On pasting -weights

Theorem 3 gives a condition when two -weights can be ``pasted' together to yield another -weight. It is subsequently used in Example 6 to give an example that shows that a necessary condition by Gohberg, Krupnik, and Spitkovsky is not sufficient.

     

Critical behavior of self-avoiding walks on fractals

Using a new graph counting technique suitable for self-similar fractals, exact 18th-order series expansions for SAWs on some Sierpinski carpets are generated. From them, the critical fugacityx _c and critical exponents _SAW and _SAW are obtained. The results show a linear dependence of the critical fugacity with the average number of bonds per site of the lattices studied. We find for some carpets with low lacunarity that _SAW<0.75, thus violating the relation _SAW(fractal) > _SAW (d) for SAWs on the fractals which are embedded in ad-dimensional Euclidean space.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

Automated molecular design: A new fragment-joining algorithm

Summary A popular first step in the problem of structure-based, de novo molecule design is to identify regions where specific functional groups or chemical entities would be expected to interact strongly. When the three-dimensional structure of the receptor is not available, it may be possible to derive a pharmacophore giving the three-dimensional relationships between such chemical groups. The task then is to design synthetically feasible molecules which not only contain the required groups, but which can also position them in the desired relative orientation. One way to do this is to first link the groups using an acyclic chain. We have investigated the application of the tweak algorithm [Shenkin, P.S. et al., Biopolymers, 26 (1987) 2053] for generating families of acyclic linkers. These linking structures can subsequently be braced using a ring-joining algorithm [Leach, A.R. and Lewis, R.A., J. Comput. Chem., 15 (1994) 233], giving rise to an even wider variety of molecular skeletons for further studies.     

Evaluation of dead time calculation in liquid chromatography using a linearization procedure for homologous series

A mathematical method for the calculation of the dead time (t_m) in HPLC was evaluated using a computer simulation approach, in which artificial perturbations were introduced to Simulated homolog retention times. The calculation was based on a modified and extended Grobler and Bálisz (GB) method. Investigated wav how the precision of the calculated t_M is affected by: statistical fluctuations in retention times and which, and how many homolog retention times are used. Based on these simulations a two-step procedure for the t_M calculation is proposed: In the first step the linearity of log t_{R, n} vs carbon number n is checked using as many homolog retention times as possible. The slope value b^o of the first linear regression in the GB method is used for the selection of homolog retention times in the final t_M calculation. In the second step the optimal selection of homologs is made and the final t_M calculation is carried out. Guidelines for homolog selection are given.     

Hole doping and superconductivity characteristics of the s=1, 2 and 3 members of the (Cu,Mo)-12s2 homologous series of layered copper oxides

Superconductivity characteristics have been systematically evaluated for a two-CuO₂-plane copper oxide system, (Cu,Mo)-12s2, upon increasing the number of fluorite-structured layers, s, between the two CuO₂ planes. Essentially single-phase samples of (Cu_0.75Mo_0.25)Sr₂YCu₂O_7+δ (s=1), (Cu_0.75Mo_0.25)Sr₂(Ce_0.45Y_0.55)₂Cu₂O_9+δ (s=2) and (Cu_0.75Mo_0.25)Sr₂(Ce_0.67Y_0.33)₃Cu₂O_11+δ (s=3) were synthesized through a conventional solid-state route in air. To make the samples superconductive an additional high-pressure oxygenation (HPO) treatment was required. Such treatment (carried out at 5 GPa and 500 °C in the presence of 75 mol% Ag₂O₂ as an oxygen source to maximize the T_c) compressed the crystal lattice for the three members of the (Cu_0.75Mo_0.25)-12s2 series equally, i.e., by 0.01 Å for the a parameter and by 0.07 Å for the c parameter per formula unit. From both Cu L-edge and O K-edge XANES spectra the s=1 sample was found to possess the highest overall hole-doping level among the HPO samples. Accordingly it exhibited the best superconductivity characteristics. With increasing s, both the T_c (s=1: 88 K, s=2: 61 K, s=3: 53 K) and H_irr values got depressed, being well explained by the trend of decreasing CuO₂-plane hole concentration with increasing s as revealed from O K-edge XANES spectra for the same samples. Hence, the present results do not suggest any significant (negative) impact on the superconductivity characteristics from the gradually thickened fluorite-structured block itself.     

Thermal degradation of polystyrene in the presence of hydrogen by catalyst in solution

For the first time, low temperature degradation (170-240 °C) of polystyrene in benzene is carried out in the presence of hydrogen using iron(III) oxide catalyst. The effect of temperature, catalyst loading and polymer loading on degradation are studied in hydrogen atmosphere. Degradation is also carried out at different initial hydrogen partial pressure. The time dependent molecular weight is calculated using viscosity average method. It is found that the degradation is enhanced considerably in the presence of hydrogen and followed random degradation chain scission. A random degradation kinetic model of Kelen [Kelen T. Polymer degradation. New York: Van Nostrand Reinhold Company; 1983.] is used to estimate the degradation rate constants. Empirical correlations are proposed to account for the effect of catalyst loading and initial hydrogen partial pressure on degradation. The true thermal degradation rate constants are calculated using these proposed correlations at given catalyst loading and initial hydrogen partial pressure with varying temperature. The frequency factor and activation energy are also determined using Arrhenius equation considering the true thermal degradation rate constants.     

Computation of suboptimal randomized strategies for steering the random motion of a point under partial observation

Consider the random motion in the plane of a pointM, whose velocityv=(v ₁,v ₂) is perturbed by an ²-valued Gaussian white noise. Only noisy nonlinear observations taken on the point location (state) are available toM. The velocityv is of the formv(y)= _u (u ₁,u ₂) _y (du), wherey denotes the value of the observed signal,U is the range of the velocity, and, for eachy, _y is a probability measure on (U). Using the available observations, the pointM wishes to steer itself into a given target set by choosing a randomized strategy ={ _y :y ²}. Sufficient conditions on weak optimal randomized strategies are derived. An algorithm for computing weak suboptimal randomized strategies is suggested, and the strategies are computed for a variety of cases.This work was partially supported by a grant from Control Data.     

Trapping of random walks on the line

Several features of the trapping of random walks on a one-dimensional lattice are analyzed. The results of this investigation are as follows: (1) The correction term to the known asymptotic form for the survival probability ton steps is O(( ₂n)^–1/3), where =–ln(1–c), andc is the trap concentration. (2) The short time form for the survival probability is found to be exp[–a(c)n ^1/2], wherea(c) is given in Eq. (21). (3) The mean-square displacement of a surviving random walker is found to go liken ^2/3for largen. (4) When the distribution of trap-free regions is changed so that very large regions are much rarer than for ideally random trap placement the asymptotic survival probability changes its dependence onn. One such model is studied.