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A feasible solution that minimizes (or maximizes) the objective function is called an optimal solution. In mathematics, conventional optimization problems are usually stated in terms of minimization. A local minimum x * is defined as an element for which there exists some δ > 0 such that
In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra.In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, [1] India, [2] China, Germany, and Italy.
The arithmetic mean, or less precisely the average, of a list of n numbers x 1, x 2, . . . , x n is the sum of the numbers divided by n: + + +. The geometric mean is similar, except that it is only defined for a list of nonnegative real numbers, and uses multiplication and a root in place of addition and division:
Restricted canonical transformations are coordinate transformations where transformed coordinates Q and P do not have explicit time dependence, i.e., = (,) and = (,).The functional form of Hamilton's equations is ˙ =, ˙ = In general, a transformation (q, p) → (Q, P) does not preserve the form of Hamilton's equations but in the absence of time dependence in transformation, some ...
Linear combinations of atomic orbitals, or the sums and differences of the atomic wavefunctions, provide approximate solutions to the Hartree–Fock equations which correspond to the independent-particle approximation of the molecular Schrödinger equation. For simple diatomic molecules, the wavefunctions obtained are represented mathematically ...
The major objectives of the ISI are [20] to facilitate research and training of Statistics, to indulge in development of statistical theory and in application of statistical techniques – in the scenarios of planning at national level and in theoretical development of natural and social sciences, to participate in the process of data collection and analysis, to operate related projects in ...
The goal is to find models in which existence of money can alter the equilibrium solutions, perhaps because the initial position of agents depends on monetary prices. Some critics of general equilibrium modeling contend that much research in these models constitutes exercises in pure mathematics with no connection to actual economies.
Later, the results were rescheduled to be declared on June 12, 2015. On 15 June 2015 the Supreme Court asked CBSE to re-conduct the AIPMT 2015 Exam within 4 weeks (by 12 July 2015). After a hearing on the pleas of CBSE, Supreme Court had decided to re-conduct exam on 25 July 2015.