Multiple Coverings of the Plane with Triangles

We prove that any 43-fold covering of the plane with translates of a triangle can be decomposed into two coverings.     

Influence of the activation temperature on structural and textural properties of NiMo/Al2O3 hydrodesulfurization catalysts

Investigations of a commercial NiMo/Al₂O₃ hydrodesulfurization (HDS) catalyst are directed towards optimization of the activation procedure of HDS catalyst concerning active phase formation and thermal stability. Structural and textural data obtained with XRD, IR-FTIR, XPS and LTNA reveal that the optimal temperature for the formation of active species on the catalyst surface and an appropriate pore structure is 300°C.     

On the definition of interfacial excesses in a system consisting of an insoluble solid adsorbent and a binary liquid mixture

The paper deals with the problem whether the interfacial excess volumeV ^σ has to be set zero in the case of the systems in question as stated by D. H. Everett, or eventually different from zero as proposed by G. Schay. First it is shown that the current operational definitions of the interfacial excess amounts as relative or reduced excesses are quite independent of the choice of the reference volume (or amount) of equilibrium bulk liquid. Everett operates with the Gibbs dividing surface, letting it coincide with the surface of the solid, the corresponding operational definition of the interfacial excess amount being then that ofn ^σ(v). It is shown that this definition, while compatible with those of the relative or reduced excesses, is not cogent. Relative and reduced excesses are usually interpreted as the values resulting when the adsorption of either one selected component or the total adsorption is set arbitrarily zero. With this interpretation, the assumptionV ^σ =0 for the total system could be maintained only by admitting an adsorption excess of the solid different from zero which appears, however, unnatural.     

Statistical properties of chaos demonstrated in a class of one-dimensional maps

One-dimensional maps with complete grammar are investigated in both permanent and transient chaotic cases. The discussion focuses on statistical characteristics such as Lyapunov exponent, generalized entropies and dimensions, free energies, and their finite size corrections. Our approach is based on the eigenvalue problem of generalized Frobenius-Perron operators, which are treated numerically as well as by perturbative and other analytical methods. The examples include the universal chaos function relevant near the period doubling threshold. Special emphasis is put on the entropies and their decay rates because of their invariance under the most general class of coordinate changes. Phase-transition-like phenomena at the border state of chaos due to intermittency and super instability are presented.     

Ab initio prediction of vibrational spectra: A database approach

Efforts to develop a database of quadratic force fields for organic molecules are described. The database is based on systematic ab initio calculations, scaled to reproduce the experimentally observed frequencies. The choice of the theoretical method, the basis sets, geometries, internal coordinates and the scaling procedure are discussed. A key point in the procedure is the automatic generation of the internal valence coordinates. This is also very advantageous for geometry optimization. The database should permit the prediction of vibrational frequencies for most organic molecules to 10–20 cm⁻¹, together with semiquantitative intensities. The accuracy is sufficient to identify unknown compounds from a list of reasonable candidates.     

Optimal Joint Distributions of Several Random Variables with Given Marginals

Solutions of a singularly perturbed vector boundary-value problem are studied under the principle assumption that the trivial solution of the unperturbed equation is stable in certain senses. This is accomplished by constructing special invariant regions in which solutions display the kind of nonuniformity known as boundary-layer behavior.     

Compatibility study between indomethacin and excipients in their physical mixtures

Thermal analysis is a routine method for analysis of drugs and substances of pharmaceutical interest. Thermogravimetry/derivative thermogravimetry (TG/DTG) and differential scanning calorimetry (DSC) are thermoanalytical methods which offer important information about the physical and chemical properties of drugs (purity, stability, phase transition, polymorphism, compatibility, kinetic analysis, etc.). This work exemplifies a general method of studying the drug-excipient interactions with the aim of predicting rapidly and inexpensively the long thermal stability of their mixtures. The TG/DTG and DSC were used as screening techniques for assessing the compatibility between indomethacin (IND) and its physical associations as binary mixtures with some common excipients. Based on their frequent use in preformulations eleven different excipients: corn starch, microcrystalline cellulose (PH 101; PH 102), colloidal silicon dioxide, lactose (monohydrate and anhydre), polyvinilpyrrolidone K30, magnesium stearate, talc, stearic acid, and manitol were blended with IND. The samples were prepared by mixing the analyte and excipients in a proportion of 1:1 (w:w). In order to investigate the possible interactions between the components, the thermal curves of IND and each selected excipient were compared with those of their 1:1 (w/w) physical mixtures. FT-IR spectroscopy and X-ray powder diffraction were used as complementary techniques to adequately implement and assist in interpretation of thermal results. On the basis of thermal results, confirmed by FT-IR and X-ray analyses, a possible interaction was found between IND with polyvinylpyrrolidone K30, magnesium stearate, and stearic acid.     

Some theoretical aspects of elastic wave modeling with a recently developed spectral element method

A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media, based on the Galerkin approach applied to a partition, in small subdomains, of the original physical domain. In this work, some mathematical aspects of the method and the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobatto collocation points are introduced. The related integration formulas are obtained. The standard error estimations and expansion convergence are discussed. An element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence, neither the global matrices nor the effective force vector is assembled. When analytical formulas are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without losing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes this method much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The first part mainly focuses on theoretical studies with a simple numerical result for the Che-byshev spectral element, and the second part, mainly with the Legendre spectral element, will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the detailed modeling example comparisons of the proposed spectral element method with a pseudo-spectral method, which will be seen in another work by Lin, Wang and Zhang.