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Lanchester's Laws
Lanchester's laws are mathematical formulas for calculating the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time, with the function depending only on A and B.Lanchester F.W., ''Mathematics in Warfare'' in ''The World of Mathematics,'' Vol. 4 (1956) Ed. Newman, J.R., Simon and Schuster, 2138–2157; anthologised from ''Aircraft in Warfare'' (1916) In 1915 and 1916 during World War I, M. Osipov and Frederick Lanchester independently devised a series of differential equations to demonstrate the power relationships between opposing forces. Among these are what is known as ''Lanchester's linear law'' (for ancient combat) and ''Lanchester's square law'' (for modern combat with long-range weapons such as firearms). As of 2017 modified variations of the Lanchester equations continue to form the basis of analysis in many of the US Army’s combat simulatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship between given quantities. The plural of ''formula'' can be either ''formulas'' (from the most common English plural noun form) or, under the influence of scientific Latin, ''formulae'' (from the original Latin). In mathematics In mathematics, a formula generally refers to an equation or inequality relating one mathematical expression to another, with the most important ones being mathematical theorems. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. However, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Battle Of Gettysburg
The Battle of Gettysburg () was a three-day battle in the American Civil War, which was fought between the Union and Confederate armies between July 1 and July 3, 1863, in and around Gettysburg, Pennsylvania. The battle, won by the Union, is widely considered the Civil War's turning point, leading to an ultimate victory of the Union and the preservation of the nation. The Battle of Gettysburg was the bloodiest battle of both the Civil War and of any battle in American military history, claiming over 50,000 combined casualties. Union Major General George Meade's Army of the Potomac defeated attacks by Confederate General Robert E. Lee's Army of Northern Virginia, halting Lee's invasion of the North and forcing his retreat.A prior attempt by Lee to invade the north culminated in the Battle of Antietam and 23,000 casualties, the most of any single day Civil War.Rawley, p. 147; Sauers, p. 827; Gallagher, ''Lee and His Army'', p. 83; McPherson, p. 665; Eicher, p. 550. Gal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lewis Fry Richardson
Lewis Fry Richardson, Fellow of the Royal Society, FRS (11 October 1881 – 30 September 1953) was an English mathematician, physicist, meteorologist, psychologist, and Pacifism, pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them. He is also noted for his pioneering work on fractals and a method for solving a system of linear equations known as modified Richardson iteration. Early life Lewis Fry Richardson was the youngest of seven children born to Catherine Fry (1838–1919) and David Richardson (1835–1913). They were a prosperous Quaker family, David Richardson operating a successful tanning and leather-manufacturing business. At age 12 he was sent to a Quaker boarding school, Bootham School in York, where he received an education in science, which stimulated an active interest in natural history. In 1898 he went on to Durham College of Science (a coll ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Petrie Multiplier
The Petrie multiplier is a thought experiment or mathematical model invented by British computer scientist Karen Petrie, and first described by Ian Gent in 2013. The multiplier "shows that if the percentage of men and women in the room who make questionable remarks to the other sex is equal, then the average number of sexist remarks experienced by members of one party scales by the square of the proportion of the offending party to the other. Mathematical formulation Gent defined the multiplier in the following terms: The Petrie multiplier corresponds to Lanchester's square law in battle and predator–prey dynamics. Expanded model The model assumes that men and women are equally sexist. Further, each sexist remark made by a man is assumed to randomly target one of the women and vice versa. A more complex analysis published in the Journal of Physics A modeled heterogeneous levels of sexism by assuming each person to make sexist remarks according to an independent Poisson proce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maneuver Warfare
Maneuver warfare, or manoeuvre warfare, is a military strategy which emphasizes movement, initiative and surprise to achieve a position of advantage. Maneuver seeks to inflict losses indirectly by envelopment, encirclement and disruption, while minimizing the need to engage in frontal combat. In contrast to attrition warfare where strength tends to be applied against strength, maneuver warfare attempts to apply strength against weakness in order to accomplish the mission. Maneuver warfare, the use of initiative, originality and the unexpected, combined with a ruthless determination to succeed, seeks to avoid opponents' strengths while exploiting their weaknesses and attacking their critical vulnerabilities and is the conceptual opposite of attrition warfare. Rather than seeking victory by applying superior force and mass to achieve physical destruction, maneuver uses preemption, deception, dislocation, and disruption to destroy the enemy's will and ability to fight. Historicall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Attrition Warfare
Attrition warfare is a form of military strategy in which one side attempts to gradually wear down its opponent to the point of collapse by inflicting continuous losses in personnel, materiel, and morale. The term ''attrition'' is derived from the Latin word , meaning "to wear down" or "to rub against", reflecting the grinding nature of the strategy. Strategic considerations Attrition warfare seeks to erode an opponent’s capacity to wage war by systematically destroying their military resources, morale, and logistics over time. This may involve guerrilla warfare, people's war, scorched earth tactics, or prolonged engagements short of a decisive battle. It contrasts with strategies such as blitzkrieg or force concentration, which aim to achieve rapid victory through overwhelming power in a single decisive engagement. As Clausewitz described, it is a strategy of exhausting the adversary’s will and capability to fight. A combatant facing a significant disadvantage may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Function
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation f(x) = \frac where The logistic function has domain the real numbers, the limit as x \to -\infty is 0, and the limit as x \to +\infty is L. The exponential function with negated argument (e^ ) is used to define the standard logistic function, depicted at right, where L=1, k=1, x_0=0, which has the equation f(x) = \frac and is sometimes simply called the sigmoid. It is also sometimes called the expit, being the inverse function of the logit. The logistic function finds applications in a range of fields, including biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, statistics, and artificial neural networks. There are various generalizations, depending on the field. History The logistic function was introduced in a series of three papers by Pier ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean of numbers is the Nth root, th root of their product (mathematics), product, i.e., for a collection of numbers , the geometric mean is defined as : \sqrt[n]. When the collection of numbers and their geometric mean are plotted in logarithmic scale, the geometric mean is transformed into an arithmetic mean, so the geometric mean can equivalently be calculated by taking the natural logarithm of each number, finding the arithmetic mean of the logarithms, and then returning the result to linear scale using the exponential function , :\sqrt[n] = \exp \left( \frac \right). The geometric mean of two numbers is the square root of their product, for example with numbers and the geometric mean is \textstyle \sqrt = The geometric mean o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fire Ants
Fire ants are several species of ants in the genus ''Solenopsis'', which includes over 200 species. ''Solenopsis'' are stinging ants, and most of their common names reflect this, for example, ginger ants and tropical fire ants. Many of the names shared by this genus are often used interchangeably to refer to other species of ant, such as the term red ant, mostly because of their similar coloration despite not being in the genus ''Solenopsis''. Both '' Myrmica rubra'' and '' Pogonomyrmex barbatus'' are common examples of non-Solenopsis ants being termed red ants. None of these common names apply to all species of ''Solenopsis'' nor exclusively to species of ''Solenopsis''; for example, several species of weaver ants of the genus '' Oecophylla'' in Southeast Asia are colloquially called "fire ants" because of their similar coloration and painful bites, but the two genera are not closely related. '' Wasmannia auropunctata'' is another unrelated ant more commonly called the "littl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Argentine Ant
The Argentine ant (''Linepithema humile'', formerly ''Iridomyrmex humilis'') is an ant native to northern Argentina, Uruguay, Paraguay, Bolivia and southern Brazil. This invasive species was inadvertently introduced by humans on a global scale and has become established in many Mediterranean climate areas, including South Africa, New Zealand, Japan, Easter Island, Australia, the Azores, Europe, Hawaii, and the continental United States. Argentine ants are significant pests within agricultural and urban settings, and are documented to cause substantial harm to communities of native arthropods, vertebrates, and plants within their invaded range. Description ''Linepithema humile'' is a small-bodied (2.2–2.6 mm) ant species, dull light to dark brown in color. Within the invasion zone, ant colonies are large and include many workers and multiple queens. Argentine ants are opportunistic with regard to nesting preferences. Colony nests have been found in the ground, in cracks in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meat Ants
The meat ant (''Iridomyrmex purpureus''), also known as the gravel ant or southern meat ant, is a species of ant endemic to Australia. A member of the genus ''Iridomyrmex'' in the subfamily Dolichoderinae, it was described by British entomologist Frederick Smith in 1858. The meat ant is associated with many common names due to its appearance, nest-building behaviour and abundance, of which its specific name, ''purpureus'', refers to its coloured appearance. It is among the best-known species of ant found throughout Australia; it occurs in almost all states and territories except for Tasmania. Its enormous distribution, aggression and ecological importance have made this ant a dominant species. The meat ant is monomorphic (occurs in a particular form), although there is evidence that certain populations can be polymorphic. It is characterised by its dark-bluish body and red head. It is a medium to large species, measuring . The workers and males are approximately the same s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
