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291.
Fabrizio Colombo Samuele Mongodi Marco Peloso Stefano Pinton 《Mathematical Methods in the Applied Sciences》2019,42(5):1662-1686
Let e?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory. 相似文献
292.
Effects of graded porous structure on local strain distribution under compression in silicone rubber
Keijiro Yoshimura Kazunori Nakano Takeshi Nishiwaki Yuki Iwama Masanobu Murata 《Journal of Polymer Science.Polymer Physics》2019,57(16):1033-1042
Silicone rubber samples with gradually changing pore sizes within the range of 70–610 μm are produced using an improved spacer method. The samples are scanned using an X‐ray computed tomography to evaluate their graded structure as compared to uniform rubber. A compressive test reveals that graded porous silicone rubber has characteristic stress–strain curves whose slope changes within a specific strain range depending on the porous structure. Analysis results of local strain based on a digital image correlation of the graded porous silicone rubber under compression demonstrate that the characteristic stress–strain properties are caused by shifts in the main deformation region in the graded structure. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1033–1042 相似文献
293.
Sarika Goyal 《Mathematische Nachrichten》2019,292(10):2189-2202
In this article, we study the eigenvalues of p‐fractional Hardy operator where , , , and Ω is an unbounded domain in with Lipschitz boundary containing 0. The weight function V may change sign and may have singular points. We also show that the least positive eigenvalue is simple and it is uniquely associated to a nonnegative eigenfunction. Moreover, we proved that there exists a sequence of eigenvalues as . 相似文献
294.
295.
296.
Wen‐ming He 《Numerical Methods for Partial Differential Equations》2019,35(6):2044-2055
In this article, we will discuss the local ultraconvergence of high‐degree finite element method based on a rectangular partition for the second‐degree elliptic problem with constant coefficients in Ω ? ?2 , u( y ) = 0 on ?Ω . Based on suitable regularity, ultraconvergence of the displacement of the extrapolated kth (k ≥ 3) degree finite element solution has been obtained by an extrapolation technique. Finally, numerical experiments are applied to demonstrate our theoretical findings. 相似文献
297.
Under the assumption that μ is a non-doubling measure on Rdwhich only satisfies the polynomial growth condition,the authors obtain the boundedness of the multilinear fractional integrals on Morrey spaces,weak-Morrey spaces and Lipschitz spaces associated with μ,which,in the case when μ is the d-dimensional Lebesgue measure,also improve the known results. 相似文献
299.
《Optimization》2012,61(8):1009-1028
Bilevel convex models are studied after being cast into a parametric programming form. This form has a lexicographic inner-outer structure where the optimal value of the outer model is optimized on the set of optimal solutions of the inner model. Optimal solutions are characterized using a Lagrangian saddle-point approach and a marginal value formula is given for the outer model. These are used to formulate a general method for finding an optimal solution by input optimization. 相似文献
300.
The octahedral (FeO6)9? and tetrahedral (FeO4)5? clusters in yttrium gallium garnet (YGG): Fe3+ system are investigated based on the 252 × 252 complete energy matrices for d5 configuration ions in trigonal and tetragonal ligand fields, moreover, the EPR and optical spectra are made unified calculation. The results indicate that the defect structures around Fe3+ centres display expansion effects at different temperatures 4.2 and 295 K, and which are close to those in YIG garnet, respectively. Simultaneously, the defect structure parameters for Fe3+ centres in YGG are determined, and the relationship between the defect structure and the temperature has been discussed. 相似文献