On spectral resolutions connected with self-adjoint differential vector-operators in a Hilbert space

We show that spectral resolutions of differential vector-operators may be represented as a specific direct sum integral operator with a kernel written in terms of generalized vector-operator eigenfunctions. Then we prove that a generalized eigenfunction measurable with respect to the spectral parameter may be decomposed using a set of analytical defining systems of coordinate operators.     

Monoid Valuations and Value Ordered Supervaluations

We complement two papers on supertropical valuation theory ([11 Izhakian , Z. , Knebusch , M. , Rowen , L. ( 2011 ). Supertropical semirings and supervaluations . J. Pure and Applied Alg. 215 ( 10 ): 2431 – 2463 . Preprint at arXiv:1003.1101 .[Crossref], [Web of Science ®] , [Google Scholar]], [12 Izhakian , Z. , Knebusch , M. , Rowen , L. ( 2013 ). Dominance and transmissions in supertropical valuation theory . Commun. Algebra 41 ( 7 ): 2736 – 2782 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]) by providing natural examples of m-valuations (= monoid valuations), and afterwards of supervaluations and transmissions between them. These supervaluations have values in totally ordered supertropical semirings, and the transmissions discussed respect the orderings. We develop the basics of the theory of such semirings and transmissions.     

Semigroups with apartness

Proving a constructive version of the Spectral Mapping Theorem, Bridges and Havea used a constructive semigroup with inequality in 8 . This motivated us to achieve a little progress in that direction. The starting point is the structure called a semigroup with apartness. Our primary objective is to prove isomorphism theorems for such constructive semigroups. In doing so our main ideas and notions come from 10 .     

格蕴涵代数的区间值(J)-模糊滤子理论

将区间值模糊集和D[0,1]上的t-模(J)应用于格蕴涵代数的滤子理论,引入格蕴涵代数的区间值,(J)-模糊(关联、正关联)滤子的概念,给出了它们的等价刻画,研究了它们之间的关系.     

基于软集合参数约简的一种启发式算法

在比较和分析了原有软集合参数约简文献的基础上,本文总结出了一些参数约简的结论,并结合参数约简的思想,提出了一种参数约简的启发式算法.同时,本文给出了该启发式算法的具体算法过程及算例,并对该算法的相关理论进行了证明.最后,将该算法的约简结果与其它两种算法进行对比分析,表明本文算法的高效性和优越性.     

Outsourcing and scheduling for two-machine ordered flow shop scheduling problems

This paper considers a two-machine ordered flow shop problem, where each job is processed through the in-house system or outsourced to a subcontractor. For in-house jobs, a schedule is constructed and its performance is measured by the makespan. Jobs processed by subcontractors require paying an outsourcing cost. The objective is to minimize the sum of the makespan and the total outsourcing cost. Since this problem is NP-hard, we present an approximation algorithm. Furthermore, we consider three special cases in which job j has a processing time requirement p_j, and machine i a characteristic q_i. The first case assumes the time job j occupies machine i is equal to the processing requirement divided by a characteristic value of machine i, that is, p_j/q_i. The second (third) case assumes that the time job j occupies machine i is equal to the maximum (minimum) of its processing requirement and a characteristic value of the machine, that is, max{p_j, q_i} (min{p_j, q_i}). We show that the first and the second cases are NP-hard and the third case is polynomially solvable.     

Precovering and Preenveloping Ideals

In [8 Salce , L. ( 1979 ). Cotorsion theories for abelian groups . Symposia Mathematica 23 : 11 – 23 . [Google Scholar]] L. Salce introduced the notion of a cotorsion pair (?, 𝒞) in the category of abelian groups. But his definitions and basic results carry over to more general abelian categories and have proven to be useful in a variety of settings. A significant result of cotorsion theory proven by Eklof and Trlifaj is that if a pair (?, 𝒞) of classes of R-modules is cogenerated by a set, then it is complete [1 Eklof , P. C. , Trlifaj , J. ( 2001 ). How to make Ext vanish . Bull. London Math. Soc. 33 : 31 – 41 .[Crossref], [Web of Science ®] , [Google Scholar]]. Recently Fu, Herzog, Guil, and Torrecillas developed the ideal approximation theory [6 Herzog , I. ( 2014 ). Phantom morphisms and Salce's Lemma . Contemp. Math. 607 : 57 – 83 .[Crossref] , [Google Scholar]], [4 Fu X. H. , Guil Asensio , P. A. , Herzog , I. , Torrecillas , B. ( 2013 ). Ideal Approximation Theory . Adv. in Math. 244 : 750 – 790 .[Crossref], [Web of Science ®] , [Google Scholar]]. In this article we look at a result motivated by the Eklof and Trlifaj argument for an ideal ? when it is generated by a set of homomorphisms.     

Flatness Properties of S-Posets

We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a consequence we show that a weakly shod algebra which is not quasi-tilted of canonical type is simply connected if and only if its first Hochschild cohomology group vanishes.     

α-Cu_2Se精细结构的球差校正扫描透射电镜表征

目前学界对Cu_2Se低温α相的结构仍未认识清楚,而解决这一问题对理解Cu_2Se在相变过程中热电性能提升等特性具有重要意义。本文首次报道了由球差校正扫描透射电镜(STEM)拍摄到的沿■带轴的原子级分辨率高角环形暗场(HAADF)像,揭示了由Se原子以多种形式有序起伏产生的复杂结构。结合电子衍射图谱,分析了包含不同层数、通过相互组合构成α-Cu_2Se晶体的多种结构变体。使用QSTEM软件对构建的结构变体进行高分辨图像模拟,得到了与实验对应的HAADF像。该工作为更全面地理解α-Cu_2Se的结构提供了新的重要信息。     

On near-wall effects in hard disk packing between two concentric cylinders

Monodisperse packing of disks in confined geometries is rarely addressed in the literature. We present some theoretical aspects of the microstructural properties of 2D static packing of disks between two concentric cylinders. In the core of the geometry, the packing is intact, while it is dilated in the vicinity of the walls as a result of the removal of overlapping disks. We have derived the formula for average packing density in concentric cylinders geometry with given ratio of the particle diameter to the gap between cylinders. It is verified and analyzed further by constructing ordered and disordered packs of monodisperse disks in computer. In this context, Voronoi tessellation is performed for the resulting packs to demonstrate the thickness of the static boundary layer where the packing is influenced by the presence of cylindrical walls.