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SUMMARY / RELATED TOPICS

Kuiper's test

Kuiper's test is used in statistics to test that whether a given distribution, or family of distributions, is contradicted by evidence from a sample of data. It is named after Dutch mathematician Nicolaas Kuiper. Kuiper's test is related to the better-known Kolmogorov–Smirnov test; as with the K-S test, the discrepancy statistics D+ and D− represent the absolute sizes of the most positive and most negative differences between the two cumulative distribution functions that are being compared. The trick with Kuiper's test is to use the quantity D+ + D− as the test statistic; this small change makes Kuiper's test as sensitive in the tails as at the median and makes it invariant under cyclic transformations of the independent variable. The Anderson–Darling test is another test that provides equal sensitivity at the tails as the median, but it does not provide the cyclic invariance; this invariance under cyclic transformations makes Kuiper's test invaluable when testing for cyclic variations by time of year or day of the week or time of day, more for testing the fit of, differences between, circular probability distributions.

The test statistic, V, for Kuiper's test is defined. Let F be the continuous cumulative distribution function, to be the null hypothesis. Denote the sample of data which are independent realisations of random variables, having F as their distribution function, by xi. Define z i = F, D + = m a x, D − = m a x, V = D + + D −. Tables for the critical points of the test statistic are available, these include certain cases where the distribution being tested is not known, so that parameters of the family of distributions are estimated. We could test the hypothesis. To test this, we would collect the dates on which the test set of computers had failed and build an empirical distribution function; the null hypothesis is. Kuiper's statistic does not change if we change the beginning of the year and does not require that we bin failures into months or the like. Another test statistic having this property is the Watson statistic, related to the Cramér–von Mises test. However, if failures occur on weekends, many uniform-distribution tests such as K-S and Kuiper would miss this, since weekends are spread throughout the year.

This inability to distinguish distributions with a comb-like shape from continuous uniform distributions is a key problem with all statistics based on a variant of the K-S test. Kuiper's test, applied to the event times modulo one week, is able to detect such a pattern. Using event times that have been modulated with the K-S test can result in different results depending on how the data is phased. In this example, the K-S test may detect the non-uniformity if the data is set to start the week on Saturday, but fail to detect the non-uniformity if the week starts on Wednesday. Kolmogorov–Smirnov test

Gun laws in Wisconsin

Gun laws in Wisconsin regulate the sale and use of firearms and ammunition in the U. S. state of Wisconsin. The Constitution of Wisconsin protects the right to bear arms in Article 1, Section 25 - "The people have the right to keep and bear arms for security, hunting, recreation or any other lawful purpose." Wisconsin has state preemption laws which forbid cities from passing firearms or knife ordinances stricter than that of state law. Localities may impose a sales or use tax, may restrict the discharge of firearms. On March 8, 2017, the Wisconsin Supreme Court ruled that Madison's Metro Transit rule forbidding firearms on public buses violated the state's preemption law, that people who are lawfully carrying arms must be allowed to carry on public buses. Wisconsin is a shall-issue state for concealed carry licensing; as of November 1, 2011, Wisconsin residents may apply for a concealed carry license through the Wisconsin Department of Justice. The law allows Wisconsin to become the 49th state in the Union to make some provision for the concealed carry of firearms by normal citizens.

Open carry is legal. It is legal for all adults who are 18 years of age or older unless they are prohibited from possession of firearms. A license is not required unless in a taxpayer-owned building or within 1000 feet of school property and not on private property. In the past, some jurisdictions have tried to prosecute open-carry by equating the open carry of handguns with disorderly conduct. On April 20, 2009 the Wisconsin Attorney General's office released a memorandum to all law enforcement agencies stating that mere open carry of a firearm was not disorderly conduct, instructed both law enforcement and the district attorneys to cease this practice. In 2011 a subsection was added to the Disorderly Conduct statute reading "Unless other facts and circumstances that indicate a criminal or malicious intent on the part of the person apply, a person is not in violation of, may not be charged with a violation of, this section for loading, carrying, or going armed with a firearm, without regard to whether the firearm is loaded or is concealed or carried."

This codified open carry. Loading, or having a loaded, uncased handgun inside a vehicle was legalized beginning November 1, 2011; the firearm must not be "hidden from ordinary observation" while inside the vehicle unless the citizen has a license. However, the Wisconsin Supreme Court ruled that a license is required to have a concealed loaded handgun within reach in a vehicle, regardless of the Safe Transport Statue removing restrictions on transporting loaded handguns. On December 7, 2011, Governor Scott Walker signed a bill passing a Castle Doctrine for Wisconsin; the bill provides criminal immunity and protection from civil suits for homeowners or business owners who use a gun in self-defense while on their property, with the presumption that any action is justified. The law is a "stand your ground" law; this applies at the user's private vehicle, at their home. Protection extends to improvements only, not bare ground; the criminal must have forcibly entered, or be in the process of attempting to forcibly enter, the defender must be present in the home, car, or business.

The Washington County DA ruled. The law does not apply if force is used against police while in the line of duty if the shooter knows or should have known that the victim was a police officer or other public safety worker; the law does not protect those who are engaged in criminal activity. Wisconsin is not a "must notify" state. If an officer is "acting in an official capacity and with lawful authority", the citizen is carrying a concealed weapon, the citizen must show both a carry license and photographic identification upon demand. WI statute 175.60 The Wisconsin Supreme Court ruled that a license is required to have a concealed loaded handgun within reach in a vehicle, regardless of the Safe Transport Statue removing restrictions on transporting loaded handguns. Beginning November 1, 2011, it is legal to load a handgun, or to transport a loaded handgun cased or uncased, in a vehicle without a license. NOTE: This does NOT apply to long guns. There is still some confusion as to whether or not an encased gun is concealed, so if it is cased, best practice is to keep the long gun out of reach.

Long guns must be "discernable to ordinary observation", since a conceal carry license does not apply. All firearms had to be unloaded & encased, & out of reach; those with a concealed carry license may conceal a pistol in a vehicle. WI statute 167.31 Pistols may be carried without a license, or concealed with a license. Long guns must be unloaded. Firearms are prohibited on commercial aircraft except in checked baggage. A discussion of federal laws is with links to and quotes from the statutes. Carry is legal on a private aircraft. With a license a user may carry or concealed. Without a license, only open carry is legal. Anyone on their own property, on-duty law enforcement officers, military personnel on active duty and their family and employees on farm tractors inside CWD eradication zones, disabled hunters with special permits meeting all the requirements. Private sales are legal. No b

Statistical physics

Statistical physics is a branch of physics that uses methods of probability theory and statistics, the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature, its applications include many problems in the fields of physics, chemistry and some social sciences, such as sociology and linguistics. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. In particular, statistical mechanics develops the phenomenological results of thermodynamics from a probabilistic examination of the underlying microscopic systems. One of the first topics in physics where statistical methods were applied was the field of mechanics, concerned with the motion of particles or objects when subjected to a force. Statistical mechanics provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a natural result of statistics, classical mechanics, quantum mechanics at the microscopic level.

Because of this history, statistical physics is considered synonymous with statistical mechanics or statistical thermodynamics. One of the most important equations in statistical mechanics is the definition of the partition function Z, a weighted sum of all possible states q available to a system. Z = ∑ q e − E k B T where k B is the Boltzmann constant, T is temperature and E is energy of state q. Furthermore, the probability of a given state, q, occurring is given by P = e − E k B T Z Here we see that very-high-energy states have little probability of occurring, a result, consistent with intuition. A statistical approach can work well in classical systems when the number of degrees of freedom is so large that the exact solution is not possible, or not useful. Statistical mechanics can describe work in non-linear dynamics, chaos theory, thermal physics, fluid dynamics, or plasma physics. Although some problems in statistical physics can be solved analytically using approximations and expansions, most current research utilizes the large processing power of modern computers to simulate or approximate solutions.

A common approach to statistical problems is to use a Monte Carlo simulation to yield insight into the properties of a complex system. Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble is described by a density operator S, a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system; this can be shown under various mathematical formalisms for quantum mechanics. One such formalism is provided by quantum logic. A significant contribution in development of statistical physics was given by Satyendra Nath Bose, James Clerk Maxwell, Ludwig Boltzmann, J. Willard Gibbs, Marian Smoluchowski, Albert Einstein, Enrico Fermi, Richard Feynman, Lev Landau, Vladimir Fock, Werner Heisenberg, Nikolay Bogolyubov, Benjamin Widom, Lars Onsager and Jeremy Chubb, Humb and others. Statistical physics is studied in the nuclear center at Los Alamos. Pentagon has organized a large department for the study of turbulence at Princeton University.

Work in this area is being conducted by Saclay, Max Planck Institute, Netherlands Institute for Atomic and Molecular Physics and other research centers. Statistical physics allowed us to explain and quantitatively describe superconductivity, turbulence, antiphlogistine, collective phenomena in solids and plasma, the structural features of liquid, it underlies the modern astrophysics. It is statistical physics that helped us to create such intensively developing study of liquid crystals and to construct a theory of phase transition and critical phenomena. Many experimental studies of matter are based on the statistical description of a system; these include the scattering of cold neutrons, X-ray, visible light, more. Statistical physics plays a major role in Physics of Solid State Physics, Materials Science, Nuclear Physics, Chemistry and Medicine, Information Theory and Technique but in those areas of technology owing to their development in the evolution of Modern Physics, it still has important applications

HMS E51

HMS E51 was a British E class submarine built ordered from Yarrow, Scotstoun but transferred to Scotts, Greenock on 3 March 1915. HMS E51 was laid down on 30 November 1916 and commissioned on 27 January 1917. E51 was sold for scrap on 13 October 1921. Like all post-E8 British E-class submarines, E51 had a displacement of 662 tonnes at the surface and 807 tonnes while submerged, she had a beam length of 22 feet 8.5 inches. She was powered by two 800 horsepower Vickers eight-cylinder two-stroke diesel engines and two 420 horsepower electric motors; the submarine had a submerged speed of 10 knots. British E-class submarines had fuel capacities of 50 tonnes of diesel and ranges of 3,255 miles when travelling at 10 knots. E51 was capable of operating submerged for five hours. E51 was armed with a 12-pounder 76 mm QF gun mounted forward of the conning tower, she had five 18 inch torpedo tubes, two in the bow, one either side amidships, one in the stern. E-Class submarines had wireless systems with 1 kilowatt power ratings.

Their maximum design depth was 100 feet. Some submarines contained Fessenden oscillator systems. Hutchinson, Robert. Jane's Submarines: War Beneath the Waves from 1776 to the Present Day. London: HarperCollins. ISBN 978-0-00-710558-8. OCLC 53783010

Geode State Park

Geode State Park is a state park of Iowa, USA, border Henry County and Des Moines County It is managed by the Iowa Department of Natural Resources. While it is named for Iowa's state rock, the geode, few can be found in the park. A display of geodes, with their mysterious crystal formations in their hollow cavities, can be seen at the park office, it is illegal to remove geodes from state parks. The prime attraction of the 1,640-acre park is Lake Geode, a 187-acre lake built in 1950. Over the years, the lake has become well known for excellent fishing for largemouth bass, crappie, channel catfish, red-eared sunfish. Geode State Park joined the Iowa park system in 1937; the spot along the Skunk River had long been a local picnicking spot. Local groups raised $4,800 to purchase 143 acres; the Civilian Conservation Corps moved onto the grounds to begin clearing trees, creating roads and building structures. In 1947, civilian construction workers returned and building resumed. In 1951, the lake, beach and CCC-reminiscent beach house were dedicated.

Opened at the time was an airstrip, making Geode the only park that invited travelers to arrive by private plane. The strip has been closed since. On Saturday, July 25, 2009, a RAGBRAI participant, Donald D. Myers from Rolla, died from injuries sustained in a crash at the bottom of the hill near Geode Lake dam at Geode State Park; some places in the area have been reported to have timber rattlesnakes. Nearby towns are 15 miles to the east; the park can be reached from Middletown on Iowa 79 or from Lowell on County Road J-20. Media related to Geode State Park at Wikimedia Commons Geode State Park

Overberg branch line

The Overberg branch line is a railway line in the Western Cape, South Africa, that runs from Cape Town through Somerset West and Caledon to Bredasdorp. The line branches from the Bellville–Stellenbosch line at Eerste River, from which it runs through Faure and Firgrove to Somerset West. From Van der Stel station in Somerset West a short line branches to the right to Strand. After leaving Somerset West the line passes through Sir Lowry's Pass Village and climbs Sir Lowry's Pass. At the summit of the pass the line reaches an elevation of 415 metres; the line passes through the fruit-farming area of Elgin before descending the Jakkals River valley to Botrivier. From Botrivier it runs across the Overberg plain through Caledon to a junction at Klipdale. From Klipdale one line continues east to Protem. Trains from Cape Town to Bredasdorp cannot pass directly through the junction at Klipdale, but must first pass around a balloon loop. Bredasdorp is the southernmost railway station in Africa; the line is single-track, electrified only as far as Strand.

Metrorail services of the Northern Line operate from Cape Town through Bellville to Strand. The railway arrived at Eerste River in 1862, as part of the construction of the Cape Town–Wellington railway line, the first in the Cape Colony. A branch to Somerset West opened by the Cape Government Railways on 21 October 1889, further to Sir Lowry's Pass Village on 1 February 1890; the Hottentots-Holland mountains were a significant obstacle to any further development, construction of a line over Sir Lowry's Pass only started on 12 July 1899. The effects of the Anglo-Boer War slowed progress, but by 1 August 1902 the line was opened to Caledon. On 16 December 1905 the short branch to Strand was opened. Two extensions of the line from Caledon were possible: eastwards towards Riviersonderend and Swellendam, with the ultimate possibility of reaching Mossel Bay. In 1906 a conference of delegates from the Overberg was unable to agree on a route for a continuation of the line. Meanwhile, by early 1906 the New Cape Central Railway, a private company, had reached Mossel Bay with its line from Worcester via Swellendam, was having difficulty running it at a profit.

Construction on an extension began in 1914, reaching Rietpoel on 5 January 1914, Klipdale on 6 April 1914, Protem on 30 June 1915. This route was Klipdale being about halfway between Riviersonderend and Bredasdorp. "Protem" means "for the time being", reflecting the intention to continue the line to Swellendam at some time in the future. Though, the NCCR was taken over by the South African Railways in 1925, making such an extension unnecessary. In the mid-1920s the SAR embarked on a new phase of railway building, as part of which the line from Klipdale junction south to Bredasdorp was opened on 19 April 1924. Boonzaaier, J. N. C. Tracks Across the Veld. ISBN 978-0-620-41711-2. South Africa Passenger Services 2009. Bruno Martin