scholarly journals A Simple Proof of the Fredholm Alternative and a Characterization of the Fredholm Operators

2001 ◽  
Vol 108 (9) ◽  
pp. 855 ◽  
Author(s):  
A. G. Ramm
Keyword(s):  
Simple Proof ◽  
Fredholm Alternative ◽  
Fredholm Operators

scholarly journals Face Numbers and Nongeneric Initial Ideals

10.37236/1882 ◽  
2006 ◽  
Vol 11 (2) ◽  
Author(s):  
Eric Babson ◽  
Isabella Novik
Keyword(s):  
Cyclic Group ◽  
Simple Proof ◽  
Prime Order ◽  
Necessary Conditions ◽  
Betti Numbers ◽  
Proper Action ◽  
Initial Ideals ◽  
The Face ◽  
Algebraic Shifting

Certain necessary conditions on the face numbers and Betti numbers of simplicial complexes endowed with a proper action of a prime order cyclic group are established. A notion of colored algebraic shifting is defined and its properties are studied. As an application a new simple proof of the characterization of the flag face numbers of balanced Cohen-Macaulay complexes originally due to Stanley (necessity) and Björner, Frankl, and Stanley (sufficiency) is given. The necessity portion of their result is generalized to certain conditions on the face numbers and Betti numbers of balanced Buchsbaum complexes.

scholarly journals Dispersive ordering results

1983 ◽  
Vol 15 (04) ◽  
pp. 889-891 ◽  
Author(s):  
James Lynch ◽  
Gillian Mimmack ◽  
Frank Proschan
Keyword(s):  
Simple Proof ◽  
Total Positivity ◽  
Sign Changes ◽  
Dispersive Ordering

A distribution F is less dispersed than a distribution G if for all . We generalize a characterization of dispersive ordering of Shaked (1982) concerning sign changes of Fc – G, where Fc is a translate of F. We then use this generalization plus total positivity to develop a simple proof of a characterization of dispersive distributions due to Lewis and Thompson (1981); a distribution H is dispersive if

scholarly journals Some Properties oflp(A,X)Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaohong Fu ◽  
Songxiao Li
Keyword(s):  
Simple Proof ◽  
Normed Space ◽  
Convex Space ◽  
Unconditional Basis ◽  
Locally Convex Space ◽  
Locally Convex

We provide a representation of elements of the spacelp(A,X)for a locally convex spaceXand1≤p<∞and determine its continuous dual for normed spaceXand1<p<∞. In particular, we study the extension and characterization of isometries onlp(N,X)space, whenXis a normed space with an unconditional basis and with a symmetric norm. In addition, we give a simple proof of the main result of G. Ding (2002).

scholarly journals Dispersive ordering results

1983 ◽  
Vol 15 (4) ◽  
pp. 889-891 ◽  
Author(s):  
James Lynch ◽  
Gillian Mimmack ◽  
Frank Proschan
Keyword(s):  
Simple Proof ◽  
Total Positivity ◽  
Sign Changes ◽  
Dispersive Ordering

A distribution F is less dispersed than a distribution G if for all .We generalize a characterization of dispersive ordering of Shaked (1982) concerning sign changes of Fc – G, where Fc is a translate of F. We then use this generalization plus total positivity to develop a simple proof of a characterization of dispersive distributions due to Lewis and Thompson (1981); a distribution H is dispersive if

scholarly journals A Characterization of Invariant Affine Connections

1960 ◽  
Vol 16 ◽  
pp. 35-50 ◽  
Author(s):  
Bertram Kostant
Keyword(s):  
Riemannian Manifold ◽  
Simple Proof ◽  
General Theorem ◽  
Transitive Group ◽  
Complete Riemannian Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Simply Connected

1. Introduction and statement of theorem. 1. In [1] Ambrose and Singer gave a necessary and sufficient condition (Theorem 3 here) for a simply connected complete Riemannian manifold to admit a transitive group of motions. Here we shall give a simple proof of a more general theorem — Theorem 1 (the proof of Theorem 1 became suggestive to us after we noted that the Tx of [1] is just the ax of [6] when X is restricted to p0, see [6], p. 539).

Uniqueness and characterization of prime models over sets for totally transcendental first-order theories

1972 ◽  
Vol 37 (1) ◽  
pp. 107-113 ◽  
Author(s):  
Saharon Shelah
Keyword(s):  
Simple Proof ◽  
Finite Sequence ◽  
The Other ◽  
Closed Field ◽  
Prime Model ◽  
First Order ◽  
Differential Field ◽  
Closed Fields ◽  
Transcendental Theory

If T is a complete first-order totally transcendental theory then over every T-structure A there is a prime model unique up to isomorphism over A. Moreover M is a prime model over A iff: (1) every finite sequence from M realizes an isolated type over A, and (2) there is no uncountable indiscernible set over A in M.The existence of prime models was proved by Morley [3] and their uniqueness for countable A by Vaught [9]. Sacks asked (see Chang and Keisler [1, question 25]) whether the prime model is unique. After proving this I heard Ressayre had proved that every two strictly prime models over any T-structure A are isomorphic, by a strikingly simple proof. From this followsIf T is totally transcendental, M a strictly prime model over A then every elementary permutation of A can be extended to an automorphism of M. (The existence of M follows by [3].)By our results this holds for any prime model. On the other hand Ressayre's result applies to more theories. For more information see [6, §0A]. A conclusion of our theorem is the uniqueness of the prime differentially closed field over a differential field. See Blum [8] for the total transcendency of the theory of differentially closed fields.We can note that the prime model M over A is minimal over A iff in M there is no indiscernible set over A (which is infinite).

On a generalization of Smirnov’s theorem with some applications

2018 ◽  
Vol 25 (2) ◽  
pp. 217-220
Author(s):  
Lasha Ephremidze ◽  
Ilya Spitkovsky
Keyword(s):  
Simple Proof ◽  
Hardy Spaces ◽  
Spectral Factorization ◽  
Matrix Functions ◽  
Rectangular Matrix ◽  
Equivalent Characterization

Abstract We present a certain generalization of Smirnov’s theorem on functions from the Hardy spaces {H_{p}} . We provide some applications of the proposed generalization. Namely, we give an equivalent characterization of outer analytic rectangular matrix functions, and give a simple proof of the uniqueness of spectral factorization of rank deficient matrices.

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