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Ind-objects in C form a category ind-C.. Two ind-objects : and : determine a functor I op x J Sets,. namely the functor ((), ()). The set of morphisms between F and G in Ind(C) is defined to be the colimit of this functor in the second variable, followed by the limit in the first variable:
The term complete partial order, abbreviated cpo, has several possible meanings depending on context. A partially ordered set is a directed-complete partial order (dcpo) if each of its directed subsets has a supremum. (A subset of a partial order is directed if it is non-empty and every pair of elements has an upper bound in the subset.)
In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset). The most familiar example is the completeness of the real numbers. A special use of the term refers to complete partial orders or complete lattices. However, many other interesting notions ...
The least-upper-bound property is one form of the completeness axiom for the real numbers, and is sometimes referred to as Dedekind completeness. [2] It can be used to prove many of the fundamental results of real analysis , such as the intermediate value theorem , the Bolzano–Weierstrass theorem , the extreme value theorem , and the Heine ...
Matrix completion of a partially revealed 5 by 5 matrix with rank-1. Left: observed incomplete matrix; Right: matrix completion result. Matrix completion is the task of filling in the missing entries of a partially observed matrix, which is equivalent to performing data imputation in statistics. A wide range of datasets are naturally organized ...
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Bash programmable completion, complete and compgen commands [4] have been available since the beta version of 2.04 [3] in 2000 [5] and offers at least Pathname and filename completion. For KornShell users, file name completion depends on the value of the EDITOR variable. If EDITOR is set to vi, you type part of the name, and then Escape, \.
Indistinguishability under non-adaptive and adaptive Chosen Ciphertext Attack (IND-CCA1, IND-CCA2) uses a definition similar to that of IND-CPA. However, in addition to the public key (or encryption oracle, in the symmetric case), the adversary is given access to a decryption oracle which decrypts arbitrary ciphertexts at the adversary's ...