Butler groups formed by factoring a completely decomposable group by a rank one group have been studied extensively. We call such groups, bracket groups. We study bracket modules over integral domains. In particular, we are interested in when any bracket $R$-module is $R$ tensor a bracket group.
A graph is called weakly perfect if its chromatic number equals its clique number. In this note a new class of weakly perfect graphs is presented and an explicit formula for the chromatic number of such graphs is given.
The aim of this paper is to rank the words of the Chinese language of the III-V centuries in a number of classes that differ in their grammatical characteristics. The classification undertaken is based on syntactic criteria.
(i) The procedure introduced here for the clustering of frequency vectors takes into account the uncertainty arising from dealing with small observed frequencies. The smaller observed absolute frequencies, the more uncertainty about the “true” probability vector. The object is not represented by a single point in the multidimensional space but rather by the fuzzy set spread around this point. Consequently, the distance between two such objects is a fuzzy value, too. The expected mean distance between two objects generally differs from the simple distance: for instance, two objects with the same frequency vectors have a positive mean distance. The exact formula for estimation of the mean distance is given; this makes the algorithmization of the proposed procedure possible. The approach corresponds to that of the Bayesian estimation. The matrix of expected mean distances is an input to the hierarchical cluster analysis. (ii) The conventional hierarchical cluster analysis investigates similarities between objects from a given class. A modified general procedure is proposed seeking analogies between two classes of objects. The “two-class cluster analysis” is applicable to any kind of objects to be clustcred; it is not confined to the herein discussed special case of frequency vectors. (iii) The development of the procedure was developed initially for the field of the psychotherapy research - investigation of relationship patterns found within verbatirn protocols of sessions using the “guided imagery”, a psychotherapy technique dealing with evoked daydrearns. This constitutes an application example.
Let $X$ be a complex space of dimension $n$, not necessarily reduced, whose cohomology groups $H^1(X,{\cal O}), \ldots , H^{n-1}(X,{\cal O})$ are of finite dimension (as complex vector spaces). We show that $X$ is Stein (resp., $1$-convex) if, and only if, $X$ is holomorphically spreadable (resp., $X$ is holomorphically spreadable at infinity). \endgraf This, on the one hand, generalizes a known characterization of Stein spaces due to Siu, Laufer, and Simha and, on the other hand, it provides a new criterion for $1$-convexity.
The paper deals with the adaptive mechanisms in differential evolution (DE) algorithm. DE is a simple and effective stochastic algorithm frequently used in solving the real-world global optimization problems. The efficiency of the algorithm is sensitive to setting its control parameters. Several adaptive approaches have appeared recently in order to avoid control-parameter tuning. A new adaptive variant of differential evolution is proposed in this study. It is based on a combination of two adaptive approaches published before. The new algorithm was tested on the well-known set of benchmark problems developed for the special session of CEC2005 at four levels of population size and its performance was compared with the adaptive variants that were applied in the design of the new algorithm. The new adaptive DE variant outperformed the others in several test problems but its efficiency on average was not better.
Serious damage may occur to concrete hydraulic structures, such as water galleries, spillways, and stilling basins, due to the abrasive erosion caused by the presence of solid particles in the flow. This underlines the importance of being capable in providing characterization of the concrete from the point of view of its vulnerability to abrasive erosion, in order to improve the design of the structure and the material selection. Nevertheless, the existing apparatus for concrete abrasive erosion testing are either far from allowing realistic simulation of the actual environment in which this phenomenon occurs, or show a large degree of complexity and cost. An alternative method has been developed with the aid of Computational Fluid Dynamics (CFD). CFD was first employed to verify the effectiveness of a new laboratory equipment. Afterwards, a parameter has been introduced which, by successful comparison against preliminary experiments, proved suitable to quantify the effect of the fluid dynamic conditions on the concrete abrasive erosion, thereby opening the way to CFD-based customization of the apparatus. In the future, the synergy of numerical and physical modelling will allow developing predictive models for concrete erosion, making it possible to reliably simulate real structures.
The present article concentrates on an analysis of the structure of the opening passages and means of address in the Amarna Letters, one of the largest sources of epistolary documents, written during the 2nd half of the 2nd millennium B.C. From the first look at the Amarna corrpus, those familiar with the topic will notice a formal structure very similar to the one found in other letters written in Peripheral Akkadian. However, the discussion on the formal structure usually limits itself to several short statements and general descriptive comments.
Numerical simulation of the 3-D topology of magnetic field lines above a Bipolar Magnetic Region (BMR) is demonstrated. In
contrast to the usually accepted description of photospheric magnetic fields by the continuous function, the new approach is tested. The BMR is represented as a specifically distributed set of discrete sources of magnetic flux. Three branches of the specific structures of potential field lines was found in different parts of the BMR. The field line structures correspond to chromospheric fibrils, prominence configurations and to coronal arches. We suppose that the field lines create the principal skeleton of the prominence phenomenon. A prominence plasma is considered inside the magnetic flux tubes. The prominence legs represent the part of the field lines rooted in the convective zone in regions with magnetic flux concentration.