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901.
A generalized finite spectral method is proposed. The method is of high-order accuracy. To attain high accuracy in time discretization, the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Her-mite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation (nonlinear convection- diffusion problem) and KdV equation (single solitary and 2-solitary wave problems), where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases. 相似文献
902.
A continuum model is presented for the motion of a domain wall in a plane 90°-domain configuration subjected to an isolated extrinsic charge near the surface of a ferroelectric single crystal. Local pinning is postulated for the kinetic law. Before the appearance of the extrinsic charge, all polarization surface charges are taken to be neutralized by environmental charges. The domain wall motion after the appearance of the extrinsic charge is assumed to proceed sufficiently fast without any significant conductive currents on the surface or in the interior of the crystal such that new surface and interface polarization charges remain unscreened and contribute to the ferroelectric anisotropy energy. A non-admissible divergence of the electric field and consequently of the local thermodynamic driving force and of the domain wall velocity appears in the model if the domain wall charged by interface polarization charges intersects the crystal surface charged by surface polarization charges under an arbitrary angle. The physically possible domain wall angle is identified using the condition of a non-divergent driving force. The ferroelectric anisotropy energy and an intrinsic surface energy of the domain wall, however, do not provide stability of the domain wall trajectory against an unlimited increase of its curvature at the surface. The problem has been solved conceptually by proper account of the domain wall bending energy. Numerical and dimensional analysis explain also why domain walls driven by extrinsic charges remain almost straight in soft ferroelectrics. 相似文献
903.
In the problem of motion of the Kowalevski top in a double force field the four-dimensional invariant submanifold of the phase space was pointed out by [Kharlamov, M.P., 2002. Mekh. Tverd. Tela 32, 33–38]. We show that the equations of motion on this manifold can be separated by the appropriate change of variables, the new variables s1, s2 being elliptic functions of time. The natural phase variables (components of the angular velocity and the direction vectors of the forces with respect to the movable basis) are expressed via s1, s2 explicitly in elementary algebraic functions. 相似文献
904.
905.
Tomoko KANEKO-ISHINO Fumitoshi ISHINO 《Proceedings of the Japan Academy. Series B, Physical and biological sciences》2015,91(10):511-538
Mammals, including human beings, have evolved a unique viviparous reproductive system and a highly developed central nervous system. How did these unique characteristics emerge in mammalian evolution, and what kinds of changes did occur in the mammalian genomes as evolution proceeded? A key conceptual term in approaching these issues is “mammalian-specific genomic functions”, a concept covering both mammalian-specific epigenetics and genetics. Genomic imprinting and LTR retrotransposon-derived genes are reviewed as the representative, mammalian-specific genomic functions that are essential not only for the current mammalian developmental system, but also mammalian evolution itself. First, the essential roles of genomic imprinting in mammalian development, especially related to viviparous reproduction via placental function, as well as the emergence of genomic imprinting in mammalian evolution, are discussed. Second, we introduce the novel concept of “mammalian-specific traits generated by mammalian-specific genes from LTR retrotransposons”, based on the finding that LTR retrotransposons served as a critical driving force in the mammalian evolution via generating mammalian-specific genes. 相似文献
906.
Let X be a compact Hausdorff space and A a Banach algebra. We investigate amenability properties of the algebra C(X,A) of all A -valued continuous functions. We show that C(X,A) has a bounded approximate diagonal if and only if A has a bounded approximate diagonal; if A has a compactly central approximate diagonal (unbounded) then C(X,A) has a compactly approximate diagonal. Weak amenability of C(X,A) for commutative A is also considered. 相似文献
907.
We characterize boundedness, compactness and weak compactness of Volterra operators acting between different weighted Banach spaces of entire functions with sup‐norms in terms of the symbol g; thus we complement recent work by Bassallote, Contreras, Hernández‐Mancera, Martín and Paul 3 for spaces of holomorphic functions on the disc and by Constantin and Peláez 16 for reflexive weighted Fock spaces. 相似文献
908.
Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients
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This paper is devoted to strictly hyperbolic systems and equations with non‐smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of generalised functions. Extending earlier results on symmetric hyperbolic systems, we introduce generalised strict hyperbolicity, construct symmetrisers, prove an appropriate Gårding inequality and establish existence, uniqueness and regularity of generalised solutions. Under additional regularity assumptions on the coefficients, when a classical solution of the Cauchy problem (or of a transmission problem in the piecewise regular case) exists, the generalised solution is shown to be associated with the classical solution (or the piecewise classical solution satisfying the appropriate transmission conditions). 相似文献
909.
We present a form of the Mean Value Theorem (MVT) for a continuous function f between metric spaces, connecting it with the possibility to choose the relation of f in a homeomorphic way. We also compare our formulation of the MVT with the classic one when the metric spaces are open subsets of Banach spaces. As a consequence, we derive a version of the Mean Value Propriety for measure spaces that also possesses a compatible metric structure. 相似文献
910.
Paolo Giordano Michael Kunzinger Hans Vernaeve 《Journal of Mathematical Analysis and Applications》2015
Based on a refinement of the notion of internal sets in Colombeau's theory, so-called strongly internal sets, we introduce the space of generalized smooth functions, a maximal extension of Colombeau generalized functions. Generalized smooth functions as morphisms between sets of generalized points form a sub-category of the category of topological spaces. In particular, they can be composed unrestrictedly. 相似文献