Kinetics of thermal oxidation of titanium carbide and its carbon nano-composites in dry air atmosphere

Results of research work on oxidation of TiC/C nano-composites in air and under non-isothermal conditions are presented. The oxidation of nano-crystalline titanium carbide as well as its carbon composites were studied using TG-DSC method in dry air atmosphere. The investigated samples were as follows: commercial TiC nano-powders from Alfa Aesar (80 nm) and carbon composites including nano-crystalline TiC (30 nm and 50, 10, 3 mass% of carbon in matrix). The measurements were executed in the Setaram thermoanalyser TG-DSC 92-15 in non-isothermal conditions, with mass samples of 30±0.2 mg and constant heating rate in the range 2–10 K min⁻¹.     

The least element property of center location on tree networks with applications to distance and precedence constrained problems

In the classicalp-center location model on a network there is a set of customers, and the primary objective is to selectp service centers that will minimize the maximum distance of a customer to a closest center. Suppose that thep centers receive their supplies from an existing central depot on the network, e.g. a warehouse. Thus, a secondary objective is to locate the centers that optimize the primary objective as close as possible to the central depot. We consider tree networks and twop-center models. We show that the set of optimal solutions to the primary objective has a semilattice structure with respect to some natural ordering. Using this property we prove that there is ap-center solution to the primary objective that simultaneously minimizes every secondary objective function which is monotone nondecreasing in the distances of thep centers from the existing central depot.Restricting the location models to a rooted path network (real line) we prove that the above results hold for the respective classicalp-median problems as well.     

Lateral beam displacements in transmitting layered structures

The lateral shift of both the reflected and the transmitted beams are examined for incidence on layered configurations. In particular, beam displacements are evaluated at a layer placed between two different semi-infinite media. We find that the reflected beam may undergo a large displacement, which occurs in either a forward or a backward direction. The transmitted beam is also substantially displaced, but its shift occurs in a forward direction only.     

Guided-wave methods for optical configurations

Guided-wave methods used in the past to treat electromagnetic problems and applications in the microwave area have recently been extended to cover work in fiber and integrated optics. The basic principles of these methods are reviewed briefly and, in particular, the “open” properties of optical configurations are contrasted to the “closed” characteristics that describe most microwave applications. These aspects are illustrated in the context of beam couplers of uniform and periodic varieties, which are shown to lend themselves to rigorous treatment by microwave guided-wave methods that include both theoretical and experimental facets.     

Dynamic proton magnetic resonance studies on complex spin systems. Non-mutual three-spin exchange in N-(trideuteriomethyl)-2-cyanoaziridine

At room temperature and below, the proton NMR spectrum of N-(trideuteriomethyl)-2-cyanoaziridine consists of two superimposed ABC patterns assignable to two N-invertomers; a single time-averaged ABC pattern is observed at 158.9°C. The static parameters extracted from the spectra in the temperature range from –40.3 to 23.2°C and from the high-temperature spectrum permit the calculation of the thermodynamic quantities ΔH⁰ = ?475±20 cal mol^?1 (?1.987 ± 0.084 kJ mol^?1) and ΔS⁰ = 0.43±0.08 cal mol^?1 K^?1 (1.80±0.33 J mol^?1 K^?1) for the cis ? trans equilibrium. Bandshape analysis of the spectra broadened by non-mutual three-spin exchange in the temperature range from 39.4–137.8°C yields the activation parameters ΔH_tc^≠ = 17.52±0.18 kcal mol^?1 (73.30±0.75 kJ mol^?1), ΔS_tc^≠ = ?2.08±0.50 cal mol^?1 K^?1 (?8.70±2.09 J mol^?1 K^?1) and ΔG_tc^≠ (300 K) = 18.14±0.03 kcal mol^?1 (75.90±0.13 kJ mol^?1) for the trans → cis isomerization. An attempt is made to rationalize the observed entropy data in terms of the principles of statistical thermodynamics.     

Improved algorithms for the multicut and multiflow problems in rooted trees

Costa et al. (Oper. Res. Lett. 31:21–27, 2003) presented a quadratic O(min (Kn,n ²)) greedy algorithm to solve the integer multicut and multiflow problems in a rooted tree. (n is the number of nodes of the tree, and K is the number of commodities). Their algorithm is a special case of the greedy type algorithm of Kolen (Location problems on trees and in the rectilinear plane. Ph.D. dissertation, 1982) to solve weighted covering and packing problems defined by general totally balanced (greedy) matrices. In this communication we improve the complexity bound in Costa et al. (Oper. Res. Lett. 31:21–27, 2003) and show that in the case of the integer multicut and multiflow problems in a rooted tree the greedy algorithm of Kolen can be implemented in subquadratic O(K+n+min (K,n)log n) time. The improvement is obtained by identifying additional properties of this model which lead to a subquadratic transformation to greedy form and using more sophisticated data structures.      

Improved versions of Tardos’ fingerprinting scheme

We study the Tardos’ probabilistic fingerprinting scheme and show that its codeword length may be shortened by a factor of approximately 4. We achieve this by retracing Tardos’ analysis of the scheme and extracting from it all constants that were arbitrarily selected. We replace those constants with parameters and derive a set of inequalities that those parameters must satisfy so that the desired security properties of the scheme still hold. Then we look for a solution of those inequalities in which the parameter that governs the codeword length is minimal. A further reduction in the codeword length is achieved by decoupling the error probability of falsely accusing innocent users from the error probability of missing all colluding pirates. Finally, we simulate the Tardos scheme and show that, in practice, one may use codewords that are shorter than those in the original Tardos scheme by a factor of at least 16.      

Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes

Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRCs are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities exponential vanish when the blocklength tends to infinity.     

Tight bounds and 2-approximation algorithms for integer programs with two variables per inequality

The problem of integer programming in bounded variables, over constraints with no more than two variables in each constraint is NP-complete, even when all variables are binary. This paper deals with integer linear minimization problems inn variables subject tom linear constraints with at most two variables per inequality, and with all variables bounded between 0 andU. For such systems, a 2-approximation algorithm is presented that runs in time O(mnU ² log(Un ² m)), so it is polynomial in the input size if the upper boundU is polynomially bounded. The algorithm works by finding first a super-optimal feasible solution that consists of integer multiples of 1/2. That solution gives a tight bound on the value of the minimum. It furthermore has an identifiable subset of integer components that retain their value in an integer optimal solution of the problem. These properties are a generalization of the properties of the vertex cover problem. The algorithm described is, in particular, a 2-approximation algorithm for the problem of minimizing the total weight of true variables, among all truth assignments to the 2-satisfiability problem.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.Research supported in part by ONR contracts N00014-88-K-0377 and N00014-91-J-1241.Research supported in part by ONR contract N00014-91-C-0026.Part of this work was done while the author was visiting the International Computer Science Institute in Berkeley, CA and DIMACS, Rutgers University, New Brunswick, NJ.