Related papers: Linear extensions of partial orders and Reverse Ma…

We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…

Lindel{\"o}f's hypothesis, one of the most important open problems in the history of mathematics, states that for large $t$, Riemann's zeta function $\zeta(1/2+it)$ is of order $O(t^{\varepsilon})$ for any $\varepsilon>0$ . It is well known…

The introduction of strings into the study of the Riemann Hypothesis provides a visualization of the genesis of zeros for the Zeta function. The method is heuristic and when originally introduced suggested strong visual evidence for the…

We present an unconditional proof that non-trivial zeros of the Riemann Zeta function must lie strictly on the critical line $\text{Re}(s) = 0.5$. By defining a recursive path of Taylor expansions originating from the domain of absolute…

In this work we continue the study of non-chaotic asymptotic correlations in many element systems and discuss the emergence of a new notion of asymptotic correlation -- partial order -- in the Choose the Leader (CL) system. Similarly to the…

We analyse various exponential off-diagonal decay rates of the elements of infinite matrices and their inverses. It is known that such decay of the elements of an infinite matrix does not imply inverse--closeness, i.e. the inverse, if…

We relate extensions of completely unitary VOAs and (commutative) Q-systems. As an application, we show that any unitary extension of a completely unitary VOA is completely unitary.

We have discussed the problem of finding the condition on coefficients of $f''+A(z)f'+B(z)f=0, \quad B(z)(\not \equiv 0)$ so that all non-trivial solutions are of infinite order. The hyper-order of these non-trivial solutions of infinite…

We consider several formalizations in the language of second-order arithmetic of "The formula $\phi$ is a theorem of $\omega$-logic", including some which have been studied in the literature and a new variant defined via a least fixed…

We use a second-order analogy $\mathsf{PRA}^2$ of $\mathsf{PRA}$ to investigate the proof-theoretic strength of theorems in countable algebra, analysis, and infinite combinatorics. We compare our results with similar results in the…

In this paper, we further consider the symmetry-based method for seeking nonlocally related systems for partial differential equations. In particular, we show that the symmetry-based method for partial differential equations is the natural…

An {\omega}-language is a set of infinite words over a finite alphabet X. We consider the class of recursive {\omega}-languages, i.e. the class of {\omega}-languages accepted by Turing machines with a B\"uchi acceptance condition, which is…

The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…

We redefine the transition function of elementary cellular automata (ECA) in terms of discrete operators. The operator representation provides a clear hint about the way systems behave both at the local and the global scale. We show that…

It is known that the behavior of the Mitchell order substantially changes at the level of rank-to-rank extenders, as it ceases to be well-founded. While the possible partial order structure of the Mitchell order below rank-to-rank extenders…

Let $\mathbb{A} = (A, \cdot)$ be a semigroup. We generalize some recent results by G. A. Freiman, M. Herzog and coauthors on the structure theory of set addition from the context of linearly orderable groups to linearly orderable…

We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…

We consider the four fragments FO2, the intersection of Sigma2 and FO2, the intersection of Pi2 and FO2, and Delta2 of first-order logic FO[<] over finite and infinite words. For all four fragments, we give characterizations in terms of…

A linear operator $T$ between two lattice-normed locally solid Riesz spaces is said to be $p_\tau$-continuous if, for any $p_\tau$-null net $(x_\alpha)$, the net $(Tx_\alpha)$ is $p_\tau$-null, and $T$ is also said to be $p_\tau$-bounded…

We investigate the mathematical structure of unit systems and the relations between them. Looking over the entire set of unit systems, we can find a mathematical structure that is called preorder (or quasi-order). For some pair of unit…