Group Actions and Elementary Number Theory

Abstract | In this article the shuffling of cards is studied by using the concept of a group action. We use some fundamental results in Elementary Number Theory to obtain formulas for the orders of some special shufflings, namely the Faro and Monge shufflings and give necessary and sufficient conditions for the Monge shuffling to be a cycle. In the final section we extend the considerations to the shuffling of multisets.

Pressure induced phase transition in metallic LaB6: A Raman study

We report high pressure Raman studies on single crystals of metallic LaB6 upto a pressure of 16.$ GPa. Raman spectra shows three lines at 680 cm(-1) (T-2g), 1120 cm(-1) (E-g) and 1258 cm(-1) (A(1g)), associated with the internal modes of B-6 molecule. The T-2g mode shows an asymmetric Fano line shape, arising from the interference between the phonon line and the electronic continuum. The line is fitted with I(omega) = I-0(q + epsilon(2))/(I + epsilon(2)) where epsilon = (omega - omega(0))/Gamma, omega(0) is the phonon frequency renormalised due to electron-phonon self energy corrections, Tis the width parameter proportional to the square of the matrix element of the electron-phonon interaction potential. The parameter a signifies the strength of interference. Most interestingly our pressure data for the T-2g mode shows a significant change in the slope of the mode frequency with pressure d omega(0)/dP and Gamma at 9.5 GPa. This clearly indicates that LaB6 undergoes a subtle phase transition at 9.5 GPa within the metallic phase.

Bases and Ideal Generators for Projective Monomial Curves

In this article we study bases for projective monomial curves and the relationship between the basis and the set of generators for the defining ideal of the curve. We understand this relationship best for curves in P-3 and for curves defined by an arithmetic progression. We are able to prove that the latter are set theoretic complete intersections.

Effect of Grain Size on Structural and Magnetic Properties of CuFe2O4 Nanograins Synthesized by Chemical Co-Precipitation

CuFe2O4 nanograins have been prepared by the chemical co-precipitation technique and calcined in the temperature range of 200-1200 degrees C for 3 h. A wide range of grain sizes has been observed in this sintering temperature range, which has been determined to be 4 to 56 nm. Formation of ferrite has also been confirmed by FTIR measurement through the presence of wide band near 600 and 430 cm(-1) for the samples in the as-dried condition. Systematic variation of wave number has been observed with the variation of the calcination temperature. B-H loops exhibit transition from superparamagnetic to ferrimagnetic state above the calcination temperature of 900 degrees C. Coercivity of the samples at lower calcination temperature of 900 degrees C reduces significantly and tends towards zero coercivity, which is suggestive of superparamagnetic transition for the samples sintered below this temperature. Frequency spectrum of the real and imaginary part of complex initial permeability have been measured for the samples calcined at different temperature, which shows wide range of frequency stability. Curie temperature, T-c has been measured from temperature dependence initial permeability at a fixed frequency of 100 kHz. Although there is small variation of T-c with sintering temperature, the reduction of permeability with temperature drastically reduce for lower sintering temperature, which is in conformity with the change of B-H loops with the variation of sintering temperatures.

Visible light photocatalytic inactivation of Escherichia coli with combustion synthesized TiO2

The photocatalytic inactivation of Escherichia coil was studied with combustion synthesized TiO2 photocatalysts in the presence of visible light. A series of 400W lamps irradiating in the visible region of the solar spectrum was used. The effect of various parameters, such as catalyst loading, light intensity, presence of inorganic ions, addition of hydrogen peroxide and pH, on the photocatalytic inactivation of E. coil was investigated. Photolysis alone had a small effect on inactivation while the dark experiment resulted in no inactivation and Ag/TiO2 showed the maximum inactivation. At a catalyst loading of 0.25 g/L, all the combustion synthesized catalysts showed better inactivation of E. coil compared to commercial Degussa P-25 (DP-25) TiO2 catalyst. An improved inactivation was observed with increasing lamp intensity and addition of H2O2. A negative effect on inactivation was observed by addition of inorganic ions such as HCO3-, SO42-, Cl-, NO3-, Na+, K+ and Ca2+. The photocatalytic inactivation of E. coli remained unaltered at different pH of the solution. The inactivation of E. coli was modeled with power law kinetics and was observed to follow first order kinetics. (C) 2012 Elsevier B.V. All rights reserved.

Phonon anomalies and structural transition in spin ice Dy2Ti2O7: a simultaneous pressure-dependent and temperature-dependent Raman study

We revisit the assignment of Raman phonons of rare-earth titanates by performing Raman measurements on single crystals of O18 isotope-rich spin ice Dy2Ti2O718 and nonmagnetic Lu2Ti2O718 pyrochlores and compare the results with their O16 counterparts. We show that the low-wavenumber Raman modes below 250 cm-1 are not due to oxygen vibrations. A mode near 200 cm-1, commonly assigned as F2g phonon, which shows highly anomalous temperature dependence, is now assigned to a disorder-induced Raman active mode involving Ti4+ vibrations. Moreover, we address here the origin of the new Raman mode, observed below TC similar to 110 K in Dy2Ti2O7, through a simultaneous pressure-dependent and temperature-dependent Raman study. Our study confirms the new mode to be a phonon mode. We find that dTC/dP = + 5.9 K/GPa. Temperature dependence of other phonons has also been studied at various pressures up to similar to 8 GPa. We find that pressure suppresses the anomalous temperature dependence. The role of the inherent vacant sites present in the pyrochlore structure in the anomalous temperature dependence is also discussed. Copyright (c) 2012 John Wiley & Sons, Ltd.

An integrated model for optimal reservoir operation for irrigation of multiple crops

An integratedm odel is developed,b asedo n seasonailn puts of reservoiri nflow and rainfall in the irrigated area, to determine the optimal reservoir release policies and irrigation allocationst o multiple crops.T he model is conceptuallym ade up of two modules. Module 1 is an intraseasonal allocation model to maximize the sum of relative yieldso f all crops,f or a givens tateo f the systemu, singl inear programming(L P). The module takes into account reservoir storage continuity, soil moisture balance, and crop root growthw ith time. Module 2 is a seasonaal llocationm odel to derive the steadys tate reservoiro peratingp olicyu sings tochastidc ynamicp rogramming(S DP). Reservoir storage, seasonal inflow, and seasonal rainfall are the state variables in the SDP. The objective in SDP is to maximize the expected sum of relative yields of all crops in a year.The resultso f module 1 and the transitionp robabilitieso f seasonailn flow and rainfall form the input for module 2. The use of seasonailn puts coupledw ith the LP-SDP solution strategy in the present formulation facilitates in relaxing the limitations of an earlier study,w hile affectinga dditionali mprovementsT. he model is applied to an existing reservoir in Karnataka State, India.

Moisture Aided Degradation of Oil Impregnated Paper Insulation in Power Transformers

The presence of moisture in oil impregnated paper insulation (OIP) is detrimental to its long time performance. Until recently, it was thought insulation ageing was only a function of temperature and electrical stress. It has now been realized that moisture in all its forms causes rapid degradation of the electrical and mechanical properties with time. In this study, insulation paper samples were conditioned for desired level of moisture and were impregnated with premium quality transformer oil. The oil impregnated samples with 1 to 3 % moisture content were aged at 90 to 130 C. The indices for determining the extent of ageing considered in this work are degree of polymerization (DP), furan, carbon monoxide and carbon dioxide content. These quantities were monitored throughout the ageing experimental run. End-of-life (EOL) criterion used here is the reduction in the value of DP. Phenomenological models for estimating the service life of insulation are proposed and are validated against actual experimental data.

Pressure Dependence of Glass Transition in As2Te3 Glass

Amorphous solids prepared from their melt state exhibit glass transition phenomenon upon heating. Viscosity, specific heat, and thermal expansion coefficient of the amorphous solids show rapid changes at the glass transition temperature (T-g). Generally, application of high pressure increases the T-g and this increase (a positive dT(g)/dP) has been understood adequately with free volume and entropy models which are purely thermodynamic in origin. In this study, the electrical resistivity of semiconducting As2Te3 glass at high pressures as a function of temperature has been measured in a Bridgman anvil apparatus. Electrical resistivity showed a pronounced change at T-g. The T-g estimated from the slope change in the resistivity-temperature plot shows a decreasing trend (negative dT(g)/dP). The dT(g)/dP was found to be -2.36 degrees C/kbar for a linear fit and -2.99 degrees C/kbar for a polynomial fit in the pressure range 1 bar to 9 kbar. Chalcogenide glasses like Se, As2Se3, and As30Se30Te40 show a positive dT(g)/dP which is very well understood in terms of the thermodynamic models. The negative dT(g)/dP (which is generally uncommon in liquids) observed for As2Te3 glass is against the predictions of the thermodynamic models. The Adam-Gibbs model of viscosity suggests a direct relationship between the isothermal pressure derivative of viscosity and the relaxational expansion coefficient. When the sign of the thermal expansion coefficient is negative, dT(g)/dP = Delta k/Delta alpha will be less than zero, which can result in a negative dT(g)/dP. In general, chalcogenides rich in tellurium show a negative thermal expansion coefficient (NTE) in the supercooled and stable liquid states. Hence, the negative dT(g)/dP observed in this study can be understood on the basis of the Adams-Gibbs model. An electronic model proposed by deNeufville and Rockstad finds a linear relation between T-g and the optical band gap (E-g for covalent semiconducting glasses when they are grouped according to their average coordination number. The electrical band gap (Delta E) of As2Te3 glass decreases with pressure. The optical and electrical band gaps are related as Delta E-g = 2 Delta E; thus, a negative dT(g)/dP is expected when As2Te3 glass is subjected to high pressures. In this sense, As2Te3 is a unique glass where its variation of T-g with pressure can be understood by both electronic and thermodynamic models.

Holographic charge diffusion in non-relativistic branes

In this paper, based on the principles of gauge/gravity duality and considering the so called hydrodynamic limit we compute various charge transport properties for a class of strongly coupled non-relativistic CFTs corresponding to z=2 fixed point whose dual gravitational counter part could be realized as the consistent truncation of certain non-relativistic Dp branes in the non-extremal limit. From our analysis we note that unlike the case for the AdS black branes, the charge diffusion constant in the non-relativistic background scales differently with the temperature. This shows a possible violation of the universal bound on the charge conductivity to susceptibility ratio in the context of non-relativistic holography. (C) 2015 The Author. Published by Elsevier B.V.

Comparative high pressure Raman studies on perfluorohexane and perfluoroheptane

High pressure Raman spectroscopic studies on perfluorohexane and perfluoroheptane have performed up to 12 GPa. Perfluorohexane under goes two pressure induced transitions: (1) liquid-solid transition at 1.6 GPa and (2) solid-solid transition at 8.2 GPa. On the contrary, perfluoroheptane under goes three phase transitions, they are as follows: (1) liquid-solid transition at 1.3 GPa, (2) intermediate solid I transition at 3 GPa, (3) solid II transition at 7 GPa. The change in slope (d omega/dP) shows that the solid I transition at 3.0 GPa could be the conversion of mid-gauche defect into trans conformers for perfluoroheptane. The pressure induced Raman spectra and the behavior of individual band with pressure shows that the solid phase comprises more than one conformer beyond crystallization. The intensity ratio for both the compounds shows that the high pressure phase beyond 8.2 and 7.0 GPa tends to have close packing with distorted all-trans conformers. (C) 2015 Elsevier B.V. All rights reserved.

A note on tetrablock contractions

A commuting triple of operators (A, B, P) on a Hilbert space H is called a tetrablock contraction if the closure of the set E = {(a(11),a(22),detA) : A = GRAPHICS] with parallel to A parallel to <1} is a spectral set. In this paper, we construct a functional model and produce a set of complete unitary invariants for a pure tetrablock contraction. In this construction, the fundamental operators, which are the unique solutions of the operator equations A - B* P = DPX1DP and B - A* P = DPX2DP where X-1, X-2 is an element of B(D-P) play a pivotal role. As a result of the functional model, we show that every pure tetrablock isometry (A, B, P) on an abstract Hilbert space H is unitarily equivalent to the tetrablock contraction (MG1*+G2z, MG2*+G1z, M-z) on H-DP*(2). (D), where G(1) and G(2) are the fundamental operators of (A*, B*, P*). We prove a Beurling Lax Halmos type theorem for a triple of operators (MF1*+F2z, MF2*+F1z, M-z), where epsilon is a Hilbert space and F-1, F-2 is an element of B(epsilon). We also deal with a natural example of tetrablock contraction on a functions space to find out its fundamental operators.

The Feedback Capacity of the Binary Erasure Channel With a No-Consecutive-Ones Input Constraint

The input-constrained erasure channel with feedback is considered, where the binary input sequence contains no consecutive ones, i.e., it satisfies the (1, infinity)-RLL constraint. We derive the capacity for this setting, which can be expressed as C-is an element of = max(0 <= p <= 0.5) (1-is an element of) H-b (p)/1+(1-is an element of) p, where is an element of is the erasure probability and Hb(.) is the binary entropy function. Moreover, we prove that a priori knowledge of the erasure at the encoder does not increase the feedback capacity. The feedback capacity was calculated using an equivalent dynamic programming (DP) formulation with an optimal average-reward that is equal to the capacity. Furthermore, we obtained an optimal encoding procedure from the solution of the DP, leading to a capacity-achieving, zero-error coding scheme for our setting. DP is, thus, shown to be a tool not only for solving optimization problems, such as capacity calculation, but also for constructing optimal coding schemes. The derived capacity expression also serves as the only non-trivial upper bound known on the capacity of the input-constrained erasure channel without feedback, a problem that is still open.