Generalized Hamming weights of three classes of linear codes

The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the generalized Hamming weights of three classes of linear codes constructed through defining sets and determine them partly for some cases. Particularly, in the semiprimitive case we solve a problem left in Yang et al. (2015) [30].     

Managing the spread of alfalfa stem nematodes (Ditylenchus dipsaci): The relationship between crop rotation periods and pest reemergence

Alfalfa is a critical cash/rotation crop in the western region of the United States, where it is common to find crops affected by the alfalfa stem nematode (ASN) (Ditylenchus dipsaci). Understanding the spread dynamics associated with this pest would allow growers to design better management programs and farming practices. This understanding is of particular importance given that there are no nematicides available against ASNs and control strategies largely rely on crop rotation to nonhost crops or by planting resistant varieties of alfalfa. In this paper, we present a basic host‐parasite model that describes the spread of the ASN on alfalfa crops. With this discrete time model, we are able to portray a relationship between the length of crop rotation periods and the time at which the density of nematode‐infested plants becomes larger than that of nematode‐free ones in the postrotation alfalfa. The numerical results obtained are consistent with farming practice observations, suggesting that the model could play a role in the evaluation of management strategies.     

Decomposition of algebraic sets and applications to weak centers of cubic systems

There are many methods such as Gröbner basis, characteristic set and resultant, in computing an algebraic set of a system of multivariate polynomials. The common difficulties come from the complexity of computation, singularity of the corresponding matrices and some unnecessary factors in successive computation. In this paper, we decompose algebraic sets, stratum by stratum, into a union of constructible sets with Sylvester resultants, so as to simplify the procedure of elimination. Applying this decomposition to systems of multivariate polynomials resulted from period constants of reversible cubic differential systems which possess a quadratic isochronous center, we determine the order of weak centers and discuss the bifurcation of critical periods.     

Asymptotic expansions of backward equations for two-time-scale Markov chains in continuous time

This work develops asymptotic expansions for solutions of systems of backward equations of time- inhomogeneous Maxkov chains in continuous time. Owing to the rapid progress in technology and the increasing complexity in modeling, the underlying Maxkov chains often have large state spaces, which make the computa- tional tasks ihfeasible. To reduce the complexity, two-time-scale formulations are used. By introducing a small parameter ε〉 0 and using suitable decomposition and aggregation procedures, it is formulated as a singular perturbation problem. Both Markov chains having recurrent states only and Maxkov chains including also tran- sient states are treated. Under certain weak irreducibility and smoothness conditions of the generators, the desired asymptotic expansions axe constructed. Then error bounds are obtained.     

Optimal ordering policy for stock-dependent demand under progressive payment scheme

In this article, a mathematical model is developed to formulate optimal ordering policies for retailer when demand is partially constant and partially dependent on the stock, and the supplier offers progressive credit periods to settle the account. The notion of progressive credit period is as follows:     

Irregularity and the period determinant for irregular singular connections on surfaces

In [6], we constructed a period pairing for flat irregular singular conncetions on surfaces. We now extend these constructions to a perfect period pairing between the irregularity complex of the connection and the complex of relative rapid decay chains. As a consequence, the period determinant of the connection decomposes as a product of a topological period determinant on the open surface and a determinant coming from the irregularity of the connection. Additionally, we deduce a method to compute the irregularity sheaf up to local isomorphism in topological terms (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transitivity and Dense Periodicity for Graph Maps

In 1984, Blokh proved [A. M. Blockh, On transitive mappings of one-dimensional branched manifolds, Differential-Difference Equations and Problems of Mathematical physics (Russian), Akad. Nauk Ukrain. SSR Inst. Mat., Kiev, 131, pp. 3–9, 1984] that any topologically transitive continuous map from a graph into itself which has periodic points has a dense set of periodic points and has positive topological entropy (in this proof a crucial role is played by the specification property, which implies these two statements). Also, he characterized the topologically transitive continuous graph maps without periodic points. Unfortunately, this clever paper is only available in Russian (except for a translation to English of the statements of the theorems without proofs—see [A. M. Blockh, The connection between entropy and transitivity for one-dimensional mappings, Uspekhi Mat. Nauk, 42(5(257)) (1987), pp. 209–210]).     

光栅周期不一致对莫尔条纹法测量扭转角的影响

为了提高用莫尔条纹法测量扭转角的测量精度,分析了光栅周期不一致对扭转角测量误差的影响。从基于莫尔条纹法测量扭转角的原理出发,论述了光栅周期不一致与测量精度的关系,讨论了引起两光栅周期不一致的两个因素,即光栅刻划误差以及两光栅栅面不平行。理论分析表明,前者是引起光栅周期不一致的主要原因。当两光栅等效周期比值β＜1.001时,在±15′的测量范围内,选择光栅周期为50 μm,莫尔条纹宽度为1 400~1 800 μm时,光栅周期不一致引起的测量误差可以控制在1.6″之内。