相关论文: Implication of the Modified Gottfried Sum Rule
Our knowledge on the nucleon spin structure has greatly improved over the last twenty years or so, but still many fundamental questions remain unsolved. I will try to review some of the puzzling aspects of the origin of the nucleon spin. I…
The sum formula is a well known relation in the field of the multiple zeta values. In this paper, we present its generalization for the Euler-Zagier multiple zeta function.
Recent results concerning solutions of the modified Helmholtz equation are reviewed; namely, various mean value properties and their corollaries, converse and inverse of these properties, and relations between these solutions and harmonic…
Certain new inequalities for the sums of factorials are presented.
Contributions of fermions to the mass of the scalar glueball $0^{++}$ are calculated at two-loop level in the framework of QCD sum rules. It obviously changes the coefficients in the operator product expansion (OPE) and shifts the mass of…
In the wake of a new kind of phase generally occurring in mesoscopic transport phenomena, we discuss the validity of Friedel sum rule in the presence of this phase. We find that the general Friedel sum rule may be violated.
One of the approaches to the Riemann Hypothesis is the Nyman-Beurling criterion. Cotangent sums play a significant role. Here we investigate the values of these cotangent sums for various shifts of the argument.
After a brief review of classical probability theory (measure theory), we present an observation (due to Sorkin) concerning an aspect of probability in quantum mechanics. Following Sorkin, we introduce a generalized measure theory based on…
In this paper we simplify the definition of the weighted sum Boolean function which used to be inconvenient to compute and use. We show that the new function has essentially the same properties as the previous one. In particular, the bound…
We present new counterexamples, which provide stronger limitations to sums-differences statements than were previously known. The main idea is to consider non-uniform probability measures.
In this article, we obtain certain estimate for the shifted convolution sum involving the Fourier coefficients of half-integral weight cusp forms.
We give two general transformations that allows certain quite general basic hypergeometric multi-sums of arbitrary depth (sums that involve an arbitrary sequence $\{g(k)\}$), to be reduced to an infinite $q$-product times a single basic…
Recently the CCFR Collaboration reported the measurement of the Gross--Llewellyn Smith sum rule %at $Q^2=3\; \mr{GeV}^2$: $\int^{1}_{0}\mr{d}F_{3}^{\nu p+\bare{\nu}p}(x,Q^2=3\;\mr{GeV}^2)= 2.50\pm 0.018(\mr{stat})$. Subsequently Kataev and…
A generalization of the definition of a one-dimensional improper integral with a finite limit is presented. The new definition extends the range of valid integrals to include integrals which were previously considered to not be integrable.…
We study several variants of Euler sums by using the methods of contour integration and residue theorem. These variants exhibit nice properties such as closed forms, reduction, etc., like classical Euler sums. In addition, we also define a…
In this lecture I address the issue of possible large distance modification of gravity and its observational consequences. Although, for the illustrative purposes we focus on a particular simple generally-covariant example, our conclusions…
Recently, several interesting proposals were made modifying the law of gravity on large scales, within a sensible relativistic formulation. This allows a precise formulation of the idea that such a modification might account for galaxy…
The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the…
In this paper some generalizations of the sum of powers of natural numbers is considered. In particular, the class of sums whose generating function is the power of the generating function for the classical sums of powers is studying. The…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.