Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book ...explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometrics, and applied mathematics, this is both an entry-level text and a valuable reference.
Due to the complexity of modeling the radiative transfer inside the accretion columns of neutron star binaries, their X-ray spectra are still commonly described with phenomenological models, e.g., a ...cut off power law. While the behavior of these models is well understood and they allow for a comparison of different sources and studying source behavior, the extent to which the underlying physics can be derived from the model parameters is very limited. During recent years, several physically motivated spectral models have been developed to overcome these limitations. Their application, however, is generally computationally much more expensive and they require a high number of parameters which are difficult to constrain. In particular, Becker & Wolff(2007) presented an analytical solution to the radiative transfer equation inside the accretion column assuming a velocity profile that is linear in the optical depth. An implementation of this model that is both fast and accurate enough to be fitted to observed spectra is available in XSPEC. The main difficulty of this implementation is that some solutions violate energy conservation and therefore have to be rejected by the user. We propose a novel fitting strategy that ensures energy conservation during theχ2-minimization which simplifies the application of the model considerably. We demonstrate this approach as well as a study of possible parameter degeneracies with a comprehensive Markov-Chain Monte Carlo analysis of the complete parameter space for a combined NuSTAR and Swift/XRT data-set of Cen X-3.The derived accretion-flow structure features a small column radius of∼63 m and a spectrum dominated by bulk-Comptonization of bremsstrahlung seed photons, in agreement with previous studies
In magnetic Cataclysmic Variables (mCVs), X-ray radiation originates from the shock heated multi-temperature plasma in the post-shock region near the white dwarf surface. These X-rays are modified by ...a complex distribution of absorbers in the pre-shock region. The presence of photo-ionized lines and warm absorber features in the soft X-ray spectra of these mCVs suggests that these absorbers are ionized. We developed the ionized complex absorber model zxipab, which is represented by a power-law distribution of ionized absorbers in the pre-shock ow. Using the ionized absorber model zxipab along with a cooling ow model and a reflection component, we model the broadband Chandra/HETG and NuSTAR spectra of two IPs: NY Lup and V1223 Sgr. We nd that this model describes well many of the H and He like emission lines from medium Z elements, which arises from the collisionally excited plasma. However the model fails to account for some of the He like triplets from medium Z elements, which points towards its photo-ionization origin. We do not find a compelling evidence for a blackbody component to model the soft excess seen in the residuals of the Chandra/HETG spectra, which could be due to the uncertainties in estimation of the interstellar absorption of these sources using Chandra/HETG data and/or excess fluxes seen in some photo-ionized emission lines which are not accounted by the cooling ow model. We describe the implications of this model with respect to the geometry of the pre-shock region in these two IPs
Provides a hands-on introduction to engineering analysis using one of the most powerful commercial general purposes finite element programs on the market. Students will find a practical and ...integrated approach that combines finite element theory with best practices for developing, verifying, validating and interpreting the results of finite element models, while engineering professionals will appreciate the deep insight presented on the program's structure and behavior. Additional topics covered include an introduction to commands, input files, batch processing, and other advanced features in ANSYS.
This study deals with mixed convection of Formula omitted-Cu-water hybrid nanofluid in a wavy channel having a circular cylinder. A two-dimensional system of partial differential equations has been ...discretized by employing Galerkin finite element method. Numerical simulations are carried out for different ranges of the governing parameters such as Reynolds number ( Formula omitted), nanoparticle volume fraction ( Formula omitted) and wave amplitude ( Formula omitted). It is inferred that Reynolds number is a key factor in this study. As it rises, the fluid behavior switches from slower to faster mode. Average Nusselt number rises at lower wavy wall and with lift coefficient ( Formula omitted). The highest average Nusselt number is achieved at Formula omitted, which is promoting the heat transfer by roughly Formula omitted. Furthermore, an enhancement in the nanoparticle volume fraction leads to the decrease in the local Nusselt number on upper wavy wall. The flow philosophy is presented in the form of isotherm contours, streamline contours and some appropriate plots.
The main goal of this work is to provide quantum parametrized Hermite-Hadamard like type integral inequalities for functions whose second quantum derivatives in absolute values follow different type ...of convexities. A new quantum integral identity is derived for twice quantum differentiable functions, which is used as a key element in our demonstrations along with several basic inequalities such as: power mean inequality, and Holder’s inequality. The symmetry of the Hermite-Hadamard type inequalities is stressed by the different types of convexities. Several special cases of the parameter are chosen to illustrate the investigated results. Four examples are presented.
We propose and analyze a class of particle methods for the Vlasov equation with a strong external magnetic field in a torus configuration. In this regime, the time step can be subject to stability ...constraints related to the smallness of Larmor radius. To avoid this limitation, our approach is based on higher-order semi-implicit numerical schemes already validated on dissipative systems 3 and for magnetic fields pointing in a fixed direction 9, 10, 12. It hinges on asymptotic insights gained in 11 at the continuous level. Thus, when the magnitude of the external magnetic field is large, this scheme provides a consistent approximation of the guiding-center system taking into account curvature and variation of the magnetic field. Finally, we carry out a theoretical proof of consistency and perform several numerical experiments that establish a solid validation of the method and its underlying concepts.
To study the temperature in a gas subjected to electromagnetic radiations, one may use the Radiative Transfer equations coupled with the Navier-Stokes equations. The problem has 7 dimensions; however ...with minimal simplifications it is equivalent to a small number of integrodifferential equations in 3 dimensions. We present the method and a numerical implementation using an H-matrix compression scheme. The result is a very fast: 50K physical points, all directions of radiation and 680 frequencies require less than 5 minutes on an Apple M1 Laptop. The method is capable of handling variable absorptioN and scattering functionS of spatial positions and frequencies. The implementation is done using htool 1 , a matrix compression library interfaced with the PDE solverfreefem++. Applications to the temperature in the French Chamonix valley is presented at different hours of the day with and without snow / clouds and with a variable absorption taken from the Gemini measurements. The result is precise enough to assert temperature differences due to increased absorption in the vibrational frequency subrange of greenhouse gasses.
Pour étudier la température dans un gaz soumis à des rayonnements électromagnétiques, on peut utiliser les équations du transfert radiatif couplées aux équations de Navier-Stokes. Le problème a 7 dimensions ; cependant, avec des simplifications minimales,on peut le réduire à un petit nombre d'équations intégro-différentielles en 3 dimensions. Nous présentons la méthode et une implémentation numérique utilisant un schéma de compression de matrice H. Le résultat est très rapide : 50K points physiques, toutes les directions de rayonnement et 680 fréquences nécessitent moins de 5 minutes sur un ordinateur portable Apple M1. Le procédé est capable de gérer des coefficients d'absorption et de diffusion dépendants des positions spatiales et des fréquences. L'implémentation se fait à l'aide de la bibliothèque htool , pour la compression de matrice à diagonales dominante, interfacée avec le solveur d'EDP freefem++. Les applications à la température dans la vallée française de Chamonix sont présentées à différentes heures de la journée avec et sans neige/nuage et avec une absorption variable tirée des mesures Gemini. Le résultat est suffisamment précis pour obtenir les différences de température dues à une absorption accrue dans une sous-gamme de fréquence vibratoire des gaz à effet de serre.
Convexity performs the appropriate role in the theoretical study of inequalities according to the nature and behavior. Its significance is raised by the strong connection between symmetry and ...convexity. In this article, we consider a new parameterized quantum fractional integral identity. By applying this identity, we obtain as main results some integral inequalities of trapezium, midpoint and Simpson's type pertaining to s-convex functions. Moreover, we deduce several special cases, which are discussed in detail. To validate our theoretical findings, an example and application to special means of positive real numbers are presented. Numerical analysis investigation shows that the mixed fractional calculus with quantum calculus give better estimates compared with fractional calculus or quantum calculus separately.
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