A Note on a Generalization of the Multiple Cover Formula and the Simple Flop

We prove a closed formula for an excess integral over the moduli space of stable maps from genus one, unmarked curves to the projective space ? ^r of degree d for any positive integers r and d. The result generalizes the multiple cover formula for ?¹. We also show that any simple ? ^r flop preserves the theory of arbitrary-genus Gromov-Witten invariants in exceptional curve classes.     

On Covers and Envelopes in Some Functor Categories

We study the existence of covers and envelopes by some special functors on the category of finitely presented modules. As an application, we characterize some important rings using these functors. We also investigate homological properties of some functors on the stable module category. The relationship between phantoms and Ext-phantoms is obtained. It is shown that every left R-module M has an Ext-phantom preenvelope f: M → N with coker(f) pure-projective. Finally, we prove that, as a torsionfree class of (mod-R, Ab), (mod-R, Ab) is generated by the FP-injective objects.     

A Note on the Radical of a Module Category

We characterize the finiteness of the representation type of an artin algebra in terms of the behavior of the projective covers and the injective envelopes of the simple modules with respect to the infinite radical of the module category. In case the algebra is representation-finite, we show that the nilpotency of the radical of the module category is the maximal depth of the composites of these maps, which is independent from the maximal length of the indecomposable modules.     

On Covers and Envelopes under Hom and Tensor Functors

Let R be a commutative ring. We investigate the relationship between (pre)covers ((pre)envelopes) of an R-module and the counterparts of the corresponding homomorphism module or tensor product module. Some applications are also given.     

Exact borel subalgebras of quasi-hereditary algebras. II

In this article, we consider the class of flat G-modules in the category of discrete modules over a profinite group G. We will appeal to a recent result of Enochs to prove that we have flat covers in this situation.     

Efficient band monitoring with sensors outer positioning

The article considers models for monitoring a band with a preset width using sensor networks shaped as disc covers. Every cover disc is a centred sensor operation area. The researchers determine a min-density band cover with the discs of one, two and three radii. The specific requirement for the cover is that the disc centres shall not be inside the band (external monitoring). Various efficient cover models are proposed and their characteristics are determined.     

滑动盖板对一维微尺度光栅红外辐射特性影响

电磁波入射到微尺度周期性结构表面时,一定条件下将在某一波段产生异常光吸收现象。基于该特性,本文提出了单边移动盖板光栅和双边移动盖板光栅两种光栅结构,并使用严格耦合波分析(RCWA)方法对TM波垂直入射的一维微尺度光栅表面辐射特性进行了分析,研究了滑动盖板的厚度和位置对光栅表面结构辐射特性的影响。结果表明,相同盖板厚度,双边移动盖板光栅形成的发射率峰较单边移动盖板光栅形成的发射率峰具有较宽的半高全宽(FWHM),但峰值较低;随盖板向关闭侧移动,高发射率峰对应波长向长波方向移动;随盖板厚度增加,发射率峰向长波方向移动,其中双边移动盖板光栅结构形成的发射率峰变宽,峰值变小。     

Geometry and combinatorics of the cutting angle method

Lower approximation of Lipschitz functions plays an important role in deterministic global optimization. This article examines in detail the lower piecewise linear approximation which arises in the cutting angle method. All its local minima can be explicitly enumerated, and a special data structure was designed to process them very efficiently, improving previous results by several orders of magnitude. Further, some geometrical properties of the lower approximation have been studied, and regions on which this function is linear have been identified explicitly. Connection to a special distance function and Voronoi diagrams was established. An application of these results is a black-box multivariate random number generator, based on acceptance–rejection approach.     

Generalized cover facet inequalities for the generalized assignment problem

The generalized assignment problem is that of finding an optimal assignment of agents to tasks, where each agent may be assigned multiple tasks and each task is performed exactly once. This is an NP-complete problem. Algorithms that employ information about the polyhedral structure of the associated polytope are typically more effective for large instances than those that ignore the structure. A class of generalized cover facet-defining inequalities for the generalized assignment problem is derived. These inequalities are based upon multiple knapsack constraints and are derived from generalized cover inequalities.