Related papers: A conjecture on some estimates for integrals

Uncertainty enters into human reasoning and inference in at least two ways. It is reasonable to suppose that there will be roles for these distinct uses of uncertainty also in automated reasoning.

Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several…

In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…

Paper is devoted to extremal problems in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. In particular, we strengthen some known result in this…

The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, the framework gives an efficient algorithm to calculate all tautological equations using only finite dimensional…

Human communication is based on a variety of inferences that we draw from sentences, often going beyond what is literally said. While there is wide agreement on the basic distinction between entailment, implicature, and presupposition, the…

Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas…

A parameter estimation problem is considered for a stochastic parabolic equation with multiplicative noise under the assumption that the equation can be reduced to an infinite system of uncoupled diffusion processes. From the point of view…

Let $K$ be a number field and $O_K$ the ring of integers of $K$. In the spirit of Siegel's theorem on integral points on affine algebraic curves, the plane Jacobian conjecture over $K$ is equivalent to the following statement: if $P,Q\in…

In 1904, Dickson [5] stated a very important conjecture. Now people call it Dickson's conjecture. In 1958, Schinzel and Sierpinski [14] generalized Dickson's conjecture to the higher order integral polynomial case. However, they did not…

We present a conjecture about partitions, with a very elementary formulation.

In this short note we present a class of conjectures on partitions of integers as summations of primes, which are extensions of Goldbach conjecture.

Pairwise comparisons between alternatives are a well-established tool to decompose decision problems into smaller and more easily tractable sub-problems. However, due to our limited rationality, the subjective preferences expressed by…

Often, one would like to determine some observable A, but can only measure some (hopefully related) observable M. This can arise, for example, in quantum eavesdropping, or when the research lab budget isn't large enough for that 100%…

In this paper we obtain a partial answer to a conjecture on the solvabilty of linear difference equations in quasianalytic Carleman classes.

In this article, we use a class of harmonic functions (maybe multi-valued) to study the equality part in a weighted version of Suita conjecture for higher derivatives and finite points case, and we obtain some sufficient and necessary…

We discuss some aspects of the theory of subelliptic estimates.

Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…

For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…