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Analytical Formulas (analytical + formula)
Selected AbstractsDiffraction-line shift caused by residual stress in polycrystal for all Laue groups in classical approximationsJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 1 2000N. C. Popa Analytical formulae for all Laue groups are derived, giving the dependence of the residual elastic strain measured by X-ray and neutron diffraction on the direction in the sample and on the Miller indices. These formulae are valid for isotropic polycrystals in the limits of the Reuss and Voigt approximations and are appropriate for Rietveld refinement. [source] Analytical formulas for the geometric and inertia quantities of the largest removable blocks around tunnelsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2007Fulvio Tonon Abstract This paper presents algorithms for determining the vertices of the maximum removable block (MB) created by a joint pyramid (JP) around a tunnel when discontinuities are fully persistent. It is shown that an MB cannot be formed by more than 4 discontinuities and this drastically limits the proliferation of rock blocks that need to be analysed. The non-convex block obtained after the MB is tunnelled through (real maximum block, RMB) is partitioned into a set of tetrahedra, and procedures are given for determining the vertices of these tetrahedra. Geometric and inertia quantities needed for stability analysis and support/reinforcement design are determined as functions of the calculated vertices' co-ordinates. These quantities are: RMB's volume, face areas, perimeter of the excavated surface, centroid and inertia tensor. The algorithms for their calculation are at least two times faster than other algorithms previously proposed in other applications. It is shown that the formulations presented by Goodman and Shi for translational analysis and by Tonon for rotatability analysis can be used to analyse the RMBs using the geometric quantities presented. A numerical example is presented among those used to verify these analytical procedures and their implementation. Copyright © 2006 John Wiley & Sons, Ltd. [source] Analytical Valuation of American Options on Jump-Diffusion ProcessesMATHEMATICAL FINANCE, Issue 1 2001Chandrasekhar Reddy Gukhal We derive analytic formulas for the value of American options when the underlying asset follows a jump-diffusion process and pays continuous dividends. They early exercise premium has a form very different form from that for diffusion processes, and this can be attributed to the discontinuous nature of the price paths. Analytical formulas are derived for several distributions of the jump amplitude. [source] Pipelines on heterogeneous systems: models and toolsCONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 9 2005F. Almeida Abstract We study the performance of pipeline algorithms in heterogeneous networks. The concept of heterogeneity is not only restricted to the differences in computational power of the nodes, but also refers to the network capabilities. We develop a skeleton tool that allows us an efficient block-cyclic mapping of pipelines on heterogeneous systems. The tool supports pipelines with a number of stages much larger than the number of physical processors available. We derive an analytical formula that allows us to predict the performance of pipelines in heterogeneous systems. According to the analytical complexity formula, numerical strategies to solve the optimal mapping problem are proposed. The computational results prove the accuracy of the predictions and effectiveness of the approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] Equilibrium and growth shapes of crystals: how do they differ and why should we care?CRYSTAL RESEARCH AND TECHNOLOGY, Issue 4-5 2005Robert F. SekerkaArticle first published online: 15 MAR 200 Abstract Since the death of Prof. Dr. Jan Czochralski nearly 50 years ago, crystals grown by the Czochralski method have increased remarkably in size and perfection, resulting today in the industrial production of silicon crystals about 30 cm in diameter and two meters in length. The Czochralski method is of great technological and economic importance for semiconductors and optical crystals. Over this same time period, there have been equally dramatic improvements in our theoretical understanding of crystal growth morphology. Today we can compute complex crystal growth shapes from robust models that reproduce most of the features and phenomena observed experimentally. We should care about this because it is likely to result in the development of powerful and economical design tools to enable future progress. Crystal growth morphology results from an interplay of crystallographic anisotropy and growth kinetics by means of interfacial processes and long-range transport. The equilibrium shape of a crystal results from minimizing its anisotropic surface free energy under the constraint of constant volume; it is given by the classical Wulff construction but can also be represented by an analytical formula based on the ,-vector formalism of Hoffman and Cahn. We now have analytic criteria for missing orientations (sharp corners or edges) on the equilibrium shape, both in two (classical) and three (new) dimensions. Crystals that grow under the control of interfacial kinetic processes tend asymptotically toward a "kinetic Wulff shape", the analogue of the Wulff shape, except it is based on the anisotropic interfacial kinetic coefficient. If it were not for long range transport, crystals would presumably nucleate with their equilibrium shape and then evolve toward their "kinetic Wulff shape". Allowing for long range transport leads to morphological instabilities on the scale of the geometric mean of a transport length (typically a diffusivity divided by the growth speed) and a capillary length (of the order of atomic dimensions). Resulting crystal growth shapes can be cellular or dendritic, but can also exhibit corners and facets related to the underlying crystallographic anisotropy. Within the last decade, powerful phase field models, based on a diffuse interface, have been used to treat simultaneously all of the above phenomena. Computed morphologies can exhibit cells, dendrites and facets, and the geometry of isotherms and isoconcentrates can also be determined. Results of such computations are illustrated in both two and three dimensions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Assessment of algorithms for the no-slip boundary condition in the lattice Boltzmann equation of BGK modelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008Yong Kweon Suh Abstract Three kinds of algorithms for the lattice Boltzmann equation of the BGK model in the implementation of the no-slip boundary condition on the wall are assessed by using the analytical formula for the slip velocity of the fully developed pressure-driven channel flow. It is shown that the bounce-back algorithm results in the spatial accuracy of 1st order, except for the case when the wall is located at half way between the two grid lines. The interpolation scheme proposed by Yu et al. (Prog. Aerospace Sci. 2003; 39:329,367) and the similar one by Bouzidi et al. (Phys. Fluids 2001; 13(11):3452,3459) are of 2nd order, but the error increases quadratically with the relaxation time. The extrapolation scheme of Guo et al. (Phys. Fluids 2002; 14(6):2007,2010) is also shown to be of 2nd order, and the error level increases linearly with the relaxation time, but it turns out that this scheme is unstable for a certain range of parameter values. Numerical experiments with various parameter sets have been performed to obtain the stability diagram. Three algorithms are then applied to a circular-Couette flow and their performance is also studied in terms of the numerical accuracy and stability. Copyright © 2008 John Wiley & Sons, Ltd. [source] Discrete thermodynamics of chemical equilibria and classical limit in thermodynamic simulationISRAEL JOURNAL OF CHEMISTRY, Issue 3-4 2007Boris Zilbergleyt This article sets forth comprehensive basic concepts of the discrete thermodynamics of chemical equilibrium as balance between internal and external thermodynamic forces. Conditions of chemical equilibrium in the open chemical system are obtained in the form of a logistic map, containing only one new parameter that defines the chemical system's resistance to external impact and its deviation from thermodynamic equilibrium. Solutions to the basic map are bifurcation diagrams that have quite traditional shape but the diagram areas feature specific meanings for chemical systems and constitute the system's domain of states. The article is focused on two such areas: the area of "true" thermodynamic equilibrium and the area of open chemical equilibrium. The border between them represents the classical limit, a transition point between the classical and newly formulated equilibrium conditions. This limit also separates regions of the system ideality, typical for isolated classical systems, and non-ideality due to the limitations imposed on the open system from outside. Numerical examples illustrating the difference between results of classical and discrete thermodynamic simulation methods are presented. The article offers an analytical formula to find the classical limit, compares analytical results with these obtained by simulation, and shows the classical limit dependence upon the chemical reaction stoichiometry and robustness. [source] Consistent treatment of inter- and intramolecular polarization in molecular mechanics calculationsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 16 2002Pengyu Ren Abstract A protocol is described for the treatment of molecular polarization in force field calculations. The resulting model is consistent in that both inter- and intramolecular polarization are handled within a single scheme. An analytical formula for removing intramolecular polarization from a set of atomic multipoles for an arbitrary static structure or conformation is given. With the help of the intramolecular polarization, these permanent atomic multipoles can then be applied in modeling alternative conformations of a molecule. Equipped with this simple technique, one can derive transferable electrostatic parameters for peptides and proteins using flexible model compounds such as dipeptides. The proposed procedure is tested for its ability to describe the electrostatic potential around various configurations of the N -methylacetamide dimer. The effect of different intramolecular polarization schemes on the accuracy of a force field model of the electrostatic potential of alanine dipeptide is investigated. A group-based scheme for including direct intramolecular polarization is shown to be most successful in accounting for the conformational dependence of electrostatic potentials. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 1497,1506, 2002 [source] PRICING AND HEDGING AMERICAN OPTIONS ANALYTICALLY: A PERTURBATION METHODMATHEMATICAL FINANCE, Issue 1 2010Jin E. Zhang This paper studies the critical stock price of American options with continuous dividend yield. We solve the integral equation and derive a new analytical formula in a series form for the critical stock price. American options can be priced and hedged analytically with the help of our critical-stock-price formula. Numerical tests show that our formula gives very accurate prices. With the error well controlled, our formula is now ready for traders to use in pricing and hedging the S&P 100 index options and for the Chicago Board Options Exchange to use in computing the VXO volatility index. [source] Energy-dependent variability from accretion flowsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2005Andrzej A. Zdziarski ABSTRACT We develop a formalism to calculate energy-dependent fractional variability (rms) in accretion flows. We consider rms spectra resulting from radial dependences of the level of local variability (as expected from the propagation of disturbances in accretion flows) assuming the constant shape of the spectrum emitted at a given radius. We consider the cases when the variability of the flow is either coherent or incoherent between different radial zones. As an example of local emission, we consider blackbody, Wien and thermal Comptonization spectra. In addition to numerical results, we present a number of analytical formulae for the resulting rms. We also find an analytical formula for the disc Wien spectrum, which we find to be a very good approximation to the disc blackbody. We compare our results to the rms spectrum observed in an ultrasoft state of GRS 1915+105. [source] [Ba6(C2H3O2)12(H2O)3.5], a new hydrate of barium acetateACTA CRYSTALLOGRAPHICA SECTION C, Issue 11 2007Gabriela Leyva A new barium acetate phase, di-,5 -acetato-tri-,4 -acetato-tri-,3 -acetato-tri-,2 -acetato-,2 -acetato-triaquahemiaquahexabarium(II), of analytical formula [Ba6(C2H3O2)12(H2O)3.5], is described. The asymmetric unit contains six independent Ba centres with coordination numbers varying from 7 to 10 arising from bonding to 12 crystallographically independent acetate ligands and four molecules of water, one of which is disordered over two sites both of occupancy 0.5. Bonding to the acetate ligands creates a completely connected three-dimensional structure. All H atoms of the water molecules participate in hydrogen bonding. [source] A Simple and reliable formula for assessment of maximum volumetric productivities in photobioreactorsBIOTECHNOLOGY PROGRESS, Issue 2 2009Jean-François Cornet Abstract This article establishes and discusses the consistency and the range of applicability of a simple but general and predictive analytical formula, enabling to easily assess the maximum volumetric biomass growth rates (the productivities) in several kinds of photobioreactors with more or less 15% of deviation. Experimental validations are performed on photobioreactors of very different conceptions and designs, cultivating the cyanobacterium Arthrospira platensis, on a wide range of volumes and hemispherical incident light fluxes. The practical usefulness of the proposed formula is demonstrated by the fact that it appears completely independent of the characteristics of the material phase (as the type of reactor, the kind of mixing, the biomass concentration,), according to the first principle of thermodynamics and to the Gauss-Ostrogradsky theorem. Its ability to give the maximum (only) kinetic performance of photobioreactors cultivating many different photoautotrophic strains (cyanobacteria, green algae, eukaryotic microalgae) is theoretically discussed but experimental results are reported to a future work of the authors or to any other contribution arising from the scientific community working in the field of photobioreactor engineering and potentially interested by this approach. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009 [source] Bivariate combined linkage and association mapping of quantitative trait lociGENETIC EPIDEMIOLOGY, Issue 5 2008Jeesun Jung Abstract In this paper, bivariate/multivariate variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL), based on combinations of pedigree and population data. Suppose that a quantitative trait locus is located in a chromosome region that exerts pleiotropic effects on multiple quantitative traits. In the region, multiple markers such as single nucleotide polymorphisms are typed. Two regression models, "genotype effect model" and "additive effect model", are proposed to model the association between the markers and the trait locus. The linkage information, i.e., recombination fractions between the QTL and the markers, is modeled in the variance and covariance matrix. By analytical formulae, we show that the "genotype effect model" can be used to model the additive and dominant effects simultaneously; the "additive effect model" only takes care of additive effect. Based on the two models, F -test statistics are proposed to test association between the QTL and markers. By analytical power analysis, we show that bivariate models can be more powerful than univariate models. For moderate-sized samples, the proposed models lead to correct type I error rates; and so the models are reasonably robust. As a practical example, the method is applied to analyze the genetic inheritance of rheumatoid arthritis for the data of The North American Rheumatoid Arthritis Consortium, Problem 2, Genetic Analysis Workshop 15, which confirms the advantage of the proposed bivariate models. Genet. Epidemiol. 2008. © 2008 Wiley-Liss, Inc. [source] A method for analysing the transient and the steady-state oscillations in third-order oscillators with shifting biasINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 5 2001A. Buonomo Abstract We provide an asymptotic method for systematically analysing the transient and the steady-state oscillations in third-order oscillators with shifting bias. The method allows us to construct the general solution of the weakly non-linear differential equation describing these oscillators through an iteration procedure of successive approximations typical of perturbation methods. The approximation to first order is obtained solving a system of two first-order non-linear differential equations in the leading terms of solution (dc component and fundamental harmonic), whereby the dominant dynamics, the stationary states and their stability can be easily analysed. Unlike existing approaches, our method also enables us to determine the higher harmonics as well as the frequency shift from the system's natural frequency in the exact solution through analytical formulae. In addition, formulae for higher-order approximations of the above quantities are determined. The proposed method is applied to a practical circuit to show its usefulness in both analysis and design problems. Copyright © 2001 John Wiley & Sons, Ltd. [source] Numerical modelling of anisotropy and eddy current effects in ferromagnetic laminations using a co-energy formulationINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5 2001L. R. Dupré Abstract The paper deals with a numerical model for the evaluation of electromagnetic fields in one steel lamination under the influence of a rotating magnetic flux, taking into account anisotropy effects. For this purpose a detailed material model, described by a differential permeability tensor, is included in the macroscopic electromagnetic field calculations in one lamination. Here, by geometrical and physical considerations, the governing Maxwell equations are reduced to a system of parabolic PDEs for the components of the magnetic field vector, under appropriate boundary and initial conditions. We present a suitable numerical approximation based upon a finite element,finite difference method, which properly takes into account the material characteristics. The study leads to a more realistic numerical modelling of the electromagnetic phenomena inside electric and magnetic conducting laminations due to anisotropy effects. Numerical results are compared with those from simplified analytical formulae. Copyright © 2001 John Wiley & Sons, Ltd. [source] Energy-dependent variability from accretion flowsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2005Andrzej A. Zdziarski ABSTRACT We develop a formalism to calculate energy-dependent fractional variability (rms) in accretion flows. We consider rms spectra resulting from radial dependences of the level of local variability (as expected from the propagation of disturbances in accretion flows) assuming the constant shape of the spectrum emitted at a given radius. We consider the cases when the variability of the flow is either coherent or incoherent between different radial zones. As an example of local emission, we consider blackbody, Wien and thermal Comptonization spectra. In addition to numerical results, we present a number of analytical formulae for the resulting rms. We also find an analytical formula for the disc Wien spectrum, which we find to be a very good approximation to the disc blackbody. We compare our results to the rms spectrum observed in an ultrasoft state of GRS 1915+105. [source] Power spectra from ,spotted' accretion discsASTRONOMISCHE NACHRICHTEN, Issue 10 2006T. Pechá Abstract We are carrying out a project to calculate power spectra of variability, assuming a model of a ,spotted' accretion disc near a black hole. We consider relativistic effects that change photon energy and produce light-bending and time-delays acting on the X-ray signal received by an observer. We assume that the life-time and the intrinsic emissivity of individual.aring events are described in terms of a simple stochastic process. This allows us to give approximate analytical formulae and compare them with numerical computations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Time-series photometric spot modelling , VI.ASTRONOMISCHE NACHRICHTEN, Issue 3 2003A new computer code, its application to 23 years of photometry of the active giant IM Pegasi Abstract We present and apply a new computer program named SpotModeL to analyze single and multiple bandpass photometric data of spotted stars. It is based on the standard analytical formulae from Budding and Dorren. The program determines the position, size, and temperature of up to three spots by minimizing the fit residuals with the help of the Marquardt-Levenberg non-linear least-squares algorithm. We also expand this procedure to full time-series analysis of differential data, just as real observations would deliver. If multi-bandpass data are available, all bandpasses can be treated simultaneously and thus the spot temperature is solved for implicitly. The program may be downloaded and used by anyone. In this paper, we apply our code to an ,23 year long photometric dataset of the spotted RS CVn giant IM Peg. We extracted and modelled 33 individual light curves, additionally, we fitted the entire V dataset in one run. The resulting spot parameters reflect the long term light variability and reveal two active longitudes on the substellar point and on the antipode. The radius and longitude of the dominant spot show variations with 29.8 and 10.4 years period, respectively. Our multicolour data suggests that the spot temperature is increasing with the brightening of the star. The average spot temperature from V, IC is 3550 ± 150 K or approximately 900 K below the effective temperature of the star. [source] A note on formulas for localized failure of frictional materials in compression and biaxial loading modesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2001Matthias Lambrecht Abstract The paper investigates aspects of the localization analysis of frictional materials. We derive closed formulas and diagrams for the inclination angle of critical discontinuity surfaces which develop in homogeneous compression and biaxial loading tests. The localization analysis is based on a Drucker,Prager-type elastoplastic hardening model for non-associated plastic flow at small strains, which we represent in spectral form. For this type of constitutive model, general analytical formulas for the so-called critical hardening modulus and the inclination angle of critical discontinuity surfaces are derived for the plane strain case. The subsequent treatment then specializes these formulas for the analysis of compression and biaxial loading modes. The key contribution here is a detailed analysis of plane strain deformation modes where the localized failure occurs after subsequent plastic flow. The derived formulas and diagrams can be applied to the checking of an accompanying localization analysis of frictional materials in finite-element computations. Copyright © 2001 John Wiley & Sons, Ltd. [source] Efficient inductance calculation for planar spiral inductors and transformers based on analytical concentric half-turn formulasINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 6 2006Wei Gao Abstract A new method to efficiently calculate the self and mutual inductances of a planar spiral inductor or a multicoil transformer is presented. Three analytical formulas are firstly derived to calculate partial inductances of concentric half-turn segments, which are then summed to the device's total inductances. The final results are quite accurate whether compared to the measurements or the numerical simulations. The method is also compatible with any script-supported circuit simulators. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006. [source] Improved design method for optimum gain pyramidal hornsINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 4 2001Kerim Güney Abstract A technique, simple and easy to use, is presented to design the optimum gain pyramidal horn. The optimum gain pyramidal horn design equation available in the literature is improved. Design parameters are computed from the simple and explicit analytical formulas. The pyramidal horn gain is determined with no path length error approximation. Several design examples are given to show the performance of the improved design technique. © 2001 John Wiley & Sons, Inc. Int J RF and Microwave CAE 11: 188,193, 2001. [source] Physical,statistical methods for determining state transition probabilities in mobile-satellite channel modelsINTERNATIONAL JOURNAL OF SATELLITE COMMUNICATIONS AND NETWORKING, Issue 3 2001S. R. Saunders Abstract Signal propagation in land mobile satellite (LMS) communication systems has for the last decade become an essential consideration, especially when high-rate data services are involved. As far as urban or suburban built-up areas are concerned, the extent of the influence is mainly restricted to the roadside obstacles, since the satellite is positioned at relatively high elevation angles in most practical situations. Probably, the most common model currently used for representing the LMS channel is the Lutz model, which uses two states to represent line-of-sight and non-line-of-sight conditions. Transitions between these states are described by transition probabilities which are a function of the environment and the satellite elevation angles. Similarly, an extension to the model allows a four-state description to be used for the states associated with a pair of satellites used in a dual-diversity configuration. Calculation of the transition probabilities then requires knowledge of the correlation between the two channels, which in turn depends on the spatial characteristics of the local environment around the mobile. In both cases, the transition probabilities have been derived basically from measurements in the past. In the new approaches described in this paper, physical,statistical principles are applied to construct analytical formulas for the probabilities of shadowing and the correlation between states. These expressions apply particularly to systems operated in built-up environments, and have been checked against numerical experiments and against direct measurements. In both cases excellent agreement is obtained. Copyright © 2001 John Wiley & Sons, Ltd. [source] Strategies to model the near-solute solvent molecular density/polarizationJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 5 2009Pei-Kun Yang Abstract The solvent molecular distribution significantly affects the behavior of the solute molecules and is thus important in studying many biological phenomena. It can be described by the solvent molecular density distribution, g, and the solvent electric dipole distribution, p. The g and p can be computed directly by counting the number of solvent molecules/dipoles in a microscopic volume centered at r during a simulation or indirectly from the mean force F and electrostatic field E acting on the solvent molecule at r, respectively. However, it is not clear how the g and p derived from simulations depend on the solvent molecular center or the solute charge and if the gF and pE computed from the mean force and electric field acting on the solvent molecule, respectively, could reproduce the corresponding g and p obtained by direct counting. Hence, we have computed g,p,gF, and pE using different water centers from simulations of a solute atom of varying charge solvated in TIP3P water. The results show that gF and pE can reproduce the g and p obtained using a given count center. This implies that rather than solving the coordinates of each water molecule by MD simulations, the distribution of water molecules could be indirectly obtained from analytical formulas for the mean force F and electrostatic field E acting on the solvent molecule at r. Furthermore, the dependence of the g and p distributions on the solute charge revealed provides an estimate of the change in g and p surrounding a biomolecule upon a change in its conformation. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009 [source] Distribution Function and Thermodynamic Potentials of a Self-Avoiding ChainMACROMOLECULAR THEORY AND SIMULATIONS, Issue 5 2006Aleksey D. Drozdov Abstract Summary: An explicit expression is derived for the distribution function of end-to-end vectors for a flexible self-avoiding chain. Based on this relation, analytical formulas are developed for the free and internal energies of a chain with excluded-volume interactions. Force,stretch relations are obtained at uniaxial tension and compression. The effects of strength of segment interactions on the shapes of the distribution function and the force-displacement diagram, as well as on the mean-square end-to-end distance and stiffness of a chain are studied numerically. The dimensionless distribution function P versus the dimensionless end-to-end vector Q* for self-repellent chains with ,,=,0.0, 0.4, 0.8, 1.2, and 1.6, from top to bottom, respectively. [source] PRICING EQUITY DERIVATIVES SUBJECT TO BANKRUPTCYMATHEMATICAL FINANCE, Issue 2 2006Vadim Linetsky We solve in closed form a parsimonious extension of the Black,Scholes,Merton model with bankruptcy where the hazard rate of bankruptcy is a negative power of the stock price. Combining a scale change and a measure change, the model dynamics is reduced to a linear stochastic differential equation whose solution is a diffusion process that plays a central role in the pricing of Asian options. The solution is in the form of a spectral expansion associated with the diffusion infinitesimal generator. The latter is closely related to the Schrödinger operator with Morse potential. Pricing formulas for both corporate bonds and stock options are obtained in closed form. Term credit spreads on corporate bonds and implied volatility skews of stock options are closely linked in this model, with parameters of the hazard rate specification controlling both the shape of the term structure of credit spreads and the slope of the implied volatility skew. Our analytical formulas are easy to implement and should prove useful to researchers and practitioners in corporate debt and equity derivatives markets. [source] A NEW METHOD OF PRICING LOOKBACK OPTIONSMATHEMATICAL FINANCE, Issue 2 2005Peter Buchen A new method for pricing lookback options (a.k.a. hindsight options) is presented, which simplifies the derivation of analytical formulas for this class of exotics in the Black-Scholes framework. Underlying the method is the observation that a lookback option can be considered as an integrated form of a related barrier option. The integrations with respect to the barrier price are evaluated at the expiry date to derive the payoff of an equivalent portfolio of European-type binary options. The arbitrage-free price of the lookback option can then be evaluated by static replication as the present value of this portfolio. We illustrate the method by deriving expressions for generic, standard floating-, fixed-, and reverse-strike lookbacks, and then show how the method can be used to price the more complex partial-price and partial-time lookback options. The method is in principle applicable to frameworks with alternative asset-price dynamics to the Black-Scholes world. [source] Global and local linear buckling behavior of a chiral cellular structurePHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 3 2005A. Spadoni Abstract This paper investigates the flat-wise compression behavior of an innovative cellular structure configuration. The considered layout has a hexagonal chiral geometry featuring cylinders, or nodes, joined by ligaments, or ribs. The resulting assembly is characterized by a number of interesting properties that can be exploited for the design of alternative honeycombs or cellular topologies to be used in sandwich construction. The flat-wise strength of the chiral geometry is investigated through classical analytical formulas for the linear buckling of thin plates and shells and a bifurcation analysis performed on a Finite Element model. The analytical expressions predict the global buckling behavior and the resulting critical loads, and can be directly compared with the results obtained from the Finite Element analysis. In addition, the Finite Element model predicts local buckling modes, which should be considered to evaluate the possible development of localized plasticity. A sensitivity study is performed to evaluate the influence of the geometry of the chiral structure on its buckling strength. The study shows that the considered topology can offer great design flexibility, whereby several parameters can be selected and modified to improve the flat-wise performance. The comparison with traditional, hexagonal centro-symmetric structural configurations concludes the paper and demonstrates the enhanced performance and the potentials of chiral noncentro-symmetric designs. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Impact and Quantification of the Sources of Error in DNA Pooling DesignsANNALS OF HUMAN GENETICS, Issue 1 2009A. Jawaid Summary The analysis of genome wide variation offers the possibility of unravelling the genes involved in the pathogenesis of disease. Genome wide association studies are also particularly useful for identifying and validating targets for therapeutic intervention as well as for detecting markers for drug efficacy and side effects. The cost of such large-scale genetic association studies may be reduced substantially by the analysis of pooled DNA from multiple individuals. However, experimental errors inherent in pooling studies lead to a potential increase in the false positive rate and a loss in power compared to individual genotyping. Here we quantify various sources of experimental error using empirical data from typical pooling experiments and corresponding individual genotyping counts using two statistical methods. We provide analytical formulas for calculating these different errors in the absence of complete information, such as replicate pool formation, and for adjusting for the errors in the statistical analysis. We demonstrate that DNA pooling has the potential of estimating allele frequencies accurately, and adjusting the pooled allele frequency estimates for differential allelic amplification considerably improves accuracy. Estimates of the components of error show that differential allelic amplification is the most important contributor to the error variance in absolute allele frequency estimation, followed by allele frequency measurement and pool formation errors. Our results emphasise the importance of minimising experimental errors and obtaining correct error estimates in genetic association studies. [source] User-level QoS and traffic engineering for 3G wireless 1xEV-DO systemsBELL LABS TECHNICAL JOURNAL, Issue 2 2003Simon C. Borst Third-generation (3G) wireless systems such as 3G1X, 1xEV-DO, and 1xEV-DV provide support for a variety of high-speed data applications. The success of these services critically relies on the capability to ensure an adequate quality of service (QoS) experience to users at an affordable price. With wireless bandwidth at a premium, traffic engineering and network planning play a vital role in addressing these challenges. We present models and techniques that we have developed for quantifying the QoS perception of 1xEV-DO users generating file transfer protocol (FTP) or Web browsing sessions. We show how user-level QoS measures may be evaluated by means of a Processor-Sharing model that explicitly accounts for the throughput gains from multi-user scheduling. The model provides simple analytical formulas for key performance metrics such as response times, blocking probabilities, and throughput. Analytical models are especially useful for network deployment and in-service tuning purposes due to the intrinsic difficulties associated with simulation-based optimization approaches. © 2003 Lucent Technologies Inc. [source] Impact of Population Substructure on Trend Tests for Genetic Case,Control Association StudiesBIOMETRICS, Issue 1 2010Gang Zheng Summary Hidden population substructure in case,control data has the potential to distort the performance of Cochran,Armitage trend tests (CATTs) for genetic associations. Three possible scenarios that may arise are investigated here: (i) heterogeneity of genotype frequencies across unidentified subpopulations (PSI), (ii) heterogeneity of genotype frequencies and disease risk across unidentified subpopulations (PSII), and (iii) cryptic correlations within unidentified subpopulations. A unified approach is presented for deriving the bias and variance distortion under the three scenarios for any CATT in a general family. Using these analytical formulas, we evaluate the excess type I errors of the CATTs numerically in the presence of population substructure. Our results provide insight into the properties of some proposed corrections for bias and variance distortion and show why they may not fully correct for the effects of population substructure. [source] | ||||||||||||||||||||||||||||||||||