A shape invariant nonseparable and nondiagonalizable two-dimensional model with anharmonic complex interaction, first studied by Cannata, Ioffe, Nishnianidze, is re-examined the purpose of providing an algebraic construction associated functions to excited-state wavefunctions, needed complete basis. The two operators A+ A-, coming from supersymmetric approach, where acts as a raising operator w...

The identity linking the Tutte polynomial with the Potts model on a graph implies the existence of a decomposition resembling that previously obtained for the chromatic polynomial. Specifically, let {Gn} be a family of bracelets in which the base graph has b vertices. Then the Tutte polynomial of Gn can be written as a sum of terms, one for each partition π of a non-negative integer ` ≤ b: (x− ...

We give asymptotic formulas for the number of biquadratic extensions of Q that admit a quadratic extension which is a Galois extension of Q with a prescribed Galois group, for example, with a Galois group isomorphic to the quaternionic group. Our approach is based on a combination of the theory of quadratic equations with some analytic tools such as the Siegel–Walfisz theorem and the double osc...

Let X ,Y are linear space. In this paper, we prove the generalized Hyers-Ulam stability of the following quartic equation n ∑ k=2 ( k ∑ i1=2 k+1 ∑ i2=i1+1 . . . n ∑ in−k+1=in−k+1 ) f ( n ∑ i=1,i =i1,...,in−k+1 xi − n−k+1 ∑ r=1 xir )

Approved for public release; distribution unlimited. An exact formula is given for the grazing angle of specular reflection from a sphere by displaying the zeros of a certain self-inversive quartic polynomial.

This paper presents an algorithm that, given a prime n, finds and verifies a proof of the primality of n in random time (lg n)4+o(1). Several practical speedups are incorporated into the algorithm and discussed in detail.

A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine integral quartic Cayley graphs on finite abelian groups. As a side result we show that there are exactly 27 connected integral Cayley graphs up to 11 vertices.

We prove Manin’s conjecture for a split singular quartic del Pezzo surface with singularity type 2A1 and eight lines. This is achieved by equipping the surface with a conic bundle structure. To handle the sum over the family of conics, we prove a result of independent interest on a certain restricted divisor problem for four binary linear forms.

In this paper we analyze and exactly compute the number of affine equivalence classes under permutations for quartic monomial rotation symmetric functions in prime and prime power dimensions.

The quartic gauge boson couplings in the SU(3) C ⊗ SU(3) L ⊗ U(1) N models are presented. We find that the couplings of four differrent gauge bosons may have unusual Lorentz structure and the couplings sastify the tree unitarity requirement at high energy limit.