The purpose of this article is to show that when a smooth manifold is given a generic metric, prime minimal two-spheres and prime minimal tori within the manifold do not have branch points. This is an analog within Riemannian geometry of a well-known theorem of Böhme and Tromba which states that solutions to the classical Plateau problem in R have no branch points for generic choice of boundary...

Local event structures and local traces are generalizations of the classical prime event structures and Mazurkiewicz’ traces in which independence is no longer a global binary property. We consider the problem of lifting the categorical connection between prime event structures and Mazurkiewicz’ traces to this more general setting. Using a generic approach it is shown how certain subcategories ...

In this paper we give a computation of the mass spectrum of mesons and baryons. By this computation we show that there is a consecutive numbering of the mass spectrum of mesons and baryons. We show that in this numbering many stable mesons and baryons are assigned with a prime

This paper defines an isomorphism, an anti-isomorphism and a Jordan isomorphism in a gamma ring and develops some important results relating to these concepts. Using these results we prove Herstein’s theorem of classical rings in case of prime gamma rings by showing that every Jordan isomorphism of a 2-torsion free prime gamma ring is either an isomorphism or an anti-isomorphism. AMS Mathematic...

The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. Mayne proved that in case there exists a nontrivial centralizing automorphism on a prime ring, then the ring is commutative. In this paper, some...

The notion of quantale, which designates a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins, appears in various areasof mathematics-in quantaloid theory, non classical logic as completion the Lindebaum algebra, and different representations spectrum C∗ algebra asmany-valued commutative topologies. To put it briefly, its importance is nolonger...

For each prime $p$, we define a $t$-structure on the category $\widehat{S^{0,0}}/\tau\text{-}\mathbf{Mod}_{harm}^b$ of harmonic $\mathbb{C}$-motivic left module spectra over $\widehat{S^{0,0}}/\tau$, whose MGL-homology has bounded Chow-Novikov degree, such that its heart is equivalent to abelian $p$-completed $BP_*BP$-comodules are concentrated in even degrees. We prove $\mathcal{D}^b({{BP}_*{B...

This paper proposes and investigates a framework for clique gossip protocols. As complete subnetworks, the existence of cliques is ubiquitous in various social, computer, and engineering networks. By clique gossiping, nodes interact with each other along a sequence of cliques. Clique-gossip protocols are defined as arbitrary linear node interactions where node states are vectors evolving as lin...

We present a family of congruences which hold if and only if a natural number n is prime. 2000 Mathematics Subject Classification: 11A51, 11A07. The subject of primality testing has been in the mathematical and general news recently, with the announcement [1] that there exists a polynomial-time algorithm to determine whether an integer p is prime or not. There are older deterministic primality ...

In this paper, we completely solve the simultaneous Diophantine equations x − az = 1, y − bz = 1 provided the positive integers a and b satisfy b−a ∈ {1, 2, 4}. Further, we show that these equations possess at most one solutions in positive integers (x, y, z) if b − a is a prime or prime power, under mild conditions. Our approach is (relatively) elementary in nature and relies upon classical re...