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The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
Theorem (Lefschetz theorem on (1,1)-classes) Any element of (,), is the cohomology class of a divisor on . In particular, the Hodge conjecture is true for H 2 {\displaystyle H^{2}} . A very quick proof can be given using sheaf cohomology and the exponential exact sequence .
Landau's fourth problem asked whether there are infinitely many primes which are of the form = + for integer n. (The list of known primes of this form is A002496 .) The existence of infinitely many such primes would follow as a consequence of other number-theoretic conjectures such as the Bunyakovsky conjecture and Bateman–Horn conjecture .
The debate concerned the nature and role of capital goods and a critique of the neoclassical vision of aggregate production and distribution. The question of whether the natural growth rate is exogenous, or endogenous to demand (and whether it is input growth that causes output growth, or vice versa), lies at the heart of the debate.
In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms.They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture.
In contract law, the lex loci contractus is the Law Latin term meaning "law of the place where the contract is made". [ 1 ] [ 2 ] It refers (in the context of conflict of laws ) to resolving contractual disputes among parties of differing jurisdictions by using the law of the jurisdiction in which the contract was created.
Business mathematics comprises mathematics credits taken at an undergraduate level by business students.The course [3] is often organized around the various business sub-disciplines, including the above applications, and usually includes a separate module on interest calculations; the mathematics itself comprises mainly algebraic techniques. [1]