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Academic literature on the topic 'Theory of distributions (Functional analysis)'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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Journal articles on the topic "Theory of distributions (Functional analysis)"

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Jakubowski, Jacek, and Maciej Wiśniewolski. "Another Look at the Hartman-Watson Distributions." Potential Analysis 53, no. 4 (November 5, 2019): 1269–97. http://dx.doi.org/10.1007/s11118-019-09806-7.

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Abstract The article deals with the Hartman-Watson distributions and presents a new approach to them by investigating a special function u. The function u is strictly related to the distribution of the exponential functional of Brownian motion appearing in the mathematical finance framework. The study of the latter leads to new explicit representations for the function u. One of them is through a new parabolic PDE. Integral relations of convolution type between Hartman-Watson distributions and modified Bessel functions are presented. It turns out that u can be represented as an integral convolution of itself and the modified Bessel function K0. Finally, excursion theory and a subordinator connected to the hyperbolic cosine of Brownian motion are involved in order to obtain yet another representation for u. Possible applications of the resulting explicit formulas are discussed, among others Monte Carlo evaluations of u.

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Bao, Nguyen Dien Quoc, Le Hoang Chien, Chau Van Tao, and Trinh Hoa Lang. "Analysis of 12C+12C scattering using different nuclear density distributions." Science and Technology Development Journal 21, no. 3 (October 16, 2018): 78–83. http://dx.doi.org/10.32508/stdj.v21i3.431.

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Elastic 12C+12C angular distributions at three bombarding energies of 102.1, 112.0 and 126.1 MeV were analyzed in the framework of optical model (OM) and compared to the experimental data. The reality of the OM analysis using the double folding potential depends on the chosen nuclear density distributions. In this work, we use two available models of nuclear density distributions obtained from the electron scattering experiments and the density functional theory (DFT). The OM results show that the former gives better description of the 12C nuclear density distribution than the latter. Therefore, the DFT should be worked on for improving the nuclear density description of 12C in the future.

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Dehay, Dominique, and Jacek Leśkow. "Functional limit theory for the spectral covariance estimator." Journal of Applied Probability 33, no. 4 (December 1996): 1077–92. http://dx.doi.org/10.2307/3214987.

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Processes that exhibit repeatability in their kth-order moments are frequently studied in signal analysis. Such repeatability can be conveniently expressed with the help of almost periodicity. In particular, almost periodically correlated (APC) processes play an important role in the analysis of repeatable signals. This paper presents a study of asymptotic distributions of the estimator of the spectral covariance function for APC processes. It is demonstrated that, for a large class of APC processes, the functional central limit theorem holds.

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Dehay, Dominique, and Jacek Leśkow. "Functional limit theory for the spectral covariance estimator." Journal of Applied Probability 33, no. 04 (December 1996): 1077–92. http://dx.doi.org/10.1017/s002190020010049x.

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Processes that exhibit repeatability in their kth-order moments are frequently studied in signal analysis. Such repeatability can be conveniently expressed with the help of almost periodicity. In particular, almost periodically correlated (APC) processes play an important role in the analysis of repeatable signals. This paper presents a study of asymptotic distributions of the estimator of the spectral covariance function for APC processes. It is demonstrated that, for a large class of APC processes, the functional central limit theorem holds.

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Zeng, Ming, Yiping Tang, Jianguo Mi, and Chongli Zhong. "Improved Direct Correlation Function for Density Functional Theory Analysis of Pore Size Distributions." Journal of Physical Chemistry C 113, no. 40 (September 11, 2009): 17428–36. http://dx.doi.org/10.1021/jp902803t.

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Fux, Samuel, Karin Kiewisch, Christoph R. Jacob, Johannes Neugebauer, and Markus Reiher. "Analysis of electron density distributions from subsystem density functional theory applied to coordination bonds." Chemical Physics Letters 461, no. 4-6 (August 2008): 353–59. http://dx.doi.org/10.1016/j.cplett.2008.07.038.

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Chesneau, Christophe. "On a Logarithmic Weighted Power Distribution: Theory, Modelling and Applications." Journal of Mathematical Sciences: Advances and Applications 67, no. 1 (October 10, 2021): 1–59. http://dx.doi.org/10.18642/jmsaa_7100122214.

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Engineers, economists, hydrologists, social scientists, and behavioural scientists often deal with data belonging to the unit interval. One of the most common approaches for modeling purposes is the use of unit distributions, beginning with the classical power distribution. A simple way to improve its applicability is proposed by the transmuted scheme. We propose an alternative in this article by slightly modifying this scheme with a logarithmic weighted function, thus creating the log-weighted power distribution. It can also be thought of as a variant of the log-Lindley distribution, and some other derived unit distributions. We investigate its statistical and functional capabilities, and discuss how it distinguishes between power and transmuted power distributions. Among the functions derived from the log-weighted distribution are the cumulative distribution, probability density, hazard rate, and quantile functions. When appropriate, a shape analysis of them is performed to increase the exibility of the proposed modelling. Various properties are investigated, including stochastic ordering (first order), generalized logarithmic moments, incomplete moments, Rényi entropy, order statistics, reliability measures, and a list of new distributions derived from the main one are offered. Subsequently, the estimation of the model parameters is discussed through the maximum likelihood procedure. Then, the proposed distribution is tested on a few data sets to show in what concrete statistical scenarios it may outperform the transmuted power distribution.

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Koshmanenko, Volodymyr. "The theory of dynamical systems of conflict in the framework of functional analysis." Збірник Праць Інституту математики НАН України 20, no. 1 (August 17, 2023): 843–72. http://dx.doi.org/10.3842/trim.v20n1.530.

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In this article, we give an introduction to the mathematical setting of problems related to the phenomenon of conflict in terms of constructions in Hilbert spaces. The struggle (conflict, game) between opponents (adversaries, players) will be represented by operator transformations of vectors in Hilbert spaces and probabilistic distributions on the territory of life resources. The phenomenon of conflict as a contradiction between opponents appears in mathematical terms as an intersection the domains of definition for operators and overlapping of corresponding measures. Conflict interaction between opponents in the physical sense is described by the specific transformation of states in a Hilbert space. In turn, this is a mapping that changes the spectral measurements. Thus, a complex dynamical system arises, which we call a dynamical system of conflict. Then the following main problems arise as fundamental questions. What reasonable law of engagement (game or war) should be adopted to resolve the initial intersections? What is a fair limiting distribution of the resource territory? In a more general formulation, solving conflict problems means the detailed describing of all possible outcomes on opponents states of the type: victories, defeats, states of equilibrium, compromises as fixed points together with their basins of attraction.

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Blackmore, Denis, and Jack G. Zhou. "Fractal Analysis of Height Distributions of Anisotropic Rough Surfaces." Fractals 06, no. 01 (March 1998): 43–58. http://dx.doi.org/10.1142/s0218348x98000067.

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A general distribution function for the heights of anisotropic engineering surfaces is obtained by extending earlier work on surface profiles. The derivation starts from a functional description of surface heights that involves fractal quantities and is comprehensive enough to include almost all of the mathematical models for surface topography that have appeared in the literature. It is found that the distribution is in the form of a Gaussian function multiplied by a convergent power series, and the terms in the series depend in a fundamental way on the fractal parameters of the surface. This distribution is used to predict the dependence of bearing-area on fractal parameters, and is compared with other approaches to anisotropic surfaces in the literature. Two truncated approximate versions of the distribution function are introduced in order to test the theoretical model against experimentally obtained distributions of engineering surfaces; the results show good agreement between theory and experiment.

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Thangarasu, S., V. Siva, A. Shameem, A. Murugan, S. Athimoolam, and S. Asath Bahadur. "Structural, Electronic, Molecular Orbital Analysis and Charge Distributions on Nitrate Salt of Guanidine through DFT and TD-DFT Methods." Asian Journal of Chemistry 33, no. 8 (2021): 1905–10. http://dx.doi.org/10.14233/ajchem.2021.23201.

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Guanidinium nitrate, a non-linear optical material has been systematically studied through quantum chemical (density functional theory and Hartree Fock) methods. Studies on Mulliken charge, Frontier molecular orbitals (FMOs) and hyperpolarizability analyses have been performed. The Mulliken population analyses were carried out for the optimized molecular geometry by HF and B3LYP methods with 6-311++G(d,p) levels. The molecular orbital parameters of guanidinium nitrate have been calculated by FMO analysis. Frontier molecular orbital (FMO) analysis indicates the electron delocalization on the guanidinium nitrate and also its low value of energy gap indicates electron transfer. Optical property has been investigated by time-dependent density functional theory (TD-DFT) calculation. The second-order hyperpolarizability value of the ion pairs is much greater than urea, which confirms the good NLO nature of guanidinium nitrate.

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Dissertations / Theses on the topic "Theory of distributions (Functional analysis)"

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Waller, Bradley A. "Properties of p-adic C^k Distributions." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1385485834.

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Kou, Kit Ian. "Paley-Wiener theorem and Shannon sampling with the Clifford analysis setting." Thesis, University of Macau, 2005. http://umaclib3.umac.mo/record=b2492153.

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Butler, Pieter-Willem. "The transfer of distributions by LULU smoothers." Thesis, Link to the online version, 2008. http://hdl.handle.net/10019/2030.

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Begum, Munni. "Estimating posterior expectation of distributions belonging to exponential and non exponential families." Virtual Press, 2001. http://liblink.bsu.edu/uhtbin/catkey/1244863.

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Bayesian principle is conceptually simple and intuitively plausible to carry out but its numerical implementation is not always straightforward. Most of the times we have posterior distributions in terms of complicated analytical funs ions and be known only up to a multiplicative constant. Hence it becomes computationally difficult to attain the marginal densities and the moments of the posterior distributions in closed form. In the present study the leading methods, both analytical and numerical, for implementing Bayesian inference has been explored. In particular, the non-iterative Monte Carlo method known as Importance Sampling has been applied to approximate the posterior expectations of the Lognormal and Cauchy distributions, belonging to the Exponential family and the non-Exponential family of distributions respectively. Sample values from these distributions have been simulated through computer programming. Calculations are done mostly by C++ programming language and Mathematica.
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Kim, Jongchul. "Generalized Function Solutions to Nonlinear Wave Equations with Distribution Initial Data." Thesis, University of North Texas, 1996. https://digital.library.unt.edu/ark:/67531/metadc278853/.

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In this study, we consider the generalized function solutions to nonlinear wave equation with distribution initial data. J. F. Colombeau shows that the initial value problem u_tt - Δu = F(u); m(x,0) = U_0; u_t (x,0) = i_1 where the initial data u_0 and u_1 are generalized functions, has a unique generalized function solution u. Here we take a specific F and specific distributions u_0, u_1 then inspect the generalized function representatives for the initial value problem solution to see if the generalized function solution is a distribution or is more singular. Using the numerical technics, we show for specific F and specific distribution initial data u_0, u_1, there is no distribution solution.

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Hasan, Abeer. "A Study of non-central Skew t Distributions and their Applications in Data Analysis and Change Point Detection." Bowling Green State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1371055538.

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Engelke, Sebastian. "Brown-Resnick Processes: Analysis, Inference and Generalizations." Doctoral thesis, Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2012. http://hdl.handle.net/11858/00-1735-0000-000D-F1B3-2.

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Kong, Fanhui. "Asymptotic distributions of Buckley-James estimator." Online access via UMI:, 2005.

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Lai, Pik-ying, and 黎碧瑩. "Lp regression under general error distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B30287844.

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Chan, Chun-man, and 陳俊文. "On a topic of Bayesian analysis using scale mixtures distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31223989.

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Books on the topic "Theory of distributions (Functional analysis)"

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Carmichael, Richard D. Distributions and analytic functions. Harlow: Longman Scientific & Technical, 1989.

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Carmichael, Richard D. Distributions and analytic functions. Harlow, Essex, England: Longman Scientific & Technical, 1989.

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Carmichael, Richard D. Distributions and analytic functions. Harlow, Essex, England: Longman Scientific & Technical, 1989.

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Kanwal, Ram P. Generalized functions: Theory and applications. 3rd ed. Boston: Birkhäuser, 2004.

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Friedlander, F. G. Introduction to the theory of distributions. 2nd ed. Cambridge, UK: Cambridge University Press, 1998.

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Grudzinski, Olaf von. Quasihomogeneous distributions. Amsterdam: North-Holland, 1991.

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Marchand, J. P. Distributions: An outline. Mineola, N.Y: Dover Publications, 2007.

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Hoskins, R. F. Delta functions: An introduction to generalised functions. 2nd ed. Chichester, UK: Horwood Pub., 2009.

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Colombeau, Jean François. Multiplication of distributions: A tool in mathematics, numerical engineering, and theoretical physics. Berlin: Springer-Verlag, 1992.

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S, Pathak R., and International Symposium on Generalized Functions and Their Applications (1991 : Vārānasi, Uttar Pradesh, India), eds. Generalized functions and their applications. New York: Plenum Press, 1993.

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Book chapters on the topic "Theory of distributions (Functional analysis)"

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Khanfer, Ammar. "Distribution Theory." In Applied Functional Analysis, 81–131. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-99-3788-2_2.

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Vogt, Dietmar. "Sequence Space Representations of Spaces of Test Functions and Distributions." In Functional Analysis, Holomorphy, and Approximation Theory, 405–43. Boca Raton: CRC Press, 2020. http://dx.doi.org/10.1201/9781003072577-18.

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Kozma, Gady, and Alexander Olevskii. "Singular Distributions and Symmetry of the Spectrum." In Operator-Related Function Theory and Time-Frequency Analysis, 107–16. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08557-9_4.

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Lang, Serge. "Distributions." In Real and Functional Analysis, 295–307. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0897-6_11.

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Reddy, B. Daya. "Distributions and Sobolev spaces." In Introductory Functional Analysis, 213–51. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0575-3_8.

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Yosida, Kôsaku. "Ergodic Theory and Diffusion Theory." In Functional Analysis, 379–418. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-61859-8_14.

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Muscat, Joseph. "Spectral Theory." In Functional Analysis, 307–43. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06728-5_14.

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Berezansky, Yuri M., Zinovij G. Sheftel, and Georgij F. Us. "Measure Theory." In Functional Analysis, 1–65. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9185-1_1.

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Muscat, Joseph. "Spectral Theory." In Functional Analysis, 345–82. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-27537-1_14.

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Botelho, Fabio. "Distributions." In Functional Analysis and Applied Optimization in Banach Spaces, 167–74. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06074-3_7.

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Conference papers on the topic "Theory of distributions (Functional analysis)"

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Alavinasab, Ali, Goodarz Ahmadi, and Ratneshwar Jha. "Nonlocal Continuum Theory Based Modeling of Carbon Nanotube Composites." In ASME 2008 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2008. http://dx.doi.org/10.1115/smasis2008-595.

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Analytical modeling of Carbon Nanotube (CNT) composite based on the nonlocal continuum theory is investigated. This approach accounts for nonlocal stress-strain relationships, that is, stress at any point in a structure is a function of strain in the entire structure. Finite element analysis of a representative volume element (RVE) of CNT composite is used to evaluate unknown constant in the nonlocal theory based solution. Stress distributions are obtained from finite element method (FEM), nonlocal theory, and standard (local) elasticity. Nonlocal theory and FEM stress distributions yield the same total force and first moment, whereas standard elasticity gives less accurate results.

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Navazi, H. M., and H. Haddadpour. "Supersonic Flutter of Functionally Graded Plates in a Thermal Environment." In ASME 8th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2006. http://dx.doi.org/10.1115/esda2006-95253.

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In this paper, an analytical investigation intended to determine the flutter margin of supersonic functionally graded panels is carried out. For this purpose, piston theory aerodynamics has been employed to model quasi-steady aerodynamic loading. The material properties of the plate are assumed to be graded continuously across the panel thickness. The variation of temperature-dependent thermoelastic properties follows a simple power-law distribution in terms of the volume fraction of the constituent materials. The effects of compressive in-plane loads and static pressure differential are studied. Both uniform and through the thickness nonlinear temperature distributions are also considered. Hamilton’s principle is used to determine the coupled partial differential equations of motion. Using Galerkin’s method, the derived equations are transformed into a set of coupled ordinary differential equations, and then solved by numerical time integration. Some examples comparing the flutter margin of FG panels with that of plates made of pure metals and pure ceramics are presented. The results of the present study are compared with those of the previous works, where finite element method was used. It is shown that the use of functionally graded materials can yield an increase or decrease of the aeroelastic stability in the supersonic flow for different regions.

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Tzou, H. S., D. W. Wang, and I. Hagiwara. "Distributed Dynamic Signal Analysis of Piezoelectric Laminated Linear and Nonlinear Toroidal Shells." In ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/ad-23715.

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Abstract Toroidal shells belong to the shells of revolution family. Dynamic sensing signals and their distributed characteristics of spatially distributed sensors or neurons laminated on thin toroidal shell structures are investigated in this study. Spatially distributed modal voltages and signal patterns are related to the meridional and circumferential membrane/bending strains, based on the direct piezoelectricity, the Gauss theorem, the Maxwell principle and the open-circuit assumption. Linear and nonlinear toroidal shells are defined based on the thin shell theory and the von Karman geometric nonlinearity. With the simplified mode shape functions defined by the Donnell-Mushtari-Vlasov theory, modal dependent distributed signals and detailed signal components of spatially distributed sensors or neurons are defined and these signals are quantitatively illustrated. Signal distributions basically reveal distinct modal characteristics of toroidal shells. Parametric studies suggest that the dominating signal component originates from the meridional membrane strains. Shell dimensions, materials, boundary conditions, natural modes, sensor locations/distributions/sizes, modal strain components, etc. all influence the spatially distributed modal voltages and signal generations.

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Darabi, Mehdi, and Rajamohan Ganesan. "Exact 3-D Stress and Stiffness Analysis of Functionally Graded Sandwich Plates Using Sampling Surfaces Method." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38400.

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In the present work, the three-dimensional analysis for the deflection and stress distributions of functionally graded ceramic–metal sandwich plates is developed based on the method of sampling surfaces (SaS). In accordance with this method, into each layer of the plate, reference surfaces that are not equally spaced and are parallel to the mid-surface of the plate are introduced, and the displacement vectors of these surfaces are chosen as unknown functions. Such a choice allows the representation of the governing equations of the proposed higher order layer-wise plate theory in a very compact form and also permits the derivation of strain–displacement relationships correctly describing all motions including the rigid-body motions of the functionally graded plate. Hence the 3D elasticity problem of the thick plate is efficiently solved. The material properties of sandwich plate’s face layer are assumed to be that of a two-constituent material that vary continuously through the thickness of the face sheet according to a power law distribution of the volume fraction of the constituents. The core layer is homogeneous and made of an isotropic ceramic material. The effects of the volume fraction of the material constituents and their distribution on the deflections and, in particular, the 3-D stress distributions as well as the effects of the length-to-width and length-to-thickness ratios of the plate are investigated. Comparison of the results of the present work with the results available in existing literature is carried out for a benchmark problem. It is shown that considering large number of SaS, which are located at interfaces and Chebyshev polynomial nodes, the accuracy of the solutions can be improved significantly wherein the error will approach zero value as the total number of surfaces in each layer become very large.

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Bellur-Ramaswamy, Ravi S., Nahil A. Sobh, Robert B. Haber, and Daniel A. Tortorelli. "Quench Process Modeling and Optimization." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-1850.

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Abstract We optimize continuous quench process parameters to produce a desired precipitate distribution in aluminum alloy extrudates. To perform this task, an optimization problem is defined and solved using a standard nonlinear programming algorithm. Ingredients of this algorithm include a cost function, constraint functions and their sensitivities with respect to the process parameters. These functions are dependent on the temperature and precipitate size which are obtained by balancing energy to determine the temperature distribution and by using a reaction-rate theory to determine a discrete precipitate particle size distribution. Both the temperature and the precipitate models are solved via the finite element method. Since we use a discrete particle size model, there are as many as 105 degrees-of-freedom per finite element node. After we compute the temperature and precipitate size distributions, we must also compute their sensitivities. This seemingly intractable computational task is resolved by using an element-by-element discontinuous Galerkin finite element formulation and a direct differentiation sensitivity analysis which allows us to perform all of the computations on a PC.

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Dayhoum, Abdallah, Alejandro Ramirez-Serrano, and Robert Martinuzzi. "Aerodynamic Optimization and Experimental Analysis of Shrouded Rotor Blades." In Vertical Flight Society 80th Annual Forum & Technology Display. The Vertical Flight Society, 2024. http://dx.doi.org/10.4050/f-0080-2024-1289.

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Unmanned Aerial Vehicles (UAVs), particularly Vertical Take-Off and Landing (VTOL) aircraft such as quad-rotors and helicopters, have gained attention for diverse applications in military and civilian domains. However, to increase applications, reducing their power consumption and their restricted payload capacity. This paper describes a method to enhance the thrust capabilities of typical shrouded rotors through a novel rotor design. Beginning with an airfoil with a high lift-to-drag ratio. Blade element momentum theory (BEMT) is used to optimize the rotor's chord and twist distributions systematically along with precise induced velocity prediction in shrouded rotors. Furthermore, a validation process requires rotor manufacturing and experimentation. BEMT harmonizes momentum and blade element theories, offering a comprehensive framework for rotor behavior modeling, especially in hovering conditions. First, second, and third degrees functions are used to express both the chord and twist distributions along the rotor radius from where the best rotor design is obtained, for this, an experimental validation is employed. The experimental tests demonstrate improved performance, especially when the rotor designed using the higher degree functions is employed. The proposed approach provides a comprehensive approach to shrouded rotor design, offering advancements.

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Hu, Dianyin, and Rongqiao Wang. "Probabilistic Analysis on Turbine Disk Under LCF-Creep." In ASME Turbo Expo 2008: Power for Land, Sea, and Air. ASMEDC, 2008. http://dx.doi.org/10.1115/gt2008-50722.

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This paper establishes a structural model of the turbine disk of a certain aero-engine subjected to loads due to centrifugal force and duration at elevated temperature, and calculates the plastic and creep deformation with finite element (FE) analysis software. During creep analysis, the Norton constitutive equation was taken into account. After the temperature field distribution of the turbine disk had been obtained, structural static analysis results showed that the maximum equivalent stress and strain appeared at the area near to the disk center, which was taken as the critical point. The Manson-Coffin formula was used to predict low cycle fatigue (LCF) life based on the calculations derived from cyclic plastic-creep analysis, and creep life was obtained by applying the Larson-Miller equation. Lognormal distributions of LCF life and creep life were used as pointed out in the literature, which mainly considered the uncertainties in material parameters. Taking the lives and loads as random variables including LCF life, creep life, fatigue load and hold time, a probabilistic analysis on the turbine disk was performed under LCF-Creep, in which a failure function was proposed based on linear cumulative damage rule (LCDR). The probabilistic method of response surface (RS) was applied to fit the regression model of the LCF-Creep life with a quadratic approximation function including cross-terms. The Monte Carlo Simulation sampling technique was employed to carry out probabilistic analysis on the turbine disk life, resulting in the conclusion that the life of turbine disk under LCF-Creep follows a lognormal distribution. Furthermore, the effect of different random variables on the disk life was investigated through sensitivity analysis in order to increase the component’s life and improve its reliability. However, studies on the distributions of loads and damage theory of the component under LCF-Creep still need to be discussed in future study.

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Katsuo, Masahide, Toshiyuki Sawa, Koji Kawaguchi, and Hiroshi Kawamura. "Axisymmetrical Thermal Stress Analysis of Laminated Composite Finite Hollow Cylinders Restricted at Both Ends in Steady State." In ASME 1996 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/imece1996-0860.

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Abstract The thermal stress distributions of laminated composite finite hollow cylinders restricted at both ends and at one end of the cylinders are analyzed using the thermoelastic displacement potential and Michell’s stress functions based on the axisymmetrical theory of elasticity. In the numerical calculations, the thermal stress distributions in the laminated composite finite hollow cylinders are examined. The effects of restrictions at the end of the cylinders on the thermal stress distributions are clarified. The analytical results are compared with the results obtained from the plain strain the ory. It can be seen that the differences in the stresses between the inner cylinder and the outer cylinder increase near the restricted end. The hoop and the axial stresses distribute discontinuously at the interface of the cylinders. The difference in the hoop stress at the interface is minimal in the case of the plain strain theory. For verification, the strains were measured and the analytical results were in fairly good agreement with the experimental results.

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Rahaeifard, M., M. H. Kahrobaiyan, S. A. Moeini, M. T. Ahmadian, and M. Hoviattalab. "Flexural Sensitivity of a V-Shaped AFM Cantilever Made of Functionally Graded Materials." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24676.

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In this paper, two lowest resonant frequencies and sensitivities of an AFM V-Shaped microcantilever made of functionally graded materials are studied. The beam is modeled by Euler-Bernoulli beam theory in which rotary inertia and shear deformation is neglected. It is assumed that the beam is made of a mixture of metal and ceramic with properties varying through the thickness of the beam. This variation is function of volume fraction of beam material constituents. The interaction between AFM tip and surface is modeled by two linear springs which expresses the normal and lateral contact stiffness. A relationship is developed to evaluate the sensitivity of FGM micro cantilever beam. Effect of volume fraction of materials and geometric parameters on resonant frequencies and sensitivities is studied. Results show that natural frequencies and sensitivities are significantly affected by volume fraction of material constituents and geometric parameters. Using these results, optimum geometric parameters and mass distributions of material constituents can be chosen so that high resolution images could be obtained.

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Song, Shaopin, and Pingsha Dong. "Analysis of Residual Stresses in Pipe Seam Welds and a Proposed Residual Stress Profile Estimation Method." In ASME 2015 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/pvp2015-45726.

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A recent comprehensive investigation into residual stress distributions in pipe and vessel longitudinal seam welds is presented in this paper, covering component wall thickness from 1/4” (6.35mm) to 10” (254mm), component radius to wall thickness ratio from 2 to 10, and linear welding heating input from low (50 J/mm) to high (6000 J/mm). Through the use of a residual stress decomposition technique, two key parameters that govern through-thickness residual stress distributions in terms of their membrane and bending content have been identified. One is component radius to wall thickness ratio (r/t) and the other is a characteristic heat input density (Q̂) having a unit of J/mm3. With these two parameters, a unified functional form for representing through-thickness residual stress profile behaviors in seam welds is proposed along with its solution procedure for applications in weld region. The simplicity of the proposed residual stress profile estimation scheme in functional form and demonstrated applicability for a wide range of r/t and Q̂ provides an effective framework for generating residual stress profile information for supporting defect assessment procedures in FFS codes and standards.

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Reports on the topic "Theory of distributions (Functional analysis)"

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Luttman, Aaron, Marylesa Howard, and Kasey Bray. Mie Scattering Analysis: Using Mie Theory to Compute Size Distribution Functions. Office of Scientific and Technical Information (OSTI), October 2017. http://dx.doi.org/10.2172/1755913.

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Luttman, Aaron, Marylesa Howard, and Kasey Bray. Mie Scattering Analysis: Using Mie Theory to Compute Size Distribution Functions. Office of Scientific and Technical Information (OSTI), October 2017. http://dx.doi.org/10.2172/1755913.

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Chernis, Tony, Niko Hauzenberger, Florian Huber, Gary Koop, and James Mitchell. Predictive Density Combination Using a Tree-Based Synthesis Function. Federal Reserve Bank of Cleveland, November 2023. http://dx.doi.org/10.26509/frbc-wp-202330.

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Bayesian predictive synthesis (BPS) provides a method for combining multiple predictive distributions based on agent/expert opinion analysis theory and encompasses a range of existing density forecast pooling methods. The key ingredient in BPS is a “synthesis” function. This is typically specified parametrically as a dynamic linear regression. In this paper, we develop a nonparametric treatment of the synthesis function using regression trees. We show the advantages of our tree-based approach in two macroeconomic forecasting applications. The first uses density forecasts for GDP growth from the euro area’s Survey of Professional Forecasters. The second combines density forecasts of US inflation produced by many regression models involving different predictors. Both applications demonstrate the benefits – in terms of improved forecast accuracy and interpretability – of modeling the synthesis function nonparametrically.

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Seccareccia, Mario, and Guillermo Matamoros. Is “Inflation First” Really “Rentiers First”? The Taylor Rule and Rentier Income in Industrialized Countries. Institute for New Economic Thinking Working Paper Series, July 2023. http://dx.doi.org/10.36687/inetwp209.

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The Taylor rule has returned as a significant policy guide amid increasingly overt political pressures for its official (and not just its implicit) adoption at the US Fed as inflation fears have come to dominate monetary policy actions both in the US and internationally in recent times. Our paper analyzes the effect of monetary policy on the functional distribution of income by reconstructing how the post-1970s “inflation first” policy commitments of central banks came to be crystallized in the Taylor rule. While there are differences among the various specifications of this “rule”, the Taylor relation is merely an offshoot of what can be described generically as the family of Wicksellian reaction functions whose implications support rentier income over time. Because of the internal logic of the Taylor rule, this has led to different interpretations such as, for example, the more Keynesian Yellen rule, which depart from the strict sense of the Taylor rule. The paper also interprets the Taylor Rule in light of Wicksell’s formulation and analyzes the potential consequence of the differences. In contrast to the strict Wicksell rule of “proportional” adjustment, our econometric findings suggest evidence that central banks adjust “over-proportionally” the benchmark money interest rate in the presence of changes in the inflation rate for the complete “inflation first” era since the 1970s until the COVID-19 crisis. They thereby strongly favored rentier incomes in their reaction functions, with the possible exception of the post-financial crisis period. To limit the pro-rentier consequences of such inflation-targeting regimes, it is important that policymakers mandate multiple objectives for central banks, as exemplified in the current US Fed’s dual mandate.

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McClure, Michael A., Yitzhak Spiegel, David M. Bird, R. Salomon, and R. H. C. Curtis. Functional Analysis of Root-Knot Nematode Surface Coat Proteins to Develop Rational Targets for Plantibodies. United States Department of Agriculture, October 2001. http://dx.doi.org/10.32747/2001.7575284.bard.

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The goal of this research was to provide a better understanding of the interface between root-knot nematodes, Meloidogyne spp., and their host in order to develop rational targets for plantibodies and other novel methods of nematode control directed against the nematode surface coat (SC). Specific objectives were: 1. To produce additional monoclonal SC antibodies for use in Objectives 2, 3, and 4 and as candidates for development of plantibodies. 2. To determine the production and distribution of SC proteins during the infection process. 3. To use biochemical and immunological methods to perturbate the root-knot nematode SC in order to identify SC components that will serve as targets for rationally designed plantibodies. 4. To develop SC-mutant nematodes as additional tools for defining the role of the SC during infection. The external cuticular layer of nematodes is the epicuticle. In many nematodes, it is covered by a fuzzy material termed "surface coat" (SC). Since the SC is the outermost layer, it may playa role in the interaction between the nematode and its surroundings during all life stages in soil and during pathogenesis. The SC is composed mainly of proteins, carbohydrates (which can be part of glycoproteins), and lipids. SC proteins and glycoproteins have been labeled and extracted from preparasitic second-stage juveniles and adult females of Meloidogyne and specific antibodies have been raised against surface antigens. Antibodies can be used to gain more information about surface function and to isolate genes encoding for surface antigens. Characterization of surface antigens and their roles in different life-stages may be an important step towards the development of alternative control. Nevertheless, the role of the plant- parasitic nematode's surface in plant-nematode interaction is still not understood. Carbohydrates or carbohydrate-recognition domains (CROs) on the nematode surface may interact with CROs or carbohydrate molecules, on root surfaces or exudates, or be active after the nematode has penetrated into the root. Surface antigens undoubtedly play an important role in interactions with microorganisms that adhere to the nematodes. Polyclonal (PC) and monoclonal (MC) antibodies raised against Meloidogyne javanica, M. incognita and other plant-parasitic nematodes, were used to characterize the surface coat and secreted-excreted products of M. javanica and M. incognita. Some of the MC and PC antibodies raised against M. incognita showed cross-reactivity with the surface coat of M. javanica. Further characterization, in planta, of the epitopes recognized by the antibodies, showed that they were present in the parasitic juvenile stages and that the surface coat is shed during root penetration by the nematode and its migration between root cells. At the molecular level, we have followed two lines of experimentation. The first has been to identify genes encoding surface coat (SC) molecules, and we have isolated and characterized a small family of mucin genes from M. incognita. Our second approach has been to study host genes that respond to the nematode, and in particular, to the SC. Our previous work has identified a large suite of genes expressed in Lycopersicon esculentum giant cells, including the partial cDNA clone DB#131, which encodes a serine/threonine protein kinase. Isolation and predicted translation of the mature cDNA revealed a frame shift mutation in the translated region of nematode sensitive plants. By using primers homologous to conserved region of DB#131 we have identified the orthologues from three (nematode-resistant) Lycopersicon peruvianum strains and found that these plants lacked the mutation.

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Rheinberger, Christoph, and Nicolas Treich. Catastrophe aversion: social attitudes towards common fates. Fondation pour une culture de sécurité industrielle, June 2016. http://dx.doi.org/10.57071/882rpq.

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In light of climate change and other existential threats, policy commentators sometimes suggest that society should be more concerned about catastrophes. This document reflects on what is, or should be, society’s attitude toward such low-probability, high-impact events. The question underlying this analysis is how society considers (1) a major accident that leads to a large number of deaths; (2) a large number of small accidents that each kill one person, where the two situations lead to the same total number of deaths. We first explain how catastrophic risk can be conceived of as a spread in the distribution of losses, or a “more risky” distribution of risks. We then review studies from decision sciences, psychology, and behavioral economics that elicit people’s attitudes toward various social risks. This literature review finds more evidence against than in favor of catastrophe aversion. We address a number of possible behavioral explanations for these observations, then turn to social choice theory to examine how various social welfare functions handle catastrophic risk. We explain why catastrophe aversion may be in conflict with equity concerns and other-regarding preferences. Finally, we discuss current approaches to evaluate and regulate catastrophic risk, with a discussion of how it could be integrated into a benefit-cost analysis framework.

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Liu, Yuzhou, Yang Zhang, Zhijia Zhang, Qiang Fu, Yin Fu, Zhixiang Li, Chenyu Zhang, and Xiaoyu Wang. Efficacy of Li-Zhong Decoction in the treatment of patients with functional dyspepsia: A protocol for systematic review and meta-analysis. INPLASY - International Platform of Registered Systematic Review and Meta-analysis Protocols, April 2022. http://dx.doi.org/10.37766/inplasy2022.4.0029.

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Review question / Objective: To evaluate the safety and efficacy of LZD in the treatment of FD. In this study, all theory is adopted the soup randomized controlled trials for the treatment of functional dyspepsia. Condition being studied: Although the disease is not life-threatening, it can take a psychological and financial toll on sufferers. At present, the efficacy of conventional treatment is not significant. Previous studies have shown that Lizhong decoction is safe and effective, but there is a lack of systematic evaluation. The purpose of this study was to systematically study the efficacy of LZD in the treatment of FD patients.

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Heymsfield, Ernie, and Jeb Tingle. State of the practice in pavement structural design/analysis codes relevant to airfield pavement design. Engineer Research and Development Center (U.S.), May 2021. http://dx.doi.org/10.21079/11681/40542.

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An airfield pavement structure is designed to support aircraft live loads for a specified pavement design life. Computer codes are available to assist the engineer in designing an airfield pavement structure. Pavement structural design is generally a function of five criteria: the pavement structural configuration, materials, the applied loading, ambient conditions, and how pavement failure is defined. The two typical types of pavement structures, rigid and flexible, provide load support in fundamentally different ways and develop different stress distributions at the pavement – base interface. Airfield pavement structural design is unique due to the large concentrated dynamic loads that a pavement structure endures to support aircraft movements. Aircraft live loads that accompany aircraft movements are characterized in terms of the load magnitude, load area (tire-pavement contact surface), aircraft speed, movement frequency, landing gear configuration, and wheel coverage. The typical methods used for pavement structural design can be categorized into three approaches: empirical methods, analytical (closed-form) solutions, and numerical (finite element analysis) approaches. This article examines computational approaches used for airfield pavement structural design to summarize the state-of-the-practice and to identify opportunities for future advancements. United States and non-U.S. airfield pavement structural codes are reviewed in this article considering their computational methodology and intrinsic qualities.

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Parkins and Leis. L51654 Spatial Densities of Stress-Corrosion Cracks in Line-Pipe Steels. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), April 1992. http://dx.doi.org/10.55274/r0010367.

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There was a need to define the spatial density of stress-corrosion crack arrays that develop in operating gas-transmission pipelines and in laboratory test specimens of line-pipe steel, to improve understanding of the factors that control the density and provide data to test models of pipeline cracking. Within the broad definition of crack density are included the locations, numbers, lengths, depths, and degree of linkage of cracks. An analysis has been conducted of location, numbers, lengths, depths, and degree of linkage of stress-corrosion crack colonies in samples from the field and from laboratory tests. This has provided data to test any model of the cracking of pipelines. Thus, it is shown that crack densities are of the order of 5 cracks/mm of distance normal to the crack length direction and that the depths and lengths of cracks are distributed according to log normal and Weibull functions. During the growth stage of cracks in a colony, their spatial distribution is not random, because of the interaction of their associated stress fields. That interaction also results in the coalescence of cracks, an extremely important part of the overall growth process, and that interaction is defined quantitatively to provide further information to which modeling must aspire.

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Ori, Naomi, and Mark Estelle. Role of GOBLET and Auxin in Controlling Organ Development and Patterning. United States Department of Agriculture, January 2012. http://dx.doi.org/10.32747/2012.7697122.bard.

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The size and shape of plant leaves are extremely diverse within and among species, and are also sensitive to growth conditions. Compound leaves, such as those of tomato, maintain morphogenetic activity during early stages of their development, enabling them to elaborate lateral appendages such as leaflets. The aim of the research project was to understand the interaction between the plant hormone auxin, the putative auxin response inhibitor ENTIRE (E, SlIAA9) and the NAM/CUC transcription factor GOBLET (GOB) in compound-leaf development in tomato (Solanum lycopersicum). The specific aims of the project were: 1. Investigation of the role of GOB in compound-leaf development. 2. Characterization of E function in auxin signaling. 3. Characterization of the role of auxin in compound-leaf development. 4. Investigation of the genetic and molecular interaction between E and GOB. 5. Investigate the role of these factors in fruit development. There were no major changes in these objectives. GOB was shown to mark and promote the boundaries between the leaf and initiating leaflets. Its accurate distribution was found to be required for proper leaflet initiation and separation. E was found to interact with the TIR1 and AFB6 proteins in an auxin-dependant manner, indicating that these are functional auxin receptors that mediate E degradation in the presence of auxin. This was further supported by the stabilization of E by a mutation in domain II of the protein, which is thought to mediate its auxin-dependant degradation. Over expression of this stabilized form in tomato leaves and characterization of the e mutant phenotype and the E expression domain indicated that E acts between initiating leaflets to inhibit auxin response and lamina growth. Generation and analysis of tomato plants expressing the auxin response reporter DR5::VENUS, and analysis of the effect of auxin microapplication or overexpression of an auxin biosynthesis gene, indicated that auxin marks the sites of leaflet initiation and promotes lamina growth. Investigation of the molecular and genetic interaction between auxin, GOB and E revealed a complex network of mutual regulation that is utilized to precisely pattern the leaf margin in a manner that enables the combination of tight control and flexibility. E, auxin and GOB were shown to affect fruit development and fruit set, and in an extension of the project are currently utilized to identify new players that affect these processes. The research project yielded enhanced understanding of the mechanisms of compound leaf patterning and provided tools that will enable the manipulation of leaf shape and fruit set.

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