Related papers: About the Kronecker Theorem

In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.

We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…

A necessary and sufficient condition is derived for the controllability of Kronecker product networks, where the factor networks are general directed graphs. The condition explicitly illustrates how the controllability of the factor…

We formulate the Hauptvermutung of Causal Set Theory in two mathematically well-defined but different ways one of which turns out to be wrong and the other one turns out to be true. A further result is that the Hauptvermutung is true if we…

The well-known Leibniz theorem (Leibniz Criterion or alternating series test) of convergence of alternating series is generalized for the case when the absolute value of terms of series are "not absolutely monotonously" convergent to zero.…

This paper investigates the strict comparison theorem under the framework of $G$-expectation, i.e., let $X\leq Y$ q.s., if $X,Y$ satisfy some additional conditions, then $\E[X]<\E[Y]$.

Let $A$ be a finite-dimensional algebra over an algebraically closed field $\Bbbk$. For any finite-dimensional $A$-module $M$ we give a general formula that computes the indecomposable decomposition of $M$ without decomposing it, for which…

We develop a technique for normalization for $\infty$-type theories. The normalization property helps us to prove a coherence theorem: the initial model of a given $\infty$-type theory is $0$-truncated. The coherence theorem justifies…

We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…

In this paper we show how to introduce a conditional to Kripke's theory of truth that respects the deduction theorem for the consequence relation associated with the theory. To this effect we develop a novel supervaluational framework,…

This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.

We prove a fixed point theorem that combines the contraction mapping principle and some Knaster-Tarski-like theorem. As a consequence we obtain an existence theorem to initial value problem for ordinary differential equation with…

In this note I provide two extensions of a particular case of the classical Poncelet theorem.

This paper has been withdrawn. Theorem 2.1 of the paper is false, as it contradicts a result of Srinvas (Crelle's J. v.381, 1987). The error in our proof is in the construction of a functor in Claim 2. What we construct does not preserve…

A graph may be the Kronecker cover in more than one way. In this note we explore this phenomenon. Using this approach we show that the least common cover of two graphs need not be unique.

This is an erratum to an earlier paper, "Generalizations of the Poincar\'e-Birkhoff theorem." An error in the statement of one of the theorems is corrected.

We prove the theorem converse to Jackson's theorem for a modulus of smoothness of the first order generalised by means of an asymmetric operator of generalised translation.

To verify the universal validity of the "two-sided" monotonicity condition introduced in [8], we will apply it to include more classical examples. The present paper selects the $L^{p}$ convergence case for this purpose. Furthermore, Theorem…

The K\"unneth Theorem for equivariant (complex) K-theory K^*_G, in the form developed by Hodgkin and others, fails dramatically when G is a finite group, and even when G is cyclic of order 2. We remedy this situation in this very simplest…

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical…