Quasiperiodicity and randomness in tilings of the plane

We define new tilings of the plane with Robinson triangles, by means of generalized inflation rules, and study their Fourier spectrum. Penrose's matching rules are not obeyed; hence the tilings exhibit new local environments, such as three different bond lengths, as well as new patterns at all length scales. Several kinds of such generalized tilings are considered. A large class of deterministic tilings, including chiral tilings, is strictly quasiperiodic, with a tenfold rotationally symmetric Fourier spectrum. Random tilings, either locally (with extensive entropy) or globally random (without extensive entropy), exhibit a mixed (discrete+continuous) diffraction spectrum, implying a partial perfect long-range order.     

Rule-based models of multivariable functions

This study is devoted to fuzzy rule based modelling of multiple-input single-output nonlinear numerical relationships. The model under investigation is viewed as a collection of conditional statements “if state Ω_i then y = g_i(x, a_i)”, i = 1, 2,…, N with Ω_i being a fuzzy relation defined in the space of the input variables. In contrast to the commonly encountered identification approach that is dwelled upon discrete experimental data, the one proposed in this study is concerned with explicitly articulated nonlinear input-output relationship. The main thrust is in the development of a fuzzy partition of the input variables completed through a sequence of fuzzy relations rather than Cartesian products of fuzzy sets. This approach allows us to maintain the number of necessary rules under control and avoid a combinatorial explosion otherwise inevitable in situations of highly multivariable functions. Introduced are criteria of separability and function variability whose objective is to guide a distribution and granularity of the linguistic labels forming the condition part of the rules.     

Fast Construction of the Fejér and Clenshaw–Curtis Quadrature Rules

We present an elegant algorithm for stably and quickly generating the weights of Fejér’s quadrature rules and of the Clenshaw–Curtis rule. The weights for an arbitrary number of nodes are obtained as the discrete Fourier transform of an explicitly defined vector of rational or algebraic numbers. Since these rules have the capability of forming nested families, some of them have gained renewed interest in connection with quadrature over multi-dimensional regions. AMS subject classification (2000) 65D32, 65T20, 65Y20     

Test of the intercombination rules on the two excited states (0 and 1) potential parameters of the second group metal atoms perturbed by inert gases

A set of intercombination rules has been used to calculate the two excited (³0 and ³1) state potential parameters ε₁₂ and R₁₂ of Hg, Cd and Zn interacting with inert gases (Xe, Kr, Ar and Ne). The results obtained with these rules are compared with various experimental and theoretical results for these molecules. The rules can be very well used for determination of the position of the potential minimum for the two states of all molecules. Concerning the well depths of the two states (³0 and ³1) of these molecules, it is observed that for the more bounded excited state ³0 some of these rules give results that are in close agreement with experimental data especially for molecules consisting of heavy atoms but for the shallow excited state ³1 these rules cannot be used.     

MV-Algebra for Cultural Rules

This paper reports preliminary results on a new area of application of quantum structures, motivated by a reading of the 2004 monograph Reasoning in Quantum Theory. Ethnographers often describe a particular culture by describing rules of social relations that they assert characterize that culture. Viable cultures exist over periods of time, that is, over sequences of “generations”. To embody this, we define a suitable set of objects and relations, and a structure on which cultural rules act as “operators” on a set of “configurations” on generations. This yields an MV-algebra of those operators. This implies that culture theory might be studied as an example of the theory of quantum structures. The author acknowledges Dick Greechie in appreciation for the many comments he offered on this paper and on the development of this line of research. Useful comments of an unidentified reviewer helped clarify results. Only the author is responsible for any errors, and for the ideas asserted. This paper was delivered at the meetings of the International Quantum Structures Association, IQSA-Malta 2006.     

Impact of flexible machines on automated manufacturing systems

Although the problem of scheduling dynamic job shops is well studied, setup and changeover times are often assumed to be negligibly small and therefore ignored. In cases where the product mix changes occur frequently, setup and changeover times are of critical importance. This paper applies some known results from the study of multi-class single-server queues with setup and changeover times to develop an approximation for evaluating the performance of job shops. It is found that the product mix, setup and changeover times, and scheduling rules affect the performance significantly, in particular at high levels of machine utilisation. This approach could be used to determine the required level of flexibility of machines and to choose an appropriate scheduling policy such that production rates remain within acceptable limits for foreseeable changes in the product mix.     

Bayesian methods in global optimization

This paper reviews methods which have been proposed for solving global optimization problems in the framework of the Bayesian paradigm.     

对(mèng)烷的~(13)C-NMR研究顺反异构体比及顺式构象平衡常数K(35℃)

本工作是在35℃下测定对(艹孟)烷(p-Menthane)(即对位甲基异丙基环已烷)的~(13)C-NMR谱。由取代基参数,经验加和规律计算各碳化学位移数值,归属各谱峰位置。由积分值得知顺式、反式对(艹孟)烷含量之比。并根据权分法计算顺式对(艹孟)烷中构象1与构象2分子数之比。结果表明顺式对(艹孟)烷中异丙基处于平展位置的构象2为主。     

The Variety of Thermal Pericyclic Reactions

The six-electron thermal pericyclic reactions are examined systematically as to the number and kind which are possible by varying both the σ shell and the combinations of different atoms in all orientations, on both a six-atom and a five-atom framework. A simple unifying nomenclature is offered for these reactions, which number in the thousands. Further, in order to comprehend this very large number of possible reactions, they are also organized systematically in terms of their value for basic synthesis operations: construction, elimination, refunctionalization, etc. The methodology is aimed at providing a basis of selection for the invention of useful new reactions. A discussion of reaction energetics leads also to an analysis of molecular features which can facilitate reaction.     

On extrapolation of Jagerman and Stetter rules

In this paper quadrature rules introduced by Jagerman [1] and Stetter [2] are considered and asymptotic expansions for the error given. This allows to make use of the Romberg extrapolation process. Such rules can be viewed as generalizations of the well-known mid-point rule. Thus, numerical examples comparing these rules are finally presented.