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In solving mathematical equations, particularly linear simultaneous equations, differential equations and integral equations, the terminology homogeneous is often used for equations with some linear operator L on the LHS and 0 on the RHS. In contrast, an equation with a non-zero RHS is called inhomogeneous or non-homogeneous, as exemplified by ...
In the field of geometric topology, a two-dimensional sphere is characterized by the fact that it is the only closed and simply-connected two-dimensional surface. In 1904, Henri Poincaré posed the question of whether an analogous statement holds true for three-dimensional shapes. This came to be known as the Poincaré conjecture, the precise ...
2.1 Mathematics. 2.2 Physics. 2.3 Chemistry. 2.4 Telecommunications engineering. 3 Lists of equations. 4 See also. ... Laws of science; Defining equation (physical ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
A word equation is a formal equality:= = between a pair of words and , each over an alphabet comprising both constants (c.f. ) and unknowns (c.f. ). [1] An assignment h {\displaystyle h} of constant words to the unknowns of E {\displaystyle E} is said to solve E {\displaystyle E} if it maps both sides of E {\displaystyle E} to identical words.
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). [2]
Sigmoid functions most often show a return value (y axis) in the range 0 to 1. Another commonly used range is from −1 to 1. A wide variety of sigmoid functions including the logistic and hyperbolic tangent functions have been used as the activation function of artificial neurons.
The Newton–Pepys problem is a probability problem concerning the probability of throwing sixes from a certain number of dice. [1]In 1693 Samuel Pepys and Isaac Newton corresponded over a problem posed to Pepys by a school teacher named John Smith. [2]