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General Expression (general + expression)
Selected AbstractsTheoretical investigation of elastic flexural properties for multistranded orthodontic archwiresJOURNAL OF BIOMEDICAL MATERIALS RESEARCH, Issue 3 2002Brian K. Rucker Abstract The bending and torsional stresses during flexure were detailed and simplified for a single twisted strand, which emulates a spring. General expressions were derived to evaluate the elastic properties (i.e., strength, stiffness, and range) of multistranded wires by combining the effects of a number of outer twisted strands, with or without an inner strand. Specific expressions were solved for single-stranded, twisted, and coaxial wires. Initially, we considered the following multistranded wire configurations: two- (twin), three- (triple), four-strand (quad) twisted, and coaxial wires. The elastic properties of the twin and quad wires were essentially subsets of the triple wire. For a given overall wire diameter (D) and helix angle (,), the ranges of multistranded wires were independent of wire configurations. By varying the , from 45 to 85°, the D from 0.394 to 0.546 mm (15.5 to 21.5 mil), and the stress at the proportional limit from 1.03 to 3.28 GPa (150 to 475 ksi), the theoretical elastic properties of triple and coaxial stainless steel wires matched many of the properties of conventional nickel titanium leveling wires. © 2002 Wiley Periodicals, Inc. J Biomed Mater Res 62: 338,349, 2002 [source] Symmetry rules and strain/order-parameter relationships for coupling between octahedral tilting and cooperative Jahn,Teller transitions in ABX3 perovskites.ACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2009The structural evolution of selected perovskites containing Jahn,Teller cations has been investigated in the light of a formal analysis of symmetry hierarchies for phase transitions driven by octahedral tilting and Jahn,Teller cooperative distortions. General expressions derived from the strain/order-parameter coupling relationships allowed by symmetry are combined with observed changes in lattice parameters to reveal details of order-parameter evolution and coupling. LuVO3, YbVO3, YVO3 and CeVO3 are representative of systems which develop Jahn,Teller ordering schemes associated with irreducible representations and of the space group . Tilting of their octahedra is associated with and . The Pnma ( tilting) ,P21/a ( tilting, Jahn,Teller order) transition below room temperature is close to second order in character. Shear strains which depend primarily on tilt angles show little variation, implying that there is only weak coupling between the tilting and Jahn,Teller order parameters. The subsequent P21/a,Pnma ( tilting, Jahn,Teller order) is first order in character, and involves either a reduction in the tilt angle or a change in the strength of tilt/Jahn,Teller order-parameter coupling. In LaMnO3, the isosymmetric Pnma ( tilting) ,Pnma ( tilting, Jahn,Teller order) transition can be described in terms of a classical first-order transition conforming to a 246 Landau expansion with negative fourth-order coefficients. Strain evolution in Ba-doped samples suggests that the transition becomes second order in character and reveals a new strain relaxation mechanism in LaMnO3 which might be understood in terms of local strain heterogeneities due to the disordering of distorted MnO6 octahedra. Transitions in PrAlO3 and La0.5Ba0.5CoO3 illustrate the transformation behaviour of systems in which the Jahn,Teller ordering scheme is associated with the irreducible representation . Overall, coupled tilting + Jahn,Teller phase transitions in perovskites conform to mean-field behaviour, consistent with the underlying role of strain in promoting long interaction lengths. [source] The graviton propagator with a non-conserved external generating sourceFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 11-12 2007E.B. Manoukian Abstract A novel general expression is obtained for the graviton propagator from Lagrangian field theory by taking into account the necessary fact that in the functional differential approach of quantum field theory, in order to generate non-linearities in gravitation and interactions with matter, the external source T,,, coupled to the gravitational field, should a priori not be conserved ,,T,,, 0, so variations with respect to its ten components may be varied independently. The resulting propagator is the one which arises in the functional approach and does not coincide with the corresponding time-ordered product of two fields and it includes so-called Schwinger terms. The quantization is carried out in a gauge corresponding to physical states with two polarization states to ensure positivity in quantum applications. [source] Optimal filtering for incompletely measured polynomial states over linear observationsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 5 2008Michael Basin Abstract In this paper, the optimal filtering problem for polynomial system states over linear observations with an arbitrary, not necessarily invertible, observation matrix is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. A transformation of the observation equation is introduced to reduce the original problem to the previously solved one with an invertible observation matrix. The procedure for obtaining a closed system of the filtering equations for any polynomial state over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular case of a third-order state equation. In the example, performance of the designed optimal filter is verified against a conventional extended Kalman,Bucy filter. Copyright © 2007 John Wiley & Sons, Ltd. [source] Isomeric hexyl-ketohydroperoxides formed by reactions of hexoxy and hexylperoxy radicals in oxygenINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 8 2003François Jorand Isomerization reactions of peroxy radicals during oxidation of long-chain hydrocarbons yield hydroperoxides, and therefore play an important role in combustion and atmospheric chemistry, because of their action as branching agents in these chain reaction processes. Different formation mechanisms and structures are involved. Three isomeric hexyl-ketohydroperoxides are formed via isomerization reactions in oxygen of either hexoxy RO or hexylperoxy RO2 radicals. In the temperature range 373,473 K, 2-hexoxy (C6H13O) radical in O2/N2 mixtures gives 2-hexanone-5-hydroperoxide via two consecutive isomerizations. The second one is a H transfer from a HC(OH) group occurring via a seven-membered ring intermediate: Its rate constant has been determined at 453 and 483 K, and the general expression can be written as Hexylperoxy C6H13O2 radical, present in n -hexane oxidation by oxygen/nitrogen mixtures in the temperature range 543,573 K, gives 2-hexanone-4-hydroperoxide, 3-hexanone-5-hydroperoxide, and 2-hexanone-5-hydroperoxide. The first two are formed through an isomerization reaction via a six-membered ring intermediate, and the last through an isomerization reaction via a seven-membered ring intermediate. The ratio of the rate constant of the isomerization reactions of RO2 radicals via a seven-membered ring intermediate to that via a six-membered ring is found to be 0.795, and the rate constant expression via a seven-membered ring intermediate is proposed: The role of these reactions in the formation of radicals in the troposphere is discussed. Other products arising in the reactional path, such as ketones, furans, and diketones, are identified. Identification of these ketohydroperoxides was made using gas chromatography/mass spectrometry with electron impact, and with NH3 (or ND3) chemical ionization. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 354,366, 2003 [source] Optimal filtering for polynomial system states with polynomial multiplicative noiseINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2006Michael Basin Abstract In this paper, the optimal filtering problem for polynomial system states with polynomial multiplicative noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of a linear state equation with linear multiplicative noise and a bilinear state equation with bilinear multiplicative noise. In the example, performance of the designed optimal filter is verified for a quadratic state with a quadratic multiplicative noise over linear observations against the optimal filter for a quadratic state with a state-independent noise and a conventional extended Kalman,Bucy filter. Copyright © 2006 John Wiley & Sons, Ltd. [source] From massacre to the genocidal processINTERNATIONAL SOCIAL SCIENCE JOURNAL, Issue 174 2002Jacques Sémelin Since the time of Raphael Lemkin's work, genocide studies have been conducted primarily at the intersection of law and social science. As a result, the term ,genocide' has frequently been employed in a normative sense, leading to considerable conceptual difficulties and debate. How can such problems be overcome? This article comes down firmly in favour of moving away from a legal approach to genocide studies. It recommends the use of non-normative vocabulary based on the concept of ,massacre', this term being suggested as a reference lexical unit. It also puts forward the more general expression ,destruction process', whose most dramatic form is massacre. Massacre is not an act of actual ,madness' but the response to what the author calls ,delusional rationality'. In that respect, he distinguishes between two destruction strategies: one aimed at a group's subjugation and the other at its eradication. It is in the latter case that one can refer to a genocidal process. This article thus considers that genocide should not be defined as a static concept but viewed rather as a particular dynamic of civilian destruction, being the product of both its perpetrators' will and of favourable circumstances. [source] Modelling of diffraction from fibre texture gradients in thin polycrystalline filmsJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 4 2007M. Birkholz Crystallographic textures in thin polycrystalline films typically exhibit a rotational symmetry, i.e. they occur as a fibre texture with the texture pole being orientated in the direction of the substrate normal. As a further characteristic of thin-film textures, it was often observed that the degree of preferred orientation increases with increasing thickness. It is shown in this work how a fibre texture gradient may be modelled in kinematical X-ray diffraction and which effects it has on the intensity mapping of the IHKL reflection, when the HKL pole is the fibre axis. A general expression for IHKL is derived for a depth-dependent fibre texture that is based on the finite Laplace transform of the texture distribution. The concept is outlined for the cosn, function to model the tilt-angle dependence of intensity, with the parameter n denoting the degree of texture. It is found that the measured intensity distribution sensitively depends on the ratio of texture gradient over X-ray attenuation coefficient. For particular cases, it is found that the maximum intensity may occur for non-zero tilt angles and thus arise at a different tilt angle from the pole of the fibre texture. [source] Retrieval of spectral and dynamic properties from two-dimensional infrared pump-probe experimentsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 9 2008Riccardo Chelli Abstract We have developed a fitting algorithm able to extract spectral and dynamic properties of a three level oscillator from a two-dimensional infrared spectrum (2D-IR) detected in time resolved nonlinear experiments. Such properties go from the frequencies of the ground-to-first and first-to-second vibrational transitions (and hence anharmonicity) to the frequency-fluctuation correlation function. This last is represented through a general expression that allows one to approach the various strategies of modeling proposed in the literature. The model is based on the Kubo picture of stochastic fluctuations of the transition frequency as a result of perturbations by a fluctuating surrounding. To account for the line-shape broadening due to pump pulse spectral width in double-resonance measurements, we supply the fitting algorithm with the option to perform the convolution of the spectral signal with a Lorentzian function in the pump-frequency dimension. The algorithm is tested here on 2D-IR pump-probe spectra of a Gly-Ala dipeptide recorded at various pump-probe delay times. Speedup benchmarks have been performed on a small Beowulf cluster. The program is written in FORTRAN language for both serial and parallel architectures and is available free of charge to the interested reader. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008 [source] Geostatistical inference under preferential samplingJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 2 2010Peter J. Diggle Summary. Geostatistics involves the fitting of spatially continuous models to spatially discrete data. Preferential sampling arises when the process that determines the data locations and the process being modelled are stochastically dependent. Conventional geostatistical methods assume, if only implicitly, that sampling is non-preferential. However, these methods are often used in situations where sampling is likely to be preferential. For example, in mineral exploration, samples may be concentrated in areas that are thought likely to yield high grade ore. We give a general expression for the likelihood function of preferentially sampled geostatistical data and describe how this can be evaluated approximately by using Monte Carlo methods. We present a model for preferential sampling and demonstrate through simulated examples that ignoring preferential sampling can lead to misleading inferences. We describe an application of the model to a set of biomonitoring data from Galicia, northern Spain, in which making allowance for preferential sampling materially changes the results of the analysis. [source] Proximity factor in image size magnification for optical instruments in generalOPHTHALMIC AND PHYSIOLOGICAL OPTICS, Issue 6 2003W. F. Harris Abstract A general expression is derived for the proximity factor in near image size magnification for an arbitrary instrument in front of an arbitrary eye. The proximity factor is a 2 × 2 matrix. The instrument and eye may be astigmatic and have decentred elements. The image on the retina may be blurred or not. The analysis is exact within the limitations of linear optics. The general results are specialized for the case of a stigmatic instrument and a stigmatic eye. The results are applied to the case of a thick, possibly bitoric, spectacle lens. The Appendix treats two numerical examples. [source] Negative longitudinal magneto-resistance of layered crystals taking into account the spin splittingPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 6 2006S. R. Figarova Abstract The influence of the spin splitting on the longitudinal magnetoresistance of a quasi-two-dimensional electron gas in layered crystals is theoretically investigated. At acoustic-phonon scattering, a general expression for the longitudinal magnetoresistance has been found. A negative longitudinal magnetoresistance due to the spin splitting has been revealed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A general expression of the polarization factor for multi-diffraction processesACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2010Kiyoaki Tanaka A general expression of the polarization factor of multi-diffracted beams is formulated. By assigning the diffracted beam direction of each diffraction process as the y axis of a Cartesian coordinate system, the polarization factor of multi-diffraction processes can be easily calculated for polarized and unpolarized beams without being limited by the number of diffraction processes. The method can be applied to processes with more than three scattering events such as multiple diffraction and extinction. [source] Internal stabilization of standard sampled-data systemsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003B. P. Lampe Prof. Dr. The paper presents necessary and sufficient conditions under which for a standard sampled-data system there exists a digital controller, that ensures the internal stability of the system. For the case of stabilizability a general expression for the set of all stabilizing controllers is given. The stabilizability conditions are formulated as divisibility of certain polynomials, controllability and observability concepts are not used. [source] From the Atomic Jump Frequencies to the Phenomenological Transport Coefficients,ADVANCED ENGINEERING MATERIALS, Issue 12 2006M. Nastar The SCMF theory based on an atomic model of atom-vacancy exchange frequencies yields general expressions of the phenomenological coefficients Lij of a multi-component alloy with any crystallographic structure. The limitations and future improvements of the Self-Consistent Mean-Field (SCMF) approach are easily related to the statistical approximation of the thermodynamic correlations and to the time-dependent effective interactions used to describe the kinetic correlations induced by the vacancy diffusion mechanism. [source] A variational r -adaption and shape-optimization method for finite-deformation elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004P. Thoutireddy Abstract This paper is concerned with the formulation of a variational r -adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configurational forces for isoparametric elements and non-linear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and non-linear elastic bodies; and the optimization of the shape of elastic inclusions. Copyright © 2004 John Wiley & Sons, Ltd. [source] Modelling Overdispersion for Complex Survey DataINTERNATIONAL STATISTICAL REVIEW, Issue 3 2001E.A. Molina Summary The population characteristics observed by selecting a complex sample from a finite identified population are the result of at least two processes: the process which generates the values attached to the units in the finite population, and the process of selecting the sample of units from the population. In this paper we propose that the resulting observations by viewed as the joint realization of both processes. We overcome the inherent difflculty in modelling the joint processes of generation and selection by exploring second moment and other simplifying assumptions. We obtain general expressions for the mean and covariance function of the joint processes and show that several overdispersion models discussed in the literature for the analysis of complex surveys are a direct consequence of our formulation, undere particular sampling schemes and population structures. Résumé Les caracté d'une population sont observées grâce à un échantillon complexe sélectionnéâ partir d'une poplation finie. Ces caractéristiques sont le résultat de l'échantillon des unités de ette population. Dans cet article, nous considérons que l'observation globale peut être vue comme une réalisation simultanée de ces deux processus. Nous tentons de surmonter la difficulté intrinsèque liée à la modélisation du double processus de génération et de sélection par une étude du moment d'ordre deux et en considérant d'autres hypothèses simplificatrices. Nous obtenons une expression générale pour la moyenne et la covariance liée au sondage complexes, sont une conséquence directe de notre formulation, losque l'on considère un plan de sondage particulier et une population ayant une structure spécifique. [source] On Haseman boundary value problem for a class of metaanalytic functions with different factors on the unit circumferenceMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2010Ying Wang Abstract In this article, the Haseman boundary value problem (bvp) is discussed for metaanalytic functions with different factors on the unit circumference. Through a series of appropriate transformations, we obtain general expressions for the solution and the condition of solvability for the problem. Copyright © 2009 John Wiley & Sons, Ltd. [source] Low-angle scattering by cylindrical structuresACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2010Girija Bhushan Mitra A theory of diffraction at small angles of scattering by a cylindrically constructed structure has been developed and general expressions for two- and three-dimensional cylindrically curved crystallites have been obtained. Modified expressions have been derived for special cases of (a) a single arc of equiangularly spaced identical atoms, (b) several coaxial arcs each having an equal number of equiangularly spaced identical atoms and (c) such arcs arranged at equal distances along the common axis of the arc, including single cylinders and multilayered cylindrical structures. From the expressions obtained, it is possible to measure the magnitudes of the radius of the cylinder, the length of the cylinder, the angular distance between the scattering atoms on each cylindrical arc, their atomic number and the radius of the hole inside each cylindrical structure when a particular tube is considered for a particular purpose or even when predicting the properties required by a nanotube for a particular purpose. [source] Moment approximation for least-squares estimators in dynamic regression models with a unit root,THE ECONOMETRICS JOURNAL, Issue 2 2005Jan F. Kiviet Summary, To find approximations for bias, variance and mean-squared error of least-squares estimators for all coefficients in a linear dynamic regression model with a unit root, we derive asymptotic expansions and examine their accuracy by simulation. It is found that in this particular context useful expansions exist only when the autoregressive model contains at least one non-redundant exogenous explanatory variable. Surprisingly, the large-sample and small-disturbance asymptotic techniques give closely related results, which is not the case in stable dynamic regression models. We specialize our general expressions for moment approximations to the case of the random walk with drift model and find that they are unsatisfactory when the drift is small. Therefore, we develop what we call small-drift asymptotics which proves to be very accurate, especially when the sample size is very small. [source] Symmetry rules and strain/order-parameter relationships for coupling between octahedral tilting and cooperative Jahn,Teller transitions in ABX3 perovskites.ACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2009Space groups, order-parameter and strain/order-parameter coupling relationships in ABX3 perovskite structures which combine cooperative Jahn,Teller distortions and octahedral tilting have been investigated from the perspective of group theory using the computer program ISOTROPY. Two common Jahn,Teller ordering schemes are associated with the irreducible representations and of the space group . A third, less-common ordering scheme is associated with . These combine with tilting instabilities associated with and to generate a predicted suite of Jahn,Teller structure types that includes many of the known structures of manganites, vanadates, Cu and Cr halides. Order-parameter coupling and possible phase transitions are described using Landau free-energy expansions, and general expressions for the relationships between symmetry-adapted spontaneous strains and particular order-parameter components are presented. These provide a general formal framework for determining structural evolution across multi-component order-parameter space and for characterizing the influence of tilting instabilities on Jahn,Teller instabilities or of Jahn,Teller ordering on octahedral tilting. [source] Analytical Expressions for Quantitative Scanning Electrochemical Microscopy (SECM)CHEMPHYSCHEM, Issue 3 2010Christine Lefrou Dr. Abstract Scanning electrochemical microscopy (SECM), is a recent analytical technique in electrochemistry, which was developed in the 1990s and uses microelectrodes to probe various surfaces. Even with the well-known disc microelectrodes, the system geometry is not as simple as in regular electrochemistry. As a consequence even the simplest experiments, the so-called positive and negative feedback approach curves, cannot be described with exact analytical expressions. This review gathers all the analytical expressions available in the SECM literature in steady-state feedback experiments. Some of them are claimed as general expressions, other are presented as approximate. Their validity is discussed in the light of the current understanding and computer facilities. [source] | |||||||||||||||||||||||||