|
Joseph Bertrand
Joseph Louis François Bertrand (; 11 March 1822 – 5 April 1900) was a French mathematician whose work emphasized number theory, differential geometry, probability theory, economics and thermodynamics. Biography Joseph Bertrand was the son of physician Alexandre Jacques François Bertrand and the brother of archaeologist Alexandre Bertrand. His father died when Joseph was only nine years old; by that time he had learned a substantial amount of mathematics and could speak Latin fluently. At eleven years old he attended the course of the École Polytechnique as an auditor. From age eleven to seventeen, he obtained two bachelor's degrees, a license and a PhD with a thesis concerning the mathematical theory of electricity, and was admitted to the 1839 entrance examination of the École Polytechnique. Bertrand was a professor at the École Polytechnique and Collège de France, and was a member of the Paris Academy of Sciences of which he was the permanent secretary for twenty-si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of cities in the European Union by population within city limits, fourth-most populous city in the European Union and the List of cities proper by population density, 30th most densely populated city in the world in 2022. Since the 17th century, Paris has been one of the world's major centres of finance, diplomacy, commerce, culture, Fashion capital, fashion, and gastronomy. Because of its leading role in the French art, arts and Science and technology in France, sciences and its early adoption of extensive street lighting, Paris became known as the City of Light in the 19th century. The City of Paris is the centre of the Île-de-France region, or Paris Region, with an official estimated population of 12,271,794 inhabitants in January 2023, or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bertrand's Box Paradox
Bertrand's box paradox is a Paradox#Quine's_classification, veridical paradox in elementary probability theory. It was first posed by Joseph Bertrand in his 1889 work Calcul des Probabilités'. There are three boxes: # a box containing two gold coins, # a box containing two silver coins, # a box containing one gold coin and one silver coin. A coin withdrawn at random from one of the three boxes happens to be a gold. What is the probability the other coin from the same box will also be a gold coin? A veridical paradox is a paradox whose correct solution seems to be counterintuitive. It may seem intuitive that the probability that the remaining coin is gold should be , but the probability is actually . Bertrand showed that if were correct, it would result in a contradiction, so cannot be correct. This simple but counterintuitive puzzle is used as a standard example in teaching probability theory. The solution illustrates some basic principles, including the Kolmogorov axioms. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Swedish Academy Of Sciences
The Royal Swedish Academy of Sciences () is one of the Swedish Royal Academies, royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for promoting natural sciences and mathematics and strengthening their influence in society, whilst endeavouring to promote the exchange of ideas between various disciplines. The goals of the academy are: * To be a forum where researchers meet across subject boundaries, * To offer a unique environment for research, * To provide support to younger researchers, * To reward outstanding research efforts, * To communicate internationally among scientists, * To advance the case for science within society and to influence research policy priorities * To stimulate interest in mathematics and science in school, and * To disseminate and popularize scientific information in various forms. Every year, the academy awards the Nobel Prizes in Nobel Prize in Physics, phy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversible Process (thermodynamics)
In thermodynamics, a reversible process is a process, involving a system and its surroundings, whose direction can be reversed by infinitesimal changes in some properties of the surroundings, such as pressure or temperature. Throughout an entire reversible process, the system is in thermodynamic equilibrium, both physical and chemical, and ''nearly'' in pressure and temperature equilibrium with its surroundings. This prevents unbalanced forces and acceleration of moving system boundaries, which in turn avoids friction and other dissipation. To maintain equilibrium, reversible processes are extremely slow ( ''quasistatic''). The process must occur slowly enough that after some small change in a thermodynamic parameter, the physical processes in the system have enough time for the other parameters to self-adjust to match the new, changed parameter value. For example, if a container of water has sat in a room long enough to match the steady temperature of the surrounding air, for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economic Equilibrium
In economics, economic equilibrium is a situation in which the economic forces of supply and demand are balanced, meaning that economic variables will no longer change. Market equilibrium in this case is a condition where a market price is established through competition such that the amount of goods or services sought by buyers is equal to the amount of goods or services produced by sellers. This price is often called the competitive price or market clearing price and will tend not to change unless demand or supply changes, and quantity is called the "competitive quantity" or market clearing quantity. Understanding economic equilibrium An economic equilibrium is a situation when the economic agent cannot change the situation by adopting any strategy. The concept has been borrowed from the physical sciences. Take a system where physical forces are balanced for instance.This economically interpreted means no further change ensues. Properties of equilibrium Three basic prope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bertrand Competition
Bertrand competition is a model of competition used in economics, named after Joseph Louis François Bertrand (1822–1900). It describes interactions among firms (sellers) that set prices and their customers (buyers) that choose quantities at the prices set. The model was formulated in 1883 by Bertrand in a review of Antoine Augustin Cournot's book ''Recherches sur les Principes Mathématiques de la Théorie des Richesses'' (1838) in which Cournot had put forward the Cournot model. Cournot's model argued that each firm should maximise its profit by selecting a quantity level and then adjusting price level to sell that quantity. The outcome of the model equilibrium involved firms pricing above marginal cost; hence, the competitive price. In his review, Bertrand argued that each firm should instead maximise its profits by selecting a price level that undercuts its competitors' prices, when their prices exceed marginal cost. The model was not formalized by Bertrand; however, the id ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antoine Augustin Cournot
Antoine Augustin Cournot (; 28 August 180131 March 1877) was a French philosopher and mathematician who contributed to the development of economics. Biography Antoine Augustin Cournot was born on August 28, 1801 in Gray, Haute-Saône. He entered the preparatory school at Collège de Gray in 1809, where he studied until the age of 15. He later studied at Collège Royal de Besançon. In 1821, he entered one of the most prestigious Grande école, the École normale supérieure. According to Agnar Sandmo: in 1823 he took a license degree in mathematics at Sorbonne University. He then became the private secretary of a field marshal who required assistance in writing his memoirs. This position left Cournot with considerable time for his own pursuits. In the course of his ten years in the field marshal's employment he took two doctoral degrees, one in mechanics and one in astronomy. In addition, he published a number of articles and even acquired a degree in law. Subsequently, Cou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cournot Competition
Cournot competition is an economic model used to describe an industry structure in which companies compete on the amount of output they will produce, which they decide on independently of each other and at the same time. It is named after Antoine Augustin Cournot (1801–1877) who was inspired by observing competition in a spring water duopoly. It has the following features: * There is more than one firm and all firms produce a homogeneous product, i.e., there is no product differentiation; * Firms do not cooperate, i.e., there is no collusion; * Firms have market power, i.e., each firm's output decision affects the good's price; * The number of firms is fixed; * Firms compete in quantities rather than prices; and * The firms are economically rational and act strategically, usually seeking to maximize profit given their competitors' decisions. An essential assumption of this model is the "not conjecture" that each firm aims to maximize profits, based on the expectation that i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oligopoly
An oligopoly () is a market in which pricing control lies in the hands of a few sellers. As a result of their significant market power, firms in oligopolistic markets can influence prices through manipulating the supply function. Firms in an oligopoly are mutually interdependent, as any action by one firm is expected to affect other firms in the market and evoke a reaction or consequential action. As a result, firms in oligopolistic markets often resort to collusion as means of maximising profits. Nonetheless, in the presence of fierce competition among market participants, oligopolies may develop without collusion. This is a situation similar to perfect competition, where oligopolists have their own market structure. In this situation, each company in the oligopoly has a large share in the industry and plays a pivotal, unique role. Many jurisdictions deem collusion to be illegal as it violates competition laws and is regarded as anti-competition behaviour. The EU com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Method Of Least Squares
The method of least squares is a mathematical optimization technique that aims to determine the best fit function by minimizing the sum of the squares of the differences between the observed values and the predicted values of the model. The method is widely used in areas such as regression analysis, curve fitting and data modeling. The least squares method can be categorized into linear and nonlinear forms, depending on the relationship between the model parameters and the observed data. The method was first proposed by Adrien-Marie Legendre in 1805 and further developed by Carl Friedrich Gauss. History Founding The method of least squares grew out of the fields of astronomy and geodesy, as scientists and mathematicians sought to provide solutions to the challenges of navigating the Earth's oceans during the Age of Discovery. The accurate description of the behavior of celestial bodies was the key to enabling ships to sail in open seas, where sailors could no longer rely on la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Errors
In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate due to the combination of variables in the function. The uncertainty ''u'' can be expressed in a number of ways. It may be defined by the absolute error . Uncertainties can also be defined by the relative error , which is usually written as a percentage. Most commonly, the uncertainty on a quantity is quantified in terms of the standard deviation, , which is the positive square root of the variance. The value of a quantity and its error are then expressed as an interval . However, the most general way of characterizing uncertainty is by specifying its probability distribution. If the probability distribution of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and professor of astronomy from 1807 until his death in 1855. While studying at the University of Göttingen, he propounded several mathematical theorems. As an independent scholar, he wrote the masterpieces '' Disquisitiones Arithmeticae'' and ''Theoria motus corporum coelestium''. Gauss produced the second and third complete proofs of the fundamental theorem of algebra. In number theory, he made numerous contributions, such as the composition law, the law of quadratic reciprocity and the Fermat polygonal number theorem. He also contributed to the theory of binary and ternary quadratic forms, the construction of the heptadecagon, and the theory of hypergeometric series. Due to Gauss' extensive and fundamental contributions to science ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
