共查询到20条相似文献,搜索用时 15 毫秒
1.
Let 1 < s < 2, λk > 0 with λk → ∞ satisfy λk+1/λk ≥ λ > 1. For a class of Besicovich functions B(t) = sin λkt, the present paper investigates the intrinsic relationship between box dimension of their graphs and the asymptotic behavior of {λk}. We show that the upper box dimension does not exceed s in general, and equals to s while the increasing rate is sufficiently large. An estimate of the lower box dimension is also established. Then a necessary and sufficient condition is given for this type of Besicovitch functions to have exact box dimensions: for sufficiently large λ, dim BΓ(B) = dim BΓ(B) = s holds if and only if limn→∞ = 1. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
Xiangyu Feng 《代数通讯》2013,41(5):1700-1708
Let R be a ring and R ω a self-orthogonal module. We introduce the notion of the right orthogonal dimension (relative to R ω) of modules. We give a criterion for computing this relative right orthogonal dimension of modules. For a left coherent and semilocal ring R and a finitely presented self-orthogonal module R ω, we show that the projective dimension of R ω and the right orthogonal dimension (relative to R ω) of R/J are identical, where J is the Jacobson radical of R. As a consequence, we get that R ω has finite projective dimension if and only if every left (finitely presented) R-module has finite right orthogonal dimension (relative to R ω). If ω is a tilting module, we then prove that a left R-module has finite right orthogonal dimension (relative to R ω) if and only if it has a special ω⊥-preenvelope. 相似文献
3.
Yuxian Geng 《Czechoslovak Mathematical Journal》2013,63(1):143-156
Let R be a left and right Noetherian ring and C a semidualizing R-bimodule. We introduce a transpose Tr c M of an R-module M with respect to C which unifies the Auslander transpose and Huang’s transpose, see Z.Y.Huang, On a generalization of the Auslander-Bridger transpose, Comm. Algebra 27 (1999), 5791–5812, in the two-sided Noetherian setting, and use Tr c M to develop further the generalized Gorenstein dimension with respect to C. Especially, we generalize the Auslander-Bridger formula to the generalized Gorenstein dimension case. These results extend the corresponding ones on the Gorenstein dimension obtained by Auslander in M. Auslander, M. Bridger, Stable Module Theory, Mem. Amer. Math. Soc. vol. 94, Amer. Math. Soc., Providence, RI, 1969. 相似文献
4.
5.
Heinz-Dieter Niessen 《Results in Mathematics》1994,26(1-2):89-98
For every λ in a complex domain G, consider on some interval I the initial value problem y′(λ,x) = A(λ,x)y(λ,x) + b(λ,x), y(λ,x0) - y0. If this problem satisfies the Carathéodory conditions for every A, then there exist locally absolutely continuous and almost everywhere differentiable solutions y(λ,· ) of the initial value problem. In general, the union N of the exceptional sets N λ ? I where y(λ, ·) is not differentiate or does not fulfill the differential equation, is not of Lebesgue measure zero. It will be shown that N is of Lebesgue measure zero provided that A and b are holomorphic with respect to λ and their integrals with respect to x are locally bounded on G × I. 相似文献
6.
We study Misiurewicz points on the parameter space about a family of rational maps Tλ concerning renormalization transformation in statistical mechanic. We determine the intersection points of the Julia set J(Tλ) and the positive real axis R+and discuss the continuity of the Hausdorff dimension HD(J(f)) about real parameter λ. 相似文献
7.
For a family {T + Nλ: λ ? [a, b]} of semilinear operators T + Nλ in L2(Ω) the solution set {(λ, uλ) ? J × D(T): Tuλ + Nλuλ = h} is investigated with respect to turning points. By Ljapunov-Schmidt-reduction and calculation of the derivatives of the bifurcation equation a class of turning points is characterized by properties of these derivatives. 相似文献
8.
Lubomir Gavrilov 《Functional Analysis and Its Applications》2013,47(3):174-186
We prove that the number of limit cycles which bifurcate from a two-saddle loop of an analytic planar vector field X 0 under an arbitrary finite-parameter analytic deformation X λ , λ ∈ (? N , 0), is uniformly bounded with respect to λ. 相似文献
9.
We consider semilinear second order elliptic Neumann problems, which are resonant both at infinity (with respect to an eigenvalue λk, k ≥ 1) and at zero (with respect to the principal eigenvalue λ0 = 0). Using techniques from Morse theory, combined with variational methods, we are able to show that the problem has at least four nontrivial smooth solutions (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
Fernando De Terán 《Linear and Multilinear Algebra》2013,61(12):1605-1628
We give a complete solution of the matrix equation AX?+?BX ??=?0, where A, B?∈?? m×n are two given matrices, X?∈?? n×n is an unknown matrix, and ? denotes the transpose or the conjugate transpose. We provide a closed formula for the dimension of the solution space of the equation in terms of the Kronecker canonical form of the matrix pencil A?+?λB, and we also provide an expression for the solution X in terms of this canonical form, together with two invertible matrices leading A?+?λB to the canonical form by strict equivalence. 相似文献
11.
Let e λ (x) be an eigenfunction with respect to the Laplace-Beltrami operator Δ M on a compact Riemannian manifold M without boundary: Δ M e λ = λ 2 e λ . We show the following gradient estimate of e λ : for every λ ≥ 1, there holds ${\lambda\|e_\lambda\|_\infty/C\leq \|\nabla e_\lambda\|_\infty\leq C\lambda\|e_\lambda\|_\infty}$ , where C is a positive constant depending only on M. 相似文献
12.
Generalized Orlicz–Lorentz sequence spaces λφ generated by Musielak‐Orlicz functions φ satisfying some growth and regularity conditions (see [28] and [33]) are investigated. A regularity condition δλ 2 for φ is defined in such a way that it guarantees many positive topological and geometric properties of λφ. The problems of the Fatou property, the order continuity and the Kadec–Klee property with respect to the uniform convergence of the space λφ are considered. Moreover, some embeddings between λφ and their two subspaces are established and strict monotonicity as well as lower and upper local uniform monotonicities are characterized. Finally, necessary and sufficient conditions for rotundity of λφ, their subspaces of order continuous elements and finite dimensional subspaces are presented. This paper generalizes the results from [19], [4] and [17]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
Teresa Martinez 《Mathematische Nachrichten》2008,281(7):978-988
We define and investigate the multipliers of Laplace transform type associated to the differential operator Lλf (θ) = –f ″(θ) – 2λ cot θf ′(θ) + λ2f (θ), λ > 0. We prove that these operators are bounded in Lp ((0, π), dmλ) and of weak type (1, 1) with respect to the same measure space, dmλ (θ) = (sin θ)2λ dθ. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
A connection between the semigroup of the Cauchy process killed upon exiting a domain D and a mixed boundary value problem for the Laplacian in one dimension higher known as the mixed Steklov problem, was established in [R. Bañuelos, T. Kulczycki, The Cauchy process and the Steklov problem, J. Funct. Anal. 211 (2004) 355-423]. From this, a variational characterization for the eigenvalues λn, n?1, of the Cauchy process in D was obtained. In this paper we obtain a variational characterization of the difference between λn and λ1. We study bounded convex domains which are symmetric with respect to one of the coordinate axis and obtain lower bound estimates for λ∗−λ1 where λ∗ is the eigenvalue corresponding to the “first” antisymmetric eigenfunction for D. The proof is based on a variational characterization of λ∗−λ1 and on a weighted Poincaré-type inequality. The Poincaré inequality is valid for all α symmetric stable processes, 0<α?2, and any other process obtained from Brownian motion by subordination. We also prove upper bound estimates for the spectral gap λ2−λ1 in bounded convex domains. 相似文献
15.
V. E. Bobkov 《Differential Equations》2014,50(6):765-776
We study the existence of nodal solutions of a parametrized family of Dirichlet boundary value problems for elliptic equations with convex-concave nonlinearities. In the main result, we prove the existence of nodal solutions u λ for λ ∈ (?∞, λ*0). The critical value λ*0 >0 is found by a spectral analysis procedure according to Pokhozhaev’s fibering method. We show that the obtained solutions form a continuous branch (in the sense of level lines of the energy functional) with respect to the parameter λ. Moreover, we prove the existence of an interval \(( - \infty ,\tilde \lambda )\) , where \(\tilde \lambda > 0\) , on which this branch consists of solutions with exactly two nodal domains. 相似文献
16.
Tiziana Cardinali Nikolaos S. Papageorgiou Paola Rubbioni 《Annali di Matematica Pura ed Applicata》2014,193(1):1-21
We consider a nonlinear Neumann logistic equation driven by the p-Laplacian with a general Carathéodory superdiffusive reaction. We are looking for positive solutions of such problems. Using minimax methods from critical point theory together with suitable truncation techniques, we show that the equation exhibits a bifurcation phenomenon with respect to the parameter λ > 0. Namely, we show that there is a λ* > 0 such that for λ < λ*, the problem has no positive solution; for λ = λ*, it has at least one positive solution; and for λ > λ*, it has at least two positive solutions. 相似文献
17.
Petter Andreas Bergh 《代数通讯》2013,41(11):3440-3450
We compute the Hochschild cohomology and homology of the algebra Λ = k 〈x, y〉/(x 2, xy + qyx, y 2) with coefficients in 1 Λψ for every degree preserving k-algebra automorphism ψ : Λ → Λ. As a result we obtain several interesting examples of the homological behavior of Λ as a bimodule. 相似文献
18.
Victor D. Didenko Natalia A. Rozhenko 《Mathematical Methods in the Applied Sciences》2014,37(15):2211-2217
A spectral problem for the Sturm–Liouville equation on the edges of an equilateral regular star‐tree with the Dirichlet boundary conditions at the pendant vertices and Kirchhoff and continuity conditions at the interior vertices is considered. The potential in the Sturm–Liouville equation is a real–valued square summable function, symmetrically distributed with respect to the middle point of any edge. If {λj}is a sequence of real numbers, necessary and sufficient conditions for {λj}to be the spectrum of the problem under consideration are established. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
19.
Let D be the diameter of a graph G and let λ1 be the largest eigenvalue of its (0, 1)-adjacency matrix. We give a proof of the fact that there are exactly 69 non-trivial connected graphs with (D + 1)λ1 ? 9. These 69 graphs all have up to 10 vertices and were recently found to be suitable models for small multiprocessor interconnection networks. We also examine the suitability of integral graphs to model multiprocessor interconnection networks, especially with respect to the load balancing problem. In addition, we classify integral graphs with small values of (D + 1)λ1 in connection with the load balancing problem for multiprocessor systems. 相似文献
20.
《Journal of Computational and Applied Mathematics》2002,139(2):253-274
Let {Snλ} denote the monic orthogonal polynomial sequence with respect to the Sobolev inner productwhere {dψ0,dψ1} is a so-called coherent pair and λ>0. Then Snλ has n different, real zeros. The position of these zeros with respect to the zeros of other orthogonal polynomials (in particular Laguerre and Jacobi polynomials) is investigated. Coherent pairs are found where the zeros of Sn−1λ separate the zeros of Snλ. 相似文献