Daily Archives: January 4, 2023

Cauchy principal value – Wikipedia

Posted: January 4, 2023 at 6:13 am

Method for assigning values to certain improper integrals which would otherwise be undefined

In mathematics, the Cauchy principal value, named after Augustin Louis Cauchy, is a method for assigning values to certain improper integrals which would otherwise be undefined.

Depending on the type of singularity in the integrand f, the Cauchy principal value is defined according to the following rules:

In some cases it is necessary to deal simultaneously with singularities both at a finite number b and at infinity. This is usually done by a limit of the form

Let C c ( R ) {displaystyle {C_{c}^{infty }}(mathbb {R} )} be the set of bump functions, i.e., the space of smooth functions with compact support on the real line R {displaystyle mathbb {R} } . Then the map

To prove the existence of the limit

Therefore, 0 1 u ( x ) u ( x ) x d x {displaystyle int _{0}^{1},{frac {u(x)-u(-x)}{x}},mathrm {d} x} exists and by applying the mean value theorem to u ( x ) u ( x ) , {displaystyle u(x)-u(-x),} we get:

And furthermore:

we note that the map

Note that the proof needs u {displaystyle u} merely to be continuously differentiable in a neighbourhood of 0 and x u {displaystyle x,u} to be bounded towards infinity. The principal value therefore is defined on even weaker assumptions such as u {displaystyle u} integrable with compact support and differentiable at 0.

The principal value is the inverse distribution of the function x {displaystyle x} and is almost the only distribution with this property:

In a broader sense, the principal value can be defined for a wide class of singular integral kernels on the Euclidean space R n {displaystyle mathbb {R} ^{n}} . If K {displaystyle K} has an isolated singularity at the origin, but is an otherwise "nice" function, then the principal-value distribution is defined on compactly supported smooth functions by

Consider the values of two limits:

This is the Cauchy principal value of the otherwise ill-defined expression

Also:

Similarly, we have

This is the principal value of the otherwise ill-defined expression

Different authors use different notations for the Cauchy principal value of a function f {displaystyle f} , among others:

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Cauchy principal value - Wikipedia

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Proud Boys | Leader, Founder, History, January 6 Attack, & Donald Trump …

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Proud Boys, neofascist white nationalist organization established in the United States in 2016. The groups members were noted for their misogynistic and anti-Semitic rhetoric, QAnon-related beliefs, their support for U.S. Pres. Donald Trump, and their propensity for street violence. The Proud Boys were designated a hate group by the Southern Poverty Law Center and were designated a terrorist organization by the governments of Canada and New Zealand.

The Proud Boys were created by Gavin McInnes, a Canadian writer and provocateur who had cofounded the magazine Voice of Montreal (later VICE) in 1994. McInnes was the most visible face of VICE as it expanded from a zine chronicling Montreal music and street fashion to an international media presence. McInnes would help define hipster culture of the early 2000s, and he was a strong influence on the magazines vulgar humour, biting tone, and conscious rejection of political correctness. By 2008 McInness public persona had transformed from contrarian gadfly to overtly far-right spokesperson, and VICE Media had forged a corporate relationship with communications giant Viacom; ties between McInnes and VICE were soon severed over what McInnes called creative differences.

McInnes subsequently explored other media ventures and speaking engagements, and his rhetoric became increasingly sexist and xenophobic. In 2010 he cofounded the advertising agency Rooster, but he was forced out of the company in 2014 after publishing a violently transphobic essay in an online magazine. McInnes became a regular contributor to white nationalist and anti-immigration websites, and in 2015 he launched The Gavin McInnes Show on a subscription-based streaming media platform. McInnes would claim that the Proud Boys were an outgrowth of social gatherings held after that show. In an article announcing the creation of the Proud Boys in September 2016, he stated that the groupwhich was open only to menconsisted of Western chauvinists who were vocal in their support for then-candidate Trump. Violence was a fundamental part of the Proud Boys from the beginning, and the groups most famous initiation ritual involved a candidate being beaten by other members until he could correctly name five breakfast cereals.

Far-right extremists were emboldened by Trumps election in November 2016, and Proud Boy Jason Kessler was the main organizer of the Unite the Right rally in Charlottesville, Virginia, in August 2017. Hundreds of white supremacists descended on the city to protest the planned removal of a statue of Confederate Gen. Robert E. Lee. On the night of August 11 a torchlit march was punctuated with chants like You will not replace us, a phrase grounded in a racist conspiracy theory, and Blood and soil, a Nazi slogan. The following day street fighting between Unite the Right marchers and anti-fascist (antifa) counter-protesters erupted in downtown Charlottesville, and a neo-Nazi drove into a crowd of counter-protesters, killing one and injuring dozens. McInnes disavowed Kessler and tried to distance himself and the Proud Boys from Charlottesville, but there was already a significant membership overlap between the Proud Boys and other white supremacist and neo-Nazi groups. Rather than condemning the events in Charlottesville, Trump prevaricated, stating that there were some very bad people among the violent white nationalists, but you also had people that were very fine people, on both sides.

Throughout the summer of 2018 the Proud Boys were involved in brawls in Portland, Oregon, and they often appeared at rallies with Patriot Prayer, a violent far-right organization based in the Pacific Northwest. The Fraternal Order of Alt-Knights, a Proud Boys paramilitary spin-off group, was active in California; its members employed homemade armour and melee weapons to provide tactical defense at right-wing rallies. In August 2018 Twitter suspended the accounts of both McInnes and the group itself, and Facebook followed suit two months later. After McInnes delivered a speech at the Metropolitan Republican Club in Manhattan in October 2018, the Proud Boys initiated a street fight with protesters that led to several arrests. The following month McInnes announced that he was leaving the Proud Boys, and he was succeeded by Henry (Enrique) Tarrio, a former FBI informant who had led both the Miami Proud Boys and a group called Latinos for Trump. In February 2019 McInnes filed a defamation lawsuit against the Southern Poverty Law Center over that organizations designation of the Proud Boys as a hate group.

As governments around the world attempted to slow the spread of the coronavirus SARS-CoV-2 pandemic in 2020, the Proud Boys participated in rallies against mitigation efforts and spread disinformation and conspiracy theories about COVID-19, the potentially deadly disease caused by the virus. Racial justice demonstrations swept the United States in the wake of the killing of George Floyd in police custody in May 2020, and the Proud Boys often appeared as armed counter-protesters at these events alongside extremist militia groups such as the Oath Keepers. On September 29, 2020, during a presidential debate with Democratic Party candidate Joe Biden, Trump was prompted to denounce white supremacist groups, but he instead seemed to offer the Proud Boys his endorsement with the statement, Proud Boys, stand back and stand by.

After Biden defeated Trump in the 2020 presidential election, Trump refused to concede and made baseless claims of election fraud. The Proud Boys were a conspicuous presence at so-called Stop the Steal rallies, and at one such event in December 2020 Tarrio set fire to a Black Lives Matter banner taken from a Black church in Washington, D.C. Tarrio was arrested on January 4, 2021, so he was not present two days later when a pro-Trump mob stormed the U.S. Capitol in an attempt to disrupt the certification of Bidens election victory. Dozens of Proud Boys from across the United States would be arrested for crimes committed during the January 6 insurrection, and in May 2021 Canada added the Proud Boys to its list of terrorist entities alongside groups such as the Taliban and the so-called Islamic State. In June 2022 Tarrio and four of his lieutenants were charged with seditious conspiracy for their role in planning and executing the attack on the Capitol. That same month New Zealand designated the Proud Boys as a terrorist organization. Jeremy Bertino, a leader of the South Carolina Proud Boys who had aided in the planning of the January 6 attack, pleaded guilty to seditious conspiracy and unlawful possession of a firearm in October 2022, in a case that was separate from the proceedings against Tarrio. As part of his plea agreement, Bertino, who faced up to 30 years in prison for the charges against him, agreed to cooperate with government investigators.

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Proud Boys attorney wants Trump’s ‘stand back and stand by’ statement kept out of trial – WUSA9.com

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Proud Boys attorney wants Trump's 'stand back and stand by' statement kept out of trial  WUSA9.com

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Progress Quotes (2035 quotes) – Goodreads

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That is the idea -- that we should all be wicked if we did not hold to the Christian religion. It seems to me that the people who have held to it have been for the most part extremely wicked. You find this curious fact, that the more intense has been the religion of any period and the more profound has been the dogmatic belief, the greater has been the cruelty and the worse has been the state of affairs. In the so-called ages of faith, when men really did believe the Christian religion in all its completeness, there was the Inquisition, with all its tortures; there were millions of unfortunate women burned as witches; and there was every kind of cruelty practiced upon all sorts of people in the name of religion.

You find as you look around the world that every single bit of progress in humane feeling, every improvement in the criminal law, every step toward the diminution of war, every step toward better treatment of the colored races, or every mitigation of slavery, every moral progress that there has been in the world, has been consistently opposed by the organized churches of the world. I say quite deliberately that the Christian religion, as organized in its churches, has been and still is the principal enemy of moral progress in the world.

You may think that I am going too far when I say that that is still so. I do not think that I am. Take one fact. You will bear with me if I mention it. It is not a pleasant fact, but the churches compel one to mention facts that are not pleasant. Supposing that in this world that we live in today an inexperienced girl is married to a syphilitic man; in that case the Catholic Church says, 'This is an indissoluble sacrament. You must endure celibacy or stay together. And if you stay together, you must not use birth control to prevent the birth of syphilitic children.' Nobody whose natural sympathies have not been warped by dogma, or whose moral nature was not absolutely dead to all sense of suffering, could maintain that it is right and proper that that state of things should continue.

That is only an example. There are a great many ways in which, at the present moment, the church, by its insistence upon what it chooses to call morality, inflicts upon all sorts of people undeserved and unnecessary suffering. And of course, as we know, it is in its major part an opponent still of progress and improvement in all the ways that diminish suffering in the world, because it has chosen to label as morality a certain narrow set of rules of conduct which have nothing to do with human happiness; and when you say that this or that ought to be done because it would make for human happiness, they think that has nothing to do with the matter at all. 'What has human happiness to do with morals? The object of morals is not to make people happy. Bertrand Russell, Why I Am Not a Christian and Other Essays on Religion and Related Subjects

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Progress Quotes (2035 quotes) - Goodreads

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Progress Software to Report Fourth Quarter 2022 Financial Results on January 17, 2023 – Marketscreener.com

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Progress Software to Report Fourth Quarter 2022 Financial Results on January 17, 2023  Marketscreener.com

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SDOT crews making progress on repairs to West Seattle low bridge – KOMO News

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SDOT crews making progress on repairs to West Seattle low bridge  KOMO News

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A look at Times Square and the progress thus far in 2023 post Hurricane Ian – FOX 4 News Fort Myers WFTX

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A look at Times Square and the progress thus far in 2023 post Hurricane Ian  FOX 4 News Fort Myers WFTX

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Basic Blackjack Strategy Charts [2021] – Generate Charts for 1-8 Decks

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Adjust The Rules

Key:

D

Double (Hit if not allowed)

DS

Double (Stand if not allowed)

Looking for a way to cut the casinos edge down to a marginal amount? Basic strategy is a mathematically calculated set of decisions that can help you win more at blackjack. The Blackjack Basic Strategy Engine above provides a simple way to memorize a variety of different profitable decisions, such as when to split, double, surrender, hit, or stand.

A standard basic strategy chart can only provide you with the strategy for one set of rules, such as dealer hits on soft 17, limiting your mastery to just one game. Our Blackjack Basic Strategy Engine allows you to quickly adjust the rules with the click of a button, calculating the optimal strategy for your selected game. The engines easy-to-read charts detail the strategy for all hard totals, soft totals, and pairs.

The engine allows you to instantly customize your strategy based on rules like surrender, double on 9, 10, or 11 only, dealer hole card styles, and any number of decks. This unique system is an incredible resource for any serious blackjack player who needs to calculate the strategy for any game they encounter.

Basic strategy will never be enough to beat the game in the long-term. Sure, youll definitely be able to win more frequently, keep your money longer, and go on a few free vacations using casino comps, but youll never make money over thousands of hours of play. For that, youll need to learn to count cards and utilize strategy deviations to beat the house edge. If youre just looking to have fun and make your money last much longer, basic strategy will do the trick.

So you want to learn basic strategy so that you can get an edge up on the tables, but youre not sure to begin. Once youve used the Blackjack Basic Strategy Engine to select the game youll play most frequently, you may be tempted to dive right into memorization, but a bit of background knowledge can help you understand the concepts behind the strategy. Lets explore a few rules that will help you along the way.

Theres more to blackjack than just hitting or standing, and those extra decisions will determine whether youre a big winner or a big loser. Your extra options are to surrender, split, or double, and their availability is determined by the rules of your game of blackjack. Also, keep in mind that even in the same casino, different tables can have different rules, so make sure to check the felt or ask the dealer about each tables rules. Never play 6:5 blackjack, and try to play S17 if it is available. Read our rules page if you need a refresher course on whateach action does.

Surrender is a rule that is becoming offered less frequently, as it is beneficial to the player. To find out if it is available at your table, you can ask your dealer or look for a sign located on the table. Before you take any other action, you should see if basic strategy recommends surrendering.

Splitting comes into play when you have an equal pair in your handfor example, two 8s, two 7s, or a jack and a queen. When you find yourself with a pair, you should check your basic strategy card to see if splitting is advantageous.

You can double on any first two cards. Generally, you will want to double when a 10 card would be beneficial to you (with a hard 11 or hard 10, for example), or when the dealer has a card with a higher than normal possibility of busting, like a 5 or a 6.

These two actions will make up the majority of your decision making. Learning when to hit or stand in every scenario is the crux of basic strategy. By memorizing basic strategy, youre memorizing the optimal, most bang-for-your-buck action with any two given cards against any dealer up card.

It may feel overwhelming to tackle every different combination of starting cards with basic strategy, but luckily there are a lot of rules of thumb that can help simplify the process. Here are some of the most important, effective, and easy to remember strategies to help you on your road to playing solid blackjack.

Surrender 16 against 9 through Ace.

Surrender 15 against a 10 only (Unless using H17 rules, then you Surrender against Ace)

Always Split Aces

Never Split Faces (10 value cards)

Always Split 8s (Unless using H17 rules, then you Surrender against an Ace)

Never Split 5s

Split a pair of 9s against a dealer 2 through 9, except a dealer 7 (since your 18 beats their 17)

Split a pair of 7s against a dealer 2 through 7, hit anything else.

Split a pair of 6s against a dealer 2 through 6, hit anything else.

Split a pair of 4s against a dealer 5 or 6 when you can double afterward, otherwise hit.

Split a pair of 3s against a dealer 2 through 7, hit anything else.

Split a pair of 2s against a dealer 2 through 7, hit anything else.

Double an 11 against everything except an Ace (Also double against Ace if playing H17 Rules)

Double a 10 against everything except a 10 or Ace

Double a hard 9 against a dealer 3 through 6.

Never double a hard 8.

Double a soft 13 or 14 against a dealer 5 or 6.

Double a soft 15 or 16 against a dealer 4 through 6.

Double a soft 17 or 18 against a dealer 3 through 6.

Double a soft 19 against a dealer 6 if using H17 rules.

Stand on 17 and up

Stand on a 13, 14, 15, or 16 against a 2 through 6, hit against any other card

Stand on a 12 against a dealer 4 through 6, hit against any other card.

Always hit anything under soft 17.

Stand on soft 19 and up.

You should study the above information in conjunction with our Blackjack Basic Strategy Engine while you practice playing blackjack. You arent ready to play in a casino yet, not by a longshot. Even if youve played before and done well, you shouldnt go back until you know basic strategy like the back of your hand.

The best way to practice is to utilize software like our Blackjack TrainerorCasino Vrit Blackjack to enhance your skills and figure out what areas youre struggling in, like surrendering or playing soft hands. Once you can play error free through a wide range of scenarios, you are ready to practice in a casino environment.

Remember, it can be a more difficult to remember perfect basic strategy when a waitress is yelling out drink orders, a pit boss is asking for your card, and players are trying to make conversation, so dont go to the casino until youre truly ready. Dont ask other players for advice, either. They deliberately go against basic strategy when the math doesnt mesh with their superstitions about the flow of the cards, and theyll often tell you how crazy you are to hit a soft 18 against a dealer 9 or 10.

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Basic Blackjack Strategy Charts [2021] - Generate Charts for 1-8 Decks

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New Zealand – The Heritage Foundation

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New Zealands economic freedom score is 80.6, making its economy the 4th freest in the 2022 Index. New Zealand is ranked 2nd among 39 countries in the AsiaPacific region, and its overall score is above the regional and world averages.

New Zealands economy was growing smartly in 2017 and 2018 but began to slow in 2019 before contracting in 2020. Growth recovered in 2021. During the past five years, economic freedom has generally been robust, although it has dipped. With higher scores for government integrity and judicial effectiveness overshadowed by score decreases in fiscal health and business freedom, New Zealand has registered an overall 3.1-point loss of economic freedom since 2017 but nevertheless remains in the top, Free Index category. The countrys indicators are generally very strong except for the burden of government spending on the economy.

IMPACT OF COVID-19: As of December 1, 2021, 44 deaths had been attributed to the pandemic in New Zealand, and the governments response to the crisis ranked 7th among the countries included in this Index in terms of its stringency. The economy contracted by 3.0 percent in 2020.

The former British colony of New Zealand is one of the AsiaPacific regions most prosperous countries. General elections in 2017 resulted in a hung parliament, enabling new Prime Minister Jacinda Arderns center-left Labor Party to return to power. She will remain in power until 2023 after winning a landslide victory in 2020 elections. Far-reaching deregulation and privatization since the 1980s have largely liberated the economy. Agriculture is important as are manufacturing, tourism, and a strong geothermal energy resource base. The ongoing trade tension between the U.S. and China is of concern to New Zealand, especially given its heavy reliance on China for export revenue. Until the present crisis, New Zealands economy had been expanding since 2010.

New Zealand recognizes and enforces secured interests in property, both movable and real. The Land Transfer Act of 2017 simplified and modernized property law. The judicial system is independent and functions well. New Zealand ranked 1st among the 180 countries surveyed in Transparency Internationals 2020 Corruption Perceptions Index. Stiff penalties against bribery of government officials and those who accept bribes are strictly enforced.

The top income tax rate is 33 percent, and the top corporate tax rate is 28 percent. Other taxes include goods and services and environmental taxes. The overall tax burden equals 32.3 percent of total domestic income. Government spending has amounted to 39.4 percent of total output (GDP) over the past three years, and budget deficits have averaged 2.3 percent of GDP. Public debt is equivalent to 41.3 percent of GDP.

The governments strict shutdowns of the economy decimated tourism. The government began to tax online businesses at 15 percent and is considering additional taxes. A wage subsidy of 80 percent of private companies salaries has kept unemployment under control during the crisis, but it also has significantly increased public debt. The government has introduced new subsidies for electric vehicles and for housing and urban development.

New Zealand has 13 preferential trade agreements in force. The trade-weighted average tariff rate is 2.5 percent, and 247 nontariff measures are in effect. Overall, openness to global trade and investment is firmly institutionalized. Banking is well established and competitive. To support the financial systems stability and liquidity during the pandemic, implementation of a higher capital reserve requirement for banks has been postponed.

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Singapore Economy: Population, GDP, Inflation, Business, Trade, FDI …

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Singapores economic freedom score is 84.4, making its economy the freest in the 2022 Index. Singapore is ranked 1st among 39 countries in the AsiaPacific region, and its overall score is above the regional and world averages.

Over the past five years, Singapores economy has grown slowly except in 2020, when it contracted. Economic freedom has been maintained at a very high level during that period, at or near the top of the Index. Singapores highly developed free-market economy owes its success in large measure to its remarkably open and corruption-free business environment, prudent monetary and fiscal policies, and a transparent legal framework. Trade freedom is strong, and well-secured property rights promote entrepreneurship and innovation effectively. The overall rule of law is undergirded by a high degree of transparency and government accountability.

IMPACT OF COVID-19: As of December 1, 2021, 726 deaths had been attributed to the pandemic in Singapore, and the governments response to the crisis ranked 77th among the countries included in this Index in terms of its stringency. The economy contracted by 5.4 percent in 2020.

Singapore is one of the worlds most prosperous nations and has both a business-friendly regulatory environment and a very low unemployment rate. Despite an active parliamentary opposition, it has been ruled by one party, the Peoples Action Party (PAP), for many decades. Prime Minister Lee Hsien Loong has led the government since 2004 and has suggested a near-term leadership transition. Although certain civil liberties remain restricted, the PAP has championed economic liberalization and international trade. Services dominate the economy, but Singapore is also a major manufacturer of electronics and chemicals and operates one of the worlds largest ports. Principal exports include integrated circuits, refined petroleum, and computers.

Although there are limitations on foreign ownership, property rights are recognized and enforced effectively. Judicial processes are reliable in business-related matters but tend to favor the government in politically sensitive cases. Singapore was ranked third out of 180 countries in Transparency Internationals 2020 Corruption Perceptions Index and is considered one of the worlds least corrupt countries. The anticorruption agency is very effective.

The top individual income tax rate is 22 percent, and the top corporate tax rate is 17 percent. Other taxes include a goods and services tax. The overall tax burden equals 13.2 percent of total domestic income. Government spending has amounted to 18.2 percent of total output (GDP) over the past three years, and budget deficits have averaged 0.5 percent of GDP. Public debt is equivalent to 128.4 percent of GDP.

Singapores business-friendly legal and tax structure, reliable infrastructure, and dependable regulatory processes provide a positive commercial environment. The government tightened restrictions on foreign labor in 2020. In 2021, the IMF estimated that government subsidies, grants, subventions, and capital injections to businesses and other organizations consume about 17 percent of GDP.

Singapore has 27 preferential trade agreements in force. The trade-weighted average tariff rate is 0.0 percent, and 182 nontariff measures are in effect. Foreign and domestic businesses are treated equally under the law, and nearly all sectors of the economy are open to 100 percent foreign ownership. The sophisticated financial sector is robust, and the number of foreign banks in the market has risen steadily.

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