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Tag Archives: realistic
All the Dirty Parts
September 3, 2017,
Categories: Contemporary, Realistic, Reviews
Tags: adult, all the dirty parts, book, contemporary, daniel handler, fiction, realistic, review
Title: All the Dirty Parts
Publisher: Bloomsbury USA
From bestselling, award-winning author Daniel Handler (aka Lemony Snicket), an eagerly anticipated, gutsy, exciting novel that looks honestly at the erotic lives and impulses of an all-too-typical young man. Cole is a boy in high school. He runs cross country, he sketches in a sketchbook, he jokes around with friends. But none of this quite matters, next to the allure of sex. "Let me put it this way," he says, "Draw a number line, with zero is, you never think about sex, and ten is, it's all you think about, and while you are drawing the line, I am thinking about sex." Cole fantasizes about whomever he's looking at. He consumes and shares pornography. And he sleeps with a lot of girls--girls who seem to enjoy it at the time and seem to feel bad about it afterwards. Cole is getting a reputation around school--a not quite savory one--which leaves him adrift and hanging out with his best friend. Which is when something startling begins to happen between them--another kind of adventure, unexpected and hot, that might be what he's been after all this time. And then he meets Grisaille. A companion piece to Handler's Why We Broke Up, the bestselling Michael J. Printz Honor novel, All The Dirty Parts is an unblinking take on the varied and ribald world of teenage desire in a culture of unrelenting explicitness and shunted communication, where queer can be as fluid as consent, where sex feels like love, but no one knows what love feels like. Structured in short chapters recalling Jenny Offill's Dept. of Speculation or Mary Robison's Why Did I Ever, the novel gives us a tender, brutal, funny, and always intoxicating portrait of an age in which the whole world is tilted through the lens of sex. "There are love stories galore," Cole tells us, "and we all know them. This isn't that. The story I'm typing is all the dirty parts."
"All the Dirty Parts" is one of those books that you will either love or hate. I'm in the LOVE camp. Warning: Don't buy this for a kid thinking "Lemony Snicket." This is not a good present from Grandma, though I can promise you it would get read.
Most of us know what it's like to wait for the dirty part in a movie, book, story your friend is telling, or even our own lives if we're honest about it. It seems like that's the good part. The genius of "All the Dirty Parts" is that is exactly what the name implies: all of the dirty parts of Cole's life. The problem is, when you only look at that, your perception of him as a person is not very good. He seems like a jerk, and probably is, but you can only he has some redeeming qualities about him since he has friends and good grades. We just don't know what they are. He doesn't even know what they are. There are a lot of things he doesn't know about himself, but I'll leave it to you to learn them.
This book is listed as an adult novel, and that is definitely the correct classification. That being said, there are a lot of lessons in literature that can be taught using it for the older young adult and new adult crowd. It's also certain to make some banned book lists and become a coveted book for teenagers to acquire. I'm ok with that. Maybe they'll accidentally learn something.
I don't normally do content warnings on adult books, but be aware that this one is filthy. The words aren't minced and the sex is graphic. Proceed at your own risk.
Mom and Mum Are Getting Married
Categories: Children's, Contemporary, Diverse Books, Realistic
Tags: book, children's, contemporary, diverse books, fiction, lgbt, marriage equality, realistic, review, same sex marriage
Title: Mom and Mum are Getting Married!
Author: Ken Setterington, Alice Priestley
Rosie is surprised to find her Mom dancing alone in the living room, but when Mom announces, "Your Mum and I are getting married!" they can't wait to start planning the big day. Friends and family come together for a celebration of love.
It's so wonderful to see a book about same-sex marriage that presents it to children as absolutely nothing other than a regular wedding… which it is. There are no judgmental family members and it's a regular party after the simple wedding. Be aware that it is a bit wordy for a picture book so take that in consideration for your child's attention span.
Trusting You & Other Lies
Categories: Contemporary, Realistic, Reviews, Romance
Tags: book, contemporary, fiction, nicole williams, realistic, review, romance, trusting you and other lies, ya, young adult
Title: Trusting You and Other Lies
Author: Nicole Williams
Publisher: Crown Books For Young Readers
USA Today and New York Times bestselling author Nicole Williams delivers a seductive summer romance worth swooning over. Perfect for fans of Sarah Dessen and Stephanie Perkins. Phoenix can't imagine anything worse than being shipped off to family summer camp. Her parents have been fighting for the past two years--do they seriously think being crammed in a cabin with Phoenix and her little brother, Harry, will make things better? On top of that, Phoenix is stuck training with Callum--the head counselor who is seriously cute but a complete know-it-all. His hot-cold attitude means he's impossible to figure out--and even harder to rely on. But despite her better judgment, Phoenix is attracted to Callum. And he's promising Phoenix a summer she'll never forget. Can she trust him? Or is this just another lie? "What elevates this novel...is the witty and realistic dialogue and excellent character development." -SLJ
"Trusting You & Other Lies" is a nice summer romance that has some teeth.
It's refreshing to see a sibling relationship that is loving and a family that is struggling in a realistic way. The teenage emotions rang true and brought back quite a bit of nostalgia, along with a lot of "glad I'm past that phase of my life" thoughts. Last but not least, there was no instalove. That is always a bonus in YA romances.
I recommend "Trusting You & Other Lies" for anyone looking for an emotional read about young relationships, both with family and romantic interests.
Language, Sexual Situations
Grendel's Guide to Love and War
June 7, 2017,
2 Comments,
Tags: a.e. kaplan, book, contemporary, fiction, grendel's guide to love and war, ptsd, realistic, review, ya, young adult
Title: Grendel's Guide to Love and War
Author: A. E. Kaplan
Publisher: Knopf Books for Young Readers
The Perks of Being a Wallflower meets Revenge of the Nerds in this tale of a teen misfit who seeks to take down the bro next door, but ends up falling for his enemy's sister and uncovering difficult truths about his family in the process. Tom Grendel lives a quiet life--writing in his notebooks, mowing lawns for his elderly neighbors, and pining for Willow, a girl next door who rejects the "manic-pixie-dream" label. But when Willow's brother, Rex (the bro-iest bro ever to don a jockstrap), starts throwing wild parties, the idyllic senior citizens' community where they live is transformed into a war zone. Tom is rightfully pissed--his dad is an Iraq vet, and the noise from the parties triggers his PTSD--so he comes up with a plan to end the parties for good. But of course, it's not that simple. One retaliation leads to another, and things quickly escalate out of control, driving Tom and Willow apart, even as the parties continue unabated. Add to that an angsty existential crisis born of selectively reading his sister's Philosophy 101 coursework, a botched break-in at an artisanal pig farm, and ten years of unresolved baggage stemming from his mother's death . . . and the question isn't so much whether Tom Grendel will win the day and get the girl, but whether he'll survive intact. "Deep and uproarious all at once . . . A clever spin on a weighty classic." --Kirkus, starred review
I'm not sure how to describe "Grendel's Guide to Love and War." It isn't as deep as it could be, considering Tom Grendel has a very difficult life, including a father suffering from severe PTSD. Yet it does evoke quite a few emotions by just skimming the surface of the issues he's dealing with. It is also hilarious. Laugh out loud hilarious. If you're looking for a fast read with a bit of an emotional roller coaster, give it a try.
All the Forever Things
Tags: all the forever things, book, contemporary, fiction, grief, jolene perry, loss, realistic, review, romance, ya, young adult
Title: All the Forever Things
Author: Jolene Perry
Publisher: Albert Whitman and Company
From growing up in the funeral home her family runs, Gabriella knows that death is a part of life and nothing is forever. Yet Bree, her best friend, has been a constant; it's always been the two of them together against the world. But when Bree starts dating a guy—the worst guy— from that ultra-popular world, suddenly she doesn't have time for Gabe anymore. Now the only one at school who wants to spend time with "Graveyard Gabe" is Hartman, the new guy, but Gabe, not wanting to lose her mind over a boyfriend the way Bree has, holds back. It takes a very strange prom night (with the family hearse instead of a limo) for Gabe to truly fall for Hartman. But when she leaves the after-prom party with him, she's not there for Bree—or for the deadly accident that happens that night. Bree survives, but will she and Gabe ever be able to rebuild their friendship?
"All the Forever Things" is a unique book that deals with deep issues in a sensitive and entertaining way.
I think every young adult or adult who is/was an outcast will be able to relate to "Graveyard Gabe," even if your family does not own a funeral home. The story is bittersweet and touches on friendship, embracing who we are, first loves, forgiveness, and death. Somehow this is all put together in a way that hurts at times but is funny and entertaining at others.
I recommend "All the Forever Things" for upper middle graders through adults who are looking for a good young adult novel that is different from the norm.
Language, Sexual Situations, Disturbing Imagery
Tags: adult, always, book, contemporary, fiction, realistic, review, romance, sarah jio
Title: Always
Author: Sarah Jio
Release Date: February 7, 2017
A gripping novel about the kind of love that never lets go, and the heart's capacity to remember, from the New York Times bestselling author of Blackberry Winter and The Violetes of March Enjoying a romantic candlelit dinner with her fianc�, Ryan, at one of Seattle's chicest restaurants, Kailey Crain can't believe her good fortune: She has a great job as a journalist and is now engaged to a guy who is perfect in nearly every way. As she and Ryan leave the restaurant, Kailey spies a thin, bearded homeless man on the sidewalk. She approaches him to offer up her bag of leftovers, and is stunned when their eyes meet, then stricken to her very core: The man is the love of her life, Cade McAllister. When Kailey met Cade ten years ago, their attraction was immediate and intense--everything connected and felt right. But it all ended suddenly, leaving Kailey devastated. Now the poor soul on the street is a faded version of her former beloved: His weathered and weary face is as handsome as Kailey remembers, but his mind has suffered in the intervening years. Over the next few weeks, Kailey helps Cade begin to piece his life together, something she initially keeps from Ryan. As she revisits her long-ago relationship, Kailey realizes that she must decide exactly what--and whom--she wants. Alternating between the past and the present, Always is a beautifully unfolding exploration of a woman faced with an impossible choice, a woman who discovers what she's willing to save and what she will sacrifice for true love. Advance praise for Always "A heartwarming story of personal growth and the power of nostalgia . . . Fans of Elin Hilderbrand and Emily Giffin should enjoy this warm and compassionate novel."--Booklist Praise for Sarah Jio Goodnight June "Sarah Jio's delightful and uplifting novel is guaranteed to melt even the toughest cynic and deserves a top rating of five stars (plus the moon)."--Historical Novels Review "A tribute to family and forgiveness."--Booklist Morning Glory "Jio explores the degree to which time and distance give comfort to those who have experienced loss [with] a depth of feeling in her writing."--Publishers Weekly "Jio has become one of the most-read women in America."--Woman's World Blackberry Winter "Compelling . . . an intoxicating blend of mystery, history, and romance."--Real Simple "Ingenious . . . imaginative."--The Seattle Times
"Always" is a sweet romance of love lost and found. I enjoyed the story but found it lacked the depth of Sarah Jio's previous books. It's still very much worth the read if you're a fan.
Maid of the King's Court
Categories: Historical, Realistic, Reviews
Tags: book, fiction, henry VIII, historical, lucy worsley, maid of the king's court, realistic, review, tudor england, ya, young adult
Title: Maid of the King's Court
Author: Lucy Worsley
Publisher: Candlewick Press
In the vibrant, volatile court of Henry VIII, can even the most willful young woman direct her own fate and follow her heart in a world ruled by powerful men?
Clever, headstrong Elizabeth Rose Camperdowne knows her duty. As the sole heiress to an old but impoverished noble family, Eliza must marry a man of wealth and title — it's the only fate for a girl of her standing. But when a surprising turn of events lands her in the royal court as a maid of honor to Anne of Cleves, Eliza is drawn into the dizzying, dangerous orbit of Henry the Eighth and struggles to distinguish friend from foe. Is her glamorous flirt of a cousin, Katherine Howard, an ally in this deceptive place, or is she Eliza's worst enemy? And then there's Ned Barsby, the king's handsome page, who is entirely unsuitable for Eliza but impossible to ignore. British historian Lucy Worsley provides a vivid, romantic glimpse of the treachery, tragedy, and thrills of life in the Tudor court.
"Maid of the King's Court" is an excellent historical fiction novel about life in the court of King Henry VIII.
While the story of Elizabeth is fictionalized, most of the facts of life at the time are as historically accurate as possible, owing to the fact that the author (Lucy Worsley) is a British historian who actually works at the castle featured in the book. I have always enjoyed reading about life in Tudor England, and this novel did not disappoint. It's also surprisingly clean considering it's about life with King Henry VIII. It does have talk about sexual situations but none involving the main character.
I highly recommend "Maid of the King's Court" to those who like historical fiction with a dash of romance.
Duels & Deception
Tags: book, cindy anstey, duels & deception, fiction, historical, realistic, review, romance, ya, young adult
Title: Duels & Deception
Author: Cindy Anstey
Publisher: Macmillan
In 1800s London, a young heiress and her lawyer are caught up in a kidnapping plot to steal her fortune, but as their investigation delves deeper and their affections for each other grow, Lydia starts to wonder what she truly wants.
I feel like I am the wrong person to review "Duels & Deception." It definitely seems like this is a case of "it isn't the book; it's me." The budding romance featured is cute and the historical elements are fascinating. It's also a very clean book for those looking for one, which is not very easy to find. The flowery prose just seemed to grate on me and kept me from enjoying it. If this seems like the type of book you will enjoy, please give it a try. Don't let my dislike sway you.
Minor Violence, Alcoholic Character
One Italian Summer
Tags: book, contemporary, fiction, keris stainton, one italian summer, realistic, review, romance, ya, young adult
Title: One Italian Summer
Author: Keris Stainton
Publisher: Hot Key Books
'Gentle and romantic. A holiday in itself.' Rainbow Rowell 'I flew through ONE ITALIAN SUMMER. It's a perfect summer read with a gorgeous setting, warm characters and a bittersweet evocation of life after tragedy.' Sophia Bennett, author of LOVE SONG Milly loves her sisters more than anything - they are her best friends. But this holiday is different. The loss of their dad has left a gaping hole in their lives that none of them know how to fill. Heartbreak is a hard thing to fix ...Still, there is plenty to keep the girls busy in Rome. A family wedding. Food, wine, parties and sun. And of course Luke ...Luke is hot, there is no way around that. And Milly will always have a crush on him. But this summer is about family, being together, and learning to live without Dad. It isn't about Luke at all ...is it?
"One Italian Summer" is a light ya romance that reads quickly but lacks much substance.
While there was an attempt at making the characters developed, I still felt somewhat removed from them, especially the love interest, Luke. There was little to no explanation of exactly why Milly was so interested in him, aside from a rather alarming amount of wanting to lick his muscles. Not going to lie, the amount of times a phrase like that was thought by her was a bit unsettling. I know this complaint may be nitpicky, but the author seems to lose track of what her characters were doing quite a bit. Characters would stand up twice in one page without sitting down, be in a car one second and in a parking lot walking to the car the next, etc. It kept pulling me out of the story.
That being said, "One Italian Summer" is still a cute romance if you're looking for a beach read that doesn't require much from you.
Language, Sexual Situations, Alcohol Use
May 19, 2017,
Categories: Contemporary, Diverse Books, Realistic, Reviews
Tags: bang, barry lyga, book, contemporary, diverse characters, fiction, realistic, review, ya, young adult
Title: Bang
Author: Barry Lyga
Publisher: Little, Brown Books for Young Readers
A heartbreaking novel about living with your worst mistake, from New York Times bestselling author Barry Lyga. A chunk of old memory, adrift in a pool of blood. Sebastian Cody did something horrible, something no one--not even Sebastian himself--can forgive. At the age of four, he accidentally shot and killed his infant sister with his father's gun. Now, ten years later, Sebastian has lived with the guilt and horror for his entire life. With his best friend away for the summer, Sebastian has only a new friend--Aneesa--to distract him from his darkest thoughts. But even this relationship cannot blunt the pain of his past. Because Sebastian knows exactly how to rectify his childhood crime and sanctify his past. It took a gun to get him into this. Now he needs a gun to get out. Unflinching and honest, Bang is as true and as relevant as tomorrow's headlines, the story of one boy and one moment in time that cannot be reclaimed.
I really wanted to like "Bang". It seems that I'm in the minority in not feeling it. Unfortunately, the book just did not resonate with me.
It isn't that there is not good writing or that the characters aren't well-developed. Both were good. The problem for me, I believe, is that so many issues were packed into one book that it didn't have time to focus on any of them enough. Gun control, Islamophobia, mental illness of several types, and the income gap are a few of the things covered.
I can't recommend "Bang", but if the blurb sounds good to you, give it a try. Maybe it's just me.
Language, Violence, Hate Speech
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Learn Food Vocabulary in English Through Pictures. Food is any substance consumed to provide nutritional support for an organism. It is usually of plant or animal origin, and contains essential nutrients, such as carbohydrates, fats, proteins, vitamins, or minerals.
Choose the correct word(s) to complete the sentences. You have 5 minutes to complete this test.
Home. At Food & Words we organise food events with a literary bent. This includes the annual writers' festival in Sydney, Food & Words, which is held in We can organise events that involve food and words for you. If you have an idea, give us a call. We're also behind Talking Cookbook, a cooking.
· In September 2010, FEMA updated the incident command system (ics) forms. These forms are intended for use as tools for the creation of the.
food food pyramid fork freezer French fries. fried fritter frosting fruit fry. Words by Theme Index. From Food and Eating Vocabulary to HOME PAGE.
Humans couldn't always easily produce "f" and "v" sounds, according to a surprising new study. The reason we can now enjoy words like "flavour" and "effervescent," say the researchers, has to do with.
English vocabulary with pictures for Food and Drinks. Food is any substance consumed to provide nutritional support for an organism. It is usually of plant or animal origin, and contains essential nutrients, such as carbohydrates, fats, proteins, vitamins, or minerals.
Find ways to describe food, as well as phrases and words for your menu or restaurant reviews. a bounty of food, each bite more delicious than the last. a common dish done uncommonly well. a crispy croquette sits atop a medley of spring vegetables.
This guide to food vocabulary provides different types of food, ways of preparing it, containers and suggestions for learning it for english learners. cooking and shopping for the food to prepare the meal is English is almost as much fun. There are many words you need to learn in order to speak.


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Home Islam: Art and Architecture
Islam: Art and Architecture
Markus Hattstein
Islam, the second largest and the youngest of the major world religions, has changed the world and left its mark on human history since the appearance of the prophet Mohammed in the seventh century. This book follows the historical development of the Islamic dynasties and regions, showing the variety of their forms of artistic expression from the beginning until today. From decorative elements of buildings to calligraphy and the embellishment of everyday objects, ornamentation, that most characteristic Islamic art form, is displayed in an extraordinary rich range of ways. The contributions of important scholars bring to life before our very eyes this culture, which belongs next to Greek and Roman antiquity as one of the pillars of our modern society. Illustrated
Publication Date: 14 Mar 2013
Publisher: Ullmann Publishing
Publication City, Country: Konigswinter, Germany
Dimensions (cm): 31.2(H) x 26.8(L)
Markus Hattstein studied sociology, philosophy and religious studies. He has written various books in the field of architecture, history of art and architecture and lives in Berlin as a freelance author and editor.

redpajama_set_name: RedPajamaCommonCrawl


text:
Yourelo Your Full Service Relocation Corp. v. City of Revere (Bankr. D. Mass.)
Business Law Business Law Insolvency Law Committee Case Updates
The following is a case update written by the Honorable Meredith Jury (United States Bankruptcy Judge, C.D. Cal., Ret.), analyzing a recent decision of interest:
After a thorough review of competing case law on the issue, a bankruptcy court in Massachusetts denied a City's request to apply the reasoning of BFP v Resolution Trust Corporation, 511 U.S. 531 (1994) (holding that the price received at a mortgage foreclosure auction satisfied the requirement for reasonably equivalent value to avoid a fraudulent transfer action) to the Massachusetts property tax strict foreclosure scheme which results in a tax taking, rather than an auction. In doing so, the court concluded that by not excepting tax sales from section 548 of the Bankruptcy Code, Congress displayed a policy choice that reasonably equivalent value must be obtained for a transfer of a debtor's property for the benefit of the unsecured creditors and a state's interest in assuring citizens pay their taxes did not trump that policy. Yourelo Your Full-Service Relocation Corp. v City of Revere (In re Yourelo Your Full-Service Relocation Corp.), 2020 WL 6927549 (Bankr. D. Mass 11/23/20). To view the opinion, click here.
Debtor Yourelo Your Full-Service Relocation Corp. (Debtor) owned real property (the Property) in the City of Revere, Massachusetts (City). In June 2017 the City assessed real estate taxes and related costs against the Property in the sum of $120,564.19. In October 2019 the City obtained a judgment from the Massachusetts Land Court and recorded the judgment with the Registry of Deeds. This recording foreclosed the Debtor's equity of redemption and transferred absolute title to the Property to the City (the Transfer). Soon thereafter the Debtor filed a chapter 11 petition in the bankruptcy court and brought an adversary proceeding against the City, asserting that the transfer was a constructive fraudulent transfer. The complaint alleged that the City had appraised the value of the Property at $684,100.00 and that the fair value of the Property was substantially greater than the amount of the foreclosed tax obligations.
The City filed a motion to dismiss the complaint, asserting that as a matter of law the Transfer could not be a fraudulent transfer because it had conducted a strict foreclosure of a tax lien in compliance with applicable state law, despite the fact that the value of the property significantly exceeded the amount of the tax debt. It argued that the bankruptcy court should adopt the reasoning of the Supreme Court in BFP (as described above) to insulate the City from potential exposure to the avoidance action. It pointed out that a "tax taking" followed by strict foreclosure is the prevailing method used to collect unpaid property taxes in Massachusetts. The Debtor distinguished the facts of BFP from the current circumstance because Massachusetts's strict foreclosure proceeding did not test the value of the Property via an auction or other due process procedure and, unlike a surplus bid in a mortgage foreclosure, the surplus goes to the City rather than the property owner.
The bankruptcy court denied the motion to dismiss and allowed the claim under section 548 for a constructive fraudulent transfer to proceed.
The court recognized that the issue before it – whether a property subject to a prepetition tax sale could be recovered by a bankruptcy estate as a fraudulent transfer – had been widely litigated around the country, with differing results. In allowing the fraudulent transfer action to proceed, it joined the majority of the courts, particularly when the state procedure did not result in a public auction. It compared the due process protections accorded to the property owner in the mortgage foreclosure setting such as happened in BFP to the procedures followed under Massachusetts law. Unlike a mortgage foreclosure which culminates after notice in a public auction, the Massachusetts tax taking required only a showing of default by the property owner after ample notice to cure and then the issuance of a judgment in favor of the City based on that default. Once the City recorded the judgment, the Debtor's interest in the Property was severed and the full value of the Property belonged to the City, creating a windfall in the present case. The court found this difference in the due process rights established by the procedure to make the reasoning of BFP inapplicable.
In reviewing the plethora of cases which came down on both sides of the issue, the court noted that if the tax foreclosure process culminated in an auction, the facts more closely resembled those in BFP and some courts found for the taxing agency, particularly if any surplus inured to the debtor. Plus, a small minority of the cases ruled that so long as the state-mandated foreclosure procedure was strictly followed, the policies supporting the state's interest in collecting its taxes outweighed those protected by the bankruptcy statute. The Massachusetts court rejected that minority view and ruled that the procedural due process protections afforded the taxpayer by the Massachusetts strict foreclosure statute do not immunize the City from the fraudulent conveyance claim. The lack of competitive bidding and exposure to market forces to obtain fair value for the Property made the presumption of "reasonably equivalent value" found in BFP inapposite here.
AUTHOR'S COMMENT
I have followed this issue at the bankruptcy court level closely (few appellate courts have addressed it; the cases seem to settle before appellate review) and agree with the majority view adopted by the Massachusetts court because it balances the ultimate need of the public agency to enforce its tax collection rights while at the same time preserving excess equity established by the property's fair value for the creditors of the estate. The Supreme Court's determination that "fair value" was received in BFP turned on the public exposure to the market and competitive bidding for the property at the auction sale, protections which are glaringly absent in the strict tax taking followed here. That the City followed the state mandated procedure precisely is insufficient due process to justify the "taking" of excess equity from the debtor and therefore its creditors in a bankruptcy.
This case can be very useful to the practitioner who faces this issue, from either side of the bar. The review of the reported cases is extensive, with a thorough collection of cases on both sides of the conflict. Included in that review is an analysis of the different outcomes depending on just how much due process is allotted under any particular state's procedures and how that has affected the ultimate determination of some courts. In addition to the collected cases, the court also cites to a recent law review article – Bartell, Tax Foreclosures as Fraudulent Transfers – Are Auctions Really Necessary, 93 AM BANKR. L.J. 681 (Winter 2019) – which might be worth a read before preparing a brief on this issue.
These materials were authored by the Hon. Meredith Jury (United States Bankruptcy Judge, C.D. Cal., Ret.) a member of the ad hoc group, with editorial contributions by Monique D. Jewett-Brewster, a shareholder-elect with Hopkins & Carley, ALC, a member of the ad hoc group and a past Chair of the CLA Business Law Section. Thomson Reuters holds the copyright to these materials and has permitted the Insolvency Law Committee to reprint them. This material may not be further transmitted without the consent of Thomson Reuters.
« California Advocates for Nursing Home Reform v. Arágon (Jan. 29, 2021, A158035) __ Cal.App.5th __ [2021 WL 321251]
MSY Trading Inc. v. Saleen Automotive, Inc. (Cal. App.) »


If you wish to see what happens when real discipline is used as a principal means to instill the correction of behavioral problems decided upon by BOTH parties in a relationship. This is what you seek.
Scarlet let's face it was naughty. She sought the discipline she recieves on this film. She actually requested that these be filmed. This film contains intense spanking.
1) Getting an 'F' in math put Scarlet's college plans in jeopardy. You will see two punishments including one of the hardest paddlings ever recorded. The next day she recieved an severe strapping for the same offense.
2) Getting a slew of parking tickets and not staying on top of it got Scarlet a long and very intense public spanking filmed in front of a few choice members of a spanking party.
3) Coming in late without calling got her a hard OTK hand spanking, paddling with wooden paddle, and then sent to bedroom for a series on straps and belts.
4) Spanked the next morning this stand up, wet bottomed HARD hand spanking involved her and a certain tattoo.
WARNING: THIS IS AN INTENSE SPANKING FILM. IT FEATURES REAL DISCIPLINARY SPANKINGS.


text:
Q: How to install python3.7-minimal in Docker container debian:stable? The Debian's python3.7-minimal package has some problem in its postinst. When i run:
docker run --name test -it debian

Ok - I can update and upgrade this minimal Debian (or Ubuntu). But the attempt to install python3 always fail.
root@89919f289349:/# apt install python3.7-minimal
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following additional packages will be installed:
  file libexpat1 libmagic-mgc libmagic1 libmpdec2 libpython3.7-minimal libpython3.7-stdlib libreadline7 libsqlite3-0 libssl1.1 mime-support python3.7 readline-common

...

Setting up file (1:5.35-4+deb10u2) ...
Setting up libpython3.7-minimal:amd64 (3.7.3-2+deb10u3) ...
Setting up python3.7-minimal (3.7.3-2+deb10u3) ...
Traceback (most recent call last):
  File "/usr/lib/python3.7/py_compile.py", line 212, in <module>
    sys.exit(main())
  File "/usr/lib/python3.7/py_compile.py", line 204, in main
    compile(filename, doraise=True)
  File "/usr/lib/python3.7/py_compile.py", line 169, in compile
    importlib._bootstrap_external._write_atomic(cfile, bytecode, mode)
  File "<frozen importlib._bootstrap_external>", line 112, in _write_atomic
PermissionError: [Errno 13] Permission denied: '/usr/lib/python3.7/__pycache__/__future__.cpython-37.pyc.139782148114224'
dpkg: error processing package python3.7-minimal (--configure):
 installed python3.7-minimal package post-installation script subprocess returned error exit status 1
Setting up libmpdec2:amd64 (2.4.2-2) ...
Setting up readline-common (7.0-5) ...
Setting up libreadline7:amd64 (7.0-5) ...
dpkg: dependency problems prevent configuration of python3.7:
 python3.7 depends on python3.7-minimal (= 3.7.3-2+deb10u3); however:
  Package python3.7-minimal is not configured yet.

dpkg: error processing package python3.7 (--configure):
 dependency problems - leaving unconfigured
Setting up libpython3.7-stdlib:amd64 (3.7.3-2+deb10u3) ...
Processing triggers for libc-bin (2.28-10) ...
Errors were encountered while processing:
 python3.7-minimal
 python3.7
E: Sub-process /usr/bin/dpkg returned an error code (1)

(The  /usr/lib/python3.7/pycache/ directory is full of previously created files)
Please note: the problem is only on my computer. Installation in the same container in another pc was successfull ... ????
How i can finish python3 installation ?

redpajama_set_name: RedPajamaStackExchange


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Batocnema africanus is een vlinder uit de familie van de pijlstaarten (Sphingidae). De wetenschappelijke naam van de soort werd in 1899 gepubliceerd door William Lucas Distant.

Pijlstaarten

redpajama_set_name: RedPajamaWikipedia


Are you worried about finding the right real estate agent to help you buy or sell your property? Do you have questions about the process of buying or selling a house?
I am focused on providing you with the best results and service in the industry. I listen carefully to understand your real estate goals and work hard to create solutions that make sense for you. Whether you are new to the market or an experienced investor, as a REALTOR® at RE/MAX of Duncan-Mill Bay, I have resources available to me with the expertise and proven track record to help you achieve your real estate goals.
Real estate is about location, location, location. Having lived in the Cowichan Valley for 25 years, I have extensive knowledge of the Duncan area and can help you find the right home or the right buyer for your home.
I am often out of the office looking at new developments, meeting with clients, and touring homes so please call or e-mail me today to set up an appointment and we can discuss your real estate needs. I look forward to working with you!


Reporting to the Chief Scientific Officer, the Senior Director of Assay Development will lead efforts to expand and optimize TARA's suite of assays and engineered tissue models by both internal efforts and the development of external partnerships. Key responsibilities include supervising and mentoring a team of lab-based scientists and collaborating with internal and external stakeholders to design and build novel models.
PhD in cell biology, pharmacology, bioengineering, biochemistry or a related area; relevant postdoctoral experience is preferred.
A minimum of 12 years of relevant industry (i.e. pharma, biotech, CRO) experience in the field of in vitro assay/product development; experience in the cardiometabolic arena is preferred.
Experience managing scientific collaborations with industry and academic peers.
Exceptional people management expertise including supervising, coaching and mentoring of direct reports.
A strong record of publications in high-impact, peer-reviewed journals and presentations at relevant research meetings and trade shows.


We are still needing donations of candy for the egg hunt. Please drop your bags of candy off at the legion by Wednesday. We will be filling the eggs Wednesday night at 6.
This coming Wednesday at 6 pm we will be filling over 2,000 eggs for the Easter Egg hunt on Saturday at 9 am. Open to all followed by a delicious breakfast!
Today we heard of the unthinkable being done to a special needs child in our home town at one of our high schools. One of the pillars of the American Legion is Children and Youth. That's why I created this Gofundme page. We can't change what happened but we can make a difference in his future! No donation is too small!


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And then Harry saw them. Dementors, at least a hundred of them, gliding in a black mass around the lake toward them. He spun around, the familiar, icy cold penetrating his insides, fog starting to obscure his vision; more were appearing out of the darkness on every side; they were encircling them….


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Album Review: Humble Tip – Free Thinking [@HumbleTip]
O'Kendrick Reid 5 years ago 45 Views
Album Review: Humble Tip – Free Thinking
Humble Tip is an artist that I have followed for quite a while. By quite a while I mean since 2009. I have more of his albums than I do of any other artist with the exceptions of Lecrae and Da T.r.u.t.h. Which in my view is not a bad place to be. I have his albums "Our Turn", "S.H.O.C.K", "Brainwashed: The Deluxe Edition, and now "FreeThinking".
So I find myself suitably equipped in giving an honest and through review of his work. Truth Nugget! "Free Thinking" is substantially different from Humble Tips earlier works. He pushes the envelope of his sound and message on this album. This installation of Humble Tip is the best Humble Tip that I have heard thus far. He is never stagnant in his sound, Humble Tip's sound has evolved and has become more formidable than any of his previous audio achievements.
"Free Thinking" is not an album that was put out to just remain current, this album shows that Humble Tip is still hungry and passionate about the Lord and his music. He wastes no time with formalities, there is no intro just a straight dive in to the songs. It is like when Mike Tyson walked to the ring, there was no intro music, no showboating, he went straight to the ring and was ready to commence bombardment. When you click play you are given the old one, two of "Lay It Down." This song is a certified anthem, the violins set the atmosphere, while the horns give a resonance of majestic splendor. The cymbals are a nice touch but are second fiddle to Humble Tip's lyrics and Young Rell's vocals. The whole song is bubbling with the aromatics of greatness. I know the word "aromatic" is often paired with the sense of smell, but that sense has to learn patience and stand in line with the others that I am not using as vigorously. I was so impressed with this song, that I could do a review on it alone. But for the sake of time and this being an album review I must move on. The next song is " Face Low, Cross High" it begins as a clap fest but morphs into this piano keyed spectacle. The drum and trumpet lines feel as though they are stomping into the sound canvas leaving depressions in their wake. The chipmuky chorus line is very catchy and is flush within the parameters of the song. This attention to detail makes Humble Tip's lyrics jump out at you. It is like having 3-D glasses on your eardrums, thus making the lyrical content very vivid.
The title track "Free Thinking" is riddled with sound of a buzzy guitar riff, that is complimented by a rock esque vibe. The track is straight and the lyrical content is pristine, it is a very solid track.
Another track that I really thought was nice is "G-Status." It has that Texas lean sound without the codeine. I guarantee you if D.J. Screw was still alive he would be all over this track. It is awesome without being chopped and screwed, so you know it would sound even better if it was. I like the track a lot. It shows Humble Tip has listened to some of the great underground pioneers and innovators such as D.J. Screw. Another plus is that the content is spot on, if you listen to the track you will know what I mean by that.
The next song I want to highlight is "My Pain" featuring Miss Jay Cole. It is the realist song that I have ever heard. Humble Tips glides his over a grand piano and church organ. It is straight lyrical and with Miss Jay Cole singing her heart out makes the song grab you and suspend you in relevance. This is without a doubt my favorite song from Humble Tip period.
The last song that I want to highlight is " Never Leave You Alone" featuring Drew Miller. This song is Praise and Worship infused with elements of Hip-Hop, which is a great mixture. Drew Miller's vocals adds this aura of worship in which you can feel the anointing flowing from the speakers. It is truly a sincere track, and as always Humble Tip delivers lyrics that make you not only reflect but stick with you. I was repeating his lyrics from the song without even recognizing I was doing it. Now that goes shows how powerful and anointing is on this song. As my Grandaddy used to say "it is hard to put something that is good down." I am definitely taking his advice to heart, because I am not putting this album down. It is permanently going to have a home at the top of my playlist. This album is a must have, and if you do not have it you need to go get it. For real, like time now.Lol. Thanks for reading, Be easy,Stay Blessed
CHECK OUT OUR RECENT INTERVIEW WITH HUMBLE TIP ON SPEAKLIFE RADIO SHOW:
*note: authors reviews do not necessarily reflect the opinions of GuerillaCross.com ownership or affiliates.
album reviewFree ThinkingHumble Tip
Previous Album Review: B-Luv - Growth [@imBLuv]
Next S.O. - Passion and Purity [@sothekid @lampmode]
O'Kendrick Reid
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How does a concept acquire its meaning? How does a learner acquire a concept? Answers are explored through historical review of two social science concepts: tolerance of ambiguity (TA) and educational technology (ET). Each of these concepts accommodates multiple interpretations. Limitations in dominant interpretations of each concept are exposed using three analytic perspectives: theoretical, ecological, and phenomenological. The first concept, TA, originally conceived as a personality trait, acquires additional meaning when re-interpreted as a metacognitive skill. As such, TA refers to an ability to cope with increasing sensitization to novel features of a phenomenon in order to redefine prior conceptual interpretations, contingent on trust and motivation. The second concept, ET, concerns the application of technology for purposes of learning. ET is popularly conflated to mean the application of computer technology; however, less intuitively, technology refers to myriad ideas and processes, including cultural, biological, and metacognitive processes. As a metacognitive strategy for conceptual change, TA can be exploited in ET theory and practice. In particular, securely experiencing the ambiguity that is inherent in a phenomenon (for example, the ambiguity inherent in a concept such as TA or ET) equips learners to overcome the restraints of prior knowledge, toward the cultivation of new knowledge.


Hollywood Boulevard honors media celebrities by putting their name within a star on the sidewalk of Walk of Fame. This star in sidewalk celebration happens almost every month in a ceremony, called "star unveiling ceremony".
When I worked on Hollywood Boluevard. I wittnessed a number of celebrities, including Kevin Costner, Britrney Spears, Nicole Kidman, Celine Dion received their stars right in front of the Dolby theather.
This week, actor, comedian Will Ferrel received his Star Unveiling Ceremony on the Sidewalk of Hollywood Boulevard.
It is really interesting to watch this ceremonies closely. It gives a chance to see celebrities up close in one of their indelible career moments. Their name will be in that star as long as the Hollywood sidewalk exists on Hollywood Boulevard.
Hollywood Rising Star App is making this ceremony imagination in its own photo layers. You can create your own imaginary star memorabilia, when you put your photo one of the Stars of Hollywood Rising Star.
This Photo App – Hollywood Rising Star gives us an immense pleasure when we see our snap on any Hollywood Walk of fame layers, it provide us imaginary celebrity status, and we can create memorabilia, keepsakes etc. This app is available on both Android/Apple platforms.
Enjoy with your Photo App and share your comments with us.


Sandvik offer a range of single, double, and triple deck screening solutions with the versatility to handle virtually every application with the utmost precision. There's often a fine line between what you can sell and what goes to waste. We understand the difference, which is why Sandvik offers a range of mobile screeners that can be matched to your specific needs.
Choose from a variety of mobile screeners designed for optimal performance and flexibility. The patented Sandvik Doublescreen technology utilizes two independent, inline screenboxes. This results in a marked increase in throughput, control and screening efficiency compared to a traditional single box design. There's a robust, durable Sandvik mobile screener for the most specialized screening applications. When a single screen won't suffice, take your pick of two or three deck models that cover the full range of screening challenges.
When uncompromising separation accuracy is a key consideration, Sandvik quality and flexibility are the key to success. Our single-screen units are the ideal answer for recycling applications and contractors. For more complex screening demands, our patented Sandvik Doublescreen system – available in double or triple deck configurations – offers unsurpassed mobile screening capabilities. Uniquely aggressive vibration actions ensure high productivity, and convenient wraparound walkways allow for quick, easy maintenance. The wide range of options available with our mobile screens give you the ability to configure your system to suit a variety of screening applications including aggregates, recycling, and sand and gravel.
As with every Sandvik product, experience, insight and technology set our screening solutions apart from the crowd.


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Gates' Measures of Effective Teaching Study: More Value-Added Madness
Teaching Profession Opinion
By Justin Baeder — December 21, 2010 5 min read
Justin Baeder
@eduleadership
The Measures of Effective Teaching project, funded to the tune of $45 million by the Gates Foundation, has released its first of four reports. While the report is full of intelligent insights, it makes a number of astounding logical leaps to justify the use of value-added teacher ratings, and I can already see how the study will be used to make the case for sloppy valued-added teacher evaluation systems.
This is an ambitious study, and a very well-designed one at that. I can't imagine a better-funded or better-designed study of teacher effectiveness measures; top-notch researchers and the use of five different measures will doubtless make this one of the stronger studies of its type. However, one of its fundamental premises is deeply flawed, and this affects the conclusions drawn throughout the report:
Second, any additional components of the evaluation (e.g., classroom observations, student feedback) should be demonstrably related to student achievement gains. p. 5
This assumption would make sense if "student achievement gains" were as legitimate and stable a construct as the study asserts. Certainly it makes sense to evaluate teachers based on how well they improve student learning, but the assumption that we can isolate teacher effects from all of the other influences on student test performance has not been borne out by research to date on value-added measurement (VAM), including the research done in the MET study itself.
In fact, every indication is that it will continue to remain impossible to isolate teacher effects from such other influences as:
Nonrandom assignment of students to teachers, which can happen due to purposeful assignment of struggling students to stronger teachers, or due to unintentional scheduling oddities (for example, if Advanced Band is offered when I teach Algebra II, I'm going to get non-band students in my Algebra II class, who may be different in significant ways from band students)
Other teachers who serve the same students, e.g. special education, gifted & talented, academic support, or other subject-area teachers whose effects may spill over into other classes
Class composition, which every teacher will tell you varies from year to year despite attempts to "balance" classes. While it's the teacher's job to create an environment conducive to learning, students do play an important role in determining the culture of a class, which can have a significant impact on learning
Despite attempts to control for such extraneous variables in value-added measurement, there is strong empirical evidence that "student achievement gains" are not stable from year to year—nor as the MET report notes, even between different sections of the same subject taught at the same time by the same teacher. As this EPI briefing paper notes,
there is broad agreement among statisticians, psychometricians, and economists that student test scores alone are not sufficiently reliable and valid indicators of teacher effectiveness to be used in high-stakes personnel decisions, even when the most sophisticated statistical applications such as value-added modeling are employed.
Specifically,
One study found that across five large urban districts, among teachers who were ranked in the top 20% of effectiveness in the first year, fewer than a third were in that top group the next year, and another third moved all the way down to the bottom 40%. Another found that teachers' effectiveness ratings in one year could only predict from 4% to 16% of the variation in such ratings in the following year. Thus, a teacher who appears to be very ineffective in one year might have a dramatically different result the following year. The same dramatic fluctuations were found for teachers ranked at the bottom in the first year of analysis. This runs counter to most people's notions that the true quality of a teacher is likely to change very little over time and raises questions about whether what is measured is largely a "teacher effect" or the effect of a wide variety of other factors.
These cited studies are not the final word, of course, so it would be reasonable for the MET study to try to improve value-added measurements in order to try to obtain more stable year-to-year ratings.
However, that does not appear to be part of the design; instead, first-year value-added scores will be treated as the "truth" against which all other measures of teacher effectiveness will be judged. But how good is this "truth"?
Let's see what the MET study found about the stability of its own value-added measures. Two types of data were available: comparisons between different sections of the same subject taught by the same teacher in the same year, and comparisons between the same class taught by the same teacher in two different years. The report states that
When the between-section or between-year correlation in teacher value-added is below .5, the implication is that more than half of the observed variation is due to transitory effects rather than stable differences between teachers. That is the case for all of the measures of value-added we calculated. We observed the highest correlations in teacher value-added on the state math tests, with a between-section correlation of .38 and a between-year correlation of .40. The correlation in value-added on the open-ended version of the Stanford 9 was comparable, .35. However, the correlation in teacher value-added on the state ELA test was considerably lower--.18 between sections and .20 between years.
In other words, the value-added score for one math class only has a 40% correlation with the same teacher's score for another class, whether taught at the same time or in a different year. For ELA, the correlation is only about 20%.
You'd think that the researchers would at this point give up on value-added and start looking for more reliable measures. Instead, we're treated to a full paragraph of logical gymnastics and implication-avoidance (emphasis mine):
Does this mean that there are no persistent differences between teachers? Not at all. The correlations merely report the proportion of the variance that is due to persistent differences between teachers. Given that the total (unadjusted) variance in teacher value-added is quite large, the implied variance associated with persistent differences between teachers also turns out to be large, despite the low between-year and between-section correlations. For instance, the implied variance in the stable component of teacher value-added on the state math test is .020 using the between-section data and .016 using the between-year data. Recall that the value- added measures are all reported in terms of standard deviations in student achievement at the student level. Assuming that the distribution of teacher effects is "bell-shaped" (that is, a normal distribution), this means that if one could accurately identify the subset of teachers with value-added in the top quartile, they would raise achievement for the average student in their class by .18 standard deviations relative to those assigned to the median teacher. Similarly, the worst quarter of teachers would lower achievement by .18 standard deviations. So the difference in average student achievement between having a top or bottom quartile teacher would be .36 standard deviations. That is far more than one-third of the black-white achievement gap in 4th and 8th grade as measured by the National Assessment of Educational Progress--closed in a single year!
So we've gone from "these results are highly unstable" to "we can eliminate the achievement gap in one year!" in the space of a single paragraph. Please leave a comment if I'm misinterpreting this part of the study, but it seems to me that if your measure is only a 20% predictor of itself, you don't have a meaningful measure at all. It's certainly true that some teachers are much, much better than others, but forgive me if I'm hesitant to trust a measure that is potentially wrong 80% of the time.
Earlier, the authors describe their plan for handling this risk: simply give VAM less weight by
scaling down (or up) the value-added measures themselves. But that's largely a matter of determining how much weight should be attached to value-added as one of multiple measures of teacher effectiveness. p. 4
Let me get this straight: If I choose to evaluate you on the basis of a coin toss, which is totally random, I know I'll be wrong 50% of the time. Therefore, the coin toss is a valid evaluation tool provided that it only counts for 50% of your overall evaluation.
Please tell me I'm reading this wrong—my background in statistics barely qualifies as graduate-level, and I'm certainly not a VAM expert. But I think I'm interpreting the authors' argument correctly.
Interestingly, student ratings are much more stable between classes and from year to year—their correlation is on the order of 67%. If anything, this first MET report provides good evidence that simply asking students about their teachers is a much better idea than going through both statistical and logical gymnastics to obtain a VAM score.
In its closing section, the report argues that VAM is useful even though its predictive power is incredibly weak. Now, if you wanted to report the utter unreliability of VAM as good news, how would you do it? The authors take this tack:
Two types of evidence—student achievement gains and student feedback—do seem to point in the same direction, with teachers performing better on one measure tending to perform better on the other measures. p. 31
In other words, the correlations between VAM and other forms of assessment are ridiculously weak, but hey, at least they're not negative. The report goes on to say that
many people simply forget all the bad decisions being made now, when there is essentially no evidence base available by which to judge performance. Every day, effective teachers are being treated as if they were the same as ineffective teachers and ineffective teachers are automatically granted tenure after two or three years on the job. Given that we know there are large differences in teacher effects on children, we are effectively mis-categorizing everyone when we treat everyone the same. Value-added data adds information. Better information will lead to fewer mistakes, not more. Better information will also allow schools to make decisions which will lead to higher student achievement.
Wow. Notice the careful wording: "Value-added data adds information. Better information..." Does it say that value-added data is better information? No, because clearly it's not. If and when we're able to obtain better information (e.g. from student ratings or more rigorous observation methods), we should certainly incorporate it into teacher evaluations. But for now, VAM doesn't give us anything useful—just a contextless number accompanied by a false sense of certainty.
In the end, what does this report tell us? Let's look at the problem the study is intended to solve: More than 99% of teachers are rated "satisfactory" every year, which should seem incredible to even the most ardent supporter of teachers. There is no doubt that principals, myself included, need to do a far better job of identifying underperforming teachers and helping them to improve (or, if that doesn't work, to exit the profession). I look forward to reading the forthcoming MET reports that tell us more about effective observations; Gates has convened some of the best minds in our country to tackle the issue. I can only hope that the effectiveness of rigorous classroom observations is not judged against the shoddy "truth" of value-added measurements.
Teacher Evaluations
The opinions expressed in On Performance are strictly those of the author(s) and do not reflect the opinions or endorsement of Editorial Projects in Education, or any of its publications.
From left to right: Whitney Aragaki, Autumn Rivera, Kurt Russell, and Joseph Welch
Teaching Profession Meet the 4 Finalists for the 2022 National Teacher of the Year
Madeline Will, January 19, 2022
Teaching Profession Sponsor Has your savings strategy changed with the times?
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The Creche Koalabird is always staring into mirrors, which leads to its reputation for vanity. But our zoologists have discovered another reason for its behavior: It is watching for space ghosts.
Each square in the Vampire, Ghost, and Zombie grids will be filled with either a letter or a diagonal mirror that's reflective on both sides. Place these letters and mirrors such that the answers to each clue or string of clues will follow a path that starts at the appropriate white letter on a black background, travels straight into the grid, bounces off each mirror it encounters (making a 90 degree turn in the proper direction), and eventually exits at the corresponding black letter on a gray background. Each square, whether it contains a letter or a mirror, will be used exactly twice.
A. 1-800-Cash-Call's is 99.25%: Abbr.
I. Slices of a pizza that's been cut four times, e.g.
J. Poi ingredient; What a gin player can take: 2 wds.
K. A source of lemons: 2 wds.
L. How some pharmaceuticals are obtained: Abbr.
N. Mash into pulp; Smooth transition; Do a lot of damage to; Part of a race; Net addresses: Abbr.
N. Himmler commanded it: Abbr.
P. First murder victim; Fertile soil; Mon's successor: Abbr.; Controversial relief org.: Abbr.
B. It's far from land: 2 wds.
C. Video game company: Abbr.
F. Happen again; Caesar's accusation: 2 wds.
Transcribe the mirrors from the other grids into this grid.
Every square that does not have a mirror will contain a Vampire, Ghost, or Zombie.
There are an equal number of each type of monster.
True to legend, Vampires cannot be seen in mirrors, and can only be seen head-on.
Ghosts cannot be seen head-on, and can only be seen in mirrors.
Zombies can always be seen.
The three shaded spaces contain the same type of monster.
No two monsters of the same type are orthogonally adjacent.
Once all the mirrors have been placed, the grid will contain two infinite loops (paths that neither enter nor exit the grid, but bounce around endlessly between mirrors). One contains two Vampires; the other contains a Vampire, a Ghost, and two Zombies.


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Airbnb stock trails Expedia in 2021, here's why
Airbnb received a rare double upgrade to a buy rating from Gordon Haskett this week. The firm sees improving trends, particularly in Europe, as a boon for the vacation-rental stock.
But Airbnb has languished this year in comparison to fast growing challenger Expedia, which owns competitor VRBO. Airbnb stock has fallen 2% in 2021, while Expedia is up 22%.
Airbnb's stock may have been a victim of a rotation away from high-priced growth stocks, according to Gina Sanchez, chief market strategist at Lido Advisors and CEO of Chantico Global.
"It just faced the mother of all stress tests, and it is offering growth, and therefore isn't necessarily value," Sanchez told CNBC's "Trading Nation" on Tuesday. "The trade for the first half of this year was growth at a reasonable price. That's what Expedia promised."
Now, Sanchez sees a move back toward bets on high growth stocks like Airbnb where higher valuations are tolerated for the prospect of future earnings.
"The trade for the second half of the year is growth, and that's really what Airbnb is setting itself up for. And so if you're looking forward rather than back, you're looking at opportunities to provide significant growth, and that's really where you have to look at Airbnb," said Sanchez.
Airbnb is not expected to post a full-year profit until 2022. Expedia, by comparison, is forecast to have rebounded back into the black this year after last year's steep loss.
Todd Gordon, founder of TradingAnalysis.com, sits on the other side of the trade. He's backing Expedia.
"I believe that the technical position of Airbnb is struggling, trying to hold that $145 IPO price from back in December, while Expedia is moving nicely higher. Expedia, if it can break above $160, that looks really, really good," Gordon said during the same interview.
Zoom In IconArrows pointing outwards
Airbnb closed Tuesday at $143.41 a share and Expedia closed at $162.02.


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The Lathe of Time
This greatly enlarged, and admittedly poor quality photograph is of a soapstone reliquary, thought to have been crafted in the fifth century BCE.
If you examine this carefully, you see that it was fashioned on some sort of lathe. Below, are other reliquaries of the type, including another view of the one above. If these were not turned on a lathe, then I do not know how else they could have been manufactured. These are solid soapstone: not "thrown" pottery. Since the earliest known illustration of a lathe, from Egypt, dates to 300 BCE, these items from 500 BCE push the lathe's invention back at least two centuries. Nicely done, are they not?
The reliquary in our first photograph, above, was discovered in January 1898 by a man named W.C. Peppe. Mr. Peppe was manager of the Birdpur Estate, in northeastern Basti District, Upper Pradesh, India. The reliquary was found inside a ruined stupa, near Piprahwa, which was a small village on this estate.
Ruined stupa at Priprahwa where reliquary discovered
Although the matter is not without controversy -- some suspect a British plot -- it is generally agreed that this reliquary held the bone relics of Shakyamuni Buddha. The following year (1899) these bone relics were presented by the (British) Government of India to King Chulalongkorn of Siam, who in turn presented portions to the Sanghas of Burma and Ceylon.
The classic bit of scholarship on Buddha's relics is "Asoka and the Buddha Relics," by T.W. Rhys Davids, Journal of the Royal Asiatic Society, 1901. He begins:
Our oldest authority, the Maha-parinibbana suttanta, which can be dated approximately in the fifth century B.C., states that after the cremation of the Buddha's body at Kusinara, the fragments that remained were divided into eight portions. These eight portions were allotted as follows:--
1. To Ajatasattu, king of Magadha.
2. To the Licchavis of Vesali.
3. To the Sakyas of Kapilavastu.
4. To the Bulis of Allakappa.
5. To the Koliyas of Ramagama.
6. To the brahmin of Vethadipa.
7. To the Mallas of Pava.
8. To the Mallas of Kusinara.
So, somebody in Kusinara went to the stone turner, acquired eight soapstone reliquaries, and divided up Buddha's bones. When all was said and done -- when breath came no more, when the fire finished its work -- the last stop was the stone turner's art. Stands to reason. Because of their metallurgical expertise, the ancient Indians were able to produce cutting tools that helped them become the finest stone sculptors the work has ever known. If you look at Indian temples, monuments, pillars, statues, and so forth, you will come to agree.
We are only awake in this human form a very short time. We have only a few potentially productive years, and then we pass away to take up some other form, some other potential. We try to cooperate with each other to achieve things, but no matter how durable these things may seem -- iron or stone -- they are all subject to decay.
Thus, we are all on the lathe of time. We are constantly spinning, and the material of life is constantly removed. Once, Shakyamuni walked the earth; next, there were bits of bone and ash in a crafted urn, buried beneath a mound.
What do you suppose Longchenpa might say?
There are many shortcomings to what has been constructed and has no substance;
Think about samsara as also being of this nature.
Once you have thus deeply felt and understood that all the sundry manifestations of an external world
Are similar to a dream or a phantasmic play,
Let everything go into the vibrant dimension of space,
Being's consistency with itself and everything else.
Now the urn is broken, the mound disturbed and weathering away. What a magical show! Men argue with each other, asking, "Is it real?"
Do not engage in affirmation or negation; dismiss your ruminations;
By going about your daily life in this manner, you will be able to take everything in stride;
Pure experience that is not something that comes into existence and goes out of existence,
But is intrinsically genuine, will come to the fore.
The lathe of time does not stop spinning for buddhas, for artisans, for foolish people like me, or thoughtful people like you.
I experienced a very deep sense of peace when I venerated those relics now enshrined in Wat Saket Ratcha Wora Maha Wihan (a.k.a. Wat Saket), a Buddhist temple (Wat) in Pom Prap Sattru Phai district, Bangkok, Thailand.
Thursday, May 20, 2010 at 7:31:00 AM GMT+8
Great blog. Great artifacts.
Thank you for an uplifting read.
Friday, May 21, 2010 at 10:34:00 PM GMT+8
Buddhist Relic Tour
http://www.maitreyaproject.org/en/relic/index.html
Weekly Tibetan Astrology: May 31 - June 6, 2010
Nyungne In Taiwan
Tibetan Roulette
Travel Season
Bhutan Boneyard Brouhaha
Free, Free, Set Them Free
The Excellent One
Only Ourselves to Blame
The Meditation Lesson
Weekly Tibetan Astrology: May 24 - May 30, 2010
The Chariot of Joy and Good Fortune
Does Samsara Really Need Janitors?
Desert Tidbits: Rattlesnake Rodeo
Twenty-Six Months
Sickest Buddhist, Redux
Unseen Dharamsala
Terbum: Tibetan Earth Treasure Vases
The Law of Cause and Effect Needs No Enforcement
Weekly Tibetan Astrology: May 3 - May 9, 2010


text:
Luke will be conducting a talk on "How to pass the SIA cabin crew interview" on 13 Feb Thursday 2020. Please visit www.ourcabincrew.com for details
IFM to work till 63
Effective this year, the IFM (Inflight Managers) are allowed to work till 63. Previously they retired at age 62. Congrats! 👍
PPS John said...
Be seeing and served by old, bald headed,fat,haggard looking and grouchy old farts :(
It is good to have older and more experienced staff on the flights.
The trick is to make people work longer so more cpf for the government to invest and lose them. After that the people will be forced to work till they drop dead and never enjoy their cpf monies.
Retiring at 63 means legs weak, eyes unfocused,teeth failing, mind stuck in certain modes. Lots of money but no physical stamina to even enjoy a nice tall drink by the poolside.
Silly people. Work & work.
Fyi IFM dont work. Klkk cbl and act busy and take 8k a mth. These pests are leeches to companys profits as are the rest of the crew.
They should be offloaded at 55 to work as hawker centre cleaners as they have a wealth of experience clearing plates and table.
Enough is enough... does not mean working longer the management will be
more forgiving. Still exposed to all the shit... and nail biting, borderline issues.
Roster issues, female proximity issues.
Leave with dignity and grace. Heads up.But yeow kuei will stay beond 100 yr old.
Hello PPS John,when you have a heart attack(hopefully you won't)who do you think will try to save your life? The old fart or the sweet young thing? Sweet young thing(male n female) will disappear in another zone and act busy(majority of the time,when announcement is made,to page for medical help).
CSS who left said...
But this don apply to female crew who are "forced to retire" at 50s - mid life crisis > menopausal, no job, no husband, no kids... that is so sad. I don understand why this is not apply for both Male n female. Discrimination BIG TIME
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Boh Tong was a Cabin Crew Executive (CCE) with SIA before his retirement in 2003. He rose from the rank of Flight Steward to CCE, a career spanning 35 years (1968 - 2003).
Boh is the author of the book "Fasten Your Seat Belts". He now spend his time blogging and helping wannabes ace the cabin crew interviews.
Union election 2019
Total no. of votes cast from Monday 2 Sep
to Tuesday 10 Sep is 3,342 (57.6% turnout rate).
No. of crew eligible to vote: about 5,800
The blogger (Boh Tong) should not be held responsible for the accuracy of the stories and contents published.
Boh Tong
Copyright Boh Tong 2019. . Simple theme. Powered by Blogger.


text:
\section{Introduction}

Let $X_{i},i=1,...,n,$ be compact (Hausdorff) topological spaces. Consider the
approximation to a continuous function $f$ on $X=X_{1}\times
\cdots \times X_{n}$ from the manifold

\begin{equation*}
M=\left\{ \sum_{i=1}^{n}g_{i}(x_{i}):g_{i}\in C(X_{i}),~~i=1,...,n\right\} .
\end{equation*}%
The approximation error is defined as the distance from $f$ to $M$:

\begin{equation*}
E(f)\overset{def}{=}dist(f,M)=\underset{g\in M}{\inf }\left\Vert
f-g\right\Vert _{C(X)}.
\end{equation*}

The well-known duality relation says that

\begin{equation*}
E(f)=\underset{\left\Vert \mu \right\Vert \leq 1}{\underset{\mu \in M^{\bot }%
}{\sup }}\left\vert \int\limits_{X}fd\mu \right\vert ,\eqno(1.1)
\end{equation*}%
where $M^{\bot }$ is the space of regular Borel measures
annihilating all functions in $M$ and $\left\Vert \mu \right\Vert$
stands for the total variation of a measure $\mu $. It should be
also noted that the $\sup $ in
(1.1) is attained by some measure $\mu ^{\ast }$ with the total variation $%
\left\Vert \mu ^{\ast }\right\Vert =1.$ We are interested in the problem: is
it possible to replace in (1.1) the class $M^{\bot }$ by some subclass of it
consisting of measures of simple structure? For the case $n=2,$ this problem
was first considered by Diliberto and Straus [4]. They showed that the
measures induced by so-called "closed lightning bolts" are sufficient for
the equality (1.1).

Let $X=X_{1}\times X_{2}$ and $\pi _{i}$ be the projections of $X$
onto $X_{i},$ $i=1,2.$ A lightning bolt (or, simply, a bolt) is a
finite ordered set $\{a_{1},...,a_{k}\}$ contained in $X$, such
that $a_{i}\neq a_{i+1}$, for $i=1,2,...,k-1$, and either $\pi
_{1}(a_{1})=\pi _{1}(a_{2}),$ $\pi _{2}(a_{2})=\pi _{2}(a_{3})$,
$\pi _{1}(a_{3})=\pi _{1}(a_{4}),...,$ or $\pi _{2}(a_{1})=\pi
_{2}(a_{2}),$ $\pi _{1}(a_{2})=\pi _{1}(a_{3})$, $\pi
_{2}(a_{3})=\pi _{2}(a_{4}),...$ A bolt $\{a_{1},...,a_{k}\}$ is
said to be closed if $k$ is an even number and the set
$\{a_{2},...,a_{k},a_{1}\}$ is also a bolt. These objects have
been exploited in a great deal of works devoted to the uniform
approximation of bivariate functions by univariate functions or the related problems,
though sometimes they appeared under the different names (see,
e.g., [2-7,9-11,13-16,18]). In [4], they were called "permissible lines".
The term "lightning bolt" is due to Arnold [1].

Let $l=\{a_{1},...,a_{2k}\}$ be a closed bolt. Consider a measure $\mu _{l}$
having atoms $\pm \frac{1}{2k}$ with alternating signs at the vertices of $l$. That is,

\begin{equation*}
\mu _{l}=\frac{1}{2k}\sum_{i=1}^{2k}(-1)^{i-1}\delta _{a_{i}}\text{ \ or \ }%
\mu _{l}=\frac{1}{2k}\sum_{i=1}^{2k}(-1)^{i}\delta _{a_{i}},
\end{equation*}%
where $\delta _{a_{i}}$ is a point mass at $a_{i}.$ It is clear that $\mu
_{l}\in M^{\bot }$ and $\left\Vert \mu _{l}\right\Vert \leq 1$. $\left\Vert
\mu _{l}\right\Vert =1$ if and only if the set of vertices of the bolt $l$
having even indices does not intersect with that having odd indices. The
following duality relation was first established by Diliberto and Straus [4]

\begin{equation*}
E(f)=\underset{l\subset X}{\sup }\left\vert \int\limits_{X}fd\mu
_{l}\right\vert ,\eqno(1.2)
\end{equation*}%
where $X=X_{1}\times X_{2}$ and the $\sup $ is taken over all closed bolts
of $X$. In fact, Diliberto and Straus obtained the formula (1.2) for the
case when $X$ is a rectangle in $\mathbb{R}^{2}$ with sides parallel to the
coordinate axis. The same result was independently proved by Smolyak (see
[18]). Yet another proof of (1.2), in the case when $X$ is a Cartesian
product of two compact Hausdorff spaces, was given by Light and Cheney
[14]. For $X$'s other than a rectangle in $\mathbb{R}^{2}$, the theorem
under some additional assumptions appeared in the works [9,11,15]. But we
shall not discuss these works here.

Golomb's paper [8] made a start of a systematic study of approximation of
multivariate functions by various compositions, including sums of univariate
functions. Golomb generalized the notion of a closed bolt to $n$-dimensional
case and obtained the analogue of formula (1.2) for the error of
approximation from the manifold $M$. The objects introduced in [8] were
called "projection cycles" and they are simply sets of the form

\begin{equation*}
p=\{b_{1},...,b_{k};~c_{1},...,c_{k}\}\subset X,\eqno(1.3)
\end{equation*}
with the property that $b_{i}\neq c_{j}$, $i,j=1,...,k$ and for all $\nu
=1,...,n,$ the group of the $\nu $-th coordinates of $c_{1},...,c_{k}$ is a
permutation of that of the $\nu $-th coordinates of $b_{1},...,b_{k}.$ Some
points in the $b$-part $\left( b_{1},...,b_{k}\right) $ or $c$-part $\left(
c_{1},...,c_{k}\right) $ of $p$ may coincide. The measure associated with $p$
is

\begin{equation*}
\mu _{p}=\frac{1}{2k}\left( \sum_{i=1}^{k}\delta
_{b_{i}}-\sum_{i=1}^{k}\delta _{c_{i}}\right).
\end{equation*}

It is clear that $\mu _{p}\in M^{\bot }$ and $\left\Vert \mu _{p}\right\Vert
=1.$ Besides, if $n=2,$ then a projection cycle is the union of closed bolts
after some suitable ordering of its points. Golomb's result states that

\begin{equation*}
E(f)=\underset{p\subset X}{\sup }\left\vert \int\limits_{X}fd\mu
_{p}\right\vert ,\eqno(1.4)
\end{equation*}%
where $X=X_{1}\times \cdots \times X_{n}$ and the $\sup $ is taken
over all projection cycles of $X$. It can be proved that in the
case $n=2,$ the formulas (1.2) and (1.4) are equivalent.
Unfortunately, the proof of (1.4) had a gap, which was many years
later pointed out by Marshall and O'Farrell [15]. But the problem if the formula (1.4) was correct, remained unsolved (see also the more recent monograph by Khavinson [11]).

In Section 2, we will construct families of normalized measures (that is,
measures with the total variation equal to $1$) on projection cycles. Each
measure $\mu _{p}$ defined above will be a member of some family. We will also consider minimal projection cycles and
measures constructed on them. By properties of these measures, we
show that Golomb's formula (1.4) is valid and even in a stronger form.

\bigskip

\section{Measures supported on projection cycles}

First we are going to give an equivalent definition of a projection cycle.
This will be useful in constructing of measures of simple structure and with
the capability to approximate an arbitrary measure in $M^{\bot }$.

In the sequel, $\chi _{a}$ will denote the characteristic function of a
single point set $\{a\}\subset \mathbb{R}$.

\bigskip

\textbf{Definition 2.1.} \textit{Let $X=X_{1}\times \cdots \times
X_{n}$ and $\pi _{i}$ be the projections of $X$ onto the sets $%
X_{i},$ $i=1,...,n.$ We say that a set $p=\{x_{1},...,x_{m}\}\subset X$ is a
projection cycle if there exists a vector $\lambda =(\lambda
_{1},...,\lambda _{m})$ with the nonzero real coordinates such that}

\begin{equation*}
\sum_{j=1}^{m}\lambda _{j}\chi _{\pi _{i}(x_{j})}=0,\text{ \ }i=1,...,n.\eqno%
(2.1)
\end{equation*}

\bigskip

Let us give some explanatory notes concerning Definition 2.1. Fix for a
while the subscript $i.$ Let the set $\{\pi _{i}(x_{j})$, $j=1,...,m\}$ have $%
s_{i}$ different values, which we denote by $\gamma _{1}^{i},\gamma
_{2}^{i},...,\gamma _{s_{i}}^{i}.$ Then (2.1) implies that

\begin{equation*}
\sum_{j}\lambda _{j}=0,
\end{equation*}%
where the sum is taken over all $j$ such that $\pi _{i}(x_{j})=\gamma
_{k}^{i},$ $k=1,...,s_{i}.$ Thus for the fixed $i$, we have $s_{i}$
homogeneous linear equations in $\lambda _{1},...,\lambda _{m}.$ The
coefficients of these equations are the integers $0$ and $1.$ By varying $i$%
, we obtain $s=\sum_{i=1}^{n}s_{i}$ such equations. Hence (2.1), in its
expanded form, stands for the system of these equations. One can observe
that if this system has a solution $(\lambda _{1},...,\lambda _{m})$ with
the nonzero real components $\lambda _{i},$ then it also has a solution $%
(n_{1},...,n_{m})$ with the nonzero integer components $n_{i},$
$i=1,...,m.$ This means that in Definition 2.1, we can replace the
vector $\lambda $ by the vector $n=(n_{1},...,n_{m})\,$, where
$n_{i}\in \mathbb{Z}\backslash \{0\},$ $i=1,...,m.$ Thus, Definition 2.1 is equivalent to the following definition.

\bigskip

\textbf{Definition 2.2.} \textit{A set
$p=\{x_{1},...,x_{m}\}\subset X$ is called a projection cycle if there exist nonzero
integers $n_{1},...,n_{m}$ such that}

\begin{equation*}
\sum_{j=1}^{m}n_{j}\chi _{\pi _{i}(x_{j})}=0,\text{ \ }i=1,...,n.\eqno(2.2)
\end{equation*}

\bigskip

\textbf{Proposition 2.3.} \textit{Definition 2.2 is equivalent to Golomb's definition of a projection cycle.}

\begin{proof} Let $p=\{x_{1},...,x_{m}\}$ be a projection cycle with respect to Definition 2.2.
By $b$ and $c$ denote the set of all points $x_{i}$ such that the integers $%
n_{i}$ associated with them in (2.2) are positive and negative
correspondingly. Write out each point $x_{i}$ $n_{i}$ times if $n_{i}>0$ and
$-n_{i}$ times if $n_{i}<0.$ Then the set $\{b;c\}$ is a projection cycle
with respect to Golomb's definition (see Introduction). The inverse is also
true. Let a set $p_{1}=\{b_{1},...,b_{k};~c_{1},...,c_{k}\}$ be a projection
cycle with respect to Golomb's definition. Here, some points $b_{i}$ or $%
c_{i}$ may be repeated. Let $p=\{x_{1},...,x_{m}\}$ stand for the set $p_{1}$%
, but with no repetition of its points. Let $n_{i}$ show how many
times $x_{i}$ appear in $p_{1}.$ We take $n_{i}$ positive if
$x_{i}$ appears in
the $b$-part of $p_{1}$ and negative if it appears in the $c$-part of $%
p_{1}. $ Clearly, the set $\{x_{1},...,x_{m}\}$ is a projection cycle with
respect to Definition 2.2, since the integers $n_{i},$ $i=1,...,m,$ satisfy
Eq. (2.2).
\end{proof}

In the sequel, we will use Definition 2.1. A pair $\left\langle p,\lambda
\right\rangle ,$ where $p$ is a projection cycle in $X$ and $\lambda $ is a
vector associated with $p$ by (2.1), will be called a "projection
cycle-vector pair" of $X.$ To each such pair $\left\langle p,\lambda
\right\rangle $ with $p=\{x_{1},...,x_{m}\}$ and $\lambda =(\lambda
_{1},...,\lambda _{m})$, we correspond the measure

\begin{equation*}
\mu _{p,\lambda }=\frac{1}{\sum_{j=1}^{m}\left\vert \lambda _{j}\right\vert }%
\sum_{j=1}^{m}\lambda _{j}\delta _{x_{j}}.\eqno(2.3)
\end{equation*}

Clearly, $\mu _{p,\lambda }\in M^{\bot }$ and $\left\Vert \mu _{p,\lambda
}\right\Vert =1$. We will also deal with measures supported on some certain subsets of projection cycles called minimal projection cycles. A projection cycle is said to be minimal if it does not contain any projection
cycle as its proper subset. For example, the set $p=%
\{(0,0,0),~(0,0,1),~(0,1,0),~(1,0,0),~(1,1,1)\}$ is a minimal projection
cycle in $\mathbb{R}^{3},$ since the vector $\lambda =(2,-1,-1,-1,1)$
satisfies Eq. (2.1) and there is no such vector for any other subset of $p$.
Adding one point $(0,1,1)$ from the right to $p$, we will also have a
projection cycle, but not minimal. Note that in this case, $\lambda $ can be
taken as $(3,-1,-1,-2,2,-1).$

\bigskip

\textbf{Remark 1.} A minimal projection cycle under the name of a "loop" was introduced in
the work of Klopotowski, Nadkarni, Rao [12].

\bigskip

To prove our main result we need some auxiliary facts.

\bigskip

\textbf{Lemma 2.4.} (1)\textit{\ The vector $\lambda =(\lambda
_{1},...,\lambda _{m})$ associated with a minimal projection cycle $%
p=(x_{1},...,x_{m})$ is unique up to multiplication by a constant.}

(2)\textit{\ If in (1), $\sum_{j=1}^{m}\left\vert \lambda _{j}\right\vert =1,
$ then all the numbers $\lambda _{j}$, $j=1,...,m,$ are rational.}

\begin{proof} Let $\lambda ^{1}=(\lambda _{1}^{1},...,\lambda
_{m}^{1})$ and $\lambda ^{2}=(\lambda _{1}^{2},...,\lambda
_{m}^{2})$ be any two vectors associated with $p.$ That is,

\begin{equation*}
\sum_{j=1}^{m}\lambda _{j}^{1}\chi _{\pi _{i}(x_{j})}=0\text{ and }%
\sum_{j=1}^{m}\lambda _{j}^{2}\chi _{\pi _{i}(x_{j})}=0,\text{ \ }i=1,...,n.
\end{equation*}%
After multiplying the second equality by $c=\frac{\lambda _{1}^{1}}{\lambda
_{1}^{2}}$ and subtracting from the first, we obtain that

\begin{equation*}
\sum_{j=2}^{m}(\lambda _{j}^{1}-c\lambda _{j}^{2})\chi _{\pi _{i}(x_{j})}=0%
\text{, \ }i=1,...,n.
\end{equation*}%
Now since the cycle $p$ is minimal, $\lambda _{j}^{1}=c\lambda _{j}^{2},$
for all $j=1,...,m.$

The second part of the proposition is a consequence of the first
part. Indeed, let $n=(n_{1},...,n_{m})$ be a vector with the
nonzero integer coordinates associated with $p.$ Then the vector
$\lambda ^{^{\prime
}}=(\lambda _{1}^{^{\prime }},...,\lambda _{m}^{^{\prime }}),$ where $%
\lambda _{j}^{^{\prime }}=\frac{n_{j}}{\sum_{j=1}^{m}\left\vert
n_{j}\right\vert },$ $j=1,...,m,$ is also associated with $p.$ All
the coordinates of $\lambda ^{^{\prime }}$ are rational and
therefore by the first part of the proposition, it is the unique
vector satisfying $\sum_{j=1}^{m}\left\vert \lambda _{j}^{^{\prime
}}\right\vert =1. $
\end{proof}

By this proposition, a minimal projection cycle $p$ uniquely (up to a sign) defines the
measure

\begin{equation*}
~\mu _{p}=\sum_{j=1}^{m}\lambda _{j}\delta _{x_{j}},\text{ \ }%
\sum_{j=1}^{m}\left\vert \lambda _{j}\right\vert =1.
\end{equation*}

\bigskip

\textbf{Lemma 2.5} (see [17]). \textit{Let $\mu $ be a normalized orthogonal measure on a
projection cycle $l\subset X$. Then it is a convex combination of normalized orthogonal measures on minimal
projection cycles of $l$. That is,}

\begin{equation*}
\mu =\sum_{i=1}^{s}t_{i}\mu _{l_{i}},\text{ }\sum_{i=1}^{s}t_{i}=1,~t_{i}>0,
\end{equation*}
\textit{where $l_{i},$ $i=1,...,s,$ are minimal projection cycles in $l.$}

\bigskip

This lemma follows from the result of Navada (see Theorem 2 of [17]): Let $S\subset X_{1}\times
\cdots \times X_{n}$ be a finite set. Then any extreme point of the convex set of measures $\mu $ on $S$, $\mu \in M^{\bot }$, $\left\Vert \mu \right\Vert \leq 1$, has its support on a minimal projection cycle contained in $S$.

\bigskip

\textbf{Remark 2.} In the case $n=2$, Lemma 2.5 was proved by Medvedev (see [11, p.77]).

\bigskip

\textbf{Lemma 2.6} (see [11, p.73]). \textit{Let $X=X_{1}\times
\cdots \times X_{n}$ and $\pi _{i}$ be the projections of $X$ onto
the sets $X_{i},$ $i=1,...,n.$ In order that a measure $\mu \in
C(X)^{\ast }$ be orthogonal to the subspace $M$, it is necessary
and sufficient that}

\begin{equation*}
\mu \circ \pi _{i}^{-1}=0,\text{ }i=1,...,n.
\end{equation*}

\bigskip

\textbf{Lemma 2.7} (see [11, p.75]). \textit{Let $\mu \in M^{\bot }$ and $%
\left\Vert \mu \right\Vert =1.$ Then there exist a net of measures $\{\mu
_{\alpha }\}\subset M^{\bot }$ weak$^{\text{*}}$ converging in $C(X)^{\ast }$
to $\mu $ and satisfying the following properties:}

1) $\left\Vert \mu _{\alpha }\right\Vert =1;$

2) \textit{The closed support of each $\mu _{\alpha }$ is a finite set.}

\bigskip

\textbf{Theorem 2.8.} \textit{The error of approximation from the manifold $%
M $ obeys the equality}
\begin{equation*}
E(f)=\underset{l\subset X}{\sup }\left\vert \int\limits_{X}fd\mu
_{l}\right\vert ,
\end{equation*}
\textit{where the $\sup $ is taken over all minimal projection cycles of
$X.$}

\begin{proof} Let $\overset{\sim }{\mu }$ be a
measure with a finite support $\{x_{1},...,x_{m}\}$ and orthogonal
to the space $M.$
Put $\lambda _{j}=\overset{\sim }{\mu }(x_{j}),$ $j=1,...m.$ By Lemma 2.6, $%
\overset{\sim }{\mu }(\pi _{i}^{-1}(\pi _{i}(x_{j})))=0,$ for all $%
i=1,...,n, $ $j=1,...,m.$ Fix the indices $i$ and $j.$ Then we have the
equation $\sum_{k}\lambda _{k}=0,$ where the sum is taken over all indices $%
k $ such that $\pi _{i}(x_{k})=\pi _{i}(x_{j}).$ Varying $%
i$ and $j,$ we obtain a system of such equations, which concisely can be
written as

\begin{equation*}
\sum_{k=1}^{m}\lambda _{k}\chi _{\pi _{i}(x_{k})}=0,\text{ \ }i=1,...,n.
\end{equation*}%
This means that the finite support of $\overset{\sim }{\mu }$ forms a
projection cycle. Therefore, a net of measures approximating the given
measure $\mu $ in Lemma 2.7 are all of the form (2.3).

Let now $\mu _{p,\lambda }$ be any measure of the form (2.3). Since $\mu
_{p,\lambda }\in M^{\bot }$ and $\left\Vert \mu _{p,\lambda }\right\Vert =1,$
we can write

\begin{equation*}
\left\vert \int\limits_{X}fd\mu _{p,\lambda }\right\vert =\left\vert
\int\limits_{X}(f-g)d\mu _{p,\lambda }\right\vert \leq \left\Vert
f-g\right\Vert ,\eqno(2.4)
\end{equation*}%
where $g$ is an arbitrary function in $M$. It follows from (2.4) that

\begin{equation*}
\underset{\left\langle p,\lambda \right\rangle }{\sup }\left\vert
\int\limits_{X}fd\mu _{p,\lambda }\right\vert \leq E(f),\eqno(2.5)
\end{equation*}%
where the $\sup $ is taken over all projection cycle-vector pairs of $X.$

Consider the general duality relation (1.1). Let $\mu _{0}$ be a measure
reaching the supremum in (1.1) and $\left\{ \mu _{p,\lambda }\right\} $ be a
net of measures of the form (2.3) approximating $\mu _{0}$ in the weak$^{%
\text{*}}$ topology of $C(X)^{\ast }.$ We have already known that this is
possible. For any $\varepsilon >0,$ there exists a measure $\mu
_{p_{0},\lambda _{0}}$ in $\left\{ \mu _{p,\lambda }\right\} $ such that

\begin{equation*}
\left\vert \int\limits_{X}fd\mu _{0}-\int\limits_{X}fd\mu _{p_{0},\lambda
_{0}}\right\vert <\varepsilon .
\end{equation*}%
From the last inequality we obtain that

\begin{equation*}
\left\vert \int\limits_{X}fd\mu _{p_{0},\lambda _{0}}\right\vert >\left\vert
\int\limits_{X}fd\mu _{0}\right\vert -\varepsilon =E(f)-\varepsilon .
\end{equation*}%
Hence,

\begin{equation*}
\underset{\left\langle p,\lambda \right\rangle }{\sup }\left\vert
\int\limits_{X}fd\mu _{p,\lambda }\right\vert \geq E(f).\eqno(2.6)
\end{equation*}%
From (2.5) and (2.6) it follows that

\begin{equation*}
\underset{\left\langle p,\lambda \right\rangle }{\sup }\left\vert
\int\limits_{X}fd\mu _{p,\lambda }\right\vert =E(f).\eqno(2.7)
\end{equation*}

By Lemma 2.5,

\begin{equation*}
\mu _{p,\lambda }=\sum_{i=1}^{s}t_{i}\mu _{l_{i}},
\end{equation*}%
where $l_{i}$, $i=1,...,s,$ are minimal projection cycles in $p$ and $%
\sum_{i=1}^{s}t_{i}=1,~t_{i}>0.$ Let $k$ be an index in the set $%
\{1,...,s\} $ such that

\begin{equation*}
\left\vert \int\limits_{X}fd\mu _{l_{k}}\right\vert =\max \left\{ \left\vert
\int\limits_{X}fd\mu _{l_{i}}\right\vert ,\text{ }i=1,...,s\right\} .
\end{equation*}%
Then

\begin{equation*}
\left\vert \int\limits_{X}fd\mu _{p,\lambda }\right\vert \leq \left\vert
\int\limits_{X}fd\mu _{l_{k}}\right\vert .\eqno(2.8)
\end{equation*}%
Now since

\begin{equation*}
\left\vert \int\limits_{X}fd\mu _{l}\right\vert \leq E(f),
\end{equation*}%
for any minimal cycle $l,$ from (2.7) and (2.8) we obtain the assertion of the
theorem.
\end{proof}

\textbf{Remark 3.} Theorem 2.8 not only proves Golomb's formula, but also improves it. Indeed, based on Proposition 2.3, one can easily observe that
the formula (1.4) is equivalent to the formula

\begin{equation*}
E(f)=\underset{\left\langle p,\lambda \right\rangle }{\sup }\left\vert
\int\limits_{X}fd\mu _{p,\lambda }\right\vert ,
\end{equation*}%
where the $\sup $ is taken over all projection cycle-vector pairs $%
\left\langle p,\lambda \right\rangle $ of $X$ provided that all the numbers $%
\lambda _{i}/ \sum_{j=1}^{m}\left\vert \lambda _{j}\right\vert $, $%
i=1,...,m,$ are rational. But by Lemma 2.4, minimal projection cycles enjoy this property.

\bigskip

redpajama_set_name: RedPajamaArXiv


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I would like to go on record however, as stating – 'terrifying' is not a quality we should consider as a superior quality for someone who will be leading us at home, at work, on a sports team, in an organization, or in presidency. It just isn't!


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