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Derived Equations (derived + equation)
Selected AbstractsSurface waves in a general anisotropic poroelastic solid half-spaceGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2004M. D. Sharma SUMMARY A method is introduced for studying surface waves in a general anisotropic poroelastic medium. The method is analogous to the one used for isotropic media and derives a complex secular equation to represent the propagation of surface waves at the stress-free plane surface of a non-dissipative porous medium. The point of importance is that the derived equation is, analytically, separable into real and imaginary parts and hence can be solved by iterative numerical methods. A root of this secular equation represents the existence of surface waves and calculates the apparent phase velocity along a given direction on the surface. Numerical work is carried out for the model of a crustal rock. The propagation of surface waves is studied numerically for the top three anisotropies (i.e. triclinic, monoclinic, orthorhombic). [source] Combination of Fragmental and Topological Descriptors for QSPR Estimations of Boiling TemperatureMOLECULAR INFORMATICS, Issue 8 2004Irina Abstract The novel QSPR equation for estimation of physicochemical properties of organic substances is proposed. This equation includes contributions depending on the counts of bonds and nonadditive contribution. The nonadditive term is represented as an explicit function of topological distances on the line graph of molecules. The original mathematical form for description of nonadditive contribution is suggested. The application of the derived equation to estimation of normal boiling temperatures for the saturated hydrocarbons (total number of compounds n=198; correlation coefficient r=0.9966; mean square deviation ,=3.4,K) has proved the effectiveness of the proposed approach. The modification of correlation equation is made for estimations of normal boiling temperatures for substances with OH and NH2 groups (n =139; r=0.9971; ,=3.9,K). [source] On the evolution of sharp fronts for the quasi-geostrophic equationCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 6 2005José Luis Rodrigo We consider the problem of the evolution of sharp fronts for the surface quasi-geostrophic (QG) equation. This problem is the analogue to the vortex patch problem for the two-dimensional Euler equation. The special interest of the quasi-geostrophic equation lies in its strong similarities with the three-dimensional Euler equation, while being a two-dimen-sional model. In particular, an analogue of the problem considered here, the evolution of sharp fronts for QG, is the evolution of a vortex line for the three-dimensional Euler equation. The rigorous derivation of an equation for the evolution of a vortex line is still an open problem. The influence of the singularity appearing in the velocity when using the Biot-Savart law still needs to be understood. We present two derivations for the evolution of a periodic sharp front. The first one, heuristic, shows the presence of a logarithmic singularity in the velocity, while the second, making use of weak solutions, obtains a rigorous equation for the evolution explaining the influence of that term in the evolution of the curve. Finally, using a Nash-Moser argument as the main tool, we obtain local existence and uniqueness of a solution for the derived equation in the C, case. © 2004 Wiley Periodicals, Inc. [source] Simplified algorithms for calculating double-couple rotationGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007Yan Y. Kagan SUMMARY We derive new, simplified formulae for evaluating the 3-D angle of earthquake double-couple (DC) rotation. The complexity of the derived equations depends on both accuracy requirements for angle evaluation and the completeness of desired solutions. The solutions are simpler than my previously proposed algorithm based on the quaternion representation designed in 1991. We discuss advantages and disadvantages of both approaches. These new expressions can be written in a few lines of computer code and used to compare both DC solutions obtained by different methods and variations of earthquake focal mechanisms in space and time. [source] A promising boundary element formulation for three-dimensional viscous flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005Xiao-Wei Gao Abstract In this paper, a new set of boundary-domain integral equations is derived from the continuity and momentum equations for three-dimensional viscous flows. The primary variables involved in these integral equations are velocity, traction, and pressure. The final system of equations entering the iteration procedure only involves velocities and tractions as unknowns. In the use of the continuity equation, a complex-variable technique is used to compute the divergence of velocity for internal points, while the traction-recovery method is adopted for boundary points. Although the derived equations are valid for steady, unsteady, compressible, and incompressible problems, the numerical implementation is only focused on steady incompressible flows. Two commonly cited numerical examples and one practical pipe flow problem are presented to validate the derived equations. Copyright © 2004 John Wiley & Sons, Ltd. [source] Mathematical framework towards the analysis of a generic traffic markerINTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 4 2007Nasser-Eddine Rikli Abstract DiffServ architecture has been widely adopted for the provision of QoS over the Internet. This makes the full understanding of its operation imperative. We believe that only mathematical analysis may have the power of such goal. As the heart of a DiffServ router is the token bucket algorithm, a generic one, with two-colours marking, is to be considered here. A mathematical framework will be first developed for its analysis. Then, assuming an input traffic with Poisson arrivals and Exponential packet lengths, and a memoryless token bucket system, the two types of generated streams will be statistically characterized through their distributions and averages. This analysis will be carried out for two types of buckets, one with infinite size and a second with finite size. It will be shown how the derived equations will allow the prediction of the output traffic streams for given bucket and input traffic stream parameters. The paper will be then complemented by conclusions and suggestions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Effective size of populations with unequal sex ratio and variation in mating successJOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 5 2002T. Nomura Summary To estimate the effective size (Ne) of populations with unequal sex ratio, a well-known formula, Ne=4NmNf/(Nm + Nf), has been frequently used, where Nm and Nf are the numbers of male and female parents, respectively. In this paper, the formula was examined under typical mating systems in animals. It was shown that the formula holds only when there are no variations in the numbers of mates (mating success) of parents of each sex. More appropriate equations were developed by accounting for the variation in mating success. It was found that for animal populations with harem mating system, an equation Ne=4NmNf/(2Nm+Nf) gives a more accurate estimate than the well-known formula. The effective population sizes of several wild, experimental and domestic animals are estimated by applying the derived equations to the published demographic and ecological data. Zusammenfassung Effektive Größe von Populationen mit ungleichem Geschlechterverhältnis und Variation im Anpaarungserfolg Zur Schätzung der effektiven Populationsgröße (Ne) mit ungleichem Geschlechterverhältnis, wurde häufig die allgemein bekannte Formel Ne=4NmNf/(Nm + Nf) verwendet, wobei Nm und Nf die Anzahl männlicher und weiblicher Eltern bezeichnen. In diesem Artikel wurde diese Formel unter verschiedenen Anpaarungssystemen überprüft. Es wurde gezeigt, daß die Formel nur zutrifft, wenn die Anzahl der angepaarten Tiere (Anpaarungserfolg) in jedem Geschlecht nicht variieren. Es wurden genauere Gleichungen entwickelt, die den Anpaarungserfolg mitberücksichtigen. Für Tierpopulationen mit Harempaarung wurde die Gleichung Ne=4NmNf/(2Nm + Nf) als genauerer Schätzer als die allgemein bekannte Formel gefunden. Die effektive Populationsgröße mehrerer Wild-, Versuchs- und Haustierpopulationen wurden mittels der abgeleiteten Gleichung und demographischen und ökologischen Daten geschätzt. [source] Principles of pharmacodynamics and their applications in veterinary pharmacologyJOURNAL OF VETERINARY PHARMACOLOGY & THERAPEUTICS, Issue 6 2004P. LEES Pharmacodynamics (PDs) is the science of drug action on the body or on microorganisms and other parasites within or on the body. It may be studied at many organizational levels , sub-molecular, molecular, cellular, tissue/organ and whole body , using in vivo, ex vivo and in vitro methods and utilizing a wide range of techniques. A few drugs owe their PD properties to some physico-chemical property or action and, in such cases, detailed molecular drug structure plays little or no role in the response elicited. For the great majority of drugs, however, action on the body is crucially dependent on chemical structure, so that a very small change, e.g. substitution of a proton by a methyl group, can markedly alter the potency of the drug, even to the point of loss of activity. In the late 19th century and first half of the 20th century recognition of these facts by Langley, Ehrlich, Dale, Clarke and others provided the foundation for the receptor site hypothesis of drug action. According to these early ideas the drug, in order to elicit its effect, had to first combine with a specific ,target molecule' on either the cell surface or an intracellular organelle. It was soon realized that the ,right' chemical structure was required for drug,target site interaction (and the subsequent pharmacological response). In addition, from this requirement, for specificity of chemical structure requirement, developed not only the modern science of pharmacology but also that of toxicology. In relation to drug actions on microbes and parasites, for example, the early work of Ehrlich led to the introduction of molecules selectively toxic for them and relatively safe for the animal host. In the whole animal drugs may act on many target molecules in many tissues. These actions may lead to primary responses which, in turn, may induce secondary responses, that may either enhance or diminish the primary response. Therefore, it is common to investigate drug pharmacodynamics (PDs) in the first instance at molecular, cellular and tissue levels in vitro, so that the primary effects can be better understood without interference from the complexities involved in whole animal studies. When a drug, hormone or neurotransmitter combines with a target molecule, it is described as a ligand. Ligands are classified into two groups, agonists (which initiate a chain of reactions leading, usually via the release or formation of secondary messengers, to the response) and antagonists (which fail to initiate the transduction pathways but nevertheless compete with agonists for occupancy of receptor sites and thereby inhibit their actions). The parameters which characterize drug receptor interaction are affinity, efficacy, potency and sensitivity, each of which can be elucidated quantitatively for a particular drug acting on a particular receptor in a particular tissue. The most fundamental objective of PDs is to use the derived numerical values for these parameters to classify and sub-classify receptors and to compare and classify drugs on the basis of their affinity, efficacy, potency and sensitivity. This review introduces and summarizes the principles of PDs and illustrates them with examples drawn from both basic and veterinary pharmacology. Drugs acting on adrenoceptors and cardiovascular, non-steroidal anti-inflammatory and antimicrobial drugs are considered briefly to provide a foundation for subsequent reviews in this issue which deal with pharmacokinetic (PK),PD modelling and integration of these drug classes. Drug action on receptors has many features in common with enzyme kinetics and gas adsorption onto surfaces, as defined by Michaelis,Menten and Langmuir absorption equations, respectively. These and other derived equations are outlined in this review. There is, however, no single theory which adequately explains all aspects of drug,receptor interaction. The early ,occupation' and ,rate' theories each explain some, but not all, experimental observations. From these basic theories the operational model and the two-state theory have been developed. For a discussion of more advanced theories see Kenakin (1997). [source] Correlation of Minimum Inhibitory Concentrations Toward Oral Bacterial Growth Based on the Abraham ModelMOLECULAR INFORMATICS, Issue 10 2006Christina Mintz Abstract The Abraham solvation parameter model is used to construct mathematical correlations for describing the minimum inhibitory concentration of organic compounds for growth inhibition toward Porphyromonas gingivalis, Selenomonas artemidis, and Streptococcus sorbrinius. The derived mathematical correlations describe the observed published inhibitory data to within an overall average standard deviation of approximately 0.30 log units. A principal component analysis, shows that the derived equations for the three growth inhibitions are quite close to each other, are near to some, but not to all, equations for aqueous toxicity toward various organisms, and are quite far from most equations for water to solvent partition. A further analysis suggests that the three growth inhibition systems behave as though a solute is transferred from water to an environment that is still quite water-like. [source] Novel corrective equations for complete estimation of human tissue lipids after their partial destruction by perchloric acid pre-treatment: high-resolution 1H-NMR-based studyNMR IN BIOMEDICINE, Issue 2 2008Niraj Kumar Srivastava Abstract Owing to the small quantity of tissue available in human biopsy specimens, aqueous and lipid components often have to be determined in the same tissue sample. Perchloric acid (PCA) used for the extraction of aqueous metabolites has a deleterious effect on lipid components; the severity of the damage is not known. In this study, human muscle tissue was first treated with PCA to extract aqueous metabolites, and the residue was then used for lipid extraction by conventional methods, i.e. the methods of Folch and Bligh & Dyer and a standardised one using methanol/chloroform (1:3, v/v) used in our laboratory. A 1H-NMR spectrum was obtained for each lipid extract. Lipid was quantified by measuring the integral area of N+ -(CH3)3 signals of phospholipids (PLs). Triacylglycerol (TG) and cholesterol (CHOL) were quantified using the -CH2 - signals of glycerol and the C18 methyl signal, respectively. This study shows that prior use of PCA caused marked attenuation of TG, PL, and CHOL. This was confirmed by recovery experiments and observation of the direct effect of PCA on the standard lipid components. On the basis of the quantity of lipid lost in each case, three novel equations (with respect to TG, PL, and CHOL) were derived. Application of these equations to lipid quantities estimated in different pathological tissues after PCA pre-treatment produced values equivalent to those estimated without PCA use. This study conclusively shows that PCA pre-treatment damages all three lipid moieties, TG, PL, and CHOL. When PCA is used in a fixed ratio to the tissue, the lipid damage is also proportional and correctable by statistically derived equations. These equations will be useful in human biopsy specimens where aqueous and lipid components have to be studied using the same tissue sample because of the small quantity available. Copyright © 2007 John Wiley & Sons, Ltd. [source] | |||||||||||||