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In this study, new master theorems and general formulas of integrals are presented and implemented to solve some complicated applications in different fields of science. The proposed theorems are considered to be generators of new problems,…
In a real expert system, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. It is important for decision making that the information present in this aggregate somehow find its way into use.…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
An integral transformation relating two inequalities in Khabibullin's conjecture is found. Another proof of this conjecture for some special values of its numeric parameters is suggested.
Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. In particular, we argue that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ for $n \to…
With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…
Given two Calabi--Yau threefolds which are believed to constitute a mirror pair, there are very precise predictions about the enumerative geometry of rational curves on one of the manifolds which can be made by performing calculations on…
In this paper we establish the following estimate \[ w\left(\left\{ x\in\mathbb{R}^{n}\,:\,\left|[b,T]f(x)\right| > \lambda\right\} \right)\leq…
A simple procedure to estimate O(alpha_s^3) and O(alpha_s^4) corrections to mass-dependent observables is conjectured. The method is tested in a number of cases where the O(alpha_s^3) contribution is exactly known, and reasonable agreement…
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
An integral formula is developed which applies to an essentially arbitrary function. An application is made to the Riemann zeta function.
The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalites for functions. This will allow us to prove a local subelliptic Sobolev inequality with the optimal…
When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…
Sufficient conditions for performing changes of the variable of integration when using the new definitions of improper integrals given in in "An Alternative Definition for Improper Integral with Infinite Limit" (arXiv:0805.3559v1) and "An…
We consider identification and inference about a counterfactual outcome mean when there is unmeasured confounding using tools from proximal causal inference (Miao et al. [2018], Tchetgen Tchetgen et al. [2020]). Proximal causal inference…
We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…
Sharp upper and lower estimates are obtained of the approximation numbers of a Sobolev embedding and an integral operator of Volterra type. These lead to asymptotic formulae for the approximation numbers and certain other s-numbers.
The paper considers estimates for some sums and products of functions of prime numbers. Several assertions on this topic have been proven. We also study extremal estimates for strongly additive and strongly multiplicative arithmetic…
The Sinc quadrature and the Sinc indefinite integration are approximation formulas for definite integration and indefinite integration, respectively, which can be applied on any interval by using an appropriate variable transformation.…
The higher order matching problem is the problem of determining whether a term is an instance of another in the simply typed $\lambda$-calculus, i.e. to solve the equation a = b where a and b are simply typed $\lambda$-terms and b is…