Related papers: On some conjectures on Generalized quadratic Gauss…
We study the regularity of densities of distributions that are polynomial images of the standard Gaussian measure on $\mathbb{R}^n$. We assume that the degree of a polynomial is fixed and that each variable enters to a power bounded by…
This paper suggests a generalized class of estimators for population mean of the qualitative study variable in simple random sampling using information on an auxiliary variable. Asymptotic expressions of bias and mean square error of the…
The aim of this paper is to study the characteristics of a general method to produce a new approximation sequence from a given one, by using suitable convex combinations.
The classical theorems relating integral binary quadratic forms and ideal classes of quadratic orders have been of tremendous importance in mathematics, and many authors have given extensions of these theorems to rings other than the…
It is shown that the sum of squares by Yates's method of weighted squares of means is equivalent to numerator sums of squares formulated by other methods. These relations are established first for hypotheses about fixed effects in a general…
A general method to express in terms of Gauss sums the number of rational points of subschemes of projective schemes over finite fields is applied to the image of the triple embedding $\mathbb{P}^1\hookrightarrow\mathbb{P}^3$. As a…
In the present paper a new mean value theorem for polynomials of special form is obtained. The case of sums on vertices of a regular polygon is studied. A criterion for a certain equation to be satisfied is obtained.
In this study we compare Ces\`{a}ro and Euler weighted mean methods of summability of sequences of fuzzy numbers with Abel and Borel power series methods of summability of sequences of fuzzy numbers. Also some results dealing with series of…
In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.
We prove some weighted sum formulas for half multiple zeta values, half finite multiple zeta values, and half symmetric multiple zeta values. The key point of our proof is Dougall's identity for the generalized hypergeometric function…
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.
In this review paper, we summarize the current state-of-art on the Strauss conjecture with nontrapping obstacles. Among others, three essential estimates are emphasized and presented: Morawetz-KSS estimates (also known as local energy…
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
In this paper, we mainly show that generalized hyperharmonic number sums with reciprocal binomial coefficients can be expressed in terms of classical (alternating) Euler sums, zeta values and generalized (alternating) harmonic numbers.
The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds…
We survey various results and conjectures concerning multiple polylogarithms and the multiple zeta function. Among the results, we announce our resolution of several conjectures on multiple zeta values. We also provide a new integral…
For two families of random polytopes we compute explicitly the expected sums of the conic intrinsic volumes and the Grassmann angles at all faces of any given dimension of the polytope under consideration. As special cases, we compute the…
The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…
We use techniques of relative algebraic K-theory to develop a common refinement of the existing theories of metrized and hermitian Galois structures in arithmetic. As a first application of this very general approach, we then use it to…
In this note, we investigate J.-C. Liu's work on truncated Gauss' square exponent theorem and obtain more truncations. We also discuss some possible multiple summation extensions of Liu's results.