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In this paper we are concerned with a non-negative integer and irreducible matrix . The main contribution is to prove that if the matrix satisfies certain spectral and algebraic constraints, the cone:is defined by linear maps , in the sense that v ∈ C is equivalent to, ϕl(v) ⩾ 0 for all l = 0, … , k − 1 (where k is the index of cyclicity of the irreducible matrix). This result allows us to characterize the dimension group generated by the matrix, it is a subgroup of endowed with an order induced by the positive cone of . 相似文献
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We consider the nonclassical symmetry of one-dimensional hyperbolic differential equations of the form ut + M(u)ux = 0. For the infinitesimal generator , it is shown that ξ is an eigenvalue of the matrix M when ϕi = 0 [Souichi M. Nonclassical symmetry and Riemann invariants. Int J Nonlinear Mech, [in press]]. In this paper, we prove a sufficient condition of a lemma. 相似文献
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《Annals of Pure and Applied Logic》2014,165(7-8):1243-1262
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《Communications in Nonlinear Science & Numerical Simulation》2005,10(8):931-934
If F : H → H is a -map in a real Hilbert space, supu ∈ B(u0,R)∥[F′(u)]−1∥ ⩽ m(R), and , then F is surjective. 相似文献
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Dennis I. Merino 《Linear algebra and its applications》2012,436(7):1960-1968
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We show that functions f in some weighted Sobolev space are completely determined by time-frequency samples along appropriate slowly increasing sequences and tending to ±∞ as . 相似文献
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Let denote the unitary Cayley graph of . We present results on the tightness of the known inequality , where and denote the domination number and total domination number, respectively, and is the arithmetic function known as Jacobsthal’s function. In particular, we construct integers with arbitrarily many distinct prime factors such that . We give lower bounds for the domination numbers of direct products of complete graphs and present a conjecture for the exact values of the upper domination numbers of direct products of balanced, complete multipartite graphs. 相似文献