Related papers: Distributions of missing sums and differences
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 paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level…
In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…
The distribution function of the sum of i.i.d. random variables of the special form is considered. Such sum describes messages posterior probabilities for random coding in binary symmetric channel. Close non-asymptotic lower and upper…
This paper presents a brief survey of the most important and the most remarkable inequalities involving the basic arithmetic functions.
We consider distributions on $\mathbb{R}$ that can be written as the sum of a non-zero discrete distribution and an absolutely continuous distribution. We show that such a distribution is quasi-infinitely divisible if and only if its…
In this paper we investigate the distribution of zeros of Boubaker polynomials.
Lazarev, Miller and O'Bryant investigated the distribution of $|S+S|$ for $S$ chosen uniformly at random from $\{0, 1, \dots, n-1\}$, and proved the existence of a divot at missing 7 sums (the probability of missing exactly 7 sums is less…
This short note provides a sharper upper bound of a well known inequality for the sum of divisors function. This is a problem in pure mathematics related to the distribution of prime numbers. Furthermore, the technique is completely…
We study pairs of consecutive odd numbers through a straightforward indexing. We focus in particular on twin primes and their distribution. With a counting argument, we calculate the limit of an alternating sum that is equal to 1 which…
The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.
In the paper, I consider appearance of unit's digits in minor totals of a few integer sequences. The sequences include the sequence of even integers, sequence of odd integers and Faulhaber polynomial at $p = 2$. Application of difference…
Contents: 1. Introduction. 2. Sum rules prior to QCD. 3. Dispersion relations. 4. Types of two point function sum rules. 5. Non-perturbative power corrections. 6. Some examples of QCD sum rules.
In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry {\it win-loss}. We present in…
We propose results of the investigation of properties of the random sums of random variables. We consider the case, where the number of summands is the first moment of an event occurrence. An integral equation is presented that determines…
This article gives a brief survey of the theory and applications of anomalies.
We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…
Distributions of the same type can be discussed in terms of distribution functions as well as their integral transforms. For continuous distributions they are equivalent. In this note it is shown that it is not so in the discrete case.
In this paper, we study the value distribution of zeros of certain nonlinear difference polynomials of entire functions of finite order.
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.