There is a construction which lies at the heart of descent theory. The combinatorial aspects of this paper concern the description of the construction in all dimensions. The description is achieved precisely for strict n-categories and outlined for weak ncategories. The categorical aspects concern the development of descent theory in low dimensions in order to provide a template for a theory in...

We construct an equivalence between the categories of vertex operator algebras and vertex operator coalgebras. We then investigate to what degree weak modules, generalized modules and ordinary modules carry corresponding comodule structures, as well as when various comodules carry module structure.

..........................................................................................................................2 Dedication.......................................................................................................................3 Acknowledgments..........................................................................................................4 Table of contents.....

GrunouetterS Strength of weak ties’ theory offers a satisfying approach to the study of integration in networks of face-to-face interaction consisting of ~~~~tip~e subgroups. The present paper tests five hypotheses of this t~~eor,v in the setting of a n~~~t~dis~ip~inary social network of bioIogica1 scientists. Considerable support for the theory is indicated: the local bridges and intergroup ti...

An alternative method for deriving water wave dispersion relations and evolution equations is to use a weak formulation. The free-surface displacement η is written as an eigenfunction expansion,

We investigate subgroups of the group PLo(I) of piecewise-linear, orientation preserving homeomorphisms of the unit interval with finitely many breaks in slope, and also subgroups of Thompson’s group F . We find geometric criteria determining the derived length of any such group, and use this criteria to classify the solvable and non-solvable subgroups of PLo(I) and of F . Let H be a subgroup o...

Let V be a 2n-dimensional vector space over a field F and Ω be a non-degenerate symplectic form on V . Denote by Hk(Ω) the set of all 2k-dimensional subspaces U ⊂ V such that the restriction Ω|U is non-degenerate. Our main result (Theorem 1) says that if n 6= 2k and max(k, n−k) ≥ 5 then any bijective transformation of Hk(Ω) preserving the class of base subsets is induced by a semi-symplectic au...

I introduce a concept of D(k)-proofness which says that a rule is nonmanipulable by the false preference relations within k distance from the sincere one. I prove that for every rule defined over all weak orders, strategyproofness is equivalent to D(k)-proofness if and only if k ≥ m − 1, where m is the number of the alternatives.

In some models, exotic baryons with strangeness and anticharm or antibeauty should exist and even be stable against strong decay. We consider the stability of such possible exotic baryons, which in the constituent quark picture are called pentaquarks (each is composed of four quarks and an antiquark). Our model is based on diquark clustering and supersymmetry in hadrons, and assumes that the sp...

Let the summatory function of the Möbius function be denoted M(x). We deduce in this article conditional results concerning M(x) assuming the Riemann Hypothesis and a conjecture of Gonek and Hejhal on the negative moments of the Riemann zeta function. The main results shown are that the weak Mertens conjecture and the existence of a limiting distribution of e−y/2M(ey) are consequences of the af...