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Using probability theory we derive an expression for the sum of a series of definite integrals involving upper incomplete Gamma functions. In the proof, a normal variance mixture distribution with Beta mixing distributions plays a crucial…
We study the properties of the set where a generalized function of bounded variation has infinite approximate limit, highlighting in this way the main geometric difference with functions of bounded variation. To this aim we prove a new…
Extended regular expressions with counting and interleaving are widely used in practice. However the related theoretical studies for this kind of expressions currently cannot meet the need of practical work. This paper develops syntax…
In this note we study the convergence of recursively defined infinite series. We explore the role of the derivative of the defining function at the origin (if it exists), and develop a comparison test for such series which can be used even…
In ``Rips complexes and covers in the uniform category'' the authors define, following James, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. Conditions for the existence of universal uniform…
In this paper we review a general proof for the irrationality property of numbers which take a certain form of infinite sums.
If an infinite non-periodic word is uniformly recurrent or is of bounded repetition, then the limit of its periodicity complexity is infinity. Moreover, there are uniformly recurrent words with the periodicity complexity arbitrarily high at…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
Repeated integration is a major topic of integral calculus. In this article, we study repeated integration. In particular, we study repeated integrals and recurrent integrals. For each of these integrals, we develop reduction formulae for…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the lower limit of inverse temperature
We generalize nonequilibrium integral equalities to situations involving absolutely irreversible processes for which the forward-path probability vanishes and the entropy production diverges, rendering conventional integral fluctuation…
This paper studies the concept of algorithmic equiresolution of a family of embedded varieties or ideals, which means a simultaneous resolution of such a family compatible with a given (suitable) algorithm of resolution in characteristic…
By introducing an auxiliary parameter, we find a new representation for Feynman integrals, which defines a Feynman integral by analytical continuation of a series containing only vacuum integrals. The new representation therefore…
Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper…
We describe the framework for the notion of a restricted inverse limit of categories, with the main motivating example being the category of polynomial representations of the group $GL_{\infty}$. This category is also known as the category…
The notion of random self-decomposability is generalized further. The notion is then extended to non-negative integer-valued distributions.
We define natural A_infinity-transformations and construct A_infinity-category of A_infinity-functors. The notion of non-strict units in an A_infinity-category is introduced. The 2-category of (unital) A_infinity-categories, (unital)…
The principal innovative idea in this paper is to transform the original complex nonlinear modeling problem into a combination of linear problem and very simple nonlinear problems. The key step is the generalized linearization of nonlinear…