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71.
The jump of the Milnor number of an isolated singularity f 0 is the minimal non-zero difference between the Milnor numbers of f 0 and one of its deformations (f s ). We prove that for the singularities in the X 9 singularity class their jumps are equal to 2. 相似文献
72.
Piotr Czop Krzysztof Mendrok Tadeusz Uhl 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(11):1541-1554
Requirements for current trains to be increasingly available have created the need to develop systems that can predict the
quality of both trains and infrastructure components. The paper presents a new approach to the detection of rail truck irregularities,
based on the measurements of bearing box acceleration during the operation of rail vehicles. The proposed procedure is based
on an inverse problem solution, estimating track irregularities from measured acceleration of the applied model of vehicle
dynamics. The simulation study of the proposed method, as well as its implementation, is presented. The method has been successfully
applied for the identification of rail irregularities on a typical Polish railroad and vehicle. 相似文献
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Tadeusz Jankowski 《Mathematische Nachrichten》1986,125(1):7-28
The aim of the present paper is to study boundary value problems with a parameter of differential equations with deviated arguments. The existence, uniqueness and continuous dependence of the solution on the right-hand side of our problem are considered. 相似文献
76.
Tadeusz Antczak 《Journal of Mathematical Analysis and Applications》2003,286(1):187-206
Invexity of a function is generalized. The new class of nonconvex functions, called B-(p,r)-invex functions with respect to η and b, being introduced, includes many well-known classes of generalized invex functions as its subclasses. Some properties of the introduced class of B-(p,r)-invex functions with respect to η and b are studied. Further, mathematical programming problems involving B-(p,r)-invex functions with respect to η and b are considered. The equivalence between saddle points and optima, and different type duality theorems are established for this type of optimization problems. 相似文献
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We study the semigroup of the symmetric α-stable process in bounded domains in R 2. We obtain a variational formula for the spectral gap, i.e. the difference between two first eigenvalues of the generator of this semigroup. This variational formula allows us to obtain lower bound estimates of the spectral gap for convex planar domains which are symmetric with respect to both coordinate axes. For rectangles, using “midconcavity” of the first eigenfunction (Bañuelos et al., Potential Anal. 24(3): 205–221, 2006), we obtain sharp upper and lower bound estimates of the spectral gap. 相似文献