We define a type of generalized asymptotic series called v-asymptotic. We show that every function with moderate growth at infinity has a v-asymptotic expansion. We also describe the set of v-asymptotic series, where a given function with moderate growth has a unique v-asymptotic expansion. As an application to random matrix theory we calculate the coefficients and establish the uniqueness of t...

General parametric solution to a family of generalized Sylvester matrix equations arising in linear system theory is presented by using the socalled generalized Sylvester mapping which has some elegant properties. The solution consists of some polynomial matrices satisfying certain conditions and a parametric matrix representing the degree of freedom in the solution. The results provide great c...

At the International Congress of Mathematicians in 1958 (Edinburgh) N.N. Bogolyubov made our common report "On some Mathematical Problems of Quantum Field Theory" [ 1 ], in which particularly a problem of a rigorous prove of dispersion relations in quantum field theory was discussed and in connection with this it was pointed out the importance of the problem of analytic extension of generalized...

We define a type of generalized asymptotic series called v-asymptotic. We show that every func­ tion with moderate growth at infinity has a v-asymptotic expansion. We also describe the set of v-asymptotic series, where a given function with moderate growth has a unique v-asymptotic ex­ pansion. As an application to random matrix theory we calculate the coefficients and establish the uniqueness ...

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

In this paper, weakly homogeneous generalized functions in the special Colombeau algebras are determined up to equality in the sense of generalized distributions. This yields characterizations that are formally similar to distribution theory. Further, we give several characterizations of equality in the sense of generalized distributions in these algebras.

A generalized approach to possibilistic clustering algorithms was proposed in [19], where the memberships are evaluated directly according to the data information using the fuzzy set theory, and the cluster centers are updated via a performance index. The computational experiments based on the generalized possibilistic clustering algorithms in [19] revealed that these clustering algorithms coul...

In this paper, we study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of generalized relative Ritt order and generalized relative Ritt lower order.

We apply the theory of Weierstrass elliptic function to study exact solutions of the generalized Benjamin-Bona-Mahony equation. By using the theory of Weierstrass elliptic integration, we get some traveling wave solutions, which are expressed by the hyperbolic functions and trigonometric functions. This method is effective to find exact solutions of many other similar equations which have arbit...

We develop a theory of Schur functions in noncommuting variables, assuming commutation relations that are satissed in many well-known associative algebras. As an application of our theory, we prove Schur-positivity and obtain generalized Littlewood-Richardson and Murnaghan-Nakayama rules for a large class of symmetric functions, including stable Schubert and Grothendieck polynomials.