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## Infinity
## Selected Abstracts## THE CONCEPT OF INFINITY AND CHINESE THOUGHT JOURNAL OF CHINESE PHILOSOPHY, Issue 4 2008JIANG YI[source] ## Infinity Goes Up On Trial: Must Immortality Be Meaningless? EUROPEAN JOURNAL OF PHILOSOPHY, Issue 1 2009Timothy ChappellFirst page of article [source] ## Descartes: God as the Idea of Infinity INTERNATIONAL JOURNAL OF SYSTEMATIC THEOLOGY, Issue 1 2008MARY-ANN CRUMPLINIt shows that because objectors ignore Descartes' opposition to the ,order of being' they are led to a binary and incorrect reading of his argument. However, by correctly following Descartes' own logic, the method of doubt can be used to prove the existence of an infinite God. [source] ## An Infinity of Little Hours: Five Young Men and Their Trial of Faith in the Western World's Most Austere Monastic Order , By Karen Klein Maguire THE HISTORIAN, Issue 4 2008Vincent L. WimbushNo abstract is available for this article. [source] ## Response of unbounded soil in scaled boundary finite-element method EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 1 2002John P. WolfAbstract The scaled boundary finite-element method is a powerful semi-analytical computational procedure to calculate the dynamic stiffness of the unbounded soil at the structure,soil interface. This permits the analysis of dynamic soil,structure interaction using the substructure method. The response in the neighbouring soil can also be determined analytically. The method is extended to calculate numerically the response throughout the unbounded soil including the far field. The three-dimensional vector-wave equation of elasto-dynamics is addressed. The radiation condition at infinity is satisfied exactly. By solving an eigenvalue problem, the high-frequency limit of the dynamic stiffness is constructed to be positive definite. However, a direct determination using impedances is also possible. Solving two first-order ordinary differential equations numerically permits the radiation condition and the boundary condition of the structure,soil interface to be satisfied sequentially, leading to the displacements in the unbounded soil. A generalization to viscoelastic material using the correspondence principle is straightforward. Alternatively, the displacements can also be calculated analytically in the far field. Good agreement of displacements along the free surface and below a prism foundation embedded in a half-space with the results of the boundary-element method is observed. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Competing Mechanisms in a Common Value Environment ECONOMETRICA, Issue 4 2000Bruno BiaisConsider strategic risk-neutral traders competing in schedules to supply liquidity to a risk-averse agent who is privately informed about the value of the asset and his hedging needs. Imperfect competition in this common value environment is analyzed as a multi-principal game in which liquidity suppliers offer trading mechanisms in a decentralized way. Each liquidity supplier behaves as a monopolist facing a residual demand curve resulting from the maximizing behavior of the informed agent and the trading mechanisms offered by his competitors. There exists a unique equilibrium in convex schedules. It is symmetric and differentiable and exhibits typical features of market-power: Equilibrium trading volume is lower than ex ante efficiency would require. Liquidity suppliers charge positive mark-ups and make positive expected profits, but these profits decrease with the number of competitors. In the limit, as this number goes to infinity, ask (resp. bid) prices converge towards the upper (resp. lower) tail expectations obtained in Glosten (1994) and expected profits are zero. [source] ## The Hope of a Critical Ethics: Teachers and Learners EDUCATIONAL THEORY, Issue 3 2004Donald Blumenfeld-JonesThe basic question of this essay is what motivates a person to act on behalf of the "ethical good"? Critical theorists (such as Max Horkheimer, Paulo Freire, and Sharon Welch) have proposed the educational development of critical rationality as the answer to this question, with Freire adding the notion of love and Welch adding the notion of "dangerous memory." These positions are both critiqued and used as a starting place for proposing a critical ethics with three bases: (1) Emmanuel Levinas's notion of ethical infinity (that is, a person is more than any category can reveal and categories entrap and harm the person), (2) the notion of creating a community based on "relational authority," and (3) the development of moral imagination. Descriptions of specific classroom situations ground the discussion in education. [source] ## On the Dynamics of Basic Growth Models: Ratio Stability vs. GERMAN ECONOMIC REVIEW, Issue 4 2009Convergence, Divergence in State SpaceBalanced growth; convergence; divergence; state space dynamics; ratio stability Abstract. We show for a class of basic growth models that convergence in ratios does not imply the pathwise convergence to the corresponding balanced growth path in the state space. We derive conditions on parameters and on the elasticity of the savings function for convergence or divergence and apply our results to the Solow model, an augmented Solow model as well as to an optimal growth model. An implication for the convergence debate is that two economies that differ only in the initial capital stock and converge in per capita terms might diverge to infinity in absolute terms. [source] ## Analytical Model for Removal of a Uniformly Distributed Single-Component NAPL Under Nonequilibrium Conditions GROUND WATER MONITORING & REMEDIATION, Issue 3 2001H.J.H. BrouwersIn this paper a simple analytical model is presented for the one-dimensional transport equation describing the removal of a uniformly distributed, single-component NAPL under nonequilibrium conditions. Both advective and dispersive transport are included in the model. The model describes two distinct stages: a solution for the time the amount of NAPL declines but the length of the NAPL-containing region remains constant, and a solution from the moment the front, behind which all NAPL is depleted, starts to move. The model is valid for both dissolution (i.e., by water) or volatilization (i.e., by air). Dissolution (or volatilization) is considered a firstorder rate process with a constant mass-transfer rate coefficient. As expected, the model approaches the solution for equilibrium conditions if the mass-transfer coefficient tends to infinity. Even though the model is based on some rigorous assumptions, the simplicity of the model makes it useful for obtaining an initial mass-transfer rate coefficient from experimental data, which can be used to estimate the time required to dissolve all NAPL, as shown for two data sets taken from the literature. [source] ## Heat transfer on tube bundles embedded horizontally in a liquid-fluidized bed HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 2 2005Kenichi HashizumeAbstract Heat transfer on tube bundles embedded horizontally in a liquid-fluidized bed was investigated experimentally. In the experiment, a total of 5 kinds of tube bundles in an equilateral triangular staggered arrangement, including a single tube, was used. Tested particles were of glass and ceramics, and their diameter range was from 2.1 to 6.0 mm. It was found that the distribution of local heat transfer coefficients around a tube depends not on the kind of particles, but on the tube pitch only, when a good fluidizing condition is maintained. Based on the experimental data, a new method was proposed to predict average heat transfer coefficient, which can be applicable for tube bundles having a tube pitch to diameter ratio of 1.2 to infinity (single tube). © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(2): 85,98, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20048 [source] ## A novel analytical solution for constant-head test in a patchy aquifer INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2006Shaw-Yang YangAbstract A mathematical model describing the hydraulic head distribution for a constant-head test performed in a well situated at the centre of a patchy aquifer is presented. The analytical solution for the mathematical model is derived by the Laplace transforms and the Bromwich integral method. The solution for the hydraulic head has been shown to satisfy the governing equations, related boundary conditions, and continuity requirements for the hydraulic head and flow rate at the interface of the patch and outer regions. An efficient numerical approach is proposed to evaluate the solution, which has an integral covering an integration range from zero to infinity and an integrand consisting the product and square of the Bessel functions. This solution can be used to produce the curves of dimensionless hydraulic head against dimensionless time for investigating the effect of the contrast of formation properties on the dimensionless hydraulic head distribution. Define the ratio of outer-region transmissivity to patch-region transmissivity as ,. The dimensionless hydraulic head for ,=0.1 case is about 2.72 times to that for ,=10 case at dimensionless large time (e.g. ,,106) when the dimensionless distance (,) equals 10. The results indicate that the hydraulic head distribution highly depends on the hydraulic properties of two-zone formations. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Semi-analytical elastostatic analysis of unbounded two-dimensional domains INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2002Andrew J. DeeksAbstract 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] ## Addressing volumetric locking and instabilities by selective integration in smoothed finite elements INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2009Nguyen-Xuan HungAbstract This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into subcells. The strain at a point is defined as a weighted average of the standard strain field over a representative domain. This yields superconvergent stresses, both in regular and singular settings, as well as increased accuracy, with slightly lower computational cost than the standard FEM. The one-subcell version that does not exhibit volumetric locking yields more accurate stresses but less accurate displacements and is equivalent to a quasi-equilibrium FEM. It is also subject to instabilities. In the limit where the number of subcells goes to infinity, the standard FEM is recovered, which yields more accurate displacements and less accurate stresses. The specific contribution of this paper is to show that expressing the volumetric part of the strain field using a one-subcell formulation is sufficient to get rid of volumetric locking and increase the displacement accuracy compared with the standard FEM when the single subcell version is used to express both the volumetric and deviatoric parts of the strain. Selective integration also alleviates instabilities associated with the single subcell element, which are due to rank deficiency. Numerical examples on various compressible and incompressible linear elastic test cases show that high accuracy is retained compared with the standard FEM without increasing computational cost. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## An appropriate quadrature rule for the analysis of plane crack problems in the boundary-element method INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2001E. E. TheotokoglouAbstract An hypersingular integral equation of a three-dimensional elastic solid with an embedded planar crack subjected to a uniform stress field at infinity is derived. The solution of the boundary-integral equation is succeeded taking into consideration an appropriate Gauss quadrature rule for finite part integrals which is suitable for the numerical treatment of any plane crack with a smooth-contour shape and permit the fast convergence for the results. The problem of a circular and of an elliptical crack in an infinite body subjected to a uniform stress field at infinity is confronted; and the stress intensity factors are calculated. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Diagonalization procedure for scaled boundary finite element method in modeling semi-infinite reservoir with uniform cross-section INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2009S. M. LiAbstract To improve the ability of the scaled boundary finite element method (SBFEM) in the dynamic analysis of dam,reservoir interaction problems in the time domain, a diagonalization procedure was proposed, in which the SBFEM was used to model the reservoir with uniform cross-section. First, SBFEM formulations in the full matrix form in the frequency and time domains were outlined to describe the semi-infinite reservoir. No sediments and the reservoir bottom absorption were considered. Second, a generalized eigenproblem consisting of coefficient matrices of the SBFEM was constructed and analyzed to obtain corresponding eigenvalues and eigenvectors. Finally, using these eigenvalues and eigenvectors to normalize the SBFEM formulations yielded diagonal SBFEM formulations. A diagonal dynamic stiffness matrix and a diagonal dynamic mass matrix were derived. An efficient method was presented to evaluate them. In this method, no Riccati equation and Lyapunov equations needed solving and no Schur decomposition was required, which resulted in great computational costs saving. The correctness and efficiency of the diagonalization procedure were verified by numerical examples in the frequency and time domains, but the diagonalization procedure is only applicable for the SBFEM formulation whose scaling center is located at infinity. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Flow of a third grade fluid due to an accelerated disk INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2010S. AsgharAbstract The magnetohydrodynamic (MHD) flow induced by non-coaxial rotation of porous disk and a third grade fluid at infinity is investigated. The disk is moving with uniform acceleration and rotating with a uniform angular velocity. Numerical solution of the governing nonlinear initial and boundary value problem is obtained. The effects of physical parameters on the velocity profiles are examined in detail. The present study shows that the constant acceleration part has a greater influence than the time part of the assumed variable velocity of the disk. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Potential flow around obstacles using the scaled boundary finite-element method INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003Andrew J. DeeksAbstract The scaled boundary finite-element method is a novel semi-analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. The method works by weakening the governing differential equations in one co-ordinate direction through the introduction of shape functions, then solving the weakened equations analytically in the other (radial) co-ordinate direction. These co-ordinate directions are defined by the geometry of the domain and a scaling centre. The method can be employed for both bounded and unbounded domains. This paper applies the method to problems of potential flow around streamlined and bluff obstacles in an infinite domain. The method is derived using a weighted residual approach and extended to include the necessary velocity boundary conditions at infinity. The ability of the method to model unbounded problems is demonstrated, together with its ability to model singular points in the near field in the case of bluff obstacles. Flow fields around circular and square cylinders are computed, graphically illustrating the accuracy of the technique, and two further practical examples are also presented. Comparisons are made with boundary element and finite difference solutions. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Identification of the inertia matrix of a rotating body based on errors-in-variables models INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 3 2010Byung-Eul JunAbstract This paper proposes a procedure for identifying the inertia matrix of a rotating body. The procedure based on Euler's equation governing rotational motion assumes errors-in-variables models in which all measurements, torque as well as angular velocities, are corrupted by noises. In order for consistent estimation, we introduce an extended linear regression model by augmenting the regressors with constants and the parameters with noise-contributed terms. A transformation, based on low-pass filtering, of the extended model cancels out angular acceleration terms in the regressors. Applying the method of least correlation to the model identifies the elements of the inertia matrix. Analysis shows that the estimates converge to the true parameters as the number of samples increases to infinity. Monte Carlo simulations demonstrate the performance of the algorithm and support the analytical consistency. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Model reference adaptive iterative learning control for linear systems INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 9 2006A. TayebiAbstract In this paper, we propose a model reference adaptive control (MRAC) strategy for continuous-time single-input single-output (SISO) linear time-invariant (LTI) systems with unknown parameters, performing repetitive tasks. This is achieved through the introduction of a discrete-type parametric adaptation law in the ,iteration domain', which is directly obtained from the continuous-time parametric adaptation law used in standard MRAC schemes. In fact, at the first iteration, we apply a standard MRAC to the system under consideration, while for the subsequent iterations, the parameters are appropriately updated along the iteration-axis, in order to enhance the tracking performance from iteration to iteration. This approach is referred to as the model reference adaptive iterative learning control (MRAILC). In the case of systems with relative degree one, we obtain a pointwise convergence of the tracking error to zero, over the whole finite time interval, when the number of iterations tends to infinity. In the general case, i.e. systems with arbitrary relative degree, we show that the tracking error converges to a prescribed small domain around zero, over the whole finite time interval, when the number of iterations tends to infinity. It is worth noting that this approach allows: (1) to extend existing MRAC schemes, in a straightforward manner, to repetitive systems; (2) to avoid the use of the output time derivatives, which are generally required in traditional iterative learning control (ILC) strategies dealing with systems with high relative degree; (3) to handle systems with multiple tracking objectives (i.e. the desired trajectory can be iteration-varying). Finally, simulation results are carried out to support the theoretical development. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## The spirit of capitalism, stock market bubbles and output fluctuations INTERNATIONAL JOURNAL OF ECONOMIC THEORY, Issue 1 2008Takashi KamihigashiE20; E32 This paper presents a representative agent model in which stock market bubbles cause output fluctuations. Assuming that utility depends directly on wealth, we show that stock market bubbles arise if the marginal utility of wealth does not decline to zero as wealth goes to infinity. Bubbles can affect output positively or negative depending on whether the production function exhibits increasing or decreasing returns to scale. In sunspot equilibria, the bursting of a bubble is followed by a sharp decline in output one period later. Various numerical examples are given to illustrate the behavior of stochastic bubbles and the relationship between bubbles and output. [source] ## Constructal tree-shaped paths for conduction and convection INTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 4 2003Adrian BejanAbstract This lecture reviews a series of recent results based on the geometric minimization of the resistance to flow between one point (source, sink) and a volume or an area (an infinity of points). Optimization is achieved by varying the geometric features of the flow path subject to volume constraints. The method is outlined by using the problem of steady volume-point conduction. Optimized first is the smallest elemental volume, which is characterized by volumetric heat generation in a low-conductivity medium, and one-dimensional conduction through a high-conductivity ,channel'. Progressively larger volumes are covered by assemblies of previously optimized constructs. Tree-shaped flow structures spring out of this objective and constraints principle. Analogous problems of fluid flow, and combined heat and fluid flow (convection, trees of fins) are also discussed. The occurrence of similar tree structures in nature may be reasoned based on the same principle (constructal theory) (Bejan, 2000). Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Davydov's solitons in a homogeneous nucleotide chain INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2010Victor D. LakhnoAbstract Charge transfer in homogeneous nucleotide chains is modeled on the basis of Holstein Hamiltonian. The path length of Davydov solitons in these chains is being studied. It is shown that in a dispersionless case, when the soliton velocity V is small, the path length grows exponentially as V decreases. In this case, the state of a moving soliton is quasisteady. In the presence of dispersion determined by the dependence ,2 = , + V,2, the path length in the region 0 < V < V0 is equal to infinity. In this case, the phonon environment follows the charge motion. In the region V > V0, the soliton motion is accompanied by emission of phonons which leads to a finite path length of a soliton. The latter tends to infinity as V , V0 + 0 and V , ,. The presence of dissipation leads to a finite soliton path length. An equilibrium velocity of soliton in an external electric field is calculated. It is shown that there is a maximum intensity of an electric field at which a steady motion of a soliton is possible. The soliton mobility is calculated for the stable or ohmic brunch. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] ## The Liapunov's second method for continuous time difference equations INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2003P. PepeArticle first published online: 10 OCT 200Abstract Among many other cases such as economic and lossless propagation models, continuous time difference equations are encountered as the internal dynamics in a class of non-linear time delay systems, when controlled by a suitable state feedback which drives the output exponentially to zero. The Liapunov's second method for these infinite dimensional systems has not been extensively investigated in the literature. This paper has the aim of filling this gap. Liapunov's second method theorems for checking the stability and the asymptotic stability of this class of infinite dimensional systems are built up, in both a finite and an infinite dimensional setting. In the finite dimensional setting, the Liapunov function is defined on finite dimensional sets. The conditions for stability are given as inequalities on continuous time. No derivatives are involved, as in the dynamics of the studied systems. In the infinite dimensional setting, the continuous time difference equation is transformed into a discrete time system evolving on an infinite dimensional space, and then the classical Liapunov theorem for the system in the new form is written. In this paper the very general case is considered, that is non-linear continuous time difference equations with multiple non commensurate delays are considered, and moreover the functions involved in the dynamics are allowed to be discontinuous, as well as the initial state. In order to study the stability of the internal dynamics in non-linear time delay feedback systems, an exogenous disturbance is added, which goes to zero exponentially as the time goes to infinity. An example is considered, from non-linear time delay feedback theory. While the results available in the literature are inconclusive as far as the stability of that example is concerned, such stability is proved to hold by the theorems developed in this paper, and is validated by simulation results. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Robust multiple-fault detection filter INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2002Robert H. ChenAbstract A new robust multiple-fault detection and identification algorithm is determined. Different from other algorithms which explicitly force the geometric structure by using eigenstructure assignment or geometric theory, this algorithm is derived from solving an optimization problem. The output error is divided into several subspaces. For each subspace, the transmission from one fault, denoted the associated target fault, is maximized while the transmission from other faults, denoted the associated nuisance fault, is minimized. Therefore, each projected residual of the robust multiple-fault detection filter is affected primarily by one fault and minimally by other faults. The transmission from process and sensor noises is also minimized so that the filter is robust with respect to these disturbances. It is shown that, in the limit where the weighting on each associated nuisance fault transmission goes to infinity, the filter recovers the geometric structure of the restricted diagonal detection filter of which the Beard,Jones detection filter and unknown input observer are special cases. Filter designs can be obtained for both time-invariant and time-varying systems. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Revisiting N -continuous density-functional theory: Chemical reactivity and "Atoms" in "Molecules" ISRAEL JOURNAL OF CHEMISTRY, Issue 3-4 2003Morrel H. CohenWe construct an internally-consistent density-functional theory valid for noninteger electron numbers N by precise definition of a density functional that is continuous in N. In this theory, charge transfer between the atoms of a heteronuclear diatomic molecule, which have been separated adiabatically to infinity, is avoided because the hardness for fractional occupation of a single HOMO spin-orbital is negative. This N -continuous density functional makes possible a variational theory of "atoms" in "molecules" that exactly decomposes the molecular electron density into a sum of contributions from its parts. The parts are treated as though isolated. That theory, in turn, gives a deep foundation to the chemical reactivity theory provided that the hardness of entities with vanishing spin density is positive, as argued to be the case here. This transition from negative to positive hardness closely parallels the transition from the Heitler-London to the Hund-Mulliken picture of molecular bonding. [source] ## Averaging probability judgments: Monte Carlo analyses of asymptotic diagnostic value JOURNAL OF BEHAVIORAL DECISION MAKING, Issue 2 2001Timothy R. JohnsonAbstract Wallsten et al. (1997) developed a general framework for assessing the quality of aggregated probability judgments. Within this framework they presented a theorem regarding the effects of pooling multiple probability judgments regarding unique binary events. The theorem states that under reasonable conditions, and assuming conditional pairwise independence of the judgments, the average probability estimate is asymptotically perfectly diagnostic of the true event state as the number of estimates pooled goes to infinity. The purpose of the present study was to examine by simulation (1) the rate of convergence of averaged judgments to perfect diagnostic value under various conditions and (2) the robustness of the theorem to violations of its assumption that the covert probability judgments are conditionally pairwise independent. The results suggest that while the rate of convergence is sensitive to violations of the conditional pairwise independence, the asymptotic properties remain relatively robust under a large variety of conditions. The practical implications of these results are discussed. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Desensitizing models using covariance matrix transforms or counter-balanced distortions JOURNAL OF CHEMOMETRICS, Issue 4 2005Rocco DiFoggioAbstract This paper presents a generalization of the Lagrange multiplier equation for a regression subject to constraints. It introduces two methods for desensitizing models to anticipated spectral artifacts such as baseline variations, wavelength shift, or trace contaminants. For models derived from a covariance matrix such as multiple linear regression (MLR) and principal components regression (PCR) models, the first method shows how a covariance matrix can be desensitized to an artifact spectrum, v, by adding ,2v,,,v to it. For models not derived from a covariance matrix, such as partial least squares (PLS) or neural network (NN) models, the second method shows how distorted copies of the original spectra can be prepared in a counter-balanced manner to achieve desensitization. Unlike earlier methods that added random distortions to spectra, these new methods never introduce any accidental correlations between the added distortions and the Y -block. The degree of desensitization is controlled by a parameter, ,, for each artifact from zero (no desensitization) to infinity (complete desensitization, which is the Lagrange multiplier limit). Unlike Lagrange multipliers, these methods permit partial desensitization so we can individually vary the degree of desensitization to each artifact, which is important when desensitization to one artifact inhibits desensitization to another. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## OATP1B1 388A>G polymorphism and pharmacokinetics of pitavastatin in Chinese healthy volunteers JOURNAL OF CLINICAL PHARMACY & THERAPEUTICS, Issue 1 2010J. Wen PhDSummary Purpose:, To investigate the contribution of the most frequent single nucleotide polymorphism (SNPs) of the organic anion transporting polypeptide 1B1 (OATP1B1) 388A>G to the pharmacokinetics of pitavastatin in Chinese healthy volunteers. Methods:, Eighteen healthy volunteers participated in this study. Group 1 consisted of nine subjects who were of 388AA wild-type OATP1B1 genotype. Group 2 consisted of seven subjects with the 388GA genotype and two 388GG homozygotes. Two milligram of pitavastatin was administered orally to the volunteers. The plasma concentration of pitavastatin was measured for up to 48 h by liquid chromatography,mass spectrometry (LC,MS). Results:, The pharmacokinetic parameters of pitavastatin were significantly different between the two genotyped groups. The concentration (Cmax) value was higher in the 388GA + 388GG group than that in the 388AA group (39·22 ± 8·45 vs. 22·90 ± 4·03 ng/mL, P = 0·006). The area under the curve to the last measurable concentration (AUC0,48) and area under the curve extrapolated to infinity (AUC0,,) of pitavastatin were lower in the 388AA group than in the 388GA + 388GG group (100·42 ± 21·19 vs. 182·19 ± 86·46 ng h/mL, P = 0·024; 108·12 ± 24·94 vs. 199·64 ± 98·70ng h/mL, P = 0·026) respectively. The oral clearance (Cl/F) was lower in the 388GA + 388GG group than that in the 388AA group (12·46 ± 4·79 vs. 19·21 ± 3·74/h, P = 0·012). The elimination of half-life (t1/2) and peak concentration times (Tmax) values showed no difference between these groups. Conclusions:, The OATP 388A>G polymorphism causes significant alterations in the pharmacokinetics of pitavastatin in healthy Chinese volunteers and this may well be clinically significant. [source] ## Relaxation Time Spectrum of Hydrogels by CONTIN Analysis JOURNAL OF FOOD SCIENCE, Issue 3 2000R. MaoABSTRACT: CONTIN is a general-purpose program for inverting noisy linear algebraic and integral equations by means of inverse Laplace transform. This study explored the application of CONTIN analysis to determine the relaxation time distribution spectra for food gels, including gellan, carrageenan, whey protein, and gelatin gels, based on stress-relaxation data. CONTIN results represent the continuous relaxation time spectra when the number of the terms in the discrete Maxwell stress-relaxation model approached infinity. The CONTIN results for gellan gels were correlated to the texture properties of gels from compression tests with respect to the effects of calcium concentrations. CONTIN analysis may be a very effective tool in elucidating the microstructural properties of a hydrogel from mechanical testing. [source] ## Evaluation of hydrophilic permeant transport parameters in the localized and non-localized transport regions of skin treated simultaneously with low-frequency ultrasound and sodium lauryl sulfate JOURNAL OF PHARMACEUTICAL SCIENCES, Issue 2 2008Joseph Kushner IVAbstract The porosity (,), the tortuosity (,), and the hindrance factor (H) of the aqueous pore channels located in the localized transport regions (LTRs) and the non-LTRs formed in skin treated simultaneously with low-frequency ultrasound (US) and the surfactant sodium lauryl sulfate (SLS), were evaluated for the delivery of four hydrophilic permeants (urea, mannitol, raffinose, and inulin) by analyzing dual-radiolabeled diffusion masking experiments for three different idealized cases of the aqueous pore pathway hypothesis. When , and , were assumed to be independent of the permeant radius, H was found to be statistically larger in the LTRs than in the non-LTRs. When a distribution of pore radii was assumed to exist in the skin, no statistical differences in ,, ,, and H were observed due to the large variation in the pore radii distribution shape parameter (3 Å to infinity). When infinitely large aqueous pores were assumed to exist in the skin, , was found to be 3,8-fold greater in the LTRs than in the non-LTRs, while little difference was observed in the LTRs and in the non-LTRs for ,. This last result suggests that the efficacy of US/SLS treatment may be enhanced by increasing the porosity of the non-LTRs. © 2007 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 97:906,918, 2008 [source] |