Related papers: A conjecture on some estimates for integrals
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…
Causal inference from observational data requires assumptions. These assumptions range from measuring confounders to identifying instruments. Traditionally, causal inference assumptions have focused on estimation of effects for a single…
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…
The arithmetic function of two variables is defined. Some properties of the function are given along with the formula that is an analog of the so-called Mobius' inversion formula. A heuristic statement is suggested.
In this paper, we prove an integral theorem for Cegrell class $\mathcal{F}(f)$ and use this result to study the $\mathcal{F}$-equivalence relation.
We look for pointwise bounds on a plurisubharmonic function near its singularity point, given the value of its generalized Lelong number with respect to a plurisubharmonic weight. To this end, an extremal problem is considered. In certain…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
In this paper, we give explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.
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,…
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today.…
We propose a conjectural $q$-analogue of the classical duality for iterated integrals on $\mathbb{P}^{1}$ minus four points, arising from the involutive M\"{o}bius transformation which exchanges the four marked points in pairs. To this end,…
We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the…
In paper this paper it is considered the summation problem for trigonometric integrals with quadratic phase. This problem considered in the papers \cite{Chub},\cite{Chax},\cite{Jabbar} in particular cases. Our results generalized the…
Let p be a polynomial in one complex variable. Smale's mean value conjecture estimates |p'(z)| in terms of the gradient of a chord from (z, p(z)) to some stationary point on the graph of $p$. The conjecture does not immediately generalise…
Khabibullin's conjecture for integral inequalities has two numeric parameters $n$ and $\alpha$ in its statement, $n$ being a positive integer and $\alpha$ being a positive real number. This conjecture is already proved in the case where…
We prove an exponential integral estimate for the quadratic partial sums of multiple Fourier series on large sets that implies some new properties of Fourier series.
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
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…