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Polish notation

Polish notation known as normal Polish notation, Łukasiewicz notation, Warsaw notation, Polish prefix notation or prefix notation, is a mathematical notation in which operators precede their operands, in contrast to the more common infix notation, in which operators are placed between operands, as well as reverse Polish notation, in which operators follow their operands. It does not need any parentheses as long; the description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924. The term Polish notation is sometimes taken to include reverse Polish notation; when Polish notation is used as a syntax for mathematical expressions by programming language interpreters, it is parsed into abstract syntax trees and can, in fact, define a one-to-one representation for the same. Because of this and related programming languages define their entire syntax in prefix notation. A quotation from a paper by Jan Łukasiewicz, Remarks on Nicod's Axiom and on "Generalizing Deduction", page 180, states how the notation was invented: I came upon the idea of a parenthesis-free notation in 1924.

I used that notation for the first time in my p. 610, footnote. The reference cited by Łukasiewicz is a lithographed report in Polish; the referring paper by Łukasiewicz Remarks on Nicod's Axiom and on "Generalizing Deduction" was reviewed by Henry A. Pogorzelski in the Journal of Symbolic Logic in 1965. Heinrich Behmann, editor in 1924 of the article of Moses Schönfinkel had the idea of eliminating parentheses in logic formulas. Alonzo Church mentions this notation in his classic book on mathematical logic as worthy of remark in notational systems contrasted to Alfred Whitehead and Bertrand Russell's logical notational exposition and work in Principia Mathematica. In Łukasiewicz's 1951 book, Aristotle's Syllogistic from the Standpoint of Modern Formal Logic, he mentions that the principle of his notation was to write the functors before the arguments to avoid brackets and that he had employed his notation in his logical papers since 1929, he goes on to cite, as an example, a 1930 paper he wrote with Alfred Tarski on the sentential calculus.

While no longer used much in logic, Polish notation has since found a place in computer science. The expression for adding the numbers 1 and 2 is written in Polish notation as + 1 2, rather than as 1 + 2. In more complex expressions, the operators still precede their operands, but the operands may themselves be expressions including again operators and their operands. For instance, the expression that would be written in conventional infix notation as × 7can be written in Polish notation as × 7Assuming a given arity of all involved operators, any well formed prefix representation thereof is unambiguous, brackets within the prefix expression are unnecessary; as such, the above expression can be further simplified to × − 5 6 7The processing of the product is deferred until its two operands are available. As with any notation, the innermost expressions are evaluated first, but in Polish notation this "innermost-ness" can be conveyed by the sequence of operators and operands rather than by bracketing.

In the conventional infix notation, parentheses are required to override the standard precedence rules, referring to the above example, moving them 5 − or removing them 5 − 6 × 7changes the meaning and the result of the expression. This version is written in Polish notation as − 5 × 6 7; when dealing with non-commutative operations, like division or subtraction, it is necessary to coordinate the sequential arrangement of the operands with the definition of how the operator takes its arguments, i.e. from left to right. For example, ÷ 10 5, with 10 left to 5, has the meaning of 10 ÷ 5, or - 7 6, with 7 left to 6, has the meaning of 7 - 6. Prefix/postfix notation is popular for its innate ability to express the intended order of operations without the need for parentheses and other precedence rules, as are employed with infix notation. Instead, the notation uniquely indicates; the operators are assumed to have a fixed arity each, all necessary operands are assumed to be explicitly given. A valid prefix expression always ends with an operand.

Evaluation can either proceed from left in the opposite direction. Starting at the left, the input string, consisting of tokens denoting operators or operands, is pushed token for token on a stack, until the top entries of the stack contain the number of operands that fits to the top most operator; this group of tokens at the stacktop is replaced by the result of executing the operator on these/this operand. The processing of the input continues in this manner; the rightmost operand in a valid prefix expression thus empties the stack, except for the result of evaluating the whole expression. When starting at the right, the pushing of tokens is performed just the evaluation is triggered by an operator, finding the appropriate number of operands that fits its arity at the stacktop. Now the leftmost token of a valid prefix expression must be an operator, fitting to the number of operands in the stack, which again yields the result; as can be seen from the description, a push-down store with no capability of arbitrary stack inspection suf

Harleyville, South Carolina

Harleyville is a town in Dorchester County, South Carolina, United States. The population was 677 at the 2010 census, up from 594 at the 2000 census. Harleyville is part of the Charleston-North Charleston-Summerville metropolitan area; as of 2018 the population is 886. Harleyville was named after the Harley family; the St. Paul Camp Ground was added to the National Register of Historic Places in 1998. Harleyville is located in northern Dorchester County at 33°12.7′N 80°26.9′W. U. S. Route 178 passes through the center of town, leading northwest 31 miles to Orangeburg and southeast 7 miles to its terminus at U. S. Route 78. South Carolina Highway 453 leads north 1 mile to Exit 177 on Interstate 26. According to the United States Census Bureau, the town has a total area of 1.2 square miles, all of it land. The Audubon's Francis Beidler forest is located just outside of town. Within the park, there are miles of boardwalks through the old four hole swamp; as of the census of 2010, there were 693 people, 250 households, 165 families residing in the town.

The population density was 601.1 people per square mile. There were 282 housing units at an average density of 285.4 per square mile. The racial makeup of the town was 59.26% White, 38.38% African American, 0.67% Native American, 0.17% from other races, 1.52% from two or more races. Hispanic or Latino of any race were 1.18% of the population. There were 250 households out of which 31.2% had children under the age of 18 living with them, 38.0% were married couples living together, 22.0% had a female householder with no husband present, 34.0% were non-families. 30.8% of all households were made up of individuals and 16.4% had someone living alone, 65 years of age or older. The average household size was 2.38 and the average family size was 2.99. In the town, the population was spread out with 28.3% under the age of 18, 7.6% from 18 to 24, 23.6% from 25 to 44, 24.6% from 45 to 64, 16.0% who were 65 years of age or older. The median age was 38 years. For every 100 females, there were 83.3 males. For every 100 females age 18 and over, there were 75.3 males.

The median income for a household in the town was $26,397, the median income for a family was $35,313. Males had a median income of $33,083 versus $21,875 for females; the per capita income for the town was $16,412. About 23.1% of families and 43.4% of the population were below the poverty line, including 25.2% of those under age 18 and 22.9% of those age 65 or over. Town of Harleyville official website

Treaty of Alcañices (1297)

The Treaty of Alcañices was made in Alcañices between King Denis of Portugal and King Fernando IV of Castile. Denis was the grandson of king Alfonso X of Castile and an administrator and not a warrior king, he went to war with the kingdom of Castile in 1295, relinquishing the villages of Serpa and Moura, but gained Olivença and reaffirmed Portugal’s possession of the Algarve and defined the modern borders between the two Iberian countries. The treaty established an alliance of friendship and mutual defense, leading to a peace of 40 years between the two nations. Fernando married Denis's daughter, Infanta Constance of Portugal, making her Queen of Castile

The Avion Newspaper

The Avion Newspaper is the student-led college newspaper of Embry-Riddle Aeronautical University in Daytona Beach, United States. The Avion publishes weekly, has a print circulation of 1,000; the newspaper has a history dating back to Embry-Riddle's earliest days in Miami. The Avion is published weekly during the fall and spring semesters, a total of 13 issues per semester, it is published bi-weekly in a total of six times. The Avion publishes three special issues: an orientation edition in late August, a Halloween Edition known as The Scaryoff, on October 31, an April Fools' Day edition known as The Avioff, on April 1; the newspaper is distributed free of charge to students, faculty and visitors. Mail subscriptions are available for $20 per year; the Avion is a division of the Embry-Riddle Student Government Association, which funds the organization. The newspaper is run by students, most of the contributors are volunteers; the Editor-in-Chief is elected by a majority vote of the newspaper's staff and receives a 25% tuition voucher for his or her services.

Executive board members are appointed by the Editor-in-Chief, each executive board member receives a 10% tuition voucher. The Avion consists of four sections; the first section consists of campus news and student opinions. The second section presents a collection of news in the aerospace industries; the third section is dedicated to the university's athletic teams. The fourth section is anchored by the entertainment page, carries the comics and classifieds. Editor-in-Chief: Rajan Khanna Managing Editor: Vipul Telang News Editor: Nicholas Hernandez Business Manager: Payton Muglia Photo Editor: Connor Adair The Avion's website The Avion's digital issues

Splatty Tomato

"Splatty Tomato" is the tenth episode and the season finale of the twenty-first season of the American animated television series South Park. The 287th overall episode of the series, it premiered on Comedy Central in the United States on December 6, 2017; the episode, which parodies support for Donald Trump among white middle-class Americans, depicts the people of South Park as they deal with sightings of President Garrison that frighten their children, likening him to the antagonists of popular works of horror, including Stranger Things and the 2017 feature film adaptation It. Subplots in the story focus on relationships among the regular and recurring characters, including the conclusion of Eric Cartman and Heidi Turner's relationship, a burgeoning romance between PC Principal and Strong Woman, with which the episode explores the themes of self-victimization and cultural views of workplace relationships; the episode's title is a reference to the icon used to denote films with low critical scores on the review aggregator website Rotten Tomatoes.

President Garrison has been spotted in South Park, frightening the young daughter of Bob White and his wife with his constant inquiries about his approval rating. According to a local law enforcement official, Officer Bright, Garrison has become desperate and dangerous since he was given a "splatty tomato" approval rating; the Whites, who remain loyal supporters of Garrison, believe that their daughter's anxieties are caused by the political liberalism of the school administrators at South Park Elementary, PC Principal and Strong Woman, complaining, "No one cares about the Whites." Sightings of Garrison continue, his presence heralded by red balloons bearing the campaign slogan "Make America Great Again", which Randy Marsh and the children of South Park realize bears similarities to Stranger Things and It. In the aftermath of his attack upon Toronto with a nuclear bomb in the previous episode, which killed over a million Canadians, Prime Minister Justin Trudeau demands that Garrison be handed over to Canada, a call to which the Canadian-born Ike Broflovski responds.

After he disappears, his brother Kyle embarks on a search, joined by his friends. Eric Cartman and his girlfriend Heidi Turner join the search, but Heidi's recent streak of abusiveness spurs Kyle to denounce the person that she has become, humbling her. At a town meeting, Mayor McDaniels tells the townspeople that Officer Bright is leading the search for Garrison; when she assures the assembled crowd that she understands that they all wish to get rid of Garrison, Bob White objects. When Randy points out to White all the things Garrison has been doing, White responds that Hillary Clinton would not have been any better; when Bright informs the public that authorities have set up a "fox trap" to capture Garrison, a fake interview with Fox News, the Whites help Garrison evade it by warning him. Randy and his neighbors search the woods, when they find a campsite, they discover in the tent PC Principal and Strong Woman in bed together; the sight of two co-workers in a relationship horrifies the others, who vomit in response.

Ike, wearing the uniform of a Canadian Mountie, captures Garrison and drags him bound and gagged back into town. This provokes Bob White to pull out a gun, but Heidi grabs it and holds Cartman at gunpoint, she blames him for the person she has become, but Heidi realizes that she has been engaging in self-victimization since she began seeing Cartman. He threatens to kill himself again, but Heidi, no longer moved by his attempts at manipulation, breaks up with him; as this occurs, Garrison escapes. Stan Marsh fears that Garrison cannot be destroyed, but Randy states that "it is up to the Whites". Dan Caffrey of The A. V. Club gave the episode a B- rating but did not like how President Garrison was used in the episode, commenting "Whenever a Trump/Garrison storyline goes nowhere, it's because Parker and Stone just don’t have that much more to say about him."Jesse Schedeen of IGN gave the episode a 7.9 out of 10 rating, commenting that the episode "didn't quite combine its many concurrent plot threads into a cohesive whole, but it did a better job of tying up loose ends than most.

And in some ways, the lack of closure in the final moments only played into the larger themes and topical humor."Joe Matar with Den of Geek gave the episode a 3.5 out of 5 stars rating, stating in his review "I don't find South Park laugh out loud funny these days and Season 21 has been weak, so'Splatty Tomato' was a nice surprise in that it was well-plotted, had some clever gags, ended with a clear moral for Heidi and the Whites:'if you always make yourself the victim, you can justify being awful.'"Jeremy Lambert with 411Mania gave the episode a 6.5 out of 10 rating, stating in his review "The episode had some funny moments. The bad 80s music played for some nice laughs and I lost it at the FOX trap, but the goal of this episode didn't seem to be'make people laugh.' It seemed to be'make people realize that America sucks right now.' Mission accomplished and Trey."Dani Di Placido with Forbes praised the episode in his review, stating "regardless of your political alignment, the overarching message from this season, to stop playing the victim, stop othering the opposing side, to just calm the hell down, is difficult to argue with.

Despite the show's reputation for reckless offensiveness, I would argue that South Park is one of the few voices of reason in the media landscape today."Ben Travers with IndieWire gave the episode a B- rating, stating in his review "Parker and Stone have always skewered everyone. They'll go after the easy targets, like Trump, the hard targets, like P. C. culture. Over 21 years, they've proven themselves smart and savvy satirists, Season 21

Stanisław Grodzicki

Stanisław Grodzicki was a Polish fighter pilot and a Major of the Polish Air Force during World War II. He fought during The Blitz in 1941 as a night fighter pilot with No. 307 Polish Fighter Squadron, flying the Boulton Paul Defiant. From November 1940 to June 1941 he was the commanding officer of the unit, he was awarded the Distinguished Flying Cross. In 1946, he was killed in an air crash when the Dakota of 435 Squadron RCAF, in which he was a passenger crashed during a bad weather landing approach to Croydon Airport, he is buried in Star Lane Cemetery, in St Mary Cray, Kent