Cauchy's integral theoremIn mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic functions in the complex plane. Essentially, it says that if is holomorphic in a simply connected domain Ω, then for any simply closed contour in Ω, that contour integral is zero.
Semi-differentiabilityIn calculus, a branch of mathematics, the notions of one-sided differentiability and semi-differentiability of a real-valued function f of a real variable are weaker than differentiability. Specifically, the function f is said to be right differentiable at a point a if, roughly speaking, a derivative can be defined as the function's argument x moves to a from the right, and left differentiable at a if the derivative can be defined as x moves to a from the left.
DerivativeIn mathematics, the derivative shows the sensitivity of change of a function's output with respect to the input. Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
Exponential integralIn mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its argument. For real non-zero values of x, the exponential integral Ei(x) is defined as The Risch algorithm shows that Ei is not an elementary function. The definition above can be used for positive values of x, but the integral has to be understood in terms of the Cauchy principal value due to the singularity of the integrand at zero.
MathematicsMathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.
José María CanoJosé Cano Andrés (born 21 February 1959) is a Spanish visual artist, musician, composer, and record producer. From 1982 to 1998, he was a member and principal composer of the Spanish pop-rock band Mecano. Since 1998, he works primarily in the visual arts. José Maria Cano was born in Madrid, and gave his first concerts as a university student there. There he met Ana Torroja, who would become the lead singer in their pop band Mecano. Their first album, also called Mecano (1981) and produced with the financial backing of his father, included the hit "Hoy No Me Puedo Levantar".
André MeyerAndré Benoît Mathieu Meyer (September 3, 1898 – September 9, 1979) was a French-American investment banker. Meyer was born to a low-income Jewish family in Paris. As a boy, he began following the workings of the stock market and out of necessity left school at age sixteen to work as a messenger at the Paris Bourse. Ambitious, he used his time to study the intricacies of stock trading and because of personnel shortages created by so many young French men serving in the military in World War I, he was able to get a job with Baur & Fils, a small Paris bank.
Mirabelle (London restaurant)Mirabelle was a restaurant in the Mayfair area of London. It opened in 1936, and became popular during the 1950s and 1960s, with some celebrities being regulars. Chef Marco Pierre White owned it from 1998 to 2007, and it earned a Michelin star in 2000 under head chef Charlie Rushton, and kept it until its closure for refurbishment in 2008. It remained closed until the site was demolished in 2016/17. The restaurant was first opened in 1936. The interior has a single main dining room, and two private dining rooms entitled the Pine Room and the Chinese Room.
LogarithmIn mathematics, the logarithm is the inverse function to exponentiation. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 103, the logarithm base 10 of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is denoted as logb (x), or without parentheses, logb x, or even without the explicit base, log x, when no confusion is possible, or when the base does not matter such as in big O notation.
Partial derivativeIn mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function with respect to the variable is variously denoted by It can be thought of as the rate of change of the function in the -direction.
Aleksandar DerokoAleksandar Deroko (Александар Дероко; 4 September 1894 – 30 November 1988) was a Serbian architect, artist, and author. He was a professor of the Belgrade University and a member of the Serbian Academy of Sciences and Arts. His great-grandfather was a Venetian named Marco de Rocco, who moved to Dubrovnik (in the Kingdom of Dalmatia) and married a local woman. Aleksandar's grandfather, Jovan, came to Belgrade to be an art teacher. On his maternal side, his great-uncle was Jovan Đorđević (1826–1900), the founder of the Serbian National Theatre in Novi Sad.
Bernhard RiemannGeorg Friedrich Bernhard Riemann (ˈɡeːɔʁk ˈfʁiːdʁɪç ˈbɛʁnhaʁt ˈʁiːman; 17 September 1826 – 20 July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis.
