Sentence examples for a system of distinct from inspiring English sources

In 1935 a mathematician, M. Hall, Jr., of the United States, proved that a necessary and sufficient condition for S1, S2,…, Sn to possess a system of distinct representatives is that, for every k n, any k of the n subsets contain between them at least k distinct elements.

The divided differences at a system of distinct points (x_{0},x_{1},ldots,x_{n}) are denoted by ([ x_{0},x_{1},ldots,x_{n};f ]).

Corollary 3.5 Let ( X, ∥ ⋅ ∥ ) be a normed linear space and let A = { a 1, …, a n } be a system of distinct points in X.

This theorem can be rephrased as follows: the collection (phantom {dot {i}!}{Z_{i}}_{i in N_{ell }}) has a system of distinct representatives if and only if the condition left bigcup_{i in M} Z_{i} right) cap Q neq emptyset holds for every set Q verifying (|overline {Q}| = |M|-1) (where (overline {Q}) denotes the complement of Q).

A classical theorem in combinatorial optimization asserts that the collection of sets (phantom {dot {i}!}{Z_{i}}_{i in N_{ell }}) has a system of distinct representatives if and only if the condition left | bigcup_{i in M} Z_{i} right | geq |M| is satisfied for every subset M of N ℓ (see in particular the seminal text by Ford and Fulkerson [9] and the book by Chvátal [4]).

In the early days of espionage, spies needed a way to exchange sensitive material in public without meeting: a system of "dead drops" was developed (distinct from a "live drop", when spies met).

Hiragana is a Japanese syllabary, a system of characters used to represent distinct Japanese sounds.[3].

Component identification during software design phase denotes a process of partitioning the functionalities of a system into distinct components.

Conceptually, Markov Chain models divide a system into distinct groups of risk factor states linked by transition probabilities, which define the likelihood that a member of one group will transition to another group over time.

Unlike the simple Brusselator, the cortical model is a complicated system comprised of distinct cortical connections.

The Moon and Earth consequently exert a strong gravitational influence on each other, forming a system having distinct properties and behaviour of its own.