For the problem (here u = u(x)) ∆u− u + αu + βu = 0, x ∈ R, lim |x|→∞ u(x) = 0 , with constants 1 ≤ p < q < r < n+2 n−2 , and α, β > 0, uniqueness of radial solution (called ground state solution) is not known. We present a procedure, which opens the way to produce computer assisted proofs of uniqueness for specific p, q, r, and n.

Recent lattice results for the energy of gluonic excitations as a function of quark separation are shown to correspond to transverse relativistic ux tube vibration modes. For large quark separations all states appear to degenerate into a few categories which are predicted uniquely, given the ground state.

We try to explain the differences in the He dipole strength function in [1] and [2]. We perform the full basis calculation of the strength function with the same renormalized interaction as in [1] and show that the size of the basis, needed for converged calculations of the He continuum spectrum, is much larger than that for the discrete spectrum. The renormalized interaction of [1] therefore c...

A dynamical theory is studied in which a scalar field φ in Einstein-Minkowski space is coupled to the four-velocity Nμ of a preferred inertial observer in that space. As a consistent requirement on this coupling we study a principle of duality invariance of the dynamical mass-term of φ at some universal length in the smalldistance regime. In the large-distance regime duality breaking can be int...

The effect of the " B " term in the interaction −χQ · Q(1 + B τ (1) · τ (2)), which was previously considered in the 0p shell, is now studied in a larger space which includes ∆N = 2 excitations. We still get a collapse of low-lying states below the conventional J = 0 + ground state when B is made sufficiently negative.

We conjecture that there exists a strong coupling limit of bosonic string theory which is related to the 26 dimensional theory in the same way that 11 dimensional M theory is related to superstring theory. More precisely, we believe that bosonic string theory is the compactification on a line interval of a 27 dimensional theory whose low energy limit contains gravity and a three-form potential....

We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in thermodynamics limit. We prove that for short strings the probability can be expressed in terms of Riemann zeta function with odd arguments.

In recognition of the 0ct)ober 1964 declaration of the International Committee of Weights and Measures that the physical measurement of time be based on a particular transition between two hyperfine levels in the ground state of cesium 133, a review of the characteristics of cesium beam atomic frequency standards is presented. This article discusses the general requirements for frequency and ti...

Let ) ( *2   L H with ) ( : 2 1 R S   , i.e.  is the boundary of the unit sphere. Let ) (s u being a   2 periodic function and  denotes the integral from 0 to  2 in the Cauchy-sense. Then for ) ( : 2     L H u with ) ( : 2 1 R S   and for real  the Fourier coefficients    dx e x u u x i   ) ( 2 1 : enable the definitions of the norms (e.g. [ILi] 11.1.5, [KBr0])