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Finite Value (finite + value)
Selected AbstractsAn infinite family of generalized Kalnajs discsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2006Guillermo A. González ABSTRACT An infinite family of axially symmetric thin discs of finite radius is presented. The family of discs is obtained by means of a method developed by Hunter and contains, as its first member, the Kalnajs disc. The surface densities of the discs present a maximum at the centre of the disc and then decrease smoothly to zero at the edge, in such a way that the mass distribution of the higher members of the family is more concentrated at the centre. The first member of the family has a circular velocity proportional to the radius, thus representing a uniformly rotating disc. On the other hand, the circular velocities of the other members of the family increase from a value of zero at the centre of the discs to a maximum and then decrease smoothly to a finite value at the edge of the discs, in such a way that, for the higher members of the family, the maximum value of the circular velocity is attained nearest the centre of the discs. [source] Analysis of parameterized quadratic eigenvalue problems in computational acoustics with homotopic deviation theoryNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 6 2006F. Chaitin-Chatelin Abstract This paper analyzes a family of parameterized quadratic eigenvalue problems from acoustics in the framework of homotopic deviation theory. Our specific application is the acoustic wave equation (in 1D and 2D) where the boundary conditions are partly pressure release (homogeneous Dirichlet) and partly impedance, with a complex impedance parameter ,. The admittance t = 1/, is the classical homotopy parameter. In particular, we study the spectrum when t , ,. We show that in the limit part of the eigenvalues remain bounded and converge to the so-called kernel points. We also show that there exist the so-called critical points that correspond to frequencies for which no finite value of the admittance can cause a resonance. Finally, the physical interpretation that the impedance condition is transformed into a pressure release condition when |t| , , enables us to give the kernel points in closed form as eigenvalues of the discrete Dirichlet problem. Copyright © 2006 John Wiley & Sons, Ltd. [source] Mean electromotive force proportional to mean flow in MILD turbulenceASTRONOMISCHE NACHRICHTEN, Issue 1 2010K.-H. Rädler Abstract In mean-field magnetohydrodynamics the mean electromotive force due to velocity and magnetic-field fluctuations plays a crucial role. In general it consists of two parts, one independent of and another one proportional to the mean magnetic field. The first part may be nonzero only in the presence of mhd turbulence, maintained, e.g., by small-scale dynamo action. It corresponds to a battery, which lets a mean magnetic field grow from zero to a finite value. The second part, which covers, e.g., the , effect, is important for large-scale dynamos. Only a few examples of the aforementioned first part of the mean electromotive force have been discussed so far. It is shown that a mean electromotive force proportional to the mean fluid velocity, but independent of the mean magnetic field, may occur in an originally homogeneous isotropic mhd turbulence if there are nonzero correlations of velocity and electric current fluctuations or, what is equivalent, of vorticity and magnetic field fluctuations. This goes beyond the Yoshizawa effect, which consists in the occurrence of mean electromotive forces proportional to the mean vorticity or to the angular velocity defining the Coriolis force in a rotating frame and depends on the cross-helicity defined by the velocity and magnetic field fluctuations. Contributions to the mean electromotive force due to inhomogeneity of the turbulence are also considered. Possible consequences of the above findings for the generation of magnetic fields in cosmic bodies are discussed (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A Solution to the Problem of Monotone Likelihood in Cox RegressionBIOMETRICS, Issue 1 2001Georg Heinze Summary. The phenomenon of monotone likelihood is observed in the fitting process of a Cox model if the likelihood converges to a finite value while at least one parameter estimate diverges to ±,. Monotone likelihood primarily occurs in small samples with substantial censoring of survival times and several highly predictive covariates. Previous options to deal with monotone likelihood have been unsatisfactory. The solution we suggest is an adaptation of a procedure by Firth (1993, Biometrika80, 27,38) originally developed to reduce the bias of maximum likelihood estimates. This procedure produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald-type tests and confidence intervals are available, but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. An empirical study of the suggested procedures confirms satisfactory performance of both estimation and inference. The advantage of the procedure over previous options of analysis is finally exemplified in the analysis of a breast cancer study. [source] Semi-analytical elastostatic analysis of unbounded two-dimensional domainsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2002Andrew J. Deeks Abstract Unbounded plane stress and plane strain domains subjected to static loading undergo infinite displacements, even when the zero displacement boundary condition at infinity is enforced. However, the stress and strain fields are well behaved, and are of practical interest. This causes significant difficulty when analysis is attempted using displacement-based numerical methods, such as the finite-element method. To circumvent this difficulty problems of this nature are often changed subtly before analysis to limit the displacements to finite values. Such a process is unsatisfactory, as it distorts the solution in some way, and may lead to a stiffness matrix that is nearly singular. In this paper, the semi-analytical scaled boundary finite-element method is extended to permit the analysis of such problems without requiring any modification of the problem itself. This is possible because the governing differential equations are solved analytically in the radial direction. The displacement solutions so obtained include an infinite component, but relative motion between any two points in the unbounded domain can be computed accurately. No small arbitrary constants are introduced, no arbitrary truncation of the domain is performed, and no ill-conditioned matrices are inverted. Copyright © 2002 John Wiley & Sons, Ltd. [source] Design for model parameter uncertainty using nonlinear confidence regionsAICHE JOURNAL, Issue 8 2001William C. Rooney An accurate method presented accounts for uncertain model parameters in nonlinear process optimization problems. The model representation is considered in terms of algebraic equations. Uncertain quantity parameters are often discretized into a number of finite values that are then used in multiperiod optimization problems. These discrete values usually range between some lower and upper bound that can be derived from individual confidence intervals. Frequently, more than one uncertain parameter is estimated at a time from a single set of experiments. Thus, using simple lower and upper bounds to describe these parameters may not be accurate, since it assumes the parameters are uncorrelated. In 1999 Rooney and Biegler showed the importance of including parameter correlation in design problems by using elliptical joint confidence regions to describe the correlation among the uncertain model parameters. In chemical engineering systems, however, the parameter estimation problem is often highly nonlinear, and the elliptical confidence regions derived from these problems may not be accurate enough to capture the actual model parameter uncertainty. In this work, the description of model parameter uncertainty is improved by using confidence regions derived from the likelihood ratio test. It captures the nonlinearities efficiently and accurately in the parameter estimation problem. Several examples solved show the importance of accurately capturing the actual model parameter uncertainty at the design stage. [source] Mixed singlet-triplet superconducting state in doped antiferromagnetsPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 2 2006A. Maci¸ag Abstract We analyze symmetry mixing in the superconducting (SC) order parameter of planar cuprates. The behavior of thermal conductivity observed in some systems doped with magnetic impurities or in some systems exposed to external magnetic field seems to indicate that such symmetry mixing takes place. We discuss this phenomenon in the framework of the spin polaron model (SPM). We assume that antiferromagnetic (AF) correlations, which are at least of short range, tend to confine motion of holes which have been created in the AF spin background. The nature of the propagation of quasiparticles which are hole-like and the nature of the interaction between quasiparticles is determined by a tendency to restore the local AF order. It is known that two holes in the t ,J model (tJ M) form bound states with dx 2,y2 or p-wave symmetry. The d-wave bound state has lower energy and is the ground state. The mixing of d-wave symmetry with p-wave symmetry takes place in the SC order parameter at some range of finite values of the doping parameter. That range lies at the applicability verge of the SPM, where AF correlation are already very short. On the other hand, these correlations may be strengthened by above mentioned external factors, which seems to explain why symmetry mixing is observed in this case. (© 2006 WILEY-VCH Verlag GmbH & Co. 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