Cubic Sieve Congruence of the Discrete Logarithm Problem, and fractional part sequences

The Cubic Sieve Method for solving the Discrete Logarithm Problem in prime fields requires a nontrivial solution to the Cubic Sieve Congruence (CSC) x(3) equivalent to y(2)z (mod p), where p is a given prime number. A nontrivial solution must also satisfy x(3) not equal y(2)z and 1 <= x, y, z < p(alpha), where alpha is a given real number such that 1/3 < alpha <= 1/2. The CSC problem is to find an efficient algorithm to obtain a nontrivial solution to CSC. CSC can be parametrized as x equivalent to v(2)z (mod p) and y equivalent to v(3)z (mod p). In this paper, we give a deterministic polynomial-time (O(ln(3) p) bit-operations) algorithm to determine, for a given v, a nontrivial solution to CSC, if one exists. Previously it took (O) over tilde (p(alpha)) time in the worst case to determine this. We relate the CSC problem to the gap problem of fractional part sequences, where we need to determine the non-negative integers N satisfying the fractional part inequality {theta N} < phi (theta and phi are given real numbers). The correspondence between the CSC problem and the gap problem is that determining the parameter z in the former problem corresponds to determining N in the latter problem. We also show in the alpha = 1/2 case of CSC that for a certain class of primes the CSC problem can be solved deterministically in <(O)over tilde>(p(1/3)) time compared to the previous best of (O) over tilde (p(1/2)). It is empirically observed that about one out of three primes is covered by the above class. (C) 2013 Elsevier B.V. All rights reserved.

Stress-state permeability relationships for clays with coarse fraction

In standard laboratory consolidation tests, only the fraction of soil passing through a particular size of the sieve, called the matrix material, is used. This size is usually restricted to 1/10 of the height of the consolidation ring. Particles larger than this size that are removed before the test may consist of gravel, fragments of rock, or other coarse materials. Hence, it is not possible to estimate the compressibility and permeability of the total material based on the compressibility and permeability behavior obtained from laboratory consolidation tests on the matrix material. In the present investigation an attempt has been made to estimate the compressibility and permeability behavior of the total material based on the compressibility and permeability behavior of the matrix material. The results indicate that the presence of coarse particles will reduce the compressibility of the soil in proportion to the coarse fraction present in the whole soil and will not affect the permeability of the soil for the range investigated. If the coarse fraction exceeds the Limiting percentage, the void ratio-vertical effective stress path will also start to deviate from the predicted path. An expression has been developed to estimate approximately the deviating pressure, and it is found to depend on the soil type as well as the percent clay fraction.

Effect of the method of preparation and pretreatment on the texture of alumina and related catalysts

The effect of the method of preparation and pretreatment on catalyst texture was investigated in the case of alumina, silica-alumina, 10 × molecular sieve and thoria catalysts. All the catalysts were characterised with respect to their specific surface area, surface acidity, pore size distribution and pore volume. The above properties were found to reflect the textural changes that might have been undergone by the catalyst surface as a result of the method of preparation and pretreatment. The method of preparation was found to influence markedly the acidity of the surface and to a lesser extent the surface area and pore size distribution. Acid-treatment was found to increase selectively the acidity of the catalyst while heat-treatment was found to decrease proportionally the acidity as well as surface area of the catalyst.

Drop formation in non-newtonian liquids under pulsed conditions

Drop formation from single nozzles under pulsed flow conditions in non-Newtonian fluids following the power law model has been studied. An existing model has been modified to explain the experimental data. The flow conditions employed correspond to the mixer—settler type of operation in pulsed sieve-plate extraction columns. The modified model predicts the drop sizes satisfactorily. It has been found that consideration of non-Newtonian behaviour is important at low pulse intensities and its significance decreases with increasing intensity of pulsation. Further, the proposed model for single orifices has been tested to predict the sizes of drops formed from a sieve-plate distributor having four holes, and has been found to predict the sizes fairly well in the absence of coalescence.

Electron-beam melting and centrifugal splat-quenching technique for rapid solidification of titanium alloys

An electron-beam melting and centrifugal splat-quenching technique for the production of microflakes of Ti-6A1-4V (wt%) alloy quenched at an average cooling rate of about 105 K sec–1 is described. The effect of substrate angle on the shape, size, microstructure and average cooling rate of the flakes of major sieve fractions is discussed. Morphologies of particles of minor sieve fractions are dealt with briefly.

Influence of non-geometrical factors on intracrystalline diffusion -- Role of sorbate-zeolite interactions

Molecular dynamics simulations on Xe in NaY and Ar in NaCaA zeolite are reported. Rates of cage-to-cage crossovers in the two zeolites exhibit trends which are contrary to that expected from geometrical considerations. The results suggest the important role of the sorbate-zeolite interactions in determining the molecular sieve properties of zeolites for small sized sorbates. The results are explained in terms of the barrier height for cage-to-cage crossover in the two zeolites.

Diffusion of sorbates in zeolites Y and A novel dependence on sorbate size and strength of sor ba t e-Zeoli t e interaction

A systematic investigation of monatomic spherical sorbates in the supercages of zeolites Y and A by molecular dynamics technique is presented. Rates of intercage diffusion, rates of cage visits, and the diffusion coefficients have been calculated as a function of the sorbate-zeolite interaction strength. These properties exhibit markedly different dependences on interaction strength for the two zeolites. The observed behavior is shown to be a consequence of the two principal mechanisms of intercage diffusion and the energetic barrier associated with them. The diffusion coefficient and other properties associated with intercage diffusion are found to be directly proportional to the reciprocal of the square of the sorbate diameter when the sorbate diameter is significantly smaller than the window diameter. As the sorbate diameter increases, a peak is observed in all the transport properties investigated including the diffusion coefficient. We call this surprising effect as the ring or levitation effect and it explains several anomalous results reported in the literature and suggests a breakdown of the geometrical criterion for diffusion of sorbates. It shows that under certain conditions nongeometrical factors play a major role and geometrical factors become secondary in the determination of the molecular sieve property. A generalized parameter has been proposed which suggests conditions under which one can expect the ring or levitation effect in any porous medium. Inverse size selectivity becomes operative under these conditions.

Mixed ionic and electronic conduction in zirconia and its applications in metallurgy

Mixed ionic and electronic conduction in Zr02-based solid electrolytes was studied.The effect of impurities and second-phase particles on the mixed conduction parameter, P,, was measured for different types of ZrOZ electrolytes. The performance of solid-state sensors incorporating ZrOZ electrolytes is sometimes limited by electronic conduction in ZrOZ, especially at temperatures >I800 K. Methods for eliminating or minimizing errors in measured emf due to electronically driven transport of oxygen anions are discussed. Examples include probes for monitoring oxygen content in liquid steel as well as the newly developed sulfur sensor based on a ZrOz(Ca0) + CaS electrolyte. The use of mixed conducting ZrOZ as a semipermeable membrane or chemically selective sieve for oxygen at high temperatures is discussed. Oxygen transport from liquid iron to CO + C& gas mixtures through a ZrOZ membrane driven by a chemical potential gradient, in the absence of electrical leads or imposed potentials, was experimentally observed.

Esterification of stearic acid with p-cresol over modified Indian bentonite clay catalysts

The esterification of stearic acid with p-cresol using modified Indian bentonite clay catalysts has been reported. The reaction was studied over exchanged clays, acid activated clays, exchanged acid activated clays, aluminium pillared clay, aluminium pillared acid activated clay, molecular sieve Al-MCM-41, zeolite H beta, ZrO2, S-ZrO2, p-TSA, montmorillonite K10, and montmorillonite KSF in o-xylene for 6 h. The catalysts were characterized by X-ray diffraction and surface area measurements. The acidity was determined by n-butylamine back-titration method and DRIFTS after pyridine adsorption. Acid activated Indian bentonite (AAIB) was found to be a better catalyst compared to other catalysts in the esterification of stearic acid with p-cresol.

Graded IR Filters: Distinguishing Between Single and Multipoint NO2 center dot center dot center dot I Halogen Bonded Supramolecular Synthons (P, Q, and R Synthons)

The NO2 center dot center dot center dot I supramolecular synthon is a halogen bonded recognition pattern that is present in the crystal structures of many compounds that contain these functional groups. These synthons have been previously distinguished as P, Q, and R types using topological and geometrical criteria. A five step IR spectroscopic sequence is proposed here to distinguish between these synthon types in solid samples. Sets of known compounds that contain the P, Q, and R synthons are first taken to develop IR spectroscopic identifiers for them. The identifiers are then used to create graded IR filters that sieve the synthons. These filters contain signatures of the individual NO2 center dot center dot center dot I synthons and may be applied to distinguish between P, Q, and R synthon varieties. They are also useful to identify synthons that are of a borderline character, synthons in disordered structures wherein the crystal structure in itself is not sufficient to distinguish synthon types, and in the identification of the NO2 center dot center dot center dot I synthons in compounds with unknown crystal structures. This study establishes clear differences for the three different geometries P, Q, and Rand in the chemical differences in the intermolecular interactions contained in the synthons. Our IR method can be conveniently employed when single crystals are not readily available also in high throughput analysis. It is possible that such identification may also be adopted as an input for crystal structure prediction analysis of compounds with unknown crystal structures.