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Probability theory

Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms; these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of these outcomes is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, stochastic processes, which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion. Although it is not possible to predict random events, much can be said about their behavior. Two major results in probability theory describing such behaviour are the law of large numbers and the central limit theorem.

As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of data. Methods of probability theory apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth-century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics; the earliest known forms of probability and statistics were developed by Arab mathematicians studying cryptography between the 8th and 13th centuries. Al-Khalil wrote the Book of Cryptographic Messages which contains the first use of permutations and combinations to list all possible Arabic words with and without vowels. Al-Kindi made the earliest known use of statistical inference in his work on cryptanalysis and frequency analysis. An important contribution of Ibn Adlan was on sample size for use of frequency analysis; the modern mathematical theory of probability has its roots in attempts to analyze games of chance by Gerolamo Cardano in the sixteenth century, by Pierre de Fermat and Blaise Pascal in the seventeenth century.

Christiaan Huygens published a book on the subject in 1657 and in the 19th century, Pierre Laplace completed what is today considered the classic interpretation. Probability theory considered discrete events, its methods were combinatorial. Analytical considerations compelled the incorporation of continuous variables into the theory; this culminated on foundations laid by Andrey Nikolaevich Kolmogorov. Kolmogorov combined the notion of sample space, introduced by Richard von Mises, measure theory and presented his axiom system for probability theory in 1933; this became the undisputed axiomatic basis for modern probability theory. Most introductions to probability theory treat discrete probability distributions and continuous probability distributions separately; the measure theory-based treatment of probability covers the discrete, continuous, a mix of the two, more. Consider an experiment that can produce a number of outcomes; the set of all outcomes is called the sample space of the experiment.

The power set of the sample space is formed by considering all different collections of possible results. For example, rolling an honest die produces one of six possible results. One collection of possible results corresponds to getting an odd number. Thus, the subset is an element of the power set of the sample space of die rolls; these collections are called events. In this case, is the event that the die falls on some odd number. If the results that occur fall in a given event, that event is said to have occurred. Probability is a way of assigning every "event" a value between zero and one, with the requirement that the event made up of all possible results be assigned a value of one. To qualify as a probability distribution, the assignment of values must satisfy the requirement that if you look at a collection of mutually exclusive events, the probability that any of these events occurs is given by the sum of the probabilities of the events; the probability that any one of the events, or will occur is 5/6.

This is the same as saying that the probability of event is 5/6. This event encompasses the possibility of any number except five being rolled; the mutually exclusive event has a probability of 1/6, the event has a probability of 1, that is, absolute certainty. When doing calculations using the outcomes of an experiment, it is necessary that all those elementary events have a number assigned to them; this is done using a random variable. A random variable is a function that assigns to each elementary event in the sample space a real number; this function is denoted by a capital letter. In the case of a die, the assignment of a number to a certain elementary events can be done using the identity function; this does not always work. For example, when flipping a coin the two possible outcomes are "heads" and "tails". In this example, the random variable X could assign to the outcome "heads" the number "0" and to the outcome "tails" the number "1" ( X ( t a i l

Bivalve shell

A bivalve shell is part of the body, the exoskeleton or shell, of a bivalve mollusk. In life, the shell of this class of mollusks is composed of valves. Bivalves are common in all aquatic locales, including saltwater, brackish water, freshwater; the shells of bivalves wash up on beaches and along the edges of lakes and streams. Bivalves by definition possess two shells or valves, a "right valve" and a "left valve", that are joined by a ligament; the two valves articulate with one another using structures known as "teeth" which are situated along the hinge line. In many bivalve shells, the two valves are symmetrical along the hinge line—when symmetrical, such an animal is said to be equivalved. If symmetrical front-to-back, the valves are said to be equilateral, are otherwise considered inequilateral; this exoskeleton serves not only for muscle attachment, but for protection from predators and from mechanical damage. The shell has several layers, is made of calcium carbonate precipitated out into an organic matrix.

It is secreted by a part of the molluscan body known as the mantle. The shells of bivalves are equal sides connected by a hinge. Bivalve shells are collected by professional and amateur conchologists and are sometimes harvested for commercial sale in the international shell trade or for use in glue, chalk, or varnish to the detriment of the local ecology; the bivalve shell is composed of two calcareous valves. The mantle, a thin membrane surrounding the body, secretes the shell valves and hinge teeth; the mantle lobes secrete the valves, the mantle crest creates the other parts. The mantle itself is attached to the shell by numerous small mantle retractor muscles, which are arranged in a narrow line along the length of the interior of the shell; the position of this line is quite visible on the inside of each valve of a bivalve shell, as a shiny line, the pallial line, which runs along a small distance in from the outer edge of each valve joining the anterior adductor muscle scar to the posterior adductor muscle scar.

The adductor muscles are. In some bivalves the mantle edges fuse to form siphons, which take in and expel water during suspension feeding. Species which live buried in sediment have long siphons, when the bivalve needs to close its shell, these siphons retract into a pocket-like space in the mantle; this feature of the internal anatomy of a bivalve is indicated on the interior of the shell surface as a pallial sinus, an indentation in the pallial line. In addition, the water flows through incurrent siphon ventrally and exit out of the body through excurrent dorsally to the body; the valves of the shell are made of either calcite or both calcite and aragonite with the aragonite forming an inner layer, as is the case with the Pteriida which have this layer in the form of nacre or mother of pearl. The outermost layer of the shell is known as the periostracum and is composed of a horny organic substance; this sometimes forms a brownish "skin" on the outside of the shell. The periostracum may start to peel off of a shell when the shell is allowed to dry out for long periods.

The shell is added to, increases in size, in two ways—by increments added to the open edge of the shell, by a gradual thickening throughout the animal's life. The two shell valves are held together at the animal's dorsum by the ligament, composed of the tensilium and resilium. In life the ligament opens the shell, the adductor muscle or muscles close the shell; when a bivalve dies, its adductor muscle relax and the resilium pushes the valves open. A few groups of bivalves are active swimmers like the scallops. In many species of cemented bivalves, the lower valve is more cupped than the upper valve, which tends to be rather flat. In some groups of cemented bivalves the lower or cemented valve is the left valve, in others it is the right valve; the oldest point of a bivalve shell is called the beak, the raised area around it is known as the umbo. The hinge area is the back of the shell; the lower, curved margin is the ventral side. The anterior or front of the shell is where the byssus and foot are located and the posterior or back of the shell is where the siphon is located.

Without being able to view these organs, determining anterior and posterior can be rather more difficult. In those animals with a siphon, the pallial sinus of the siphon, which will be present on both the left and right valves, will point towards the animal's posterior— such valves are called sinopalliate. Shells without a pallial sinus are termed integripalliate— such animals have a byssal notch present on the anterior end of the right valve, the anterior auricles or "wings" of both valves will be either larger than, or equal to, the posterior ones; such valves may have a dist

Rock 'n' Roll (Motörhead album)

Rock'N' Roll is the eighth studio album by the band Motörhead, released 5 September 1987, their last studio album with the GWR label, as more legal issues enthralled the band with yet another label. Reaching only No. 34 in the UK Albums Chart, Rock'N' Roll was, in that respect, the worst performing of all of Motörhead's Top 40 chart hits. It would see the return of'classic line up' drummer "Philthy Animal" Taylor, albeit only for a few more years before being fired. In 1987, Motörhead appeared in the Peter Richardson film Eat the Rich, which starred the regular cast of The Comic Strip and Motörhead bassist/vocalist Lemmy Kilmister himself in a small part as "Spider"; the band supplied six songs for the soundtrack as well. As the band was about to film their cameo, drummer Pete Gill was fired and Phil "Philthy Animal" Taylor rejoined after having quit in 1984. In his autobiography White Line Fever, Lemmy states the sacking of Gill was a long time coming: ".. Peter was his own worst enemy, he was another one.

He went up against me on a couple of decisions, he was making Phil and Wurzel upset too. I got tired of him moaning, so when he kept us waiting while he hung around in the lobby of his hotel for twenty minutes while he read the paper or something, the proverbial last straw. I know it sounds trivial, but most flare-ups in families are, aren't they? And a band is a family.." Lemmy adds that he knew Taylor, playing with Frankie Miller and ex-Thin Lizzy guitarist Brian "Robbo" Robertson, wanted to come back. Rock'N' Roll would be the final album recorded by Motörhead on the GWR label and the last before Lemmy would relocate from the UK to Los Angeles. Rock'N' Roll was produced by the band and Guy Bidmead at Master Rock Studios and Redwood Studios in London. In the Motörhead documentary The Guts and the Glory, guitarist Phil Campbell states, "I like it. It's not a great album but... There's things on there I like, a lot of good things I like." Campbell adds that the studio manager informed them that the studio they were recording in was owned by Michael Palin, Motörhead – who were all huge Monty Python fans – invited Palin to come down and do a recitation for the album.

Palin showed up dressed in a 1940s cricketer outfit, with a V-necked sweater and his hair all brushed to one side. Lemmy remembers Palin walking in and saying, "Hello, what sort of thing are we going to do now, then?" and Lemmy answering "Well, you know in The Meaning of Life, there was this speech that began'Oh Lord — .'" Palin replied "Ah! Give me some cathedral!" and went in and recorded the'Oh Lord, look down upon these people from Motörhead' speech. The song "Eat the Rich" was written for the Richardson film and a music video was released as well. In his 2002 memoir, Lemmy assesses the album: ".. Anyhow, with Pete gone, we gave Phil Taylor his job back, it was a mistake in retrospect... things weren't the same, I should have known they wouldn't be... Rock'N' Roll is a fair album, but it isn't one of our best... Our biggest mistake was choosing Guy Bidmead to produce it, he was just an engineer so we were pretty much producing ourselves... And Wurzel was having a bad time personally... In addition to all of this, we didn't have enough time to do the songs properly and when that happens you're pretty much wasting your time.."

As with the previous two albums it was not a commercial success though Lemmy had appeared in a comedy film by the same name as the single, the sound track to, "Eat The Rich". It continued the downwards momentum of the band into the late eighties, with no original release until 1991, when they made the 1916 album. Lemmy writes that Rock'N' Roll has some great songs, like "Dogs," "Boogeyman," and "Traitor", which they played "for years," but overall it just didn't seem to work. According to Joel McIver's 2011 Motörhead biography Overkill: The Untold Story of Motörhead, a court case between the band and GWR was sparked over the choice of a summer single in 1988. Joe Petagno had other ideas for the cover of this album: ".. I had this great nobody wanted to listen to me; the original Rock'N' Roll sleeve was supposed to be going up. I said, "Look, the tongue goes up; this thing is lifting off...it was supposed to be rocketing. So it was like a bomb. A projectile of some sort; when I finished it, they said,'We can't have it going up, it doesn't make any sense'.

So it's coming down. Couldn't convince them; this fucking band....." While calling Motörhead "a rock & roll band in the purest sense," Eduardo Rivadavia of AllMusic concedes: "..the songwriting here is rather uninspired for the band's standards, the one-two punch of the phenomenal title track and the amusing'Eat the Rich' are over too soon.." In 2011 Motörhead biographer Joel McIver wrote: ".. Put bluntly, it's far from Motörhead's finest work, although like all of their albums it has some scintillating high points –'Dogs','Traitor' and'Stone Deaf Forever' among them.." Rock'N' Roll renewed commercial hope for Motörhead in the United States, with Lemmy moving to Los Angeles after the recording of this album permanently. The fans in the States appeared willing to see this band live and buy their albums whereas Britain is criticised as having lost interest in Motörhead. All tracks are written by Kilmister, Campbell, Taylor; the spoken word "Blessing" by Michael Palin is listed on some version as track 5

Ken Baston

Kenneth Charles Baston is an Australian politician, a current Liberal Party member of the Western Australian Legislative Council representing the Mining and Pastoral Region. First elected to parliament at the 2005 state election, Baston was elevated to Cabinet following the 2013 state election, held the positions of Minister for Agriculture and Food and Minister for Fisheries until March 2016. Baston described his childhood—growing up on a sheep station, run by his parents on the coast north west of Carnarvon, Western Australia—as idyllic, he completed his early education by correspondence before heading to boarding school in Perth to complete his education. Following his schooling in Perth, he ran the Ella Valla sheep station on a pastoral lease 90 kilometres south of Carnarvon, exporting wool and meat. Baston won preselection for the region for the 2008 election and was chosen to be listed second on the ballot paper for the Liberal Party, after Norman Moore

Hacker-Pschorr Brewery

Hacker-Pschorr is a brewery in Munich, formed in 1972 out of the merger of two breweries and Pschorr. Hacker was founded in 1417, 99 years before the enactment of the Reinheitsgebot Purity Law of 1516; as one of six breweries located within Munich's city limits, its beers are among those served at Oktoberfest. In the late 18th century, Joseph Pschorr bought the Hacker brewery from his father-in-law Peter-Paul Hacker, he subsequently founded a separate brewery under his own name. His two sons, Georg Pschorr and Matthias Pschorr Sr. divided his estate by each taking control of one of the two separate breweries. In 1972, Hacker and Pschorr merged to form Hacker-Pschorr, but the beers were sold as separate brands well after 1975; when Crown Prince Ludwig I of Bavaria was to celebrate his wedding in Munich in 1810, he decided it was an occasion for all of Bavaria to celebrate. He commissioned Josef Pschorr the brewmaster of the Hacker-Pschorr brewery, among other Munich brewers, to develop special brews to commemorate the occasion.

Subsequent annual celebrations evolved into the city of Munich’s Oktoberfest, attended by over six million people each year, who in 2011 consumed over six million litres of beer. By Munich law, only the six breweries within the city limits of Munich are invited to serve their beer at Oktoberfest. Hacker-Pschorr is one of the six, as is Paulaner. Today’s event is held on land donated by Josef Pschorr. Prior to 2009, Hacker-Pschorr was imported to the U. S. via Star Brand Imports, based in New York and part of Heineken International. In 2009, Paulaner HP USA, of Littleton, took over the import business of Hacker-Pschorr and Paulaner in the United States. Hacker-Pschorr produces 15 different products, some of them are only seasonally available. Hacker-Pschorr Weisse is the company's flagship beer. Hacker-Pschorr Official U. S. Hacker-Pschorr Website Official U. S. Hacker-Pschorr Blog Documents and clippings about Hacker-Pschorr Brewery in the 20th Century Press Archives of the ZBW

Arabesques (short story collection)

Arabesques are collected works written and compiled by Nikolai Gogol, first published in January 1835. The collection consists of two parts, diverse in content, hence its name: ″arabesques,″ a special type of Arabic design where lines wind around each other. Articles on chronicles, art and as well as few works of fiction merge the collection into one piece. Articles represent Gogol's ideas about literature and art. In A Few Words About Pushkin, for instance, he describes Pushkin as one of the greatest Russian poets and sets task for Russian literature to be fulfilled. In On Little Russian Songs Gogol gave his estimation of Ukrainian folk arts, and in an article about Karl Bryullov's painting The Last Day of Pompeii he assessed the phenomenon of Russian art. «Гоголь. Арабески» на сайте «Лаборатория фантастики»