Exact controllability of generalized Hammerstein type equation

In this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation $$ x(t) = int_0^t h(t,s)u(s)ds+ int_0^t k(t,s,x)f(s,x(s))ds, quad 0 leq t leq T less than infty, $$ where, the state $x(t)$ lies in a Hilbert space $H$ and control $u(t)$ lies another Hilbert space $V$ for each time $t in I=[0,T]$, $T$ greater than 0. We establish the controllability result under suitable assumptions on $h, k$ and $f$ using the monotone operator theory.

Evidence of residual entropy in the cubic spinel Zn2TiO4

The standard free energies of formation of Zn2Ti04 and ZnTi03 have been determined in the temperature range 930° to i ioo'x from electromotive force measurements on reversible solid oxide galvanic cells;Ag-5at%znll I Pt, + CaO-Zr02 ZnO I II Ag-5at%Zn Y20r Th02 CaO-Zr02 + ,Pt Zn2Ti04+ ZnTi03 and II Ag-5at%Zn CaO-Zr02 + ,Pt ZnTi03+ Ti02 The values may be expressed by the equations,2ZnO (wurtz) + Ti02(rut) -> Zn2Ti04(sp), f:!:.Go = -750-2-46T (±75)cal;ZnO(wurtz) +Ti02(rut) -> ZnTi03(ilmen) ,f:!:.Co = -]600-0·]99T(±50)cal.Combination of the free energy values with the calorimetric heat of formation, and low-temperature and high-temperature heat capacity of Zn2Ti04 reported in literature, suggests a residual entropy of ],9 (±0·6) cal K-1 mol ? for the cubic spinel. Ideal mixing of Zn2+ and Ti4+ ions on the octahedral sites would result in a configurational contribution to the entropy of 2· 75 cal K-1 rnol ".The difference is indicative of short-range ordering of cations on octahedral sites.

An entropy meter based on the thermoelectric potential of a nonisothermal solid electrolyte cell

The theory, design, and performance of a solid electrolyte twin thermocell for the direct determination of the partial molar entropy of oxygen in a single-phase or multiphase mixture are described. The difference between the Seebeck coefficients of the concentric thermocells is directly related to the difference in the partial molar entropy of oxygen in the electrodes of each thermocell. The measured potentials are sensitive to small deviations from equilibrium at the electrodes. Small electric disturbances caused by simultaneous potential measurements or oxygen fluxes caused by large oxygen potential gradients between the electrodes also disturb the thermoelectric potential. An accuracy of ±0.5 calth K−1 mol−1 has been obtained by this method for the entropies of formation of NiO and NiAl2O4. This “entropy meter” may be used for the measurement of the entropies of formation of simple or complex oxides with significant residual contributions which cannot be detected by heat-capacity measurements.

The standard enthalpy and entropy of formation of Rh2O3 - A third-law optimization

The standard Gibbs energy of formation of Rh203 at high temperature has been determined recently with high precision. The new data are significantly different from those given in thermodynamic compilations.Accurate values for enthalpy and entropy of formation at 298.15 K could not be evaluated from the new data,because reliable values for heat capacity of Rh2O3 were not available. In this article, a new measurement of the high temperature heat capacity of Rh2O3 using differential scanning calorimetry (DSC) is presented.The new values for heat capacity also differ significantly from those given in compilations. The information on heat capacity is coupled with standard Gibbs energy of formation to evaluate values for standard enthalpy and entropy of formation at 289.15 K using a multivariate analysis. The results suggest a major revision in thermodynamic data for Rh2O3. For example, it is recommended that the standard entropy of Rh203 at 298.15 K be changed from 106.27 J mol-' K-'given in the compilations of Barin and Knacke et al. to 75.69 J mol-' K". The recommended revision in the standard enthalpy of formation is from -355.64 kJ mol-'to -405.53 kJ mol".

Generalized distributive law for ML decoding of STBCs

The Generalized Distributive Law (GDL) is a message passing algorithm which can efficiently solve a certain class of computational problems, and includes as special cases the Viterbi's algorithm, the BCJR algorithm, the Fast-Fourier Transform, Turbo and LDPC decoding algorithms. In this paper GDL based maximum-likelihood (ML) decoding of Space-Time Block Codes (STBCs) is introduced and a sufficient condition for an STBC to admit low GDL decoding complexity is given. Fast-decoding and multigroup decoding are the two algorithms used in the literature to ML decode STBCs with low complexity. An algorithm which exploits the advantages of both these two is called Conditional ML (CML) decoding. It is shown in this paper that the GDL decoding complexity of any STBC is upper bounded by its CML decoding complexity, and that there exist codes for which the GDL complexity is strictly less than the CML complexity. Explicit examples of two such families of STBCs is given in this paper. Thus the CML is in general suboptimal in reducing the ML decoding complexity of a code, and one should design codes with low GDL complexity rather than low CML complexity.

The generalized Onsager model for the secondary flow in a high-speed rotating cylinder

The generalizations of the Onsager model for the radial boundary layer and the Carrier-Maslen model for the end-cap axial boundary layer in a high-speed rotating cylinder are formulated for studying the secondary gas flow due to wall heating and due to insertion of mass, momentum and energy into the cylinder. The generalizations have wider applicability than the original Onsager and Carrier-Maslen models, because they are not restricted to the limit A >> 1, though they are restricted to the limit R e >> 1 and a high-aspect-ratio cylinder whose length/diameter ratio is large. Here, the stratification parameter A = root m Omega(2)R(2)/2k(B)T). This parameter A is the ratio of the peripheral speed, Omega R, to the most probable molecular speed, root 2k(B)T/m, the Reynolds number Re = rho w Omega R(2)/mu, where m is the molecular mass, Omega and R are the rotational speed and radius of the cylinder, k(B) is the Boltzmann constant, T is the gas temperature, rho(w) is the gas density at wall, and mu is the gas viscosity. In the case of wall forcing, analytical solutions are obtained for the sixth-order generalized Onsager equations for the master potential, and for the fourth-order generalized Carrier-Maslen equation for the velocity potential. For the case of mass/momentum/energy insertion into the flow, the separation-of-variables procedure is used, and the appropriate homogeneous boundary conditions are specified so that the linear operators in the axial and radial directions are self-adjoint. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order and second-order in the radial and axial directions for the Onsager equation, and fourth-order and second-order in the axial and radial directions for the Carrier-Maslen equation) are determined. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations. The comparison reveals that the boundary conditions in the simulations and analysis have to be matched with care. The commonly used `diffuse reflection' boundary conditions at solid walls in DSMC simulations result in a non-zero slip velocity as well as a `temperature slip' (gas temperature at the wall is different from wall temperature). These have to be incorporated in the analysis in order to make quantitative predictions. In the case of mass/momentum/energy sources within the flow, it is necessary to ensure that the homogeneous boundary conditions are accurately satisfied in the simulations. When these precautions are taken, there is excellent agreement between analysis and simulations, to within 10 %, even when the stratification parameter is as low as 0.707, the Reynolds number is as low as 100 and the aspect ratio (length/diameter) of the cylinder is as low as 2, and the secondary flow velocity is as high as 0.2 times the maximum base flow velocity. The predictions of the generalized models are also significantly better than those of the original Onsager and Carrier-Maslen models, which are restricted to thin boundary layers in the limit of high stratification parameter.

A generalized network alignment for three-source three-destination multiple unicast networks with delays

The concept of interference alignment when extended to three-source three-destination instantaneous multiple unicast network for the case where, each source-destination pair has a min-cut of 1 and zero-interference conditions are not satisfied, is known to achieve a rate of half for every source-destination pair under certain conditions [6]. This was called network alignment. We generalize this concept of network alignment to three-source three-destination multiple unicast (3S-3D-MU) networks with delays, without making use of memory at the intermediate nodes (i.e., nodes other than the sources and destinations) and using time varying Local Encoding Kernels (LEKs). This achieves half the rate corresponding to the individual source-destination min-cut for some classes of 3S-3D-MU network with delays which do not satisfy the zero-interference conditions.

A Generalized Enthalpy Update Scheme for Solidification of a Binary Alloy with Solid Phase Movement

A generalized enthalpy update scheme is presented for evaluating solid and liquid fractions during the solidification of binary alloys, taking solid movement into consideration. A fixed-grid, enthalpy-based method is developed such that the scheme accounts for equilibrium as well as for nonequilibrium solidification phenomena, along with solid phase movement. The effect of solid movement on the solidification interface shape and macrosegregation is highlighted.

On Generalized Reed-Muller Expansions

The generalized Reed-Muller expansions of a switching function are generated using a single Boolean matrix and step-by-step shifting of the principal column.

Noncommutative vortices and instantons from generalized Bose operators

Generalized Bose operators correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the generalized Bose operator. When used in conjunction with the noncommutative ADHM construction, we find that these new instantons are in general not unitarily equivalent to the ones currently known in literature.

Magnetic Field Dependence of Entropy And Specific Heat of YBa2Cu3O7-delta Superconductors

The change in thermodynamic quantities (e. g., entropy, specific heat etc.) by the application of magnetic field in the case of the high-T-c superconductor YBCO system is examined phenomenological by the Ginzburg-Landau theory of anisotropic type-II superconductors. An expression for the change in the entropy (Delta S) and change in specific heat (Delta C) in a magnetic field for any general orientation of an applied magnetic field B-a with respect to the crystallographic c-axis is obtained. The observed large reduction of specific heat anomaly just below the superconducting transition and the observed variation of entropy with magnetic field are explained quantitatively.

Generalized method for assessment of compressibility of rockfill material

Examination of experimental data of the modelled rockfill materials using parallel gradation technique has revealed that the plots of logarithm of strain at failure against logarithm of confining pressure are linear. Also, a trend of increase in failure strain with increase in confining pressure and maximum size of the particle have been observed. The approach presented in this paper highlights the prediction of volume change properties of rockfill materials over a range of confining pressures and particle sizes based on the results of only two tests carried out at two different confining pressures for a maximum particle size of modelled material with the use of parallel gradation technique. Two test approach and its application in modelling of rockfill materials to estimate its volume change behaviour is illustrated by means of a selected experimental data available in the literature.

Generalized frequent episodes in Event Sequences

Discovering patterns in temporal data is an important task in Data Mining. A successful method for this was proposed by Mannila et al. [1] in 1997. In their framework, mining for temporal patterns in a database of sequences of events is done by discovering the so called frequent episodes. These episodes characterize interesting collections of events occurring relatively close to each other in some partial order. However, in this framework(and in many others for finding patterns in event sequences), the ordering of events in an event sequence is the only allowed temporal information. But there are many applications where the events are not instantaneous; they have time durations. Interesting episodesthat we want to discover may need to contain information regarding event durations etc. In this paper we extend Mannila et al.’s framework to tackle such issues. In our generalized formulation, episodes are defined so that much more temporal information about events can be incorporated into the structure of an episode. This significantly enhances the expressive capability of the rules that can be discovered in the frequent episode framework. We also present algorithms for discovering such generalized frequent episodes.

Transport in nanoporous zeolites: Relationships between sorbate size, entropy, and diffusivity

Molecular dynamics simulations have been performed on monatomic sorbates confined within zeolite NaY to obtain the dependence of entropy and self-diffusivity on the sorbate diameter. Previously, molecular dynamics simulations by Santikary and Yashonath J. Phys. Chem. 98, 6368 (1994)], theoretical analysis by Derouane J. Catal. 110, 58 (1988)] as well as experiments by Kemball Adv. Catal. 2, 233 (1950)] found that certain sorbates in certain adsorbents exhibit unusually high self-diffusivity. Experiments showed that the loss of entropy for certain sorbates in specific adsorbents was minimum. Kemball suggested that such sorbates will have high self-diffusivity in these adsorbents. Entropy of the adsorbed phase has been evaluated from the trajectory information by two alternative methods: two-phase and multiparticle expansion. The results show that anomalous maximum in entropy is also seen as a function of the sorbate diameter. Further, the experimental observation of Kemball that minimum loss of entropy is associated with maximum in self-diffusivity is found to be true for the system studied here. A suitably scaled dimensionless self-diffusivity shows an exponential dependence on the excess entropy of the adsorbed phase, analogous to excess entropy scaling rules seen in many bulk and confined fluids. The two trajectory-based estimators for the entropy show good semiquantitative agreement and provide some interesting microscopic insights into entropy changes associated with confinement.

On maximum entropy and minimum KL-divergence optimization by Grobner basis methods

In this paper we study constrained maximum entropy and minimum divergence optimization problems, in the cases where integer valued sufficient statistics exists, using tools from computational commutative algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. We give an implicit description of maximum entropy models by embedding them in algebraic varieties for which we give a Grobner basis method to compute it. In the cases of minimum KL-divergence models we show that implicitization preserves specialization of prior distribution. This result leads us to a Grobner basis method to embed minimum KL-divergence models in algebraic varieties. (C) 2012 Elsevier Inc. All rights reserved.