Related papers: The simplified weighted sum function and its avera…
We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…
In this paper, we investigate the asymptotics of a class of weighted sums over multiplicative functions and apply our results to deduce a stronger asymptotic form of Yitang Zhang's smoothened GPY sieve with coefficient expressions that are…
The main purpose of present paper is to determine some lower bounds for the quotient of the normalized hyper-Bessel function and its partial sum, as well as for the quotient of the derivative of normalized hyper-Bessel function and its…
The definition of weighted entropy allows for easy calculation of the entropy of the mixture of measures. In this paper we investigate the problem of equivalent definition of the general entropy function in weighted form. We show that under…
We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained…
Combining several independent measurements of the same physical quantity is one of the most important tasks in metrology. Small samples, biased input estimates, not always adequate reported uncertainties, and unknown error distribution make…
Properties of weighted averages are studied for the general case that the individual measurements are subject to hidden correlations and have asymmetric statistical as well as systematic errors. Explicit expressions are derived for an…
This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
Soft extrapolation refers to the problem of recovering a function from its samples, multiplied by a fast-decaying window and perturbed by an additive noise, over an interval which is potentially larger than the essential support of the…
In this exploratory note we ask the question of what a measure of performance for all tasks is like if we use a weighting of tasks based on a difficulty function. This difficulty function depends on the complexity of the (acceptable)…
Recently, Deshpande et al. introduced a new measure of the complexity of a Boolean function. We call this measure the "goal value" of the function. The goal value of $f$ is defined in terms of a monotone, submodular utility function…
In this paper, we give more general definitions of weighted means and MN-convex functions. Using these definitions, we also obtain some generalized results related to properties of MN-convex functions. The importance of this study is that…
We provide new upper bounds for sums of certain arithmetic functions in many variables at polynomial arguments and, exploiting recent progress on the mean-value of the Erd\H os-Hooley $\Delta$-function, we derive lower bounds for the…
In this article, we define a special function called the Bigamma function. It provides a generalization of Euler's gamma function. Several algebraic properties of this new function are studied. In particular, results linking this new…
It is well-known that Sobol indices, which count among the most popular sensitivity indices, are based on the Sobol decomposition. Here we challenge this construction by redefining Sobol indices without the Sobol decomposition. In fact, we…
We generalize and extend the ideas in a recent paper of Chiarelli, Hatami and Saks to prove new bounds on the number of relevant variables for boolean functions in terms of a variety of complexity measures. Our approach unifies and refines…
In this paper, we study the average of shifted sum for general multiplicative functions. As applications, we prove non-trivial upper bounds for weighted averages of shifted convolutions involving $GL(2)$ and $GL(3)$ Fourier coefficients…
In this paper we show that a methodology based on a sampling with the Gaussian function of kind $h\,{e^{ - {{\left( {t/c} \right)}^2}}}/\left( {{c}\sqrt \pi } \right)$, where ${c}$ and $h$ are some constants, leads to the Fourier transform…
In this paper we introduce a method which allows us to study properties of the random uniform simplicial complex. That is, we assign equal probability to all simplicial complexes with a given number of vertices and then consider properties…