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We consider the question whether, given a countable family of lattices in a locally compact abelian group G, there exist functions such that the resulting generalized shift-invariant system is a tight frame of . This paper develops a new approach to the study of generalized shift-invariant system via almost periodic functions, based on a novel unconditional convergence property. From this theory, we derive characterizing relations for tight and dual frame generators, we introduce the system bandwidth as a measure of the total bandwidth a generalized shift-invariant system can carry, and we show that the so-called Calderón sum is uniformly bounded from below for generalized shift-invariant frames. Without the unconditional convergence property, we show, counter intuitively, that even orthonormal bases can have arbitrary small system bandwidth. Our results show that the question of existence of frame generators for a general lattice system is rather subtle and depends on analytical and algebraic properties of the lattice system. 相似文献
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《Discrete Mathematics》2022,345(10):113004
Let G be a graph. We say that G is perfectly divisible if for each induced subgraph H of G, can be partitioned into A and B such that is perfect and . We use and to denote a path and a cycle on t vertices, respectively. For two disjoint graphs and , we use to denote the graph with vertex set and edge set , and use to denote the graph with vertex set and edge set . In this paper, we prove that (i) -free graphs are perfectly divisible, (ii) if G is -free with , (iii) if G is -free, and (iv) if G is -free. 相似文献
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In this paper, we generalize the notion of functional graph. Specifically, given an equation with variables X and Y over a finite field of odd characteristic, we define a digraph by choosing the elements in as vertices and drawing an edge from x to y if and only if . We call this graph as equational graph. In this paper, we study the equational graph when choosing with a polynomial over and λ a non-square element in . We show that if f is a permutation polynomial over , then every connected component of the graph has a Hamiltonian cycle. Moreover, these Hamiltonian cycles can be used to construct balancing binary sequences. By making computations for permutation polynomials f of low degree, it appears that almost all these graphs are strongly connected, and there are many Hamiltonian cycles in such a graph if it is connected. 相似文献
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Abraham Rueda Zoca 《Journal of Mathematical Analysis and Applications》2022,505(1):125447
We study the presence of L-orthogonal elements in connection with Daugavet centers and narrow operators. We prove that if and is a Daugavet center with separable range then, for every non-empty -open subset W of , it follows that contains some L-orthogonal to Y. In the context of narrow operators, we show that if X is separable and is a narrow operator, then given and any non-empty -open subset W of then W contains some L-orthogonal u so that . In the particular case that is separable, we extend the previous result to . Finally, we prove that none of the previous results holds in larger density characters (in particular, a counterexample is shown for under the assumption ). 相似文献
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Let be a rational expression of degree three over the finite field . We count the irreducible polynomials in , of a given degree, that have the form for some . As an example of application of our results, we recover the number of irreducible transformation shift registers of order three, which were computed by Jiang and Yang in 2017. 相似文献
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Let be the finite field of order q. Let G be one of the three groups , or and let W be the standard n-dimensional representation of G. For non-negative integers m and d we let denote the representation of G given by the direct sum of m vectors and d covectors. We exhibit a minimal set of homogeneous invariant polynomials such that for all cases except when and or . 相似文献
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《Journal of Pure and Applied Algebra》2023,227(2):107189
For the Schur superalgebra over a ground field K of characteristic zero, we define the symmetrizer of the ordered pairs of tableaux of the shape λ. We show that the K-span of all symmetrizers has a basis consisting of for and semistandard. In particular, if and only if λ is an -hook partition. In this case, the S-superbimodule is identified as , where and are left and right irreducible S-supermodules of the highest weight λ.We define modified symmetrizers and show that their -span forms a -form of . We show that every modified symmetrizer is a -linear combination of modified symmetrizers for semistandard. Using modular reduction to a field K of characteristic , we obtain that has a basis consisting of modified symmetrizers for and semistandard. 相似文献
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《Discrete Mathematics》2022,345(5):112805
Given a graph H and an integer , let be the smallest number of colors C such that there exists a proper edge-coloring of the complete graph with C colors containing no k vertex-disjoint color isomorphic copies of H. In this paper, we prove that where is the 1-subdivision of the complete graph . This answers a question of Conlon and Tyomkyn (2021) [4]. 相似文献
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Benjamin Kennedy 《Journal of Differential Equations》2019,266(4):1865-1898
We consider the real-valued differential equation with state-dependent delay, where f is strictly monotonic in its second argument. We describe a class of such equations for which a version of the Poincaré–Bendixson theorem holds. 相似文献