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Just as the class P is defined in terms of polynomial running time, the class EXPTIME is the set of all decision problems that have exponential running time. In other words, any problem in EXPTIME is solvable by a deterministic Turing machine in O (2 p ( n ) ) time, where p ( n ) is a polynomial function of n .
In 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 .
Plot of the Chebyshev polynomial of the first kind () with = in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D. The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as () and ().
Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation.
In mathematics, the Gaussian or ordinary hypergeometric function 2 F 1 (a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases.
By the Artin–Wedderburn theorem, a central simple algebra is the matrix ring of a division ring; thus, each similarity class is represented by a unique division ring. For example, Br( k ) is trivial if k is a finite field or an algebraically closed field (more generally quasi-algebraically closed field ; cf. Tsen's theorem ).
In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space.
Based on this property, the class of graphs (and multigraphs) for which every cycle basis is weakly fundamental can be characterized by five forbidden minors: the graph of the square pyramid, the multigraph formed by doubling all edges of a four-vertex cycle, two multigraphs formed by doubling two edges of a tetrahedron, and the multigraph ...