A complete and equal computational complexity classification of compaction and retraction to all graphs with at most four vertices and some general results

A very close relationship between the compaction, retraction, and constraint satisfaction problems has been established earlier providing evidence that it is likely to be difficult to give a complete computational complexity classification of the compaction and retraction problems for reflexive or bipartite graphs. In this paper, we give a complete computational complexity classification of the compaction and retraction problems for all graphs (including partially reflexive graphs) with four or fewer vertices. The complexity classification of both the compaction and retraction problems is found to be the same for each of these graphs. This relates to a long-standing open problem concerning the equivalence of the compaction and retraction problems. The study of the compaction and retraction problems for graphs with at most four vertices has a special interest as it covers a popular open problem in relation to the general open problem. We also give complexity results for some general graphs. The compaction and retraction problems are special graph colouring problems, and can also be viewed as partition problems with certain properties. We describe some practical applications also.     

Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels

We consider a multiuser multiple-input multiple- output (MIMO) Gaussian broadcast channel (BC), where the transmitter and receivers have multiple antennas. Since the MIMO BC is in general a nondegraded BC, its capacity region remains an unsolved problem. We establish a duality between what is termed the "dirty paper" achievable region (the Caire-Shamai (see Proc. IEEE Int. Symp. Information Theory, Washington, DC, June 2001, p.322) achievable region) for the MIMO BC and the capacity region of the MIMO multiple-access channel (MAC), which is easy to compute. Using this duality, we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the MIMO BC. We also show that the dirty paper achievable region achieves the sum-rate capacity of the MIMO BC by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the MIMO BC.     

A normalized analytical solution for the capacitance associated with uniformly doped semiconductors at equilibrium

A normalized solution for determining the capacitance associated with uniformly doped semiconductors at equilibrium is presented here. The present formulation allows the application of this solution to both the MIS surface problem as well as PN step junction problem under equilibrium conditions, subject to Boltzmann approximation. For the surface case the results are in normalized analytic form in agreement with previous analyses. For the junction case a better estimation of the depletion layer thickness results in an analytic expression which performs better than that based on the depletion approximation.     

Dissolution system for Nifedipine Sustained Release Formulations

An in-vitro system for evaluating Nifedipine sustained release formulations has been developed. Two systems were evaluated to simulate sink conditions and correlate the system with flow through dissolution system in mechanism. For the purpose of evaluation two commercial brands were studied. The acidic biphasic system was found to be good for in-vitro dissolution rate evaluation of sustained release nifedipine tablets. It can be successfully utilized for routine quality control work.     

Antimicrobial activity of silica coated silicon nano-tubes (SCSNT) and silica coated silicon nano-particles (SCSNP) synthesized by gas phase condensation

Silica-coated, silicon nanotubes (SCSNTs) and silica-coated, silicon nanoparticles (SCSNPs) have been synthesized by catalyst-free single-step gas phase condensation using the arc plasma process. Transmission electron microscopy and scanning tunneling microscopy showed that SCSNTs exhibited a wall thickness of less than 1 nm, with an average diameter of 14 nm and a length of several 100 nm. Both nano-structures had a high specific surface area. The present study has demonstrated cheaper, resistance-free and effective antibacterial activity in silica-coated silicon nano-structures, each for two Gram-positive and Gram-negative bacteria. The minimum inhibitory concentration (MIC) was estimated, using the optical densitometric technique, and by determining colony-forming units. The MIC was found to range in the order of micrograms, which is comparable to the reported MIC of metal oxides for these bacteria. SCSNTs were found to be more effective in limiting the growth of multidrug-resistant Staphylococcus aureus over SCSNPs at 10 μg/ml (IC 50 = 100 μg/ml).     

Buckling of vibrations of shear-flexible orthotropic plates subjected to mixed boundary conditions

An approximate technique is presented for the analysis of buckling and vibrations of free-form, orthotropic, shear-flexible (‘Mindlin’) plates subject to mixed boundary conditions. The method falls into the category of Rayleigh/ Ritz-techniques; however, by using Lagrangian multipliers to ‘relax’ the geometric boundary conditions, the selection of appropriate trial functions is made considerably simpler. Accuracy and reliability of the proposed technique is demonstrated on the basisof several sample problems.     

Control of properties during the growth of a large number of (Y,Sm)3(Ga,Fe)5O12 films from the same melt

For the growth of a large number of (Y, Sm)₃(Ga, Fe)₅O₁₂ films from the same melt, we describe the drift and methods to control the drift in film properties, so that the films are suitable for making magnetic bubble memory devices. The melt was based on PbO-B₂O₃ flux. The film thickness h and the characteristic length l were kept at around 5.4 μm and 0.54 μm respectively. The desired h was achieved by adjusting the growth time. The desired values for l were achieved by adjusting the growth temperature and by periodically adding small amounts of Ga₂O₃. The lattice constant was kept within the specified limits by periodic additions of Y₂O₃. Using these techniques we were able to grow more than a hundred films, out of which ～ 85% were acceptable for device fabrication. Based on the deduced values for the composition of our films, we have calculated the melt depletion resulting from the growth of a single film. We find that the experimentally determined additions of Ga₂O₃ and Y₂O₃ that gave us good control over film properties are almost equal to the calculated depletions for these two oxides.     

Breakdown and capacitance properties of hyperabrupt epitaxial Schottky barrier diodes

An analysis of the breakdown and capacitance properties of punch-through hyperabrupt epitaxial Schottky barrier diodes has been carried out. Results are given for the dependence of breakdown voltage of such a device on surface concentration and epitaxial layer thickness. Design curves are given for epitaxial hyperabrupt schottky varactor diodes. The design procedure yields an optimal impurity profile in which just-punch-through occurs at the highest voltage of operation. This gives a maximum dynamic range of operation still keeping the series resistance to a minimum. A corrected boundary condition to determine the profile constants associated with an n/n⁺ (high/low) junction is also given.     

Synthesis, Densification, and Phase Evolution Studies of Al2O3–Al2TiO5–TiO2 Nanocomposites and Measurement of Their Electrical Properties

Alumina–aluminum titanate–titania (Al₂O₃–Al₂TiO₅–TiO₂) nanocomposites were synthesized using alkoxide precursor solutions. Thermal analysis provided information on phase evolution from the as-synthesized gel with an increase in temperature. Calcination at 700°C led to the formation of an Al₂O₃–TiO₂ nanocomposite, while at a higher temperature (1300°C) an Al₂O₃–Al₂TiO₅–TiO₂ nanocomposite was formed. The nanocomposites were uniaxially compacted and sintered in a pressureless environment in air to study the densification behavior, grain growth, and phase evolution. The effects of nanosize particles on the crystal structure and densification of the nanocomposite have been discussed. The sintered nanocomposite structures were also characterized for dielectric properties.     

Reverse osmotic properties of the membranes prepared from the polycondensate of 2,5-pyridinedicarboxylic acid chloride and malonyl dihydrazide

Summary The membrane performance of the polycondensates derived from 2,5-pyridinedicarboxylic acid chloride and malonyl dihydrazide was studied in reverse osmosis. It depended on drying time, and the kind and amount of a cross-linking agent and an inorganic additive. The membrane strength generally exceeded that of a cellulose acetate membrane. The rejection difference between transition and alkali metal salts was discussed in terms of complexation and the molecular size of the additive. A potential application was suggested for the separation between the two metals through the membrane of a large rejection difference.