Related papers: Oscillatory integrals with phases arising from alg…
We introduce an algebra given by quadratic relations in an algebra of polynomials in an infinite number of variables. Using this algebra, we prove some explicit formulas for the Sturm sequence of a polynomial.
For a polynomial P, we consider the sequence of iterated integrals of ln P(x). This sequence is expressed in terms of the zeros of P(x). In the special case of ln(1 + x^2), arithmetic properties of certain coefficients arising are…
In a seminal work of A. N. Varchenko, the behavior at infinity of oscillatory integrals with real analytic phase is precisely investigated by using the theory of toric varieties based on the geometry of the Newton polyhedron of the phase.…
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
The sharp range of $L^p$-estimates for the class of H\"ormander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of…
We derive a family of singular iterated maps--closely related to Poincare maps--that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solitary wave collisions depends on the transfer of energy to…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
Highly oscillatory integrals of composite type arise in electronic engineering and their calculations is a challenging problem. In this paper, we propose two Gaussian quadrature rules for computing such integrals. The first one is…
In this paper, we develop an explicit method to express finite algebraic numbers (in particular, certain idempotents among them) in terms of linear recurrent sequences, and give applications to the characterization of the splitting primes…
The gravitational neutrino oscillation problem is studied by considering the Dirac Hamiltonian in a Riemann-Cartan space-time and calculating the dynamical phase. Torsion contributions which depend on the spin direction of the mass…
We demonstrate existence of solitary waves of synchrony in one-dimensional arrays of identical oscillators with Laplacian coupling. Coarse-grained description of the array leads to nonlinear equations for the complex order parameter, in the…
Berry phase of simple harmonic oscillator is considered in a general representation. It is shown that, Berry phase which depends on the choice of representation can be defined under evolution of the half of period of the classical motions,…
We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this form over a totally real extension of odd degree. We prove…
We obtain results describing the behavior of the action of rotation generators on polynomials over a commutative ring. We also explore harmonic polynomials in a purely algebraic setting.
In this paper we study the problem of quantizing theories defined over a nonclassical configuration space. If one follows the path-integral approach, the first problem one is faced with is the one of definition of the integral over such…
An oscillator algebra and the associated Fock space with reflecting boundary and generalized statistics are constructed and is generalized to the multicomponent case. The oscillator algebra depends manifestly on the reflection factor and…
The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.
Developing the ideas of Bressler and Soibelman and of Karabegov, we introduce a notion of an oscillatory module on a symplectic manifold which is a sheaf of modules over the sheaf of deformation quantization algebras with an additional…
We prove a theorem on algebraic osculation and we apply our result to the Computer Algebra problem of polynomial factorization. We consider X a smooth completion of the complex plane and D an effective divisor supported on the boundary of…
In this paper we present a straightforward systematic method for the exact and approximate calculation of integrals that appear in formulas for the period of anharmonic oscillators and other problems of interest in classical mechanics.