Related papers: Some Useful Integral Representations for Informati…
Word meaning has different aspects, while the existing word representation "compresses" these aspects into a single vector, and it needs further analysis to recover the information in different dimensions. Inspired by quantum probability,…
Generalized summability results are obtained regarding formal solutions of certain families of linear moment integro-differential equations with time variable coefficients. The main result leans on the knowledge of the behavior of the…
We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation…
We generalize the Umbral Calculus of G-C. Rota by studying not only sequences of polynomials and inverse power series, or even the logarithms studied in, but instead we study sequences of formal expressions involving the iterated logarithms…
We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard's theorem for moment functionals is proven. The notion of semi-classical bilinear functionals is introduced as a generalization…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
Using standard tools of harmonic analysis, we state and solve the problem of moments for non-negative measures supported on the unit ball of a Sobolev space of multivariate periodic trigonometric functions. We describe outer and inner…
We use recurrence equations (alias difference equations) to enumerate the number of formula-representations of positive integers using only addition and multiplication, and using addition, multiplication, and exponentiation, where all the…
We introduce a new functional representation of probability density functions (PDFs) of non-negative random variables via a product of a monomial factor and linear combinations of decaying exponentials with complex exponents. This…
This paper presents new existence, dual representation, and approximation results for the information projection in the infinite-dimensional setting for moment inequality models. These results are established under a general specification…
We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle…
This paper deals with the moment problem on a (not necessarily finitely generated) commutative unital real algebra $A$. We define moment functionals on $A$ as linear functionals which can be written as integrals over characters of $A$ with…
Let $A$ be a vector space of real valued functions on a non-empty set $X$ and $L:A\rightarrow\mathbb{R}$ a linear functional. Given a $\sigma$-algebra $\mathcal{A}$, of subsets of $X$, we present a necessary condition for $L$ to be…
It is an old idea to replace averages of observables with respect to a complex weight by expectation values with respect to a genuine probability measure on complexified space. This is precisely what one would like to get from complex…
In the paper, the family of conformal four-point ladder diagrams in arbitrary space-time dimensions is considered. We use the representation obtained via explicit calculation using the operator approach and conformal quantum mechanics to…
In this paper, we investigate an example of summation of non-logarithmic singularities of a specific type in a two-dimensional non-linear sigma model. As a result of the study, we obtained an explicit formula, which, upon formal expansion…
We study the moments of the function that counts the number of representations of an integer as sums of two prime squares. We refine some of the previous arguments and apply the Selberg sieve to get an unconditional upper bound for all…
The moments of Bessel functions and Bessel-trigonometric functions play a basic role in many practical problems and numerical analysis. This paper presents a complete analysis for these moments based on the recursive relations of Bessel…
We introduce a new formalism for computing expectations of functionals of arbitrary random vectors, by using generalised integration by parts formulae. In doing so we extend recent representation formulae for the score function introduced…