On the regular representation of an (essentially) finite 2-group

The regular representation of an essentially finite 2-group G in the 2-category 2Vectk of (Kapranov and Voevodsky) 2-vector spaces is defined and cohomology invariants classifying it are computed. It is next shown that all hom-categories in Rep2Vectk(G) are 2-vector spaces under quite standard assumptions on the field k, and a formula giving the corresponding “intertwining numbers” is obtained which proves they are symmetric. Finally, it is shown that the forgetful 2-functor ω:Rep2Vectk(G)→2Vectk is representable with the regular representation as representing object. As a consequence we obtain a k-linear equivalence between the 2-vector space of functors from the underlying groupoid of G to Vectk, on the one hand, and the k-linear category End(ω) of pseudonatural endomorphisms of ω, on the other hand. We conclude that End(ω) is a 2-vector space, and we (partially) describe a basis of it.     

On resistance of graphs

An edge-coloring of a graph G with integers is called an interval coloring if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. It is known that not all graphs have interval colorings, and therefore it is expedient to consider a measure of closeness for a graph to be interval colorable. In this paper we introduce such a measure (resistance of a graph) and we determine the exact value of the resistance for some classes of graphs.     

Analysis of solid solutions stability in scheelite-type molybdates and tungstates

Mutual solubility of bivalent metal molybdates and tungstates with scheelite structure was theoretically estimated by calculating formation enthalpies and the maximal decomposition temperatures of solid solutions at different temperatures. The theoretical stability of continuous solid solutions in binary systems of bivalent metal molybdates and tungstates was found to be higher than reported literature data. After cooling down continuous substitution solid solution should remain in following systems: CaMoО₄–CdMoО₄, SrMoО₄–MMoО₄ (M=Ba, Pb), BaMoО₄–PbMoО₄, SrWO₄–MWO₄ (M=Ca, Pb), and BaWO₄–PbWO₄. There is a probability that at room temperature in systems CaMoО₄–SrMoО_4, CaWO₄–PbWO₄, and BaWO₄–SrWO₄ the single homogeneity region may decompose to limited solid solutions. It was shown experimentally that a continuous series of scheelite-structure solid solutions M_1−xM^I_xТO₄ can be formed via citrate synthesis at temperatures below 500°С.     

Global Solutions of Shock Reflection by Wedges for the Nonlinear Wave Equation

When a plane shock hits a wedge head on, it experiences a reflection-diffraction process and then a self-similar reflected shock moves outward as the original shock moves forward in time. In this paper, shock reflection by large-angle wedges for compressible flow modeled by the nonlinear wave equation is studied and a global theory of existence, stability and regularity is established. Moreover, C ^0,1 is the optimal regularity for the solutions across the degenerate sonic boundary.     

A method for group decision-making based on determining weights of decision makers using TOPSIS

In general, weights of decision makers (DMs) play a very important role in multiple attribute group decision-making (MAGDM), how to measure the weights of DMs is an interesting research topic. This paper presents a new approach for determining weights of DMs in group decision environment based on an extended TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method. We define the positive ideal solution as the average of group decision. The negative ideal solution includes two parts: left and right negative ideal solution, which are the minimum and maximum matrixes of group decision, respectively. We give an example to illustrate the developed approach. Finally, the advantages and disadvantages of this study are also compared.     

关于Clifford半群上的fuzzy同余

利用半群fuzzy同余的概念,讨论一类特殊的完全正则半群,即Clifford半群上的fuzzy同余.研究该类半群上fuzzy同余的性质.在此基础上,给出Clifford半群上fuzzy同余的性质和特征,得到Cllifford半群上fuzzy同余为fuzzy消去同余的充要条件.     

对称广义中心对称矩阵的左右逆特征值问题

研究了对称广义中心对称矩阵的左右逆特征值问题,利用矩阵的奇异值分解(SVD)得到了问题的通解表达式.并由此考虑了解集合对给定矩阵的最佳逼近.     

Observation of regular defects formed on the surface of PbTe thin films grown by molecular beam epitaxy

Regular shape defects on the surface of PbTe thin films grown by molecular beam epitaxy (MBE) were studied by scanning electron microscope (SEM). Two types of regular shape defects were observed on Te-rich PbTe films grown at substrate temperature T ≥ 235 °C with a beam flux ratio of Te to PbTe (R_f) to be 0.5 and at 280 °C with a R_f ≥ 0.4, which include cuboids and triangular pyramids. The formation mechanism of the observed regular shape defects is interpreted as following: They are the outcome of fast growth rate along {1 0 0} crystal planes that have the lowest surface energy and the enclosure of the {1 0 0} crystal planes. The formation of the regular shape defects in the growth of PbTe needs appropriate substrate temperature and Te-rich ambience. However, when R_f is decreased low enough to make the films slightly Pb-rich, triangular pits that originate from the insufficient glide of the threading dislocations along the main 〈1 1 0〉 {1 0 0} glide system of PbTe in Cottrell atmosphere, will be the main feature on the film surface.     

EVALUATING THE IMPACT OF ENVIRONMENTAL POLICY ON THE TREND BEHAVIOR OF US EMISSIONS OF NITROGEN OXIDES AND VOLATILE ORGANIC COMPOUNDS

The nature of this paper is a practical application of a proper time‐series methodology to evaluate policy impacts when there is uncertainty about the data being difference‐stationary (DS) or trend‐stationary (TS). We use this methodology to examine the trend behavior of two air pollutants, nitrogen oxides (NO_X) and volatile organic compounds (VOC). In particular, we concentrate on answering two questions. First, were there breaks in the trends of NO_X and VOC emissions around the same time environmental policies such as the Clean Air Act Amendments (CAAA) of 1970 were passed? And second, accounting for possible breaks are the US emissions of NO_X and VOC TS or DS? Our empirical results show a clear evidence of a trend shift in NO_X and VOC emissions at the time the CAAA of 1970 were passed, implying that this policy has been effective in reducing air pollution emissions, as well as additional breaks that correspond to other events and environmental policies before and after 1970. The unit root tests indicate that NO_X are DS irrespective of the number of breaks in the trend whereas results for VOC emissions depend on the number of breaks assumed.     

Squarefree P-modules and the cd-index

In this paper, we introduce a new algebraic concept, which we call squarefree P-modules. This concept is inspired from Karu's proof of the non-negativity of the cd-indices of Gorenstein* posets, and supplies a way to study cd-indices from the viewpoint of commutative algebra. Indeed, by using the theory of squarefree P-modules, we give several new algebraic and combinatorial results on CW-posets. First, we define an analogue of the cd-index for any CW-poset and prove its non-negativity when a CW-poset is Cohen–Macaulay. This result proves that the h-vector of the barycentric subdivision of a Cohen–Macaulay regular CW-complex is unimodal. Second, we prove that the Stanley–Reisner ring of the barycentric subdivision of an odd dimensional Cohen–Macaulay polyhedral complex has the weak Lefschetz property. Third, we obtain sharp upper bounds of the cd-indices of Gorenstein* posets for a fixed rank generating function.