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## Analytic Expression (analytic + expression)
## Selected Abstracts## Equilibrium theory analysis of rectifying PSA for heavy component production AICHE JOURNAL, Issue 8 2002Armin D. EbnerAn isothermal equilibrium theory analysis, based on linear isotherms and a binary feed stream, was carried out to evaluate the feasibility of a rectifying PSA process for producing a pure heavy component at high recovery. Analytic expressions were derived to describe the performance of this process at the periodic state. The performance was also analyzed in terms of the different concentration and velocity profiles exhibited during various cycle steps that included the analysis of complex shock and simple wave interactions. Based on a parametric study, periodic behavior was established for a wide range of process conditions; and a design study with the PCB activated carbon,H2,CH4 system at 25°C further demonstrated the feasibility of a rectifying PSA cycle for producing a 100% CH4 stream from a dilute feed stream (y = 0.01) with a respectable recovery (80%), and reasonable process conditions. It also demonstrated the potential usefulness of an actual rectifying PSA process for bulk gas separation and purification. [source] ## Momentum and heat transfer over a continuously moving surface with a parallel free stream in a viscoelastic fluid NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2010T. HayatAbstract The flow and heat transfer characteristics for a continuous moving surface in a viscoelastic fluid are investigated. Constitutive equations of viscoelastic fluid obey the second-grade model. Analytic expressions to velocity and temperature have been developed by employing homotopy analysis method. The criterion to the convergence of the solution is properly discussed. Furthermore, the values of skin friction coefficient and the local Nusselt number have been computed and discussed. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 [source] ## RAPID EVOLUTIONARY ESCAPE BY LARGE POPULATIONS FROM LOCAL FITNESS PEAKS IS LIKELY IN NATURE EVOLUTION, Issue 6 2005Daniel M. WeinreichAbstract Fitness interactions between loci in the genome, or epistasis, can result in mutations that are individually deleterious but jointly beneficial. Such epistasis gives rise to multiple peaks on the genotypic fitness landscape. The problem of evolutionary escape from such local peaks has been a central problem of evolutionary genetics for at least 75 years. Much attention has focused on models of small populations, in which the sequential fixation of valley genotypes carrying individually deleterious mutations operates most quickly owing to genetic drift. However, valley genotypes can also be subject to mutation while transiently segregating, giving rise to copies of the high fitness escape genotype carrying the jointly beneficial mutations. In the absence of genetic recombination, these mutations may then fix simultaneously. The time for this process declines sharply with increasing population size, and it eventually comes to dominate evolutionary behavior. Here we develop an analytic expression for Ncrit, the critical population size that defines the boundary between these regimes, which shows that both are likely to operate in nature. Frequent recombination may disrupt high-fitness escape genotypes produced in populations larger than Ncrit before they reach fixation, defining a third regime whose rate again slows with increasing population size. We develop a novel expression for this critical recombination rate, which shows that in large populations the simultaneous fixation of mutations that are beneficial only jointly is unlikely to be disrupted by genetic recombination if their map distance is on the order of the size of single genes. Thus, counterintuitively, mass selection alone offers a biologically realistic resolution to the problem of evolutionary escape from local fitness peaks in natural populations. [source] ## Network dimensioning at the call level for the always-on network INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 9 2004Soracha NananukulAbstract It is becoming common for the network to provide always-on access services, where subscribers are guaranteed that their call requests will never be blocked. This paper studies the call-level link dimensioning for the always-on network with single-class traffic. The call-level QoS requirement is expressed in terms of the probability of a poor-quality call, which is the probability that a call experiences packet-level QoS violation at any time during its duration, as opposed to the probability of blocking in the network with call admission control (CAC). The system is modelled as the M/M/infinite system with finite population and an analytic expression for the probability of a poor-quality call is derived based on performability analysis. The effects of the call-level traffic characteristics on the required link resources are studied. It is also shown that the call-level link dimensioning for the always-on network needs more link resources than the network with CAC, and the call-level link dimensioning based on the analytic expression can be used to conservatively dimension the always-on network with arbitrarily distributed call holding time and inter-call time. The paper also studies the problem of estimating the call-level traffic characteristics when the knowledge of call boundaries is not available. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Asymmetric power distribution: Theory and applications to risk measurement JOURNAL OF APPLIED ECONOMETRICS, Issue 5 2007Ivana KomunjerTheoretical literature in finance has shown that the risk of financial time series can be well quantified by their expected shortfall, also known as the tail value-at-risk. In this paper, I construct a parametric estimator for the expected shortfall based on a flexible family of densities, called the asymmetric power distribution (APD). The APD family extends the generalized power distribution to cases where the data exhibits asymmetry. The first contribution of the paper is to provide a detailed description of the properties of an APD random variable, such as its quantiles and expected shortfall. The second contribution of the paper is to derive the asymptotic distribution of the APD maximum likelihood estimator (MLE) and construct a consistent estimator for its asymptotic covariance matrix. The latter is based on the APD score whose analytic expression is also provided. A small Monte Carlo experiment examines the small sample properties of the MLE and the empirical coverage of its confidence intervals. An empirical application to four daily financial market series reveals that returns tend to be asymmetric, with innovations which cannot be modeled by either Laplace (double-exponential) or Gaussian distribution, even if we allow the latter to be asymmetric. In an out-of-sample exercise, I compare the performances of the expected shortfall forecasts based on the APD-GARCH, Skew- t -GARCH and GPD-EGARCH models. While the GPD-EGARCH 1% expected shortfall forecasts seem to outperform the competitors, all three models perform equally well at forecasting the 5% and 10% expected shortfall. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Analytic determination of workspace and singularities in a parallel pointing system JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 1 2002Raffaele Di GregorioThis paper studies a parallel pointing system, named U-2PUS, used in biomechanic and aerospace applications. In the literature, U-2PUS position analysis has already been solved in closed form, whereas simple and efficient tools to address workspace determination and singularity locations are still lacking. In this paper, the analytic expression of the U-2PUS workspace is derived, and a bidimensional representation of the workspace is proposed. The U-2PUS mobility analysis is addressed, and a singularity locus analytic expression, explicitly containing the manipulator geometric parameters and the end-effector orientation parameters, is derived. Moreover, it is shown that the U-2PUS singularity locus can be represented by curves (singularity curves) on a Cartesian plane having the U-2PUS generalized coordinates on the coordinate axes. Finally, the presented singularity conditions are geometrically interpreted. © 2002 John Wiley & Sons, Inc. [source] ## Forecasting with k -factor Gegenbauer Processes: Theory and Applications JOURNAL OF FORECASTING, Issue 8 2001L. FerraraAbstract This paper deals with the k -factor extension of the long memory Gegenbauer process proposed by Gray et al. (1989). We give the analytic expression of the prediction function derived from this long memory process and provide the h -step-ahead prediction error when parameters are either known or estimated. We investigate the predictive ability of the k -factor Gegenbauer model on real data of urban transport traffic in the Paris area, in comparison with other short- and long-memory models. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## PID control performance assessment: The single-loop case AICHE JOURNAL, Issue 6 2004Byung-Su KoAbstract An iterative solution is developed for the calculation of the best achievable (minimum variance) PID control performance and the corresponding optimal PID setting in an existing control loop. An analytic expression is derived for the closed-loop output as an explicit function of PID setting. The resulting benchmark allows for realistic performance assessment of an existing PID control loop, especially when the control loop fails to meet the minimum variance performance. A PID performance index is then defined based on the PID performance bound, and its confidence interval is estimated. A series of simulated examples are used to demonstrate the utility of the proposed method. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1211,1218, 2004 [source] ## Spontaneous bremsstrahlung effect in the nonrelativistic electron scattering by a nucleus in the field of pulsed light wave LASER PHYSICS LETTERS, Issue 6 2009A.A. Lebed'Abstract The theory of nonresonant spontaneous bremsstrahlung by a nonrelativistic electron scattered by a nucleus in the field of a pulsed light wave is developed. The electron interaction with a Coulomb potential of a nucleus is considered in the first order of perturbation theory (the Born approximation), and the interaction with an external pulsed field is taken into account accurately. The approximation is examined when the pulsewidth is considerably greater than the characteristic time of wave oscillations. For the range of moderately strong fields the analytic expression for the nonresonant differential cross-section was obtained, which has the form of a sum over partial differential crosssections. It is shown, that in the case of nonrelativistic electron energy the partial cross-section is not factorable on the crosssection of electron-nucleus spontaneous bremsstrahlung in the absence of the external field and the emission-absorption probability of a certain number of wave photons. It is concluded, that the total cross-section of spontaneous bremsstrahlung of an electron scattered by a nucleus in the field of pulsed light wave summing over all possible partial processes differs essentially from the cross-section of electron-nucleus spontaneous bremsstrahlung in the absence of the external field. (© 2009 by Astro Ltd., Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA) [source] ## A Mathematical Model for Photopolymerization From a Stationary Laser Light Source MACROMOLECULAR THEORY AND SIMULATIONS, Issue 1 2005Michael F. PerryAbstract Summary: A mathematical model of photopolymerization is presented for a stationary laser. Termination by radical combination and radical trapping is considered. Using simplifying assumptions, we derive analytical equations for the concentration of photoinitiator and monomer in the system. With these equations, we show that the light intensity and the initial amount of photoinitiator highly influence the polymerization process and determine the shape of the polymer that is formed. We also provide an analytic expression to determine the amount of polymer formed during dark reactions. Percent conversion of monomer as a function of time at z,=,0 and r,=,0 (Data from Table 1). [source] ## , -model and cooling flows in X-ray clusters of galaxies MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2000Stefano EttoriThe spatial emission from the core of cooling-flow clusters of galaxies is inadequately described by a , -model. Spectrally, the central region of these clusters is well approximated with a two-temperature model, where the inner temperature represents the multiphase status of the core and the outer temperature is a measure of the ambient gas temperature. Following this observational evidence, I extend the use of the , -model to a two-phase gas emission, where the two components coexist within a boundary radius rcool and the ambient gas alone fills the volume shell at a radius above rcool. This simple model still provides an analytic expression for the total surface brightness profile (Note in the first term the different sign with respect to the standard , -model.) Based upon a physically meaningful model for the X-ray emission, this formula can be used (i) to improve significantly the modelling of the surface brightness profile of cooling flow clusters of galaxies when compared to the standard , -model results, (ii) to constrain properly the physical characteristics of the intracluster plasma in the outskirts, like, e.g., the ambient gas temperature. [source] ## Mean,variance efficiency with extended CIR interest rates APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 1 2010René FerlandAbstract We study a mean,variance investment problem in a continuous-time framework where the interest rates follow Cox,Ingersoll,Ross dynamics. We construct a mean,variance efficient portfolio through the solutions of backward stochastic differential equations. We also give sufficient conditions under which an explicit analytic expression is available for the mean,variance optimal wealth of the investor. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Explicit expressions for 3D boundary integrals in potential theory, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2009S. Nintcheu FataAbstract On employing isoparametric, piecewise linear shape functions over a flat triangular domain, exact expressions are derived for all surface potentials involved in the numerical solution of three-dimensional singular and hyper-singular boundary integral equations of potential theory. These formulae, which are valid for an arbitrary source point in space, are represented as analytic expressions over the edges of the integration triangle. They can be used to solve integral equations defined on polygonal boundaries via the collocation method or may be utilized as analytic expressions for the inner integrals in the Galerkin technique. In addition, the constant element approximation can be directly obtained with no extra effort. Sample problems solved by the collocation boundary element method for the Laplace equation are included to validate the proposed formulae. Published in 2008 by John Wiley & Sons, Ltd. [source] ## Extrapolation methods for improving convergence of spherical Bessel integrals for the two-center Coulomb integrals INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 11 2006Hassan SafouhiAbstract Multi-center two-electron Coulomb integrals over Slater-type functions are required for any accurate molecular electronic structure calculations. These integrals, which are numerous, are to be evaluated rapidly and accurately. Slater-type functions are expressed in terms of the so-called B functions, which are best suited to apply the Fourier transform method. The Fourier transform method allowed analytic expressions for these integrals to be developed. Unfortunately, the analytic expressions obtained turned out to be extremely difficult to evaluate accurately due to the presence of highly oscillatory spherical Bessel integrals. In this work, we used techniques based on nonlinear transformation and extrapolation methods for improving convergence of these oscillatory spherical Bessel integrals. These techniques, which led to highly efficient and rapid algorithms for the numerical evaluation of three- and four-center two-electron Coulomb and exchange integrals, are now shown to be applicable to the two-center two-electron Coulomb integrals. The numerical results obtained for the molecular integrals under consideration illustrate the efficiency of the algorithm described in the present work compared with algorithms using the epsilon (,) algorithm of Wynn and Levin's u transform. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] ## Spin Echo Analysis of Restricted Diffusion under Generalized Gradient Waveforms for Spherical Pores with Relaxivity and Interconnections ISRAEL JOURNAL OF CHEMISTRY, Issue 1-2 2003Brett N. RylandThe problem of restricted diffusion in spherical pores is examined under conditions of finite gradient pulse width in pulsed gradient spin echo (PGSE)-NMR experiments. Closed form analytic expressions are derived, and the case of interconnected pores is briefly examined. An expression, based on the pore hopping approximation, is presented that predicts the echo attenuation for diffusion between pores under any gradient waveform. [source] ## The small-angle scattering structure functions of the single tetrahedron JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3-1 2003W. GilleBasic properties of the SAS correlation function , (r) and related functions are represented for a tetrahedron of edge length a. An interval splitting into four basic r -intervals in a sequence of cases for averaging the intersection volume between two tetrahedrons has been performed. Remarkably simple analytic expressions result in the first r -interval. Indeed, ,(r) is a polynomial of degree three. The coefficients are given explicitly. The asymptotic expansion I(h) is compared with the exact scattering intensity I(h). [source] ## Factorized approach to nonlinear MPC using a radial basis function model AICHE JOURNAL, Issue 2 2001Sharad BhartiyaA new computationally efficient approach for nonlinear model predictive control (NMPC) presented here uses the factorability of radial basis function (RBF) process models in a traditional model predictive control (MPC) framework. The key to the approach is to formulate the RBF process model that can make nonlinear predictions across a p-step horizon without using future unknown process measurements. The RBF model avoids error propagation from use of model predictions us input in a recursive or iterative manner. The resulting NMPC formulation using the RBF model provides analytic expressions for the gradient and Hessian of the controller's objective function in terms of RBF network parameters. Solution of the NMPC optimization problem is simplifed significantly by factorization of the RBF model output into terms containing only known and unknown parts of the process. [source] ## On the use of non-local prior densities in Bayesian hypothesis tests JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2010Valen E. JohnsonSummary., We examine philosophical problems and sampling deficiencies that are associated with current Bayesian hypothesis testing methodology, paying particular attention to objective Bayes methodology. Because the prior densities that are used to define alternative hypotheses in many Bayesian tests assign non-negligible probability to regions of the parameter space that are consistent with null hypotheses, resulting tests provide exponential accumulation of evidence in favour of true alternative hypotheses, but only sublinear accumulation of evidence in favour of true null hypotheses. Thus, it is often impossible for such tests to provide strong evidence in favour of a true null hypothesis, even when moderately large sample sizes have been obtained. We review asymptotic convergence rates of Bayes factors in testing precise null hypotheses and propose two new classes of prior densities that ameliorate the imbalance in convergence rates that is inherited by most Bayesian tests. Using members of these classes, we obtain analytic expressions for Bayes factors in linear models and derive approximations to Bayes factors in large sample settings. [source] ## Testing the modified Press,Schechter model against N -body simulations MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2001Andreu RaigA modified version of the extended Press,Schechter model for the growth of dark-matter haloes was introduced in two previous papers, with the aim of explaining the mass,density relation shown by haloes in high-resolution cosmological simulations. In this model, major mergers are well separated from accretion, thereby allowing a natural definition of halo formation and destruction. This makes it possible to derive analytic expressions for halo formation and destruction rates, the mass accretion rate and the probability distribution functions of halo formation times and progenitor masses. The stochastic merger histories of haloes can be readily derived and easily incorporated into semi-analytical models of galaxy formation, thus avoiding the usual problems encountered in the construction of Monte Carlo merger trees from the original extended Press,Schechter formalism. Here we show that the predictions of the modified Press,Schechter model are in good agreement with the results of N -body simulations for several scale-free cosmologies. [source] ## Analysis of algebraic systems arising from fourth-order compact discretizations of convection-diffusion equations NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2002Ashvin GopaulAbstract We study the properties of coefficient matrices arising from high-order compact discretizations of convection-diffusion problems. Asymptotic convergence factors of the convex hull of the spectrum and the field of values of the coefficient matrix for a one-dimensional problem are derived, and the convergence factor of the convex hull of the spectrum is shown to be inadequate for predicting the convergence rate of GMRES. For a two-dimensional constant-coefficient problem, we derive the eigenvalues of the nine-point matrix, and we show that the matrix is positive definite for all values of the cell-Reynolds number. Using a recent technique for deriving analytic expressions for discrete solutions produced by the fourth-order scheme, we show by analyzing the terms in the discrete solutions that they are oscillation-free for all values of the cell Reynolds number. Our theoretical results support observations made through numerical experiments by other researchers on the non-oscillatory nature of the discrete solution produced by fourth-order compact approximations to the convection-diffusion equation. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 155,178, 2002; DOI 10.1002/num.1041 [source] |