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Polynomial SOS. In mathematics, a form (i.e. a homogeneous polynomial) h ( x) of degree 2 m in the real n -dimensional vector x is sum of squares of forms (SOS) if and only if there exist forms of degree m such that. Every form that is SOS is also a positive polynomial, and although the converse is not always true, Hilbert proved that for n = 2 ...
SOS-convexity. A multivariate polynomial is SOS-convex (or sum of squares convex) if its Hessian matrix H can be factored as H (x) = ST (x) S (x) where S is a matrix (possibly rectangular) which entries are polynomials in x. [1] In other words, the Hessian matrix is a SOS matrix polynomial. An equivalent definition is that the form defined as g ...
Signs of trigonometric functions in each quadrant. All Students Take Calculus is a mnemonic for the sign of each trigonometric functions in each quadrant of the plane. The letters ASTC signify which of the trigonometric functions are positive, starting in the top right 1st quadrant and moving counterclockwise through quadrants 2 to 4.
In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is where b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term "base" denotes any side, and "height" denotes the length of a perpendicular ...
a.e. – almost everywhere. AFSOC - Assume for the sake of contradiction. Ai – Airy function. AL – Action limit. Alt – alternating group (Alt (n) is also written as A n.) A.M. – arithmetic mean. AP – arithmetic progression. arccos – inverse cosine function. arccosec – inverse cosecant function.
Viète. de Moivre. Euler. Fourier. v. t. e. In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.
Hinge theorem. In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the ...
Glossary of mathematical symbols. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various ...