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991.
992.
Hans‐Peter Gittel 《Mathematical Methods in the Applied Sciences》2000,23(15):1347-1372
This paper continues considerations of transonic potential flow problems by variational methods. A functional which is associated with a boundary value problem for the (full) potential equation and which possesses a real physical meaning is minimized over a class of admissible functions. These functions have to satisfy a non‐linear local entropy condition and a certain boundness constraint. Though this class is not a compact set of the underlying Hilbert space and though the functional need not be convex, the existence of a solution to the established variational problem can be proved by direct methods of the calculus of variations. Furthermore, some properties of minimizers concerning uniqueness, relation to the potential equation, and behaviour on supersonic regions are derived. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
993.
In Ref. 1, Yang et al presented characterizations of prequasi-invex functions, semistrictly prequasi-invex functions, and strictly prequasi-invex functions, respectively, under a certain set of conditions. In this note, we show that the same results or even more general ones can be obtained under weaker assumptions. 相似文献
994.
It is shown that a critical set in a Latin square of order n≥8 has to have at least elements. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 419–432, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10028 相似文献
995.
A boundary value problem for a second-order nonlinear singularly perturbed differential equation is considered for the case in which there is variation of stability caused by the intersection of roots of the degenerate equation. By the method of differential inequalities, we prove the existence of a solution such that the limit solution is nonsmooth. Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 354–362, March, 1998. This research was partially supported by the Russian Foundation for Basic Research under grant No. 96-01-00694. 相似文献
996.
One of the most important problems in topology is the minimization (in some sense) of obstructions to extending a partial map , i.e., of a subsetF ⊂ Z/A such thatf can be globally extended to its complement. It is shown that ifZ is a fixed metric space with dimZ ≤ n andp, q ≥−1 are fixed numbers, then obstructions to extending all partial maps can be concentrated in preselected fairly thin subsets ofZ. Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 803–812, December 1997 Translated by O. V. Sipacheva 相似文献
997.
We consider anti‐periodic boundary value problems for two classes of special second order impulsive differential equations. On the basis of several important impulsive differential inequalities, by using the monotone iterative technique coupled with lower and upper solutions, we obtain sufficient conditions to guarantee the existence and uniqueness of solutions for such problems. Further, we give two examples to illustrate our conclusions. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
998.
Carlos Escudero Robert Hakl Ireneo Peral Pedro J. Torres 《Mathematical Methods in the Applied Sciences》2014,37(6):793-807
The existence of stationary radial solutions to a partial differential equation arising in the theory of epitaxial growth is studied. It turns out that the existence or not of such solutions depends on the size of a parameter that plays the role of the velocity at which mass is introduced into the system. For small values of this parameter, we prove the existence of solutions to this boundary value problem. For large values of the same parameter, we prove the nonexistence of solutions. We also provide rigorous bounds for the values of this parameter, which separate existence from nonexistence. The proofs come as a combination of several differential inequalities and the method of upper and lower functions applied to an associated two‐point boundary value problem. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
999.
The well‐known “Janson's inequality” gives Poisson‐like upper bounds for the lower tail probability when X is the sum of dependent indicator random variables of a special form. We show that, for large deviations, this inequality is optimal whenever X is approximately Poisson, i.e., when the dependencies are weak. We also present correlation‐based approaches that, in certain symmetric applications, yield related conclusions when X is no longer close to Poisson. As an illustration we, e.g., consider subgraph counts in random graphs, and obtain new lower tail estimates, extending earlier work (for the special case ) of Janson, ?uczak and Ruciński. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 219–246, 2016 相似文献
1000.
In this article, we analyze the lower bound property of the discrete eigenvalues by the rectangular Morley elements of the biharmonic operators in both two dimension (2D) and three dimension (3D). The analysis relies on an identity for the errors of eigenvalues. We explore a refined property of the canonical interpolation operators and use it to analyze the key term in this identity. In particular, we show that such a term is of higher order for 2D, and is negative and of second order for 3D, which causes a main difficulty. To overcome it, we propose a novel decomposition of the first term in the aforementioned identity. Finally, we establish a saturation condition to show that the discrete eigenvalues are smaller than the exact ones. We present some numerical results to demonstrate the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1623–1644, 2015 相似文献