On a double degenerate fourth-order parabolic equation

The existence of solutions to a fourth-order p-Laplacian equation with boundary degeneracy is studied. For the purpose of solving the corresponding non-degenerate (with respect to the coefficient of fourth-order term) regularized problem, a fourth-order semi-discrete elliptic problem with homogeneous boundary conditions is established and its existence and uniqueness are obtained by the functional minimization method. It follows that the approximate solutions of the non-degenerate parabolic problem are constructed and the corresponding existence and uniqueness are discovered by a limit procedure from the energy estimation method and a compactness argument. Finally, the existence and regularity of solutions for the problem with boundary degeneracy is obtained by using a regularization parameter vanishing limit.     

Degeneracy Subgraph of the Lemke Complementary Pivot Algorithm and Anticycling Rule

In this paper, we use the theory of degeneracy graphs recently developed by Gal et al. to introduce a graph for studying the adjacency of almost complementary feasible bases, some of which may be degenerate, which are of interest in the context of the linear complementarity problem. We study the structure of this graph with particular reference to the possibility of cycling and various anticycling rules in the Lemke complementary pivoting algorithm. We consider the transition node pivot rule introduced by Geue and show that this rule helps in avoiding cycling in the Lemke complementary pivoting algorithm under a suitable assumption.     

Quantum mechanical Hamiltonians with large ground-state degeneracy

Nonrelativistic Hamiltonians with large, even infinite, ground-state degeneracy are studied by connecting the degeneracy to the property of a Dirac operator. We then identify a special class of Hamiltonians, for which the full space of degenerate ground states in any spatial dimension can be exhibited explicitly. The two-dimensional version of the latter coincides with the Pauli Hamiltonian, and recently-discussed models leading to higher-dimensional Landau levels are obtained as special cases of the higher-dimensional version of this Hamiltonian. But, in our framework, it is only the asymptotic behavior of the background ‘potential’ that matters for the ground-state degeneracy. We work out in detail the ground states of the three-dimensional model in the presence of a uniform magnetic field and such potential. In the latter case one can see degenerate stacking of all 2d Landau levels along the magnetic field axis.     

Lowest breathing mode of bosonic helium clusters

We analyze various microscopic calculations of vibrational frequencies for ⁴He_N clusters, N = 3-728. The lowest breathing frequency with total angular momentum J = 0 varies smoothly as a function of N, with a maximum around N = 50-120. Received 11 July 2001     

A note on paper “Implicit and explicit secular equations for Rayleigh waves in two-dimensional anisotropic media”

The paper is devoted to correcting structure of the representation for Rayleigh waves at non-semisimple degeneracy of the fundamental matrix. The incorrect representation was given in a paper “Implicit and explicit secular equations for Rayleigh waves in two-dimensional anisotropic media” by Cerv and Plesek (2013) .     

Paired-phonon analysis of impurities in bose fluids

Summary The paired-phonon analysis for boson mixtures is employed in conjunction with the hypernetted-chain approximation to study the ground-state properties of an impurity embedded in liquid⁴He. Chemical potentials, volume coefficients and other thermodynamic quantities as well as some of the most interesting optimal correlation functions are calculated for various impurities interacting with the⁴He background atoms via Lennard-Jones potentials of differing strength. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.