A mathematical model of a solute release from a planar polymer matrix is presented and the analytical solution in terms of the Fox H function is given. The equation of space-time-fractional diffusion and a generalized...
详细信息
A mathematical model of a solute release from a planar polymer matrix is presented and the analytical solution in terms of the Fox H function is given. The equation of space-time-fractional diffusion and a generalized Fick's law are used in the paper. Three particular cases, the standard diffusion, the time-fractional and the space-fractional diffusions are discussed in detail. The model and the solution are the generalization of the previous works and include them as special cases.
Obstacles K and L in R-d (d >= 2) are considered that are finite disjoint unions of strictly convex domains with C-3 boundaries. We show that if K and L have (almost) the same scattering length spectrum, or (almost...
详细信息
Obstacles K and L in R-d (d >= 2) are considered that are finite disjoint unions of strictly convex domains with C-3 boundaries. We show that if K and L have (almost) the same scattering length spectrum, or (almost) the same travelling times, then K = L.
We construct an asymptotic solution of the first boundary-value problem for a linear singularly perturbed system of hyperbolic partial differential equations with degeneration.
We construct an asymptotic solution of the first boundary-value problem for a linear singularly perturbed system of hyperbolic partial differential equations with degeneration.
We present a Friedmann-Robertson-Walker quantum cosmological model in the presence of Chaplygin gas and perfect fluid for early and late time epochs. In this work, we consider perfect fluid as an effective potential a...
详细信息
We present a Friedmann-Robertson-Walker quantum cosmological model in the presence of Chaplygin gas and perfect fluid for early and late time epochs. In this work, we consider perfect fluid as an effective potential and apply Schutz's variational formalism to the Chaplygin gas which recovers the notion of time. These give rise to Schrodinger-Wheeler-DeWitt equation for the scale factor. We use the eigenfunctions in order to construct wave packets and study the time dependent behavior of the expectation value of the scale factor using the many-worlds interpretation of quantum mechanics. We show that contrary to the classical case, the expectation value of the scale factor avoids singularity at quantum level. Moreover, this model predicts that the expansion of Universe is accelerating for the late times. (c) 2007 Elsevier B.V. All rights reserved.
We consider an arbitrary selfadjoint operator in a separable Hilbert space. To this operator we construct an expansion in generalized eigenfunctions, in which the original Hilbert space is decomposed as a direct integ...
详细信息
We consider an arbitrary selfadjoint operator in a separable Hilbert space. To this operator we construct an expansion in generalized eigenfunctions, in which the original Hilbert space is decomposed as a direct integral of Hilbert spaces consisting of general eigenfunctions. This automatically gives a Plancherel type formula. For suitable operators on metric measure spaces we discuss some growth restrictions on the generalized eigenfunctions. For Laplacians on locally finite graphs the generalized eigenfunctions are exactly the solutions of the corresponding difference equation.
We introduce a class of multidimensional Schrodinger operators with elliptic potential which generalize the classical Lame operator to higher dimensions. One natural example is the Calogero-Moser operator, others are ...
详细信息
We introduce a class of multidimensional Schrodinger operators with elliptic potential which generalize the classical Lame operator to higher dimensions. One natural example is the Calogero-Moser operator, others are related to the root systems and their deformations. We conjecture that these operators are algebraically integrable, which is a proper generalization of the finite-gap property of the Lame operator. Using earlier results of Braverman, Etingof and Gaitsgory, we prove this under additional assumption of the usual, Liouville integrability. In particular, this proves the Chalykh-Veselov conjecture for the elliptic Calogero-Moser problem for all root systems. We also establish algebraic integrability in all known two-dimensional cases. A general procedure for calculating the Bloch eigenfunctions is explained. It is worked out in detail for two specific examples: one is related to the B-2 case, another one is a certain deformation of the A(2) case. In these two cases we also obtain similar results for the discrete versions of these problems, related to the difference operators of Macdonald-Ruijsenaars type.
We study the volume of nodal sets for eigenfunctions of the Laplacian on the standard torus in two or more dimensions. We consider a sequence of eigenvalues 4 pi(2) E with growing multiplicity N -> infinity, and co...
详细信息
We study the volume of nodal sets for eigenfunctions of the Laplacian on the standard torus in two or more dimensions. We consider a sequence of eigenvalues 4 pi(2) E with growing multiplicity N -> infinity, and compute the expectation and variance of the volume of the nodal set with respect to a Gaussian probability measure on the eigenspaces. We show that the expected volume of the nodal set is const root E. Our main result is that the variance of the volume normalized by root E is bounded by O(1/root N), so that the normalized volume has vanishing fluctuations as we increase the dimension of the eigenspace.
For a fractional ordinary differential equation with the Dzhrbashyan-Nersesyan operator, we prove a theorem on the existence and uniqueness of a solution of a boundaryvalue problem with shift.
For a fractional ordinary differential equation with the Dzhrbashyan-Nersesyan operator, we prove a theorem on the existence and uniqueness of a solution of a boundaryvalue problem with shift.
We study uniquely ergodic dynamical systems over locally compact, sigma-compact Abelian groups. We characterize uniform convergence in Wiener/Wintner type ergodic theorems in terms of continuity of the limit. Our resu...
详细信息
We study uniquely ergodic dynamical systems over locally compact, sigma-compact Abelian groups. We characterize uniform convergence in Wiener/Wintner type ergodic theorems in terms of continuity of the limit. Our results generalize and unify earlier results of Robinson and Assani respectively. We then turn to diffraction of quasicrystals and show how the Bragg peaks can be calculated via a Wiener/Wintner type result. Combining these results we prove a version of what is sometimes known as the Bombieri/Taylor conjecture. Finally, we discuss various examples including deformed model sets, percolation models, random displacement models, and linearly repetitive systems.
Conditions for the n-fold completeness of the system of root functions(eigenfunctions and associated functions) of the pencil (1), (2) in L_2(0, 1) (see [1, p. 10~2; 2])were obtained in [3]. In the lack of n-fold comp...
详细信息
Conditions for the n-fold completeness of the system of root functions(eigenfunctions and associated functions) of the pencil (1), (2) in L_2(0, 1) (see [1, p. 10~2; 2])were obtained in [3]. In the lack of n-fold completeness, the problem on conditions for the k-foldcompleteness (0 < k < n) of the system of root functions arises.
暂无评论