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1.
Characterizations of the containment of a convex set either in an arbitrary convex set or in the complement of a finite union
of convex sets (i.e., the set, described by reverse-convex inequalities) are given. These characterizations provide ways of
verifying the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated
systems. The convex sets considered in this paper are the solution sets of an arbitrary number of convex inequalities, which
can be either weak or strict inequalities. Particular cases of dual characterizations of set containments have played key
roles in solving large scale knowledge-based data classification problems where they are used to describe the containments
as inequality constraints in optimization problems. The idea of evenly convex set (intersection of open half spaces), which
was introduced by W. Fenchel in 1952, is used to derive the dual conditions, characterizing the set containments. 相似文献
2.
Nguyen Minh Chuong Bui Kien Cuong 《Proceedings of the American Mathematical Society》2004,132(12):3589-3597
A class of Cauchy problems for interesting complicated periodic pseudodifferential equations is considered. By the Galerkin-wavelet method and with weak solutions one can find sufficient conditions to establish convergence estimates of weak Galerkin-wavelet solutions to a Cauchy problem for this class of equations.
3.
Durand William A.Pham Ngoc Dinh 《Journal of Mathematical Analysis and Applications》2003,282(1):95-106
An electromagnetic diffraction problem in a wedge shaped region is reduced to a system of coupled functional difference equations by means of Sommerfeld integrals and Malyuzhinets theorem. By introducing an integral operator it is shown that the solutions of this system of functional equations can be defined in terms of integral representations whose kernels are solutions of a singular integral equation of Cauchy-Carleman type for which an explicit solution is given. 相似文献
4.
Z. Szeglowski H. Bruchertseifer V. B. Brudanin G. V. Buklanov O. Constantinescu Dinh Thi Lien V. P. Domanov L. I. Guseva M. Hussonnois G. S. Tikhomirova I. Zvara Yu. Ts. Oganessian 《Journal of Radioanalytical and Nuclear Chemistry》1994,186(4):353-359
The short-lived isotopes of W and their descendants have been isolated from the products of the bombardment of144Sm with24Mg by a fast continuous ion-exchange method, using HF solution media. The feasibility of this method for isolation of element 106 is discussed. 相似文献
5.
6.
New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method. 相似文献
7.
Soluble catalysts for the Juliá-Colonna asymmetric epoxidation reaction have been constructed in three different ways, using NH2-PEG-OMe as the support system: suitable solvents have been identified and it is shown that the degree of helicity of the conjugates correlates with the extent of conversion and (to a lesser extent) the enantioselectivity of epoxidation. 相似文献
8.
Bui An Ton 《Mathematical Methods in the Applied Sciences》1988,10(4):351-366
Let g is a positive increasing function with 1?g(0). The existence of a unique solution of the Navier-Stokes flow associated with Kε,γ and the convergence of the solution to that of the Euler equations as the viscosity goes to zero are established. 相似文献
9.
Z. Szeglowski H. Bruchertseifer V. B. Brudanin G. V. Buklanov O. Constantinescu Dinh Thi Lien V. P. Domanov L. I. Guseva M. Hussonnois G. S. Tikhomirowa I. Zvara Yu. Ts. Oganessian 《Journal of Radioanalytical and Nuclear Chemistry》1996,212(1):35-42
Some short-lived isotopes of Hf, Ta and W, synthesized at the U-400 cyclotron of JINR-Dubna, have been isolated using a previously elaborated fast continuous method of chemical isolation of element 104 from nuclear reaction products. The products were transported by a NaCl aerosol jet, from the irradiated targets to a separation device in which Hf, Ta and W were isolated by using three coupled ion-exchange columns. 相似文献
10.
In the paper, we describe a polynomial time algorithm that, for every input graph, either outputs the minimum bisection of the graph or halts without output. More importantly, we show that the algorithm chooses the former course with high probability for many natural classes of graphs. In particular, for every fixedd≧3, all sufficiently largen and allb=o(n 1?1/[(d+1)/2]), the algorithm finds the minimum bisection for almost alld-regular labelled simple graphs with 2n nodes and bisection widthb. For example, the algorithm succeeds for almost all 5-regular graphs with 2n nodes and bisection widtho(n 2/3). The algorithm differs from other graph bisection heuristics (as well as from many heuristics for other NP-complete problems) in several respects. Most notably:
- the algorithm provides exactly the minimum bisection for almost all input graphs with the specified form, instead of only an approximation of the minimum bisection,
- whenever the algorithm produces a bisection, it is guaranteed to be optimal (i.e., the algorithm also produces a proof that the bisection it outputs is an optimal bisection),
- the algorithm works well both theoretically and experimentally,
- the algorithm employs global methods such as network flow instead of local operations such as 2-changes, and
- the algorithm works well for graphs with small bisections (as opposed to graphs with large bisections, for which arbitrary bisections are nearly optimal).