v 1 3 N ov 1 99 8 Eigenvalue bounds for a class of singular potentials in N dimensions Richard

Exact solutions for semirelativistic problems with non-local potentials

It is shown that exact solutions may be found for the energy eigenvalue problem generated by the class of semirelativistic Hamiltonians of the form H = √ m2 + p2+ V̂ , where V̂ is a non-local potential with a separable kernel of the form V(r, r′) = −∑i=1 vifi(r)gi(r). Explicit examples in one and three dimensions are discussed, including the Yamaguchi and Gauss potentials. The results are used to...

ar X iv : h ep - t h / 94 10 11 8 v 2 2 2 N ov 1 99 4 WILSON LOOPS , qq̄ and 3 q POTENTIALS , BETHE – SALPETER EQUATION

On Complementary Distance Signless Laplacian Spectral Radius and Energy of Graphs

Let $D$ be a diameter and $d_G(v_i, v_j)$ be the distance between the vertices $v_i$ and $v_j$ of a connected graph $G$. The complementary distance signless Laplacian matrix of a graph $G$ is $CDL^+(G)=[c_{ij}]$ in which $c_{ij}=1+D-d_G(v_i, v_j)$ if $ineq j$ and $c_{ii}=sum_{j=1}^{n}(1+D-d_G(v_i, v_j))$. The complementary transmission $CT_G(v)$ of a vertex $v$ is defined as $CT_G(v)=sum_{u in ...

ar X iv : h ep - t h / 97 11 12 7 v 1 1 7 N ov 1 99 7 1 Supersymmetry in Dimensions Beyond Eleven

Spacetime superalgebras with 64 or less number of real supercharges, containing the type IIB Poincaré superal-gebra in (9, 1) dimensions and the N = 1 Poincaré superalgebra in (10, 1) are considered. The restriction D ≤ 14, and two distinct possibilities arise: The N = (1, 0) superalgebra in (11, 3) dimensions, and the N = (2, 0) super-algebra in (10, 2) dimensions. Emphasizing the former, we d...

ar X iv : h ep - t h / 99 11 17 0 v 2 2 3 N ov 1 99 9 AEI - 1999 - 38 hep - th / 9911170 Yang - Mills Integrals

Abstract. SU(N) Yang-Mills integrals form a new class of matrix models which, in their maximally supersymmetric version, are relevant to recent non-perturbative definitions of 10-dimensional IIB superstring theory and 11-dimensional M-theory. We demonstrate how Monte Carlo methods may be used to establish important properties of these models. In particular we consider the partition functions as...