‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

The forward direction singularity of the non-relativistic Coulomb S-matrix is examined and discussed. The relativistic Coulomb S-matrix to order e is shown to have a similar singularity.

Third order Coulomb correction to t ¯ t threshold cross section * We report on our result of third order Coulomb correction to the cross section σ(e + e − → t ¯ t) near threshold. Analytic expression for the Coulomb energy and wave function at the origin are obtained. We discuss the significance of the Coulomb correction to the threshold cross section and heavy quarkonium phenomenology. 1. Thre...

The influence of long-range Coulomb interactions on the properties of onedimensional (1D) strongly correlated electron systems in vicinity of the metalinsulator phase transition is considered. It is shown that unscreened repulsive Coulomb forces lead to the formation of a 1D Wigner crystal in the metallic phase and to the transformation of the square-root singularity of the compressibility (cha...

Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three dimensional gauge theories, ba...

We construct the dual supergravity description of strongly coupled, large N , eightsupercharge gauge theories with fundamental hypermultiplets at points on the mixed CoulombHiggs branch. With certain assumptions about unknown couplings of D-branes to supergravity, this construction gives the correct metric on the hypermultiplet (Higgs-branch) component the moduli space, which decouples from the...

Two-loop contributions to the electromagnetic form factors are calculated in the kinematic regime close to the fermion-antifermion threshold. The results are presented in an expansion in the velocity of the fermions in the c.m. frame up to next-to-next-to leading order in. The existence of a new Coulomb singularity logarithmic in , which is closely related to the O(2 ln) corrections known from ...

Quantum mechanical models and practical calculations often rely on some exactly solvable models like the Coulomb and the harmonic oscillator potentials. The D dimensional generalized Coulomb potential contains these potentials as limiting cases, thus it establishes a continuous link between the Coulomb and harmonic oscillator potentials in various dimensions. We present results which are necess...

Quantum mechanical models and practical calculations often rely on some exactly solvable models like the Coulomb and the harmonic oscillator potentials. The D dimensional generalized Coulomb potential contains these potentials as limiting cases, thus it establishes a continuous link between the Coulomb and harmonic oscillator potentials in various dimensions. We present results which are necess...

With a help of the Schwinger — DeWitt expansion analytical properties of the evolution operator kernel for the Schrödinger equation in time variable t are studied for the Coulomb and Coulomb-like (which behaves themselves as 1/|~q| when |~q| → 0) potentials. It turned out to be that the Schwinger — DeWitt expansion for them is divergent. So, the kernels for these potentials have additional (bey...