منابع مشابه
Local Invertibility in Subrings of C*{x)
It is known that the maximal ideals in the rings C(X) and C*(X) of continuous and bounded continuous functions on X, respectively, are in one-to-one correspondence with j3X. We have shown previously that the same is true for any ring A(X) between C(X) and C*(X). Here we consider the problem for rings A(X) contained in C'{X) which are complete rings of functions (that is, they contain the consta...
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Using a novel Wintner-type formulation of the classical Peano’s existence theorem [Math. Ann. 37 (1890), 182-228], we enhance Ważewski’s result on invertibility of maps defined on closed balls [Ann. Soc. Pol. Math. 20 (1947), 81-125] securing the size of the domain of invertibility that agrees with the bounds derived by John [Comm. Pure Appl. Math. 21 (1968), 77-110] and Sotomayor [Z. Angew. Ma...
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Suppose that m,n ∈ N and that A : R → R is a linear operator. It is shown here that if k, r ∈ N satisfy k < r 6 rank(A) then there exists a subset σ ⊆ {1, . . . ,m} with |σ| = k such that the restriction of A to R ⊆ R is invertible, and moreover the operator norm of the inverse A−1 : A(R) → R is at most a constant multiple of the quantity √ mr/((r − k) ∑m i=r si(A) 2), where s1(A) > . . . > sm(...
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In cryptosystem theory, it is well-known that a logical mapping that returns the same value that was used as its argument can be inverted with a zero failure probability in linear time. In this paper, however, I show that such a mapping, while trivially assigning a logical state to itself, comes up against an impassable entropy wall such that its computational path is undone inside the threshol...
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The invertibility of the rules of a sequent calculus is important for guiding proof search and can be used in some formalised proofs of Cut admissibility. We present sufficient conditions for when a rule is invertible with respect to a calculus. We illustrate the conditions with examples. It must be noted we give purely syntactic criteria; no guarantees are given as to the suitability of the ru...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1964
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-54-1-15-25