1, -1;
   * Eigenvactors: Even function, Odd function
6. Parity applied to operators
   a. Apply to position operator,

      .. math:: \hat \Pi^\dagger \hat X \hat \Pi = -\hat X

      Proof:

      .. math:: \bra{x}\hat \Pi ^\dagger \hat X \hat \Pi \ket{x'} = \bra{-x}\hat X \ket{-x'}= -x'\delta(x-x') = \bra{x}(-\hat X)\ket{x'}

   b. Apply to momentum operator,

      .. math:: \hat \Pi^\dagger \hat p \hat \Pi = -\hat p

      Proof: Similar to the previous one, just change x basis to momentum basis.

7. Symmetry related to Hamiltonian.

   .. math:: \left[ \hat \Pi , \hat H  \right] = 0

   When this happens, parity of Hamiltonian won't change the wave function. Or the wave function should have an specific parity for 1D problem.

Classical Limit of QM
========================

Ehrenfest's Theorem
---------------------

Schrödinger equation and its adjoint

.. math::

   i\hbar \frac{\d }{\d t} \ket{\psi(t)} = \hat H \ket{\psi(t)}

   -i\hbar \frac{\d }{\d t} \bra{\psi(t)} = \bra{\psi(t)} \hat H

For any observable :math:`\hat \Omega`,

.. math::
   \frac{\d }{\d t}\left<\hat \Omega \right > & =  \left( \frac{\d}{\d t}\bra{\psi(t)}\right)  \hat \Omega \ket{\psi(t)} + \bra{\psi(t)} \dot{\hat \Omega} \ket{\psi(t)} + \bra{\psi(t)} \hat \Omega \left( \frac{\d}{\d t}\ket{\psi(t)}\right)  \\
   & =  \frac{1}{i\hbar} \left ( - \bra{\psi(t)} \hat H \hat\Omega \ket{\psi(t)} +\bra{\psi(t)} \hat\Omega \hat H \ket{\psi(t)} \right) + \bra{\psi(t)} \dot{\hat \Omega} \ket{\psi(t)} \\
   & =  \frac{1}{i\hbar} \bra{\psi(t)}\left[\hat\Omega,\hat H\right] \ket{\psi(t)}+\bra{\psi(t)} \dot{\hat \Omega} \ket{\psi(t)}

This is called Ehrenfest's Theorem.

Simple Example of Ehrenfest's Theorem
"""""""""""""""""""""""""""""""""""""""

Suppose we have a system with Hamiltonian

.. math:: \hat H = \frac{\hat p^2}{2m} + V(\hat x)

We need to figure some commutators first.

.. math::
   2m \left[ \hat x, \hat H \right] =\left[\hat x, \hat p^2\right] = \hat x \hat p\hat p - \hat p \hat p \hat x = \hat x \hat p \hat p -\hat p \hat x \hat p + \hat p \hat x \hat p - \hat p \hat p \hat x  = \left[\hat x , \hat p\right]\hat p + \hat p \left[ \hat x,\hat p\right]  = 2 i \hbar \hat p

.. math::
   \left[\hat p, \hat H\right] = \left[\hat p, V(\hat x) \right] = \left[\hat p, \sum_0^\infty \frac{V^{(n)}}{n!}\hat x^n\right] =\cdots =-i\hbar V'(\hat x)

1. Position average

   .. math::
      \frac{\d }{\d t} \left< \hat x \right> & =  \frac{1}{i\hbar} \bra{\psi(t)} \left[ \hat x, \hat H \right]\ket{\psi(t)} \\
      & =   \frac{\left< \hat p \right>}{m}

   We are familiar with this in classical mechanics.
2. Momentum average

   .. math::
      \frac{\d}{\d t} \left<\hat p\right> & =  \frac{1}{i\hbar} \bra{\psi(t)} \left[\hat p, \hat H\right] \ket{\psi(t)} \\
      & =  \frac{1}{i\hbar} \bra{\psi(t)}  (-i\hbar V'(\hat x))  \ket{\psi(t)}  \\
      & =  -\left< V'(\hat x) \right>

   In classical mechanics, the derivative of potential is force. And the result is just like Newton's 2n Law except the right hand side is not exactly like a force which should be :math:`-\frac{\d}{\d x} \left< V(\hat x) \right>`.

What does :math:`-\left< V'(\hat x)\right>` mean
"""""""""""""""""""""""""""""""""""""""""""""""""""

Suppose the potential area is fairly small and distributed around some coordinate :math:`x_0=\left< \hat x \right>`, we can do Taylor expansion around :math:`x_0`.

.. math::
   < V(\hat x)> & =  V(x_0)   +  V'(x_0) < (x - x_0)> + V''(x_0)<(x-x_0)^2> /2 + \cdots \\
   & =  V(x_0) + 0 + V''(x_0) (\Delta x)^2 + \cdots

If the uncertainty is small enough, every term except the first one becomes small. So to the lowest order, average of potential is approximately the potential at :math:`x_0`.

Similarly, the average of first derivative of potential :math:`<V'(\hat x)>` is approximately :math:`V'(x_0)`.

These gives us a hint for the previous result we got for the time evolution of average momentum. The result reduces to classical mechanics one as long as we keep the lowest order of Taylor expansion. Those higher order terms show the quantum effect.

Picture
-----------

We can see deeper into Ehrenfest's Theorem through Heisenberg Picture of quantum mechanics.

Schrödinger & Heisenberg Pictures
""""""""""""""""""""""""""""""""""""

Pictures are the ways we look at the evolution of systems.

Schrödinger Picture
^^^^^^^^^^^^^^^^^^^^

In Schrödinger picture the states are evolving with time.

.. math:: i\hbar \frac{\d}{\d t} \ket{\psi} _ S = \hat H \ket{\psi} _ S

And for time independent Hamiltonian,

.. math:: \ket{\psi}_S = U^\dagger \ket{\psi _ 0} _ S

Heisenberg Picture
^^^^^^^^^^^^^^^^^^^^

In Heisenberg Picture, the states do not change with time.

.. math:: \ket{\psi} _ H = \ket{\psi_0} _ H ,

and of course the initial is the same with Schrödinger Picture,

.. math:: \ket{\psi_0} _ H = \ket{\psi _ 0} _ S .

How do we relate to Heisenberg Picture to Schrödinger Picture? Through investigation of observables. We should have the same observation results in both Pictures.

.. math::
   {} _ H \bra{\psi} \hat \Omega _ H \ket{\psi} _ H & =  {} _ S \bra{\psi} \hat \Omega _ S \ket{\psi} _ S \\
   {} _ H \bra{\psi} \hat \Omega _ H \ket{\psi} _ H & =  {} _ S \bra{\psi _ 0} \hat U^\dagger \hat \Omega _ S  \hat U \ket{\psi _ 0} _ S \\
   \hat \Omega _ H & =  \hat U^\dagger \hat \Omega _ S \hat U

So the operators change with time in Heisenberg Picture.

Ehrenfest's Theorem in Heisenberg Picture
""""""""""""""""""""""""""""""""""""""""""""

.. math::
   \frac{\d }{\d t} \hat \Omega _ H = \frac{1}{i\hbar } \left[ \hat \Omega _ H, \hat H \right] + \hat U ^ \dagger \frac{\partial }{\partial t} \Omega _ H \hat U

This can be easily proved by throwing every definition need in to it. We also need the following equations.

.. math:: \frac{\d }{\d t} \hat U = \frac{\d }{\d t} e^{-i\hat H t /\hbar} = \frac{\hat H}{i\hbar} \hat U

And REMEMBER that propagator commute with time independent Hamiltonian, so

.. math::
   \hat H = \hat U^\dagger \hat U \hat H = \hat U^ \dagger \hat U \hat U \equiv \hat H _ H

So this Ehrenfest's Theorem can also be written as

.. math::
   \frac{\d }{\d t} \hat \Omega _ H = \frac{1}{i\hbar } \left[ \hat \Omega _ H, \hat H _ H \right] + \hat U ^ \dagger \frac{\partial }{\partial t} \Omega _ H \hat U

We can **define**

.. math::
   \frac{\partial}{\partial t}\hat  \Omega _ H \equiv \hat U^\dagger  \frac{\partial }{\partial t}\hat  \Omega _ S \hat U  ,

which is the time derivative of operator in Heisenberg Picture.

**Reminder: The time derivative of an observable (average) depends not only the time derivative of itself, but also the commutator of the observable and Hamiltonian.**

Example of Ehrenfest's Theorem in Heisenberg Picture
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

We will show why it is better to work in Heisenberg Picture to show the meanings of Ehrenfest's Theorem.

Suppose we have a Hamiltonian in Heisenberg Picture,

.. math:: \hat H_H = \frac{\hat p _ H^2 }{2m} + V(\hat x _ H) .

Time derivative of position operator

.. math:: \frac{\d}{\d t} \hat x _ H = \frac{1}{i\hbar} \left[\hat x _ H, \hat H _ H \right ] = \frac{\hat p _ H}{m}

Time derivative of momentum operator

.. math:: \frac{\d}{\d t} \hat p_H = \frac{1}{i\hbar } \left[ \hat p _ H, \hat H \right] = - V'(\hat x_H)

So the operator in Heisenberg Picture just have a sense of the physical quantities in classical mechanics. That's why we like it.

Comparison of Picutres
""""""""""""""""""""""""""""""

.. figure:: assets/images/picutres-comparison.png
   :align: center

   Comparison of different pictures. Notice that in Dirac picture, :math:`\hat W_I = \hat U_0 ^{-1}\hat W \hat U_0`, :math:`\ket{\psi(t)}_I = \hat U_I \ket{\psi(0)}_I`. A markdown file that is used to make this table can be downloaded `here <assets/pictureQM.md>`_ .

Conservation
---------------

We say a observable is conserved if the corresponding operator commutes with Hamiltonian,

.. math:: \left[ \hat \Omega, \hat H \right]=0

1. Energy
Hamiltonian always commutes with itself.

.. math:: \frac{\d}{\d t} \left<\epsilon \right> = \bra{\psi} \left( \frac{\partial }{\partial t} \hat H \right) \ket{\psi}

If Hamiltonian is time independent, then energy is conserved. (If Hamiltonian is tide dependent, energy is not conserved. This is kind of obvious in classical mechanics.)

What is the nature of time dependence
"""""""""""""""""""""""""""""""""""""""

We can see this by looking at a simple example.

Assume we have a system with energy eigenstates :math:`\ket{\epsilon _ n}`, and initially,

.. math:: \ket{\psi _ 0} = \sum_n C _ n \ket{\epsilon _ n} .

So

.. math:: \ket{\psi(t)} = \sum _ n C _ n e^{-i\epsilon _ n t/\hbar} \ket{\epsilon _ n} .

We can calculate the expectation value of some operator :math:`\hat \Omega`,

.. math::
   \left< \omega (t) \right> =  \sum _ {n,m} \left( C _ n^ * e^{i\epsilon _ n t/\hbar } \bra{\epsilon _ n} \right)  \hat \Omega \left( C _ m e^{-i \epsilon _ m t/\hbar} \ket{\epsilon _ m} \right) = \sum _ {n,m} C _ n ^* C _ m e^{-i(\epsilon _ m - \epsilon _ n) t/\hbar} \bra{\epsilon _ n} \hat \Omega \ket{\epsilon _ m}

If :math:`\ket{\epsilon _ n}` are also the eigenvectors of :math:`\hat \Omega`, then

.. math:: \bra{\epsilon _ n} \hat \Omega \ket{\epsilon _ m} = \omega _ m \delta _ {n,m}

And the expectation value

.. math:: \left<  \omega (t) \right> = \sum _ {n} C _ n^* C _ n \omega _ n

**The important thing is that the time dependence of this expectation value actually arise from this term**

.. math:: e^{-i(\epsilon _ m - \epsilon _ n)t/\hbar} .

As it is so important, we call

.. math:: (\epsilon _ m - \epsilon _ n)/\hbar

**Bohr frequency**.

Harmonic Oscillators
=====================

Why Harmonic Oscillators
--------------------------

Many systems can reduce to it. Use Taylor expansion for the potential and redefine parameters we will find harmonic oscillators in the potential.

Hamiltonian for 1D is

.. math::
   \hat H = \frac{\hat p^2}{2m} + \frac{1}{2} k \hat x^2

Standard Solution
--------------------

We can use polynomial expansion for part of the solution.

Dimension Schrodinger Equation
""""""""""""""""""""""""""""""""

First step is always finding out the characteristic length scale and characteristic energy scale. Assume we have an characteristic length :math:`\eta` and characteristic energy scale :math:`\epsilon_0`. Through uncertainty principle we know only for dimensional analysis

.. math::
   \left[\hat p\right]=\frac{\hbar}{\eta}

Kinetic energy and potential energy have the same dimension

.. math::
   \frac{\hbar^2}{\eta^2 m}=k \eta^2 ,

so we have

.. math::
   \eta = \sqrt{\frac{\hbar}{m\omega}}

with :math:`\omega^2=k/m`. A dimensional analysis shows that :math:`\epsilon_0=\hbar\omega`.

Now we can define dimensionless variables,

.. math::
   z=x/\eta, e=\epsilon/\epsilon_0

The time independent Schrodinger equation in position basis is

.. math::
   -\hbar^2 \frac{\mathrm d^2}{\mathrm dx^2}\psi'' /m + k x^2 = 2\epsilon \psi .

Using those characteristic scales, we can rewrite this equation into a dimensionless one, which is

.. math::
   \psi''+(2e-z^2)\psi = 0

in which :math:`\psi'=\frac{\mathrm d}{\mathrm dz}\psi`.

Take Limits
""""""""""""""""""""

We need to look at the behavior of the solutions before we can guess a proper general solution.

:math:`z\rightarrow \infty`, we have :math:`\psi''-z^2\psi=0`. Solution to this equation is :math:`\psi(z)~ e^{-z^2/2}`.

The solution of the the equation should be in the form

.. math::
   \psi(z) = u(z) e^{-z^2/2}  .

Insert this to time independent Schrodinger equation, we can get the equation of :math:`u(z)`.

.. math::
   u'' - 2 z u' +(2e-1) u = 0

Polynomial Method
"""""""""""""""""""""

The simplest form of :math:`u(z)` is polynomial,

.. math::
   u(z) = \sum _ {n=0}^{\infty} u _ n z^n  .

Put this back to equation of u, we can get the recursion relation,

.. math::
   (n + 2)(n+1) u _ {n+2} = \left[ 2n - (2e - 1) \right] u _ n   .

If :math:`u_0` and :math:`u_1` are given, we can get the whole polynomial.

Notice that we have definite parity here. So :math:`u _ 1` branch vanish because they are even.

:math:`u_0` is set by the normalization condition.

Terminate The Series
""""""""""""""""""""""

The series blow up if it doesn't terminate. So we need to terminate the series using the following relation,

.. math::
   2e - 1 = 2n .

Then we have the energy levels, which is :math:`e=n+1/2`.

Complete Series
""""""""""""""""

By picking proper normalization factor, we can write down the energy levels and corresponding wave functions. In fact, this polynomial can be found in mathematical phyisics books.

.. math::
   H _ {n+1} = 2 z H _n -n H _ {n-1}

Tricky Solution
-----------------

Find out the characteristic length and energy

.. math::
   \eta = \sqrt{\frac{\hbar }{m\omega }} \\
   \epsilon = \hbar \omega \\
   \omega = \sqrt{\frac{k}{m}}

One way to get the intrinsic length without writing down the dimensions of each quantity is to use the following relation

.. math::
   \left[ E \right] = \left[ m \omega^2 \hat x^2 \right] \\
   \hbar \omega = m \omega^2 \eta^2 \\\
   \eta = \sqrt{ \frac{\hbar}{m\omega} }

Or if we are given the Hamiltonian in terms of :math:`k`,

.. math::
   \left[ \frac{\hat p^2}{2m} \right] = \left[ k \hat x^2 \right] \\
   \frac{\hbar^2 / \eta^2 }{m} = k\eta^2 \\
   \eta = \sqrt{\hbar}{ \sqrt{m k} } = \sqrt{ \hbar }{ m \omega }

Rewrite the Hamiltonian

.. math::
   \hat H & =  \frac{1}{2m} \left[ \left(\frac{\hat p}{\hbar/\eta}\right)^2 \left(\frac{\hbar}{\eta}\right)^2 + \frac{1}{2} m \omega^2 \left( \frac{\hat x}{\eta} \right)^2 \right] \\
   & =  \frac 1 2 \hbar \omega \left[ \left(\frac{\hat p}{\hbar/\eta}\right)^2 + \left(\frac{\hat x}{\eta}\right)^2 \right]    \\
   & =  \frac 1 2 \hbar \omega \left( \frac{\hat x}{\eta} - i \frac{\hat p}{\hbar/\eta}   \right) \left( \frac{\hat x}{\eta} + i\frac{\hat p}{\hbar/\eta}  \right)  - \frac{i}{\hbar} \left[\hat x, \hat p\right]    \\
   & =  \frac 1 2 \hbar \omega (\sqrt 2 \hat a^\dagger \sqrt 2 \hat a + 1) \\
   & =  \hbar \omega \left( \hat a^\dagger \hat a + \frac 1 2\right)

Now we can define :math:`\hat a^\dagger \hat a = \hat N`, which is just like an operator for (energy) quanta numbers.

An impoertan relation is

.. math::
   \left[\hat a, \hat a^\dagger\right] = 1 \\
   \left[\hat a, \hat N\right] = \hat a

The eigen equation for this weird energy quanta number operator is

.. math::
   \hat N \ket{n} = n \ket{n}

To find out the eigen state of :math:`\hat a` and :math:`\hat a^\dagger`, we try this,

.. math::
   \hat N (\hat a \ket{n}) = (n-1) (\hat a \ket{n})  \\
   \hat N (\hat a^\dagger \ket{n}) = (n+1) (\hat a^\dagger \ket{n})

This means :math:`\hat a \ket{n}` and :math:`\hat a^\dagger \ket{n}` are also eigen states of :math:`\hat N`.

The next step is very crucial. Since :math:`\hat a \ket{n}` and :math:`\hat a^\dagger \ket{n}` are eigen states of :math:`\hat N`, we know that

.. math::
   \hat a \ket{n} = C1 \ket{n} \\
   \hat a^\dagger \ket{n} = C2 \ket{n}

Then our next step is to find out what are :math:`C1` and :math:`C2` exactly.

They way of finding them is to use invariant quantities, such as the inner product. Here we use average of :math:`\hat N` operator.

.. math::
   \hat a \ket{n} = \sqrt n \ket{n-1}  \\
   \hat a^\dagger \ket{n} = \sqrt{n+1} \ket{n+1}

Final step is to constrain on :math:`n`, which should be integrals. This is true because we need a cut off for the eigen equation of :math:`\hat N`, whose avarage is n and it should be non negative.

.. math::
   \bra{n}\hat N \ket{n} \ge 0

leads to :math:`n\ge 0`. To get this proper cut off, :math:`n` should be integer because if it's not, according to

.. math::
   \hat a \ket{n} = \sqrt n \ket{n-1}

n can go to negative numbers. If n is positive integer,

.. math::
   \hat a \ket{1} = \ket{0}  \\
   \hat a \ket{0} = 0 \ket{0}

show an cut off at 0.

We can even find out the wave functions of these :math:`\ket{n}` by finding the ground state first and apply :math:`\hat a^\dagger` to the ground state.

Ground state in :math:`{\ket{x}}` basis can be found by solving the differential equation,

.. math::
   \bra{x} \hat a \ket{0} = 0

..

  Very important:

  * The Hermitian conjugate of :math:`\hat a \ket{n}` is :math:`\bra{n} \hat a^\dagger`.
  * Hermitian conjugate of :math:`\hat a \hat a^\dagger` is :math:`\hat a \hat a^dagger`. This can be a trap. Hermitian conjugate is the complex conjugate AND TRANSPOSE!

Semiclassical
-------------------

Classical
""""""""""""""""""""""

In phase space, the trajectory of phase space points ( {:math:`x/\eta` and :math:`p/(\hbar/\eta)`} ) is on a circle of radius :math:`x_{max}/\eta`.

Quantum semiclassical
"""""""""""""""""""""""

Key points:

1. What is the trajectory of :math:`\left<\hat x/\eta\right>` and :math:`\left<\hat p/(\hbar/\eta)\right>`
2. Can we make the trajectory just like the classical case by choosing some special conditions?
3. What do these special cases mean?

* Expectation value of creation and annihilation operators

Apply Ehrenfest theorem to annihilation operator,

.. math::
   i\hbar \frac{\mathrm d}{\mathrm d t} \avg{\hat a(t)} = \bra{\psi} \left[ \hat a(t), \hat H \right] \ket{\psi} = \hbar \omega \avg{\hat a(t)}

Excellent. Now we can solve out :math:`\avg{\hat a(t)}`, which is

.. math::
   \avg{\hat a(t)} = \alpha_0 \exp(-i\omega t)

Take the hermitian conjugate,

.. math::
   \avg{\hat a^\dagger (t)} = \alpha_0^* \exp(i\omega t)

* Expectation value of position and momentum

With these two operators, we can find out the average of :math:`\hat x` and :math:`\hat p` because

.. math::
   \hat x = \eta \frac{1}{\sqrt 2} \left( \hat a^\dagger + \hat a\right)\\
   \hat p = \frac{\hbar}{\eta} i \frac{1}{\sqrt 2} \left(\hat a^\dagger - \hat a \right) ,

we have

.. math::
   \avg{\hat x(t)} = \eta \frac{1}{\sqrt 2} \left( \avg{\hat a^\dagger (t)} + \avg{\hat a(t)} \right) \\
   \avg{\hat p(t)} = \frac{\hbar}{\eta} i \frac{1}{\sqrt {2} } \left( \avg{\hat a^\dagger (t) - \avg{\hat a(t)}} \right)

We can have a look at these two averages,

.. math::
   \frac{\avg{\hat x(t)} }{\eta} = \frac{1}{\sqrt{2} } \left[ (\alpha_0 + \alpha_0^*)\cos(\omega t) + i (\alpha_0^* - \alpha_0 ) \sin(\omega t) \right] \\
   \frac{\avg{\hat p(t)}}{\hbar/\eta} = \frac{1}{\sqrt{2}} \left[ (\alpha_0 + \alpha_0^*) \sin(\omega t) + i( \alpha_0 - \alpha_0^*)\cos(\omega t) \right]

It is obvious that the average reduces to classical case if :math:`\alpha_0 = \alpha_0^*`. **But this is too strong for a semiclassical limit.**

* Coherent state

**Coherent state is the eigenstate of creation operator. Its wave package has the smallest spread allowed by quantum mechanics.**

**The most special part about coherent state is that the system stays on coherent state if it start with coherent state.**

.. math::
   \hat a \ket{\alpha(t)} = \alpha(t) \ket{\alpha(t)}

Take the hermitian conjugate,

.. math::
   \bra{\alpha(t)} \hat a^\dagger  = \bra{\alpha(t)}\alpha(t)^*

At :math:`t=0`, we have

.. math::
   \bra{\psi(0)} N \ket{\psi(0)} = \vert \alpha_0 \vert ^2

That is to say, energy should be

.. math::
   \bra{\psi(0)} \hat H \ket{\psi(0)} = \hbar \omega \left( \vert \alpha_0 \vert^2 + \frac{1}{2} \right)

Initially, we also have

.. math::
   \bra{\psi(0)} (\hat a - \alpha_0)^\dagger (\hat a-\alpha_0) \ket{\psi(0)} = 0

This means

.. math::
   \hat a \ket{\psi(0)} = \alpha_0 \ket{\psi(0)}

* Coherent state expanded using energy eigenstates

(This result)

(To Be Finished...)

redpajama_set_name: RedPajamaGithub


Raid Time! in Kingdom Hearts Unchained χ / Union χ is the only quest of the eleventh Weekly Raid Event series of Event Quests, available from January 1 to 6, 2018.
This page was last edited on 1 January 2019, at 14:53.


ChaplainBill - I agree that the number is low, especially as you are a very experienced i-MiEV driver. First, I would do as PV1 suggested and then refrain from leadfooting to see what happens. It may take a few full-recharge cycles (from two bars or less) to get your i-MiEV's internal battery capacity calculation recalibrated. If I were a betting person (Heaven forbid), I'd be willing to bet she'll quickly start acting normal.
Whereas I occasionally see sub-50 RR after a full recharge (after high-speed freeway runs), I also got RR=84 yesterday after a 40-mile drive down to the coast. The possible range variability is hard for non-EVers to fathom.
Ran some heat, drove on the highway, and got stuck on my driveway (again). 3 bars and 9 miles RR remaining, but only managed 35.7 miles. Gotta love single digit temperatures...and 20 MPH wind.
Thank you for sharing your own experiences with the new battery replacement concerns I expressed. I will be more patient. The battery seems much stronger, not losing power as fast, and recharging downhill much better than my failed battery. I will keep the car and may leave my new Bolt in Oregon for a couple more road trips, to get the miles and time up so I will not have to pay new car tax when I ship it to Hawaii later next year.
Today's driving - starting RR was 64, heat off although I had preheated for a few minutes.
35 miles actual driving, not much heat used on the 7 mile trip to work. some heat used in the middle 20 mile lunch trip. Full blast heat on the way home. Pulled in to the garage with 2 flashing bars and 6 miles left on the RR with the heat running.
ChaplainBill wrote: I was getting only 32 miles RR with a full charge at home. I took it to the dealer and gave them copies of news articles about battery problems at the battery manufacturer and the $30 million dollar settlement to make it right in Japan.
They tested for weeks, over and over, techs from Japan, etc. and FINALLY agreed to replace my battery when they also got only 32 miles RR at their shop!
My new battery seems stronger, does not go down as quickly while driving my normal route, but the RR has only increased to 45 miles MAX in the two weeks since I have had it back. This vehicle had 85-90 mile RR consistently when new. Is my computer system in the car confused and does not recognize the new battery?
I almost gave up on my I-Miev, and in my weakness ordered a new Chevy Bolt which I hope to pick up in Portland before the end of the year for another tax credit, and a EV with a 238 mile range!!! I have an early deposit in on a Tesla 3, but felt I could not wait that long to get back into a dependable EV. I will enjoy a coastal road trip with the new Bolt before shipping it to my home in Hawaii... Aloha!
We did a few family trips over the summer and hypermiling on the highway we could just manage a 56 mile drive to my moms house, and did the round trip a few times.
I have been taking to my miev to work lately, and working late allows me to go full speed for 15.4 miles, and 3 miles city no traffic on the way home at night. I charge fully at home and work.
Note: no heat or AC used. 20 minutes of headlights is only 1/25th of a bar.
The next morning after charging, my RR has been 28 and 31 on different days. I was surprised that I was using up 12 bars to go 18.4 miles. Either my excel range calculations are wrong, or my battery is degraded. OK, the excel has some estimated unknowns, but if I would keep going full speed on the freeway I would drain the battery in less than 25 miles, whereas my excel predicts 40 miles. That's a huge difference!
OK, the colder winter temperature would drop the range about 6% (85F to 55F) based on air density only.
But I think there may be battery degradation. I have 35k miles on the odo, with a lot of that city driving.
I may have to go to the dealer like ChaplainBill.
Yup, sounds about right. Full speed = 81mph, and at that speed the drag force is enormous!


text:
Q: Converting multiple columns variable into dummy variables I'm thinking to convert multiple columns of categorical variables in a data frame to dummy variables using pandas. The code below works, but it seems too long. May I know how do I combine these 3 lines in a single line of code, please? Thank you
X = pd.get_dummies(df.height, prefix=['height'])

Y = pd.get_dummies(df.weight, prefix=['weight'])

Z = pd.get_dummies(df.age, prefix=['age'])**

A: You can use:
pd.get_dummies(data=df, columns=["height", "weight", "age"])

redpajama_set_name: RedPajamaStackExchange


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Paris Saint-Germain are ready to make a big move to sign Barcelonastriker Luis Suarez as they target a new strike partner for Neymar, according to reports in Spain.
The Brazilian rather infamously fell out with Edinson Cavani last season, with the two players warring over set-piece duties, and the French giants are keen to avoid any more dramas next season by separating the pair.
There had been suggestions that Real Madrid would try to bring Neymar to the Bernabeu, though now appear fixated on Kylian Mbappe, so it is Cavani who will make way.
According to Spanish publication Sport, PSG will look to sell Cavani and bring in Suarez instead, having already gained Neymar's approval.
The Brazilian - who is resigned to staying in France for another season - spent three prolific years alongside Suarez at Barcelona and the pair are quoted as having a 'good feeling' with each other.
PSG are conscious of the fact that Cavani is 31-years-old and have been looking for a new, world-class No.9 and believe Suarez ticks all the boxes despite being the same age.
After exiting the World Cup in the quarter-finals and missing much of the second half of the season through injury, Neymar feels he needs a strong campaign to cement his status as a Ballon d'Or contender and thinks Suarez is the strike partner to help him achieve that.
Cavani, meanwhile, is already garnering attention from old club Napoli, with new boss Carlo Ancelotti ready to greenlight a move to bring the Uruguayan back to Naples.
Mbappe could also leave the club this summer, with Real Madrid having made the teenager their preferred choice to replace Cristiano Ronaldo should he join Juventus this summer.


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I read your website letters daily and think you do a fantastic job. Thanks so much.
I ... thought it might be nice for folks to see what Park City, Utah is like in the winter and summer. I work at Deer Valley Resort and Sylvia (Hall Hammond - '66) works at Westgate next to the Canyons. We live close by in Deer Mountain. My passion is skiing, of course, or we would not be living in such cold weather. The summers are awesome, especially if one likes camping in the high Uinta Mountains. Park City is a lovely small town. Our main attractions, besides the beauty of the mountains, are special events such as the Sundance Film Festival, 4th of July parade on Main Street and opening and closing of the ski season. Trout fishing and golf are a weekly event in the summers. Small towns are great and relatively crime free!
I have attached several pictures of the seasons which may be of interest to some. Feel free to contact us for anything from skiing to fishing. I will even try to help those who really want to be ski bums like me but are afraid to go for it.
Thanks, Phil! These images are gorgeous!
I am sending you a few pictures I took this week of The Canyons and Deer Valley Resort as well as a few from my home. Please feel free to do as you wish with them and at your convenience. Thanks again for the PC website.
but expecting several storms starting Wednesday 2-20-08.
Thanks, Phil! These images are breathtaking as well!
I meant to send you one of these pictures. Really cool and dangerous work building a lift on the side of a mountain.
Check out my favorite wild rabbit snuggling up next to my window well. He stayed for two days there.
I am sending a few of the pictures from this weekend's camping trip in the Wasatch National Forest in the Uinta Mountains.
I hope these pictures may give my typhoon friends a view of the rest of the country.
We camped at Lost Creek which is approximately 10 thousand feet. It was 70 degrees during the day and very cold at night.
The moose was at our camp site for most of the day. I fished the Bear River but could not find any fish!
Thanks, Phil! These images are also breathtaking!
Utah, We Love Thee, was written by Evan Stephens as Utah was obtaining statehood. Utah had experienced great changes from the arrival of the pioneers in 1847 to long awaited statehood in 1896. The size of the territory had diminished while settlements spread throughout the land, Utah's citizens included people from a variety of countries, cultures and religions. Technology had advanced from handcarts and candles to streetcars and electric lights. On January 4, 1896 Utah entered the Union. The people had great celebrations! 'Utah, We Love Thee' was adopted by the Utah State Legislature on February 19, 1917. Because statehood was on the mind of the composer, there are many references to Utah taking its rightful place in the union.
The first Utah State Song (now State Hymn), entitled Utah, We Love Thee written by Evan Stephens, was adopted by the State Legislature on February 17, 1937, to become effective on February 24, 1937 (Utah Code). The author builds the theme of this song about Utah's mountains, sunny skies, State flag, pioneers, and closes by predicting that Utah will grow along the lines of wealth, peace, fame, and glory. He also stresses the great love of the people of Utah for their State. This song with words and music was published by the Deseret Sunday School Union, Salt Lake City, Utah, in 1917.
Thy luster shines afar, Utah, we love thee!
God guarded, evermore, Utah, we love thee!