Enumerating semifields

In 1960, Kleinfeld published representatives for all of the isomorphism classes of 16 element semifields, [E. Kleinfeld, Techniques for Enumerating Veblen-Wedderburn Systems, J. ACM 7 (1960) 330–337]. It is not entirely clear how Kleinfeld generated some of his results, but it is likely that it was similar to the approach that Walker used in 1962 to generate representative for the isotopism classes of 32 element semifields, [R. J. Walker, Determination of Division Algebras With 32 Elements, Proc. Sympos. Appl. Math. XV (1963) 8385]. This paper introduces an alternative notation for publication which is both simple and practical, and which leads to an alternative method which was used to verify Kleinfeldʼs results.     

A branch-and-cut algorithm for the Multiple Steiner TSP with Order constraints

The paper deals with a problem motivated by survivability issues in multilayer IP-over-WDM telecommunication networks. Given a set of traffic demands for which we know a survivable routing in the IP layer, our purpose is to look for the corresponding survivable topology in the WDM layer. The problem amounts to Multiple Steiner TSPs with order constraints. We propose an integer linear programming formulation for the problem and investigate the associated polytope. We also present new valid inequalities and discuss their facial aspect. Based on this, we devise a Branch-and-cut algorithm and present preliminary computational results.     

Resonant Auger spectroscopy of poly(4-hydroxystyrene)

The electronic structure of poly(4-hydroxystyrene) (PHS), which presents strong similarities with that of phenol, has been studied via resonant Auger spectroscopy. Spectator shifts and relative intensities of participator channels are extracted from our data. Symmetry considerations on the occupied and unoccupied molecular orbitals (MO) are helpful in the assignment of the resonating valence band structures of PHS. However they are clearly not sufficient to explain the MO intensities when close-lying intermediate electronic states are involved, as interference effects may play an important role.     

The Fifth and Sixth Coefficients of the Characteristic Polynomial of a Graph

It is well known that the coefficients of the characteristic polynomial of a graph G are determined by the elementary subgraphs of G; in particular there are simple expressions for the four higest coefficients. Here we use an enumeration of elementary subgraphs called k-matchings to obtain expressions for the next two coefficients.     

Topologies and Laplacian spectra of a deterministic uniform recursive tree

The uniform recursive tree (URT) is one of the most important models and has been successfully applied to many fields. Here we study exactly the topological characteristics and spectral properties of the Laplacian matrix of a deterministic uniform recursive tree, which is a deterministic version of URT. Firstly, from the perspective of complex networks, we determine the main structural characteristics of the deterministic tree. The obtained vigorous results show that the network has an exponential degree distribution, small average path length, power-law distribution of node betweenness, and positive degree-degree correlations. Then we determine the complete Laplacian spectra (eigenvalues) and their corresponding eigenvectors of the considered graph. Interestingly, all the Laplacian eigenvalues are distinct.     

Analytical control of the preparation of single crystal materials by inductively coupled plasma atomic emission spectrometry

The present paper shows that inductively coupled plasma atomic emission spectrometry (ICP-AES) and the Q concept, in accordance with Boumans and Vrakking [Spectrochim. Acta Part B 43 (1988) 69] can be used in the determination of a large number of dopants with different characteristics (charge and ionic radius) in the single crystals of potassium titanylphosphate [KTiOPO₄], some of its structural analogues and potassium gadolinium tungstate [KGd (WO₄)₂]. The basic conclusion from the analytical data obtained in this work is that the incorporation of Me⁺, Me²⁺, Me³⁺, Me⁴⁺ and Me⁵⁺ ions in the crystal lattice depend on its ionic radii. The effect of the ionic charge of the dopant ions is negligible. The light on the regularities of dopant incorporation in the crystal lattice was thrown and hence on the possibilities of modifying the properties of the single crystal materials.     

Number-Phase Quantization and Deriving Energy-Level Gap of Two LC Circuits with Mutual-Inductance

For two LC circuits with mutual-inductance, we introduce a new quantization scheme in the context of number- phase quantization through the standard Lagrangian formalism. The commutative relation between the charge operator and the magnetic flux operator is derived. Then we use the Heisenberg equation of motion to obtain the current and voltage equation across the inductance and capacity. The results clearly show how the current and voltage in a single LC circuit are affected by the circuit parameters and inductance coupling coettlcient. In addition, adopting invariant eigen-operator method the energy-level gap of the dynamic Hamiltonian which describes two LC circuits with mutual-inductance is obtained.     

An empirical study of Chinese language networks

Chinese is spoken by the largest number of people in the world, and it is regarded as one of the most important languages. In this paper, we explore the statistical properties of Chinese language networks (CLNs) within the framework of complex network theory. Based on one of the largest Chinese corpora, i.e. People’s Daily Corpus, we construct two networks (CLN1 and CLN2) from two different respects, with Chinese words as nodes. In CLN1, a link between two nodes exists if they appear next to each other in at least one sentence; in CLN2, a link represents that two nodes appear simultaneously in a sentence. We show that both networks exhibit small-world effect, scale-free structure, hierarchical organization and disassortative mixing. These results indicate that in many topological aspects Chinese language shapes complex networks with organizing principles similar to other previously studied language systems, which shows that different languages may have some common characteristics in their evolution processes. We believe that our research may shed some new light into the Chinese language and find some potentially significant implications.     

Least-squares estimates in fuzzy regression analysis

Regression is a very powerful methodology for forecasting, which is considered as an essential component of successful OR applications. In this paper an idea stemmed from the classical least squares is proposed to handle fuzzy observations in regression analysis. Based on the extension principle, the membership function of the sum of squared errors is constructed. The fuzzy sum of squared errors is a function of the regression coefficients to be determined, which can be minimized via a nonlinear program formulated under the structure of the Chen–Klein method for ranking fuzzy numbers. To illustrate how the proposed method is applied, three cases, one crisp input-fuzzy output, one fuzzy input-fuzzy output, and one non-triangular fuzzy observations, are exemplified. The results show that the least-squares method of this paper is able to determine the regression coefficients with better explanatory power. Most important, it works for all types of fuzzy observations, not restricted to the triangular one.     

An X-ray and TEM study of inhomogeneous ordering in AlxGa1−xN layers grown by MOCVD

Ordering along the c-axis has been observed both by high resolution X-ray diffraction and transmission electron microscopy in Al_xGa_1−xN grown by low pressure metal-organic vapor phase epitaxy on sapphire (0001). Beside the disordered alloy, AlGaN₂ (1:1), and Al_0.25Ga_0.75N (3:1), there is an additional type with a quite large unit cell. In the latter, the c parameter is six times larger than that of the disordered alloy.