相关论文: Some functional equations originating from number …
The results of the Young experiment can be analyzed either by classical or Quantum Physics. The later one though leads to a more complete interpretation, based on two different patterns that appear when one works either with single or…
Hypercomputational formal theories will, clearly, be both structurally and foundationally different from the formal theories underpinning computational theories. However, many of the maps that might guide us into this strange realm have…
We discuss a method for computing the generating function for the multiplicity distribution in field theories with strong time dependent external sources. At leading order, the computation of the generating function reduces to finding a…
Our previous work (math.QA/9808015) introduces the basic notions and announces some results on function theory in the quantum disc. The present paper establishes a relationship between those results and the quantum groups theory.
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
We show that the single-particle Green's functions used in many body theory have an elegant description in the form of hyperfunctions. We summarize the necessary hyperfunction concepts. We show that the analytical properties and the…
The so-called polynomial equations play an important role both in algebra and in the theory of functional equations. If the unknown functions in the equation are additive, relatively many results are known. However, even in this case, there…
Particular solutions of the Benney equations are constructed. Their properties are discussed.
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
The Leah-Hamiltonian, $H(x,y)=y^2/2+3x^{4/3}/4$, is introduced as a functional equation for $x(t)$ and $y(t)$. By means of a nonlinear transformation to new independent variables, we show that this functional equation has a special class of…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
Field-theoretic construction of functional representations of solutions of stochastic differential equations and master equations is reviewed. A generic expression for the generating function of Green functions of stochastic systems is put…
We obtain some new formulae to compute the first derivative of confluent and biconfluent Heun functions under the minimal assumption of fixing only one parameter. These results together with the Lagrangian formulation of a general…
We present some recent progresses on Heun functions, gathering results from classical analysis up to elliptic functions. We describe Picard's generalization of Floquet's theory for differential equations with doubly periodic coefficients…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
The paper investigates the role of data, hypotheses and mathematical methods that can be used in the discovery of a law y=fo(u), relating variables u and y of a physical phenomenon, making use of experimental measurements of such variables.…
After a short introduction to effective field theories, most of their features are illustrated using the top decay. The effects of heavy new physics on the top decay are computed and the constraints on the coefficients of the dimension-six…
For a wide class of nonlinear equations a perturbative solution is constructed. This class includes equations of motion of field theories. The solution possesses a graphical representation in terms of diagrams. To illustrate the formalism…
Given a semigroup $S$ equipped with an involutive automorphism $\sigma$, we determine the complex-valued solutions $f,g,h$ of the functional equation \begin{equation*}f(x\sigma(y))=f(x)g(y)+g(x)f(y)+h(x)h(y),\,\,x,y\in S,\end{equation*} in…