Search results for "polynomial"

Fourier transform spectroscopy and direct potential fit of a shelflike state: application to E(4)1Σ(+) KCs.

2011

The paper presents high-resolution experimental study and a direct potential construction of a shelflike state E(4)(1)Σ(+) of the KCs molecule converging to K(4(2)S) + Cs(5(2)D) atomic limit; such data are of interest for selecting optical paths for producing and monitoring cold polar diatomics. The collisionally enhanced laser induced fluorescence (LIF) spectra corresponding to both spin-allowed E(4)(1)Σ(+) → X(1)(1)Σ(+) and spin-forbidden E(4)(1)Σ(+) → a(1)(3)Σ(+) transitions of KCs were recorded in visible region by Fourier transform spectrometer with resolution of 0.03 cm(-1). Overall about 1650 rovibronic term values of the E(4)(1)Σ(+) state of (39)K(133)Cs and (41)K(133)Cs isotopologu…

Numerical investigations of single mode gyrotron equation

2009

A stationary problem with the integral boundary condition arising in the mathematical modelling of a gyrotron is numerically investigated. The Chebyshev's polynomials of the second kind are used as the tool of calculations. The main result with physical meaning is the possibility to determine the maximal value of electrons efficiency. First published online: 14 Oct 2010

Correspondence between some metabelian varieties and left nilpotent varieties

2021

Abstract In the class of left nilpotent algebras of index two it was proved that there are no varieties of fractional polynomial growth ≈ n α with 1 α 2 and 2 α 3 instead it was established the existence of a variety of fractional polynomial growth with α = 7 2 . In this paper we investigate similar problems for varieties of commutative or anticommutative metabelian algebras. We construct a correspondence between left nilpotent algebras of index two and commutative metabelian algebras or anticommutative metabelian algebras and we prove that the codimensions sequences of the corresponding algebras coincide up to a constant. This allows us to transfer the above results concerning varieties of…

Computing with Rational Symmetric Functions and Applications to Invariant Theory and PI-algebras

2012

The research of the first named author was partially supported by INdAM. The research of the second, third, and fourth named authors was partially supported by Grant for Bilateral Scientific Cooperation between Bulgaria and Ukraine. The research of the fifth named author was partially supported by NSF Grant DMS-1016086.

Knot Theory, Jones Polynomial and Quantum Computing

2005

Knot theory emerged in the nineteenth century for needs of physics and chemistry as these needs were understood those days. After that the interest of physicists and chemists was lost for about a century. Nowadays knot theory has made a comeback. Knot theory and other areas of topology are no more considered as abstract areas of classical mathematics remote from anything of practical interest. They have made deep impact on quantum field theory, quantum computation and complexity of computation.

Polynomials generated by linear operators

2004

We study the class of Banach algebra-valued n n -homogeneous polynomials generated by the n t h n^{th} powers of linear operators. We compare it with the finite type polynomials. We introduce a topology w E F w_{EF} on E , E, similar to the weak topology, to clarify the features of these polynomials.

On an Inequality for Trigonometric Polynomials In Several Variables

1990

Publisher Summary This chapter presents trigonometric polynomials in n variables. Using the methods of approximation theory, an inequality can be extended to almost periodic functions and to still more general classes of functions as in the case for Bohr's inequality. However, no analogous result exists in the case of two variables. For the solution of problems containing small divisors, the estimate has to be completed by theorems concerning the best approximation of holomorphic functions by trigonometric polynomials in polystrips. The chapter also presents equations to provide an estimate for a differential operator.

Complex Numbers and Polynomials

2016

As mentioned in Chap. 1, for a given set and an operator applied to its elements, if the result of the operation is still an element of the set regardless of the input of the operator, then the set is said closed with respect to that operator.

On the zeros of Jacobi polynomials

1994

Some Numerical Invariants of Multilinear Identities

2017

We consider non-necessarily associative algebras over a field of characteristic zero and their polynomial identities. Here we describe most of the results obtained in recent years on two numerical sequences that can be attached to the multilinear identities satisfied by an algebra: the sequence of codimensions and the sequence of colengths.