Results 1 - 10 of 31473
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[en] In this paper we continue the investigation of finite XXZ spin chains with periodic boundary conditions and odd number of sites, initiated in our previous article (Stroganov Yu. G. 2001 J. Phys. A: Math. Gen. 34 L179-85). As it turned out, for a special value of the asymmetry parameter Δ=-1/2 the Hamiltonian of the system has an eigenvalue, which is exactly proportional to the number of sites E=-3N/2. Using Mathematica we have found explicitly the corresponding eigenvectors for N≤17. The obtained results support the conjecture our paper that this special eigenvalue corresponds to the ground state vector. We make a lot of conjectures concerning the correlations of the model. Many remarkable relations between the wavefunction components are noted. It turns out, for example, that the ratio of the largest component to the least one is equal to the number of the alternating sign matrices. (author)
[en] Constraints on the position of singularities on the boundary of a connected component of the complement to a wave front are studied. The boundary of the component is assumed to be the compact boundary of a manifold, and the front is assumed to have only stable corank 1 singularities at points of the boundary. Under these assumptions linear relations are found between the Euler numbers of the manifolds of singularities on the boundary of a fixed component. In particular, all universal linear relations between the Euler numbers of the manifolds of singularities on the boundaries of elliptic and hyperbolic connected components of the complement to a front are found.
[en] We present a general technique for constructing nonlocal transparent boundary conditions for one-dimensional Schroedinger-type equations. Our method supplies boundary conditions for the θ-family of implicit one-step discretizations of Schroedinger's equation in time. The use of Mikusinski's operator approach in time avoids direct and inverse transforms between time and frequency domains and thus implements the boundary conditions in a direct manner. 14 refs., 9 figs
[en] The implementation of essential boundary conditions in C1 finite element analysis requires proper treatment of both the boundary conditions on second-order differentials of the solution and the curvature of the domain boundary. A method for the imposition of essential boundary conditions using straight elements (where the elements are not deformed to approximate a curved domain) is described. It is shown that pre-multiplication of the matrix equation by the local rotation matrix at each boundary node is not the optimal transformation. The uniquely optimal transformation is found, which does not take the form of a similarity transformation due to the non-orthogonality of the transformation to curved coordinates.
[en] We prove an -estimate for the homogenization of an elliptic operator in a domain with a Neumann boundary condition on the boundary . The coefficients of the operator are rapidly oscillating over different groups of variables with periods of different orders of smallness as . We assume minimal regularity of the data, which makes it possible to impart to the result the meaning of an estimate in the operator -norm for the difference of the resolvents of the original and homogenized problems. We also find an approximation to the resolvent of the original problem in the operator -norm. Bibliography: 24 titles.
[en] A study of all the observed and well-defined sector boundaries from January 1957 to February 1975, published by Svalgaard (1974, 1975a, b), indicated that sector boundary key-dates, transformed into Bartels' days, have a significant preference to occur on certain days of the solar rotation. The electric distribution of these sector boundaries give some Bartels' days that are 'empty' of cases, while on other days there is a significant excess over the average. Using this effect, we can predict, in high levels of significance, the possible occurence of a (+,-) or (-,+) boundary within particular days of the solar rotation. (orig.)
[en] In this research, the differential quadrature method is employed to investigate the nonlocal vibration of nanobeam resting on various types of Winkler elastic foundations such as constant, linear, parabolic, and sinusoidal types. The nanobeam is modeled with Winkler elastic foundation considering the elastic coefficient varying along the axis of the nanobeam. Within the framework of Euler–Bernoulli beam theory, first order strain gradient model is incorporated to compute the frequency parameters for Hinged-Hinged (H–H) and Clamped-Hinged (C–H) boundary conditions. A convergence study is also performed to demonstrate the efficiency, adequacy, and reliability of the method. Further, the results are compared with available data of previously published research in special cases showing robust agreement. Likewise, the effects of the nonlocal parameter, strain gradient parameter, non-uniform parameters, and Winkler modulus parameter on the frequency parameters are studied comprehensively. (paper)
[en] A general method proposed by Raszillier to obtain constraints on low energy Compton scattering parameters in terms of upper bounds on the cross sections above photoproduction threshold, is shown to give optimal results