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Using the usual notations for a triangle (see the figure at the upper right), where a, b, c are the lengths of the three sides, A, B, C are the vertices opposite those three respective sides, α, β, γ are the corresponding angles at those vertices, s is the semiperimeter, that is, s = a + b + c / 2 , and r is the radius of the inscribed circle, the law of cotangents states that
Open problems on word-representable graphs can be found in, [3] [8] [9] [10] and they include: Characterise (non-)word-representable planar graphs. Characterise word-representable near-triangulations containing the complete graph K 4 (such a characterisation is known for K 4-free planar graphs [17]). Classify graphs with representation number 3.
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
The algorithmic problem of model checking concerns testing whether a given graph models a given sentence. The algorithmic problem of satisfiability concerns testing whether there exists a graph that models a given sentence. Although both model checking and satisfiability are hard in general, several major algorithmic meta-theorems show that ...
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The points labelled 1, Sec(θ), Csc(θ) represent the length of the line segment from the origin to that point. Sin(θ), Tan(θ), and 1 are the heights to the line starting from the x-axis, while Cos(θ), 1, and Cot(θ) are lengths along the x-axis starting from the origin.
A man who carried out a "vicious and violent attack" during riots has been jailed for almost three years. Ameer Khalile, 25, stamped on his victim's head during public disorder that broke out in ...
Cases of norovirus — the virulent, wildly contagious virus that causes vomiting and diarrhea — are increasing in the U.S., the Centers for Disease Control says, reporting double the amount of ...
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