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Exact Results (exact + result)
Selected AbstractsLEVERAGE ADJUSTMENTS FOR DISPERSION MODELLING IN GENERALIZED NONLINEAR MODELSAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 4 2009Gordon K. Smyth Summary For normal linear models, it is generally accepted that residual maximum likelihood estimation is appropriate when covariance components require estimation. This paper considers generalized linear models in which both the mean and the dispersion are allowed to depend on unknown parameters and on covariates. For these models there is no closed form equivalent to residual maximum likelihood except in very special cases. Using a modified profile likelihood for the dispersion parameters, an adjusted score vector and adjusted information matrix are found under an asymptotic development that holds as the leverages in the mean model become small. Subsequently, the expectation of the fitted deviances is obtained directly to show that the adjusted score vector is unbiased at least to,O(1/n). Exact results are obtained in the single-sample case. The results reduce to residual maximum likelihood estimation in the normal linear case. [source] Thermal photon dispersion law and modified black-body spectraANNALEN DER PHYSIK, Issue 4 2009J. Ludescher Abstract Based on the postulate that photon propagation is governed by an SU(2) gauge principle we numerically compute the one-loop dispersion for thermalized photon propagation on the radiatively induced mass shell. Formerly, the dispersion was addressed by assuming p2 = 0. While this approximation turns out to be excellent for temperatures , 2 TCMB the exact result exhibits a much faster (power-like) shrinking of the gap in the black-body spectral intensity with rising temperature. Our previous statements on anomalous large-angle CMB temperature-temperature correlations, obtained in the approximation p2 = 0, remain valid. [source] Exact results in a non-supersymmetric gauge theoryFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 6-7 2004A. Armoni We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gauge theory with a Dirac fermion in the anti-symmetric tensor representation. We argue that, at large N and in a large part of its bosonic sector, this theory is non-perturbatively equivalent to ,, = 1 SYM, so that exact results established in the latter (parent) theory also hold in the daughter orientifold theory. In particular, the non-supersymmetric theory has an exactly calculable bifermion condensate, exactly degenerate parity doublets, and a vanishing cosmological constant (all this to leading order in 1 / N). [source] On the absence of large-order divergences in superstring theoryFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 1 2003S. Davis The genus-dependence of multi-loop superstring amplitudes is estimated at large orders in perturbation theory using the super-Schottky group parameterization of supermoduli space. Restriction of the integration region to a subset of supermoduli space and a single fundamental domain of the super-modular group suggests an exponential dependence on the genus. Upper bounds for these estimates are obtained for arbitrary N-point superstring scattering amplitudes and are shown to be consistent with exact results obtained for special type II string amplitudes for orbifold or Calabi-Yau compactifications. The genus-dependence is then obtained by considering the effect of the remaining contribution to the superstring amplitudes after the coefficients of the formally divergent parts of the integrals vanish as a result of a sum over spin structures. The introduction of supersymmetry therefore leads to the elimination of large-order divergences in string perturbation theory, a result which is based only on the supersymmetric generalization of the Polyakov measure and not the gauge group of the string model. [source] Application of a new differential quadrature methodology for free vibration analysis of platesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2003G. Karami Abstract A new methodology is introduced in the differential quadrature (DQ) analysis of plate problems. The proposed approach is distinct from other DQ methods by employing the multiple boundary conditions in a different manner. For structural and plate problems, the methodology employs the displacement within the domain as the only degree of freedom, whereas along the boundaries the displacements as well as the second derivatives of the displacements with respect to the co-ordinate variable normal to the boundary in the computational domain are considered as the degrees of freedom for the problem. Employing such a procedure would facilitate the boundary conditions to be implemented exactly and conveniently. In order to demonstrate the capability of the new methodology, all cases of free vibration analysis of rectangular isotropic plates, in which the conventional DQ methods have had some sort of difficulty to arrive at a converged or accurate solution, are carried out. Excellent convergence behaviour and accuracy in comparison with exact results and/or results obtained by other approximate methods were obtained. The analogous DQ formulation for a general rectangular plate is derived and for each individual boundary condition the general format for imposing the given conditions is devised. It must be emphasized that the computational efforts of this new methodology are not more than for the conventional differential quadrature methods. Copyright © 2002 John Wiley & Sons, Ltd. [source] Free vibrations of shear-flexible and compressible arches by FEMINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2001Przemyslaw Litewka Abstract The purpose of this paper is to analyse free vibrations of arches with influence of shear and axial forces taken into account. Arches with various depth of cross-section and various types of supports are considered. In the calculations, the curved finite element elaborated by the authors is adopted. It is the plane two-node, six-degree-of-freedom arch element with constant curvature. Its application to the static analysis yields the exact results, coinciding with the analytical ones. This feature results from the use of the exact shape functions in derivation of the element stiffness matrix. In the free vibration analysis the consistent mass matrix is used. It is obtained on the base of the same functions. Their coefficients contain the influences of shear flexibility and compressibility of the arch. The numerical results are compared with the results obtained for the simple diagonal mass matrix representing the lumped mass model. The natural frequencies are also compared with the ones for the continuous arches for which the analytically determined frequencies are known. The advantage of the paper is a thorough analysis of selected examples, where the influences of shear forces, axial forces as well as the rotary and tangential inertia on the natural frequencies are examined. Copyright © 2001 John Wiley & Sons, Ltd. [source] Linear discriminant analysis in network traffic modellingINTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 1 2006Bing-Yi Zhang Abstract It is difficult to give an accurate judgement of whether the traffic model fit the actual traffic. The traditional method is to compare the Hurst parameter, data histogram and autocorrelation function. The method of comparing Hurst parameter cannot give exact results and judgement. The method of comparing data histogram and autocorrelation only gives a qualitative judgement. Based on linear discriminant analysis we proposed a novel arithmetic. Utilizing this arithmetic we analysed some sets of data with large and little differences. We also analysed some sets of data generated by network simulator. The analysis result is accurate. Comparing with traditional method, this arithmetic is useful and can conveniently give an accurate judgement for complex network traffic trace. Copyright © 2005 John Wiley & Sons, Ltd. [source] Simple methods for convection in porous media: scale analysis and the intersection of asymptotesINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 10 2003Adrian Bejan Abstract This article outlines the basic rules and promise of two of the simplest methods for solving problems of convection in porous media. First, scale analysis is the method that produces order-of-magnitude results and trends (scaling laws) for concrete and applicable results such as heat transfer rates, flow rates, and time intervals. Scale analysis also reveals the correct dimensionless form in which to present more exact results produced by more complicated methods. Second, the intersection of asymptotes method identifies the correct flow configuration (e.g. Bénard convection in a porous medium) by intersecting the two extremes in which the flow may exist: the many cells limit, and the few plumes limit. Every important feature of the flow and its transport characteristics is found at the intersection, i.e. at the point where the two extremes compete and find themselves in balance. The intersection is also the flow configuration that minimizes the global resistance to heat transfer through the system. This is an example of the constructal principle of deducing flow patterns by optimizing the flow geometry for minimal global resistance. The article stresses the importance of trying the simplest method first, and the researcher's freedom to choose the appropriate problem solving method. Copyright © 2003 John Wiley & Sons, Ltd. [source] Distributed Gaussian discrete variable representationINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2005Hasan Karabulut Abstract A discrete variable representation (DVR) made from distributed Gaussians gn(x) = e, (n = ,,, ,, ,) and its infinite grid limit is described. The infinite grid limit of the distributed Gaussian DVR (DGDVR) reduces to the sinc function DVR of Colbert and Miller in the limit c , 0. The numerical performance of both finite and infinite grid DGDVRs and the sinc function DVR is compared. If a small number of quadrature points are taken, the finite grid DGDVR performs much better than both infinite grid DGDVR and sinc function DVR. The infinite grid DVRs lose accuracy due to the truncation error. In contrast, the sinc function DVR is found to be superior to both finite and infinite grid DGDVRs if enough grid points are taken to eliminate the truncation error. In particular, the accuracy of DGDVRs does not get better than some limit when the distance between Gaussians d goes to zero with fixed c, whereas the accuracy of the sinc function DVR improves very quickly as d becomes smaller, and the results are exact in the limit d , 0. An analysis of the performance of distributed basis functions to represent a given function is presented in a recent publication. With this analysis, we explain why the sinc function DVR performs better than the infinite grid DGDVR. The analysis also traces the inability of Gaussians to yield exact results in the limit d , 0 to the incompleteness of this basis in this limit. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] In situ diffraction strain analysis of elastically deformed polycrystalline thin films, and micromechanical interpretationJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2009D. Faurie In situ tensile tests have been carried out under synchrotron radiation on supported gold (Au) thin films exhibiting a pronounced crystallographic texture. The 2, shift of X-ray diffraction lines has been recorded for different specimen orientations and several loading levels in the elastic domain. The data obtained demonstrate the large strain heterogeneities generated within the specimen because of the intergranular interactions associated with the large elastic anisotropy of Au grains. To interpret these results, the use of a multi-scale micromechanical approach is unavoidable. The theoretical background of such methods is described, and the points where exact results can be obtained and where approximations have to be introduced are highlighted. It is shown that the Vook,Witt model, for which a general formulation is provided, is the exact solution for polycrystals exhibiting a laminate microstructure, which is a significant departure from the standard thin-film microstructures. Among several standard models used in the field, the self-consistent model is the only one that reproduces the experimental data correctly. This is achieved by accounting for the actual crystallographic texture of the specimen, and assuming pancake-shaped two-point statistics for the morphological texture. A discussion of the limitations of this approach, originally developed for bulk materials, is given for the specific case of thin films. [source] Enveloping triangulation method for detecting internal cavities in proteins and algorithm for computing their surface areas and volumesJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 3 2009Ján Bu Abstract Detection and quantitative characterization of the internal cavities in proteins remain an important topic in studying protein structure and function. Here we propose a new analytical method for detecting the existence of cavities in proteins. The method is based on constructing the special enveloping triangulation enclosing the cavities. Based on this method, we develop an algorithm and a fortran package, CAVE, for computing volumes and surface areas of cavities in proteins. We first test our method and algorithm in some artificial systems of spheres and find that the calculated results are consistent with exact results. Then we apply the package to compute volumes and surface areas of cavities for some protein structures in the Protein Data Bank. We compare our calculated results with those obtained by some other methods and find that our approach is reliable. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009 [source] Profit Maximizing Warranty Period with Sales Expressed by a Demand FunctionQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 3 2007Shaul P. Ladany Abstract The problem of determining the optimal warranty period, assumed to coincide with the manufacturer's lower specification limit for the lifetime of the product, is addressed. It is assumed that the quantity sold depends via a Cobb,Douglas-type demand function on the sale price and on the warranty period, and that both the cost incurred for a non-conforming item and the sale price increase with the warranty period. A general solution is derived using Response Modeling Methodology (RMM) and a new approximation for the standard normal cumulative distribution function. The general solution is compared with the exact optimal solutions derived under various distributional scenarios. Relative to the exact optimal solutions, RMM-based solutions are accurate to at least the first three significant digits. Some exact results are derived for the uniform and the exponential distributions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Neuartige vernagelte Lamellen-StützwandBAUTECHNIK, Issue 8 2004Hermann Lohmiller Dr.-Ing. Aus der Reihe von verschiedenen bepflanzbaren, dauerhaften Sicherungen von Geländeeinschnitten wird eine neuartige Lamellen-Stützwand beschrieben. Sie zeichnet sich dadurch aus, daß sie aus horizontalen, im Erdreich verankerten Stahlbetongurten besteht, in deren Schutz die endgültige Aushubsohle erreicht wird, und daran später von unten nach oben fortschreitend, befestigten Fertigteil-Lamellen. Die Verankerungen bestehen vorzugsweise aus schlaffen Nägeln Es können aber auch Spannanker verwendet werden. Die Vorzüge dieser Bauweise werden hervorgehoben. Ein ausgeführtes Beispiel wird mit mehreren Fotos dargestellt und beschrieben. Anschließend wird auf die Besonderheiten eines vom Verfasser entwickelten Computer-Programms hingewiesen, mit dem nicht nur die beschriebene Konstruktion, sondern auch alle anderen vernagelten Stützwände, insbesondere die mit Spritzbeton verkleideten, berechnet werden können. Dabei werden neue Wege beschritten, die zu schnelleren und genaueren Ergebnissen führen. New nailed lamellar retaining wall. A new nailed lamellar retaining wall will be described, which belong in the category of various permanent safeguards designed to prevent the earth behind the sides of an excavation cut from moving, and into which plants can be fitted. They are characterized by horizontal walers made out of reinforced concrete, which are anchored in the earth and support the sides of an excavation so that its final bottom can be reached, and by prefabricated lamellas attached to these walers at some later date starting at the bottom and going up to the top. Preferred means of anchoring are non-prestressed nails. However, prestressed anchors can also be used. Advantages of this construction are highlighted. An example of the mentioned walls that has been put into practice is given and described through various photographs. The particularities of a computer program developed by the author are then briefly presented, which enables not only the described construction but also all other nailed retaining walls to be calculated, notably those walls coated with shotcrete. New approaches are explored here which bring about quicker and more exact results. [source] | ||||||||||||||||