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Quantum computers are widely believed have an advantage over classical computers, and some have even published some empirical evidence that this is the case. However, these publications do not include a rigorous proof of this advantage,…
We obtain a criterion for an analytic subset of a Euclidean space to contain points of differentiability of a typical Lipschitz function, namely, that it cannot be covered by countably many sets, each of which is closed and purely…
A method for estimating the merit factors of sequences will be provided. The result is also effective in determining the nonexistence of certain infinite collections of cyclic difference sets and cyclic matrices and associated binary…
Our theme is that not every interesting question in set theory is independent of $ZFC$. We give an example of a first order theory $T$ with countable $D(T)$ which cannot have a universal model at $\aleph_1$ without CH; we prove in $ZFC$ a…
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…
It is shown, that the only reason for possibility of using microcanonical ensemble is that there are probabilistic processes in microworld, that are not described by quantum mechanic. On a simple example it is demonstrated, that canonical…
A folklore argument shows that Frattini's characterization of non-generators works in the framework of algebraic partially ordered sets. We provide characterizations of non-generators in arbitrary partially ordered sets. The validity of…
Let $C$ be the middle-third Cantor set. We show that \[\left\{\frac{1}{n!}: n\in\mathbb{N}\right\}\cap C=\left\{1, \frac{1}{5!}\right\}.\] This answers a question recently posed by Jiang [J. Lond. Math. Soc., 2026, published online]. Our…
We point out that a sequence of natural numbers is the dimension sequence of a subproduct system if and only if it is the cardinality sequence of a word system (or factorial language). Determining such sequences is, therefore, reduced to a…
Ontology-based query answering with existential rules is well understood and implemented for positive queries, in particular conjunctive queries. The situation changes drastically for queries with negation, where there is no agreed-upon…
We give a necessary and sufficient condition to achieve the most uncertain exponent in the fractal uncertainty principle of discrete Cantor sets. The condition will be described as distributed spectral pairs, which is a generalization of…
Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…
The non-Hermitian formalism is used at present in many papers for the description of open quantum systems. A special language developed in this field of physics which makes it difficult for many physicists to follow and to understand the…
In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…
Binomial Theorem for (N+n)^r is described with non-commuting variables N and n.
A Q-set is an uncountable set of reals all of whose subsets are relative $G_\delta$ sets. We prove that, for an arbitrary uncountable cardinal kappa, there is consistently a Q-set of size $\kappa$ whose square is not Q. This answers a…
Different features have different relevance to a particular learning problem. Some features are less relevant; while some very important. Instead of selecting the most relevant features using feature selection, an algorithm can be given…
The Catalan numbers are well-known to be the answer to many different counting problems, and so there are many different families of sets whose cardinalities are the Catalan numbers. We show how such a family can be given the structure of a…
A set of first-order formulas, whatever the cardinality of the set of symbols, is equivalent to an independent set.
The best developed formulation of closed system quantum theory that handles multiple-time statements, is the consistent (or decoherent) histories approach. The most important weaknesses of the approach is that it gives rise to many…