The moduli space of regular stable maps

We prove that the moduli space of regular stable maps in a complex manifold admits a natural complex orbifold structure. Our proof is based on Hardy decompositions and Fredholm intersection theory. The authors would like to thank the referee for his/her diligent work. We are grateful for the careful attention to detail in the report.     

Coinvariants and the regular representation of a cyclic P-group

We consider an indecomposable representation of a cyclic p-group ${Z_{p^r}}$ over a field of characteristic p. We show that the top degree of the corresponding ring of coinvariants is less than ${\frac{(r^2+3r)p^r}{2}}$ . This bound also applies to the degrees of the generators for the invariant ring of the regular representation.     

K5的弧传递循环正则覆盖

-个图称为弧传递的,如果它的自同构群在其弧集合上作用传递.冯衍全等已经决定了4阶完全图K4的弧传递循环正则覆盖,本文给出了5阶完全图K5的弧传递循环正则覆盖的分类.     

Regular cyclic coverings of regular affine maps

The regular coverings of regular affine algebraic maps are considered, and a large family of totally ramified coverings—the so-called Steinberg and Accola coverings—are fully classified.     

Every finitely generated regular field extension has a stable transcendence base

A fieldK is called stable if every finitely generaed regular field extensionF/K has a transcendence basex ₁, …,x _n with the following properties: The field extensionF/K(x ₁,…,x _n ) is separable and the Galois hull ofF/K(x ₁,…,x _n ) remains regular overK, i.e.K is algebraically closed in . We prove in this paper thatevery field is stable. This generalizes results from [FJ1] and [GJ] which prove that fields of characteristic 0 and infinite perfect fields are stable, respectively. [G] showed that finite fields are stable in dimension 1, i.e. every finitely generated regular field extension of transcendence degree 1 over a finite field has a stable transcendence base. In the last section of this paper we apply the theorem to the construction of PAC fields with additional properties. A fieldK is called PAC if every absolutely irreducible variety overK has at least oneK-rational point.     

Strongly regular graphs from reducible cyclic codes

Journal of Algebraic Combinatorics - Let p be a prime number. Reducible cyclic codes of rank 2 over $$\mathbb {Z}_{p^m}$$ are shown to have exactly two Hamming weights in some cases. Their weight...     

Functions of regular variation and freely stable laws

Freely stable laws and their domains of attraction are characterized using the theory of functions of regular variation. The results show a complete analogy with classical probability. In fact they can be used to provide an alternative proof of the corresponding classical arguments. The first author was supported in part by a grant from the National Science Foundation.     

Free energy of a regular stable polymer network at small finite deformations

The equilibrium small finite deformations of a regular polymer network are considered. The free energy of the network is described in the form of a series expansion in small displacements of the network points from the equilibrium position. The general dependence of the free energy on the strain invariants thus obtained coincides with the Mooney expression for the free energy only in the first approximation. Aspects of the mechanical behavior of the material associated with this difference are discussed.Branch of the Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow Oblast. Translated from Mekhanika Polimerov, No. 4, pp. 615–618, July–August, 1971.     

The lattice of regular subsemigroups of a regular semigroup

It is shown that all regular subsemigroups of an arbitrary regular semigroup form a lattice. The properties of this lattice are investigated.     

The Newton-Kleinman method for the optimal control of stable weakly regular linear systems

We give an algorithm to find the approximate solution of the linear-quadratic optimal control problem for stable weakly regular linear systems. This algorithm can be understood as a generalization of the Newton-Kleinman method known from the finite-dimensional theory. The central characteristic of our approach is the possibility to solve problems with unbounded control and observation operators, which is motivated by partial differential equations with boundary control and observation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Generators of the group of principal units of a cyclic p-extension of a regular local field

Suppose k is a local field that is an extension of the field of p -adic numbers of degree n and does not contain a primitive p -th root of 1, and suppose K/k is a cyclic p-extension with Galois group G. The group E of principal units of K is a multiplicatively written module over the group ring =_p[G], where _p is the ring of p-adic integers. It was shown by Borevich (Ref. Zh. Mat., 1965, 3A256) that the -module E has a system of n+1 generators, of which n–1 are free and two are connected by certain relations. In the present paper these -generators are constructed explicitly and their arithmetical characteristics indicated.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 71, pp. 16–23, 1977.     

The deficiency of a regular graph

A proper edge coloring c:E(G)→Z of a finite simple graph G is an interval coloring if the colors used at each vertex form a consecutive interval of integers. Many graphs do not have interval colorings, and the deficiency of a graph is an invariant that measures how close a graph comes to having an interval coloring. In this paper we search for tight upper bounds on the deficiencies of k-regular graphs in terms of the number of vertices. We find exact values for 1?k?4 and bounds for larger k.     

Entire cyclic homology of stable continuous trace algebras

A central result in this paper is the computation of the entirecyclic homology of canonical smooth subalgebras of stable continuoustrace C*-algebras having smooth manifolds M as their spectrum.More precisely, the entire cyclic homology is shown to be canonicallyisomorphic to the continuous periodic cyclic homology for thesealgebras. By an earlier result of the authors, one concludesthat the entire cyclic homology of the algebra is canonicallyisomorphic to the twisted de Rham cohomology of M.     

The variation of a stable path is stable

Summary Let X(t) be a separable symmetric stable process of index . Let P be a finite partition of [0,1], and a collection of partitions. The variation of a path X(t) is defined in three ways in terms of the sum collection . Under certain conditions on and on the parameters and , the distribution of the variation is shown to be a stable law. Under other conditions the distribution of the variational sum converges to a stable distribution.The author wishes to thank Prof. J. Chover for several helpful suggestions.     

Branching random walks,stable point processes and regular variation

Using the theory of regular variation, we give a sufficient condition for a point process to be in the superposition domain of attraction of a strictly stable point process. This sufficient condition is used to obtain the weak limit of a sequence of point processes induced by a branching random walk with jointly regularly varying displacements. Because of heavy tails of the step size distribution, we can invoke a one large jump principle at the level of point processes to give an explicit representation of the limiting point process. As a consequence, we extend the main result of Durrett (1983) and verify that two related predictions of Brunet and Derrida (2011) remain valid for this model.