Related papers: A Version of Koml\'os Theorem for Additive Set Fun…
We give an extension of the Fekete's Subadditive Lemma for a set of submultiplicative functionals on countable product of compact spaces. Our method can be considered as an unfolding of the ideas [1]Theorem 3.1 and our main result is an…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
This paper offers a mathematical invention that shows how to convert integrated quantiles, which often appear in risk measures, into integrated cumulative distribution functions, which are technically more tractable from various…
{The first version of this text was written and submitted to a journal on April, 12, 2018. This second version was submitted on April, 9, 2019.} We investigate the existence of subsets $A$ and $B$ of $\mathbb{N}:=\{0,1,2,\dots\}$ such that…
In the consistent histories formulation of quantum theory, the probabilistic predictions and retrodictions made from observed data depend on the choice of a consistent set. We show that this freedom allows the formalism to retrodict…
This paper establishes an abstract Korovkin-type approximation theorem in general spaces, extending the framework of approximation theory to accommodate broader contexts. A critical result supporting this theorem is the proof that any…
Using relativized ordinal analysis, we give a proof-theoretic characterization of the provably total set-recursive-from-$\omega$ functions of KPl and related theories.
The usual nonnegative modulus function is based on addition. A natural different modulus function on the set of positive reals is introduced. Arguments for results for series through the usual modulus function are transformed to arguments…
Additive combinatorics is built around the famous theorem by Szemer\'edi which asserts existence of arithmetic progressions of any length among the integers. There exist several different proofs of the theorem based on very different…
The problem of estimating a parameter of a quantum system through a series of measurements performed sequentially on a quantum probe is analyzed in the general setting where the underlying statistics is explicitly non-i.i.d. We present a…
P\'olya's enumeration theorem is concerned with counting labeled sets up to symmetry. Given a finite group acting on a finite set of labeled elements it states that the number of labeled sets up to symmetry is given by a polynomial in the…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…
Existence of long arithmetic progression in sumsets and subset sums has been studied extensively in the field of additive combinatorics. These additive combinatorics results play a central role in the recent progress of fundamental problems…
Let G be any additive abelian group with cyclic torsion subgroup, and let A, B and C be finite subsets of G with cardinality n>0. We show that there is a numbering {a_i}_{i=1}^n of the elements of A, a numbering {b_i}_{i=1}^n of the…
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…
Combinatorial interpretation of the fibonomial coefficients as a number of choices of specific finite subsets of an infinite partially ordered set of not binomial type is proposed. This partially ordered set is here defined via…
We establish a law of the iterated logarithm (LIL) for the set of real numbers whose $n$-th partial quotient is bigger than $\alpha_n$, where $(\alpha_n)$ is a sequence such that $\sum 1/\alpha_n$ is finite. This set is shown to have…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic's relativistic equations are obtained in the presence of electromagnetic fields for…