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《Applied Mathematics Letters》2007,20(7):835-837
It is shown that every planar graph with no separating triangles is a subgraph of a Hamiltonian planar graph; that is, Whitney’s theorem holds without the assumption of a triangulation. 相似文献
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Dale W. Lick 《Annali di Matematica Pura ed Applicata》1966,72(1):267-274
Summary See the introduction. 相似文献
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The Cauchy problem for an ordinary differential equation coupled with a hysteresis operator is studied. Under physically reasonable assumptions on the forcing term, uniqueness of solutions is shown without assuming Lipschitz continuity of the hysteresis curves. The result is true for any kind of hysteresis operators with monotone curves of motion.
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Michael Eichmair Pengzi Miao Xiaodong Wang 《Calculus of Variations and Partial Differential Equations》2012,43(1-2):45-56
In this note, we prove the following generalization of a theorem of Shi and Tam (J Differ Geom 62:79–125, 2002): Let (Ω, g) be an n-dimensional (n ≥ 3) compact Riemannian manifold, spin when n?>?7, with non-negative scalar curvature and mean convex boundary. If every boundary component Σ i has positive scalar curvature and embeds isometrically as a mean convex star-shaped hypersurface ${{\hat \Sigma}_i \subset \mathbb{R}^n}$ , then $$ \int\limits_{\Sigma_i} H \ d \sigma \le \int\limits_{{\hat \Sigma}_i} \hat{H} \ d {\hat \sigma} $$ where H is the mean curvature of Σ i in (Ω, g), ${\hat{H}}$ is the Euclidean mean curvature of ${{\hat \Sigma}_i}$ in ${\mathbb{R}^n}$ , and where d σ and ${d {\hat \sigma}}$ denote the respective volume forms. Moreover, equality holds for some boundary component Σ i if, and only if, (Ω, g) is isometric to a domain in ${\mathbb{R}^n}$ . In the proof, we make use of a foliation of the exterior of the ${\hat \Sigma_i}$ ’s in ${\mathbb{R}^n}$ by the ${\frac{H}{R}}$ -flow studied by Gerhardt (J Differ Geom 32:299–314, 1990) and Urbas (Math Z 205(3):355–372, 1990). We also carefully establish the rigidity statement in low dimensions without the spin assumption that was used in Shi and Tam (J Differ Geom 62:79–125, 2002). 相似文献
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A decomposition theorem for Jacobi forms 总被引:1,自引:0,他引:1
Joachim Dulinski 《Mathematische Annalen》1995,303(1):473-498
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Sergey A. Denisov 《Proceedings of the American Mathematical Society》2004,132(3):847-852
We prove Rakhmanov's theorem for Jacobi matrices without the additional assumption that the number of bound states is finite. This result solves one of Nevai's open problems.
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In this note, we give an extension of the Mittag-Leffler theorem for some elements of a Banach algebra with unit. 相似文献
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Chen Guijing 《应用数学学报(英文版)》1984,1(1):2-7
A theorem of Lai, Robbins and Wei[7] is extended to a more general form to contain all the known results in the literature about the strong consistency of the least squares estimates of the progression coefficients in linear models with nonrandom regressors, and improvement is made on some of these results. 相似文献
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Kernel theorems for spaces of Cauchy ultradistribution, supported by an n-dimensional tube and cone of the product type, are investigated. 相似文献
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The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel. 相似文献
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Claudie Hassenforder 《Journal of Theoretical Probability》1988,1(2):205-209
If is a probability on , the set of distributions ofa+pX wherea,p>0 andX has distribution is called the type of . F. B. Knight has shown that if a type has no atom and if it is invariant byi:x–1/x, the type must be the Cauchy one. We show here thati can be replaced by any Cayley nonaffine function.
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Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We investigate new orthogonal polynomials by adding to the Jacobi matrixrnew rows and columns, so that the original Jacobi matrix is shifted downward. Thernew rows and columns contain 2rnew parameters and the newly obtained orthogonal polynomials thus correspond to an upward extension of the Jacobi matrix. We give an explicit expression of the new orthogonal polynomials in terms of the original orthogonal polynomials, their associated polynomials, and the 2rnew parameters, and we give a fourth order differential equation for these new polynomials when the original orthogonal polynomials are classical. Furthermore we show how the 1?orthogonalizing measure for these new orthogonal polynomials can be obtained and work out the details for a one-parameter family of Jacobi polynomials for which the associated polynomials are again Jacobi polynomials. 相似文献
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M. Hemdaoui 《Rendiconti del Circolo Matematico di Palermo》2000,49(3):435-444
Dans cette note, nous montrons qu’il est possible d’étendre le théorème de factorisation de Weierstrass pour certains éléments d’une algèbre de BanachA. 相似文献
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E. A. Karatsuba 《Computational Mathematics and Mathematical Physics》2017,57(11):1822-1842
A new method is devised to study the atomic inversion in the model of a two-level atom interacting with a single quantized mode of the (initially coherent) electromagnetic field in an ideal resonant cavity. The method is based on number-theoretic results applied to the approximation of special series, specifically, on the functional equation for Jacobi theta functions and the ATS theorem. New asymptotic formulas are derived, with the help of which the behavior of the atomic inversion function on various time intervals can be determined in detail depending on the parameters of the system. 相似文献
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