Related papers: A simple expression for the terms in the Baker-Cam…
The exact semiclassical quantization condition represents a cumbersome series expansion, so that only the main term of it is usually taken into account. We propose a way to find next terms without new additional calculations. Results are…
We prove by using simple number-theoretic arguments formulae concerning the number of elements of a fixed order and the number of cyclic subgroups of a direct product of several finite cyclic groups. We point out that certain multiplicative…
An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator generating an iterative…
Using Jacobi's identity we derive a simple expression for the Bessel functions of integer order in terms of combinations of powers and hyperbolic functions of the same argument.
A simple version for the extension of the Taylor theorem to the operator functions was found. The expansion was done with respect to a value given by a diagonal matrix for the non-commutative case, and the coefficients are given both by…
In earlier work the authors obtained integral formulas for probabilities for a single particle in the asymmetric simple exclusion process. Here formulas are obtained for joint probabilities for several particles. In the case of a single…
In this paper we provide an algorithm, similar to the simplex algorithm, which determines a rational cp-factorization of a given matrix, whenever the matrix allows such a factorization. This algorithm can be used to show that every integral…
We give an exact coefficients formula of any infinite product of power series with constant term equal to $1$, by using structures from partitions of integers and permutation groups. This is an universal theorem for various of Binomial-type…
A "simple trace formula" is used to derive an asymptotic result for class numbers of complex cubic orders.
Recently a new proof was given for Beurling's Ingham type theorem on one-dimensional nonharmonic Fourier series, providing explicit constants. We improve this result by applying a short elementary method instead of the previous complex…
Wolstenholme's type summations involve certain powers of all residues $k$ modulo some prime number $p$. We first consider the sums of double or triple products of certain powers of all residues, e.g., the sums of the terms $(a+k)^m(b+k)^n$…
By giving the definition of the sum of a series indexed by a set on which a group acts, we prove that the sum of the series that defines the Riemann zeta function, the Epstein zeta function, and a few other series indexed by $\Z^k$ has an…
We show that the characters of tilting modules can be used, in a concrete and explicit way, to obtain the simple characters of a connected reductive algebraic group $G$ over an algebraically closed field $\Bbbk$ of characteristic $p$, for…
A derived version of Maschke's theorem for finite groups is proved: the derived categories, bounded or unbounded, of all blocks of the group algebra of a finite group are simple, in the sense that they admit no nontrivial recollements. This…
Some power series representations of the modified Bessel functions (McDonald functions $K_{\alpha}$) are derived using the relatively little known formalism of fractional derivatives. The resulting summation formulae are believed to be new.
This paper presents very simple and easy integration-free proofs in the context of Weierstrass's theory of functions, of the Maximum and Minimum Modulus Principles and Gutzmer-Parseval Inequalities for polynomials and for functions…
The statement ``no nonabelian simple group can be obtained from a nonsimple group by adding one generator and one relator" 1) is equivalent to the Kervaire--Laudenbach conjecture; 2) becomes true under the additional assumption that the…
In this note we give an elementary demonstration of the fact that AB=I implies BA=I for square matrices A,B with coefficients in a field K. By elementary we mean that our proof follows from the very definitions of matrix and product of a…
We give a Laurent series proof of the Habsieger-Kadell $q$-Morris identity, which is a common generalization of the $q$-Morris identity and the Aomoto constant term identity. The proof allows us to extend the theorem for some additional…
We prove that a Hamilton-Jacobi equation in 1D with periodic forcing has a set of generalized solutions such that each solution is a sum of linear and continuous periodic functions; we also give a condition of uniqueness of this solution in…