Enumeration Approach for Linear Complementarity Problems Based on a Reformulation-Linearization Technique

In this paper, we consider the linear complementarity problem (LCP) and present a global optimization algorithm based on an application of the reformulation-linearization technique (RLT). The matrix M associated with the LCP is not assumed to possess any special structure. In this approach, the LCP is formulated first as a mixed-integer 0–1 bilinear programming problem. The RLT scheme is then used to derive a new equivalent mixed-integer linear programming formulation of the LCP. An implicit enumeration scheme is developed that uses Lagrangian relaxation, strongest surrogate and strengthened cutting planes, and a heuristic, designed to exploit the strength of the resulting linearization. Computational experience on various test problems is presented.     

Synthesis and properties of polyamides of p-phenylenedioxydiacetic acid

Several polyamides of p-phenylenedioxydiacetic acid (PDDA) were synthesized by the low-temperature solution polycondensation techniques. Six different diamines were condensed independently with p-phenylenedioxydiacetyl chloride (PDC) in a mixture of N-methyl pyrolidone (NMP) and hexamethyl phosphoramide (HMPA). The polymers were obtained in 80–95% yield and possessed inherent viscosities in the range 0.32–0.81 dL/g. The polymers were characterized by infrared (IR) and H¹-NMR spectra. The solubility, density, crystallinity, and thermal stability of the polyamides were also determined. A model diamide (MDA-1) was also synthesized from aniline and PDC to confirm the formation of polyamides from diamines.     

Hadamard excitation sculpting.

An approach to Hadamard phase encoding and editing in an excitation sculpting experiment is presented. When band- and/or frequency-selective experiments are performed at more than one site using excitation sculpting, use of Hadamard excitation sculpting (HEX sculpting) will reduce the total measuring time to achieve a target S/N. The application of HEX sculpting is demonstrated using selective 1D and NOESY1D experiments.     

Multifunctional antigens of A. fumigatus and specific antibodies

The majority of Aspergillus-induced infections in man are caused by the pathogenic fungus A. fumigatus, which secretes biologically and immunologically active glycosylated and nonglycosylated proteins. The complexity in the antigenic structure of A. fumigatus and the varying host immune responses lead to a wide spectrum of clinical conditions such as allergic bronchopulmonary aspergillosis (ABPA), aspergilloma, and invasive aspergillosis. It is reported that 15-20% of allergic asthmatics suffer from Aspergillus-induced allergies. The incidence of opportunistic infections, including Aspergillus infections, has risen because of the increase in the incidence of HIV and tuberculosis. Allergic bronchopulmonary aspergillosis is an immunologically significant clinical form where type I and type III hypersensitivity reactions are involved in pathogenesis. High levels of specific IgE and IgG antibodies in these patients are of diagnostic value. Molecular characterization of certain immunodominant allergens and antigens of A. fumigatus revealed the presence of complex carbohydrate moieties, heat-shock proteins, enzyme activities such as elastase, protease, catalase, dismutase, and cytotoxic ribonuclease. A Con A binding allergen/antigen (45 kDa) and Con A nonbinding allergen/antigen (18 kDa, Asp fI) have a multifunctional nature. The multifunctional nature of these antigens may play an important role in the pathogenesis of the disease. Significant amounts of a major allergen/antigen of molecular weight 18 kDa is excreted in large amounts through the urine of patients with invasive aspergillosis. Studies on the structure-function relationship of the 18-kDa allergen/antigen revealed the involvement of tryptophan residues in binding with monoclonal antibodies (MAbs). Also, the histidine residues and cysteine disulfide bonds of the 18-kDa allergen are involved in its catalytic activity. The high load of multifunctional antigens in the serum of patients for prolonged periods, the presence of high levels of specific antibodies, and the absence of protective antibodies in ABPA patients have necessitated studies on the functional properties of the antibodies. The present study shows significant immunoreactivity of antibodies in patients of ABPA to fibronectin and collagen. Analysis of IgG antibodies from the patients of ABPA showed the presence of DNA-cleaving activity. These observations offer a new line of thinking in understanding the mechanism of pathogenesis of Aspergillus-induced clinical manifestations, and may lead to novel approaches to intervention in the inflammation and infection caused by fungal pathogens.     

Nonequilibrium Phase Transition in a Model of Diffusion, Aggregation, and Fragmentation

We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact, and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady-state mass distribution decays exponentially for large mass in one phase. In the other phase, the mass distribution decays as a power law accompanied, in addition, by the formation of an infinite aggregate. The model is solved exactly within a mean-field approximation which keeps track of the distribution of masses. In one dimension, by mapping to an equivalent lattice gas model, exact steady states are obtained in two extreme limits of the parameter space. Critical exponents and the phase diagram are obtained numerically in one dimension. We also study the time-dependent fluctuations in an equivalent interface model in (1+1) dimension and compute the roughness exponent and the dynamical exponent z analytically in some limits and numerically otherwise. Two new fixed points of interface fluctuations in (1+1) dimension are identified. We also generalize our model to include arbitrary fragmentation kernels and solve the steady states exactly for some special choices of these kernels via mappings to other solvable models of statistical mechanics.     

Bubbling and large-scale structures in avalanche dynamics

Using a simple lattice model for granular media, we present a scenario of self-organization that we term self-organized structuring where the steady state has several unusual features: (1) large-scale spatial and/or temporal inhomogeneities and (2) the occurrence of a nontrivial peaked distribution of large events which propagate like "bubbles" and have a well-defined frequency of occurrence. We discuss the applicability of such a scenario for other models introduced in the framework of self-organized criticality.     

Rapid reduction of alkyl tosylates with lithium triethylborohydride. A convenient and advantageous procedure for the deoxygenation of simple and hindered alcohols. Comparison of various hydride reagents

Lithium triethylborohydride (super-hydride) in tetrahydrofuran reduces the p-toluenesulfonates of primary and secondary alcohols to the corresponding alkanes in excellent yields. The reaction is general and applicable even to tosylates derived from cycloalkanols, hindered alcohols, and polyhydroxy derivatives. Examination of the scope of the reaction and comparison with the results realized with other hydridic reducing agents reveals the advantages of this new procedure.     

Infrared absorption spectra of ethyl,n-propyl andn-butyl stearates

X-ray K-line intensity ratiosα ₂/α ₁,β ₃/β ₁ andβ ₂ ^II /β ₂ ^I have been calculated following the method due to Payne which accounts for the retardations. In addition screening has been included. It is found thatα-line intensity ratios are given best by Sommerfeld screening but that Slater screening is better for theβ-lines. Field theoretically corrected energies have also been used and it is found that the agreement is less favourable. The necessity of including the potentials corresponding to these effects as perturbations to the wavefunctions has been pointed out.     

Localised vibrations due to substitutional impurities in calcium fluoride

The localized modes in CaF₂ due to the introduction of substitutional impurities have been investigated using the greens functions method. The weakening of the nearest neighbour interaction in all the alkaline earth fluorides, is estimated from the infrared absorption spectra on localized modes in these crystals. The splitting of the localized modes in CaF₂, due to the presence of additional Sr²⁺ or Ba²⁺ impurities is estimated and satisfactory agreement exists between theory and experiment, within the limits of the simplifications in our calculations.