Journal articles: '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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Abe, Kazunori, Nouman Zobby, and Hikari Fujii. "Petrophysical Characterizations of Shale Gas Reservoirs of the Ranikot Formation in the Lower Indus Basin, Pakistan." EPI International Journal of Engineering 3, no. 2 (January 22, 2021): 103–7. http://dx.doi.org/10.25042/epi-ije.082020.02.

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The complex pore structure with nano-pores of shale gas reservoirs has an impact on the hydrocarbon storage and transport systems. We examined the pore structure of the shales of the Ranikot Formation in the Lower Indus Basin, Pakistan to investigate the full scaled pore size distributions by using a combination of techniques, mercury injection capillary pressure analysis and low pressure gas adsorption methods using N2 and CO2. Isotherm curves obtained N2 and CO2 adsorptions were interpreted using density functional theory analysis for describing the nano-scaled pore size distributions. The pore geometry of the shales was estimated to be slit-type from the isotherm hysteresis loop shape. The pore size distributions determined the density functional theory showed the dominant pore size of below around 10 nm. The Micro-scale effects such as slippage and adsorption/desorption also significantly influence the gas flow in nano-pore structure. The gas flow regimes in shales are classified into four types Darcy flow, slip flow, transition flow, Knudsen flow based on the value of the Knudsen number. Applying the specific reservoir conditions in Ranikot shale and pore size distribution to the Knudsen number, the gas flow regimes of the Ranikot shales were estimated mostly within the transition and slip flow.

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Ayanbayev, Birzhan, Ilja Klebanov, Han Cheng Lie, and T. J. Sullivan. "Γ -convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems." Inverse Problems 38, no. 2 (December 28, 2021): 025005. http://dx.doi.org/10.1088/1361-6420/ac3f81.

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Abstract The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a maximum a posteriori (MAP) estimator. The MAP estimator essentially coincides with the (regularised) variational solution to the inverse problem, seen as minimisation of the Onsager–Machlup (OM) functional of the posterior measure. An open problem in the stability analysis of inverse problems is to establish a relationship between the convergence properties of solutions obtained by the variational approach and by the Bayesian approach. To address this problem, we propose a general convergence theory for modes that is based on the Γ-convergence of OM functionals, and apply this theory to Bayesian inverse problems with Gaussian and edge-preserving Besov priors. Part II of this paper considers more general prior distributions.

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Astaiza-Gómez, José Gabriel. "Hypothesis testing with explosive time series. An approach to the theory of the functional central limit theorem." Journal de Ciencia e Ingeniería 16, no. 1 (June 1, 2024): 13–25. http://dx.doi.org/10.46571/jci.2024.1.3.

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Dealing with uncertainty about the true data generating process requires a differentiated perspective of the distributions in hypothesis testing. In particular, the realizations, or the observed data, generated by interactions that are naturally ordered in time, posits a need for a differentiated analysis with respect to the standard statistics available for hypothesis testing. The Functional Central Limit Theorem provides a framework that enables the researcher to build a statistic that fits his data and hypothesis at hand. In this paper I show some of the necessary conditions under which the popular t-statistic properly condenses the information of the underlying distribution as well as the additional tools available when the t distribution is not suitable for hypothesis testing.

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Zhang, Yichao. "Transitivity Analysis of Hillary Clinton’s and Donald Trump’s First Television Debate." International Journal of Applied Linguistics and English Literature 6, no. 7 (October 10, 2017): 65. http://dx.doi.org/10.7575/aiac.ijalel.v.6n.7p.65.

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Halliday holds that all cultures reflect some universal meta-functions in the languages and proposes three such meta-functions: ideational, interpersonal, and textual. This paper employs the transitivity theory in Halliday’s Systemic Functional Linguistics to analyze the first television debate between Hillary Clinton and Donald Trump. Specifically, through a quantitative analysis, this paper tries to find the answers for the next two questions: First, what are the distributions of six processes used by the two candidates; are there any similarities and differences or some rules in the distribution? Second, what are the reasons of such distributions, and what are the functions of the distributions of different processes and main participants in helping the speakers to convey their intentions? The main findings show that material processes, relational process and mental processes are relatively dominate in both candidates’ speeches; while compared with Hillary, Trump tends to use more existential processes. In political discourse, the speakers measure their words with special caution to interact with people, to expresses their attitudes and judgments, and to influence the viewpoints and behavior of the audience, which is mainly the realization of the interpersonal function.

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Shama, Mustafa S., Farid El Ktaibi, Jamal N. Al Abbasi, Christophe Chesneau, and Ahmed Z. Afify. "Complete Study of an Original Power-Exponential Transformation Approach for Generalizing Probability Distributions." Axioms 12, no. 1 (January 7, 2023): 67. http://dx.doi.org/10.3390/axioms12010067.

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In this paper, we propose a flexible and general family of distributions based on an original power-exponential transformation approach. We call it the modified generalized-G (MGG) family. The elegance and significance of this family lie in the ability to modify the standard distributions by changing their functional forms without adding new parameters, by compounding two distributions, or by adding one or two shape parameters. The aim of this modification is to provide flexible shapes for the corresponding probability functions. In particular, the distributions of the MGG family can possess increasing, constant, decreasing, “unimodal”, or “bathtub-shaped“ hazard rate functions, which are ideal for fitting several real data sets encountered in applied fields. Some members of the MGG family are proposed for special distributions. Following that, the uniform distribution is chosen as a baseline distribution to yield the modified uniform (MU) distribution with the goal of efficiently modeling measures with bounded values. Some useful key properties of the MU distribution are determined. The estimation of the unknown parameters of the MU model is discussed using seven methods, and then, a simulation study is carried out to explore the performance of the estimates. The flexibility of this model is illustrated by the analysis of two real-life data sets. When compared to fair and well-known competitor models in contemporary literature, better-fitting results are obtained for the new model.

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Regazzini, Eugenio, Alessandra Guglielmi, and Giulia Di Nunno. "Theory and numerical analysis for exact distributions of functionals of a Dirichlet process." Annals of Statistics 30, no. 5 (October 2002): 1376–411. http://dx.doi.org/10.1214/aos/1035844980.

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Feichtinger, Hans G. "A Sequential Approach to Mild Distributions." Axioms 9, no. 1 (February 24, 2020): 25. http://dx.doi.org/10.3390/axioms9010025.

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The Banach Gelfand Triple ( S 0 , L 2 , S 0 ′ ) ( R d ) consists of S 0 ( R d ) , ∥ · ∥ S 0 , a very specific Segal algebra as algebra of test functions, the Hilbert space L 2 ( R d ) , ∥ · ∥ 2 and the dual space S 0 ′ ( R d ) , whose elements are also called “mild distributions”. Together they provide a universal tool for Fourier Analysis in its many manifestations. It is indispensable for a proper formulation of Gabor Analysis, but also useful for a distributional description of the classical (generalized) Fourier transform (with Plancherel’s Theorem and the Fourier Inversion Theorem as core statements) or the foundations of Abstract Harmonic Analysis, as it is not difficult to formulate this theory in the context of locally compact Abelian (LCA) groups. A new approach presented recently allows to introduce S 0 ( R d ) , ∥ · ∥ S 0 and hence ( S 0 ′ ( R d ) , ∥ · ∥ S 0 ′ ) , the space of “mild distributions”, without the use of the Lebesgue integral or the theory of tempered distributions. The present notes will describe an alternative, even more elementary approach to the same objects, based on the idea of completion (in an appropriate sense). By drawing the analogy to the real number system, viewed as infinite decimals, we hope that this approach is also more interesting for engineers. Of course it is very much inspired by the Lighthill approach to the theory of tempered distributions. The main topic of this article is thus an outline of the sequential approach in this concrete setting and the clarification of the fact that it is just another way of describing the Banach Gelfand Triple. The objects of the extended domain for the Short-Time Fourier Transform are (equivalence classes) of so-called mild Cauchy sequences (in short ECmiCS). Representatives are sequences of bounded, continuous functions, which correspond in a natural way to mild distributions as introduced in earlier papers via duality theory. Our key result shows how standard functional analytic arguments combined with concrete properties of the Segal algebra S 0 ( R d ) , ∥ · ∥ S 0 can be used to establish this natural identification.

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Chang, Joel Q. L., and Vincent Y. F. Tan. "A Unifying Theory of Thompson Sampling for Continuous Risk-Averse Bandits." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 6 (June 28, 2022): 6159–66. http://dx.doi.org/10.1609/aaai.v36i6.20564.

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This paper unifies the design and the analysis of risk-averse Thompson sampling algorithms for the multi-armed bandit problem for a class of risk functionals ρ that are continuous and dominant. We prove generalised concentration bounds for these continuous and dominant risk functionals and show that a wide class of popular risk functionals belong to this class. Using our newly developed analytical toolkits, we analyse the algorithm ρ-MTS (for multinomial distributions) and prove that they admit asymptotically optimal regret bounds of risk-averse algorithms under the CVaR, proportional hazard, and other ubiquitous risk measures. More generally, we prove the asymptotic optimality of ρ-MTS for Bernoulli distributions for a class of risk measures known as empirical distribution performance measures (EDPMs); this includes the well-known mean-variance. Numerical simulations show that the regret bounds incurred by our algorithms are reasonably tight vis-à-vis algorithm-independent lower bounds.

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Lastoskie, Christian, Keith E. Gubbins, and Nicholas Quirke. "Pore size distribution analysis of microporous carbons: a density functional theory approach." Journal of Physical Chemistry 97, no. 18 (May 1993): 4786–96. http://dx.doi.org/10.1021/j100120a035.

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Dubey, Paromita, and Hans-Georg Müller. "Fréchet analysis of variance for random objects." Biometrika 106, no. 4 (October 29, 2019): 803–21. http://dx.doi.org/10.1093/biomet/asz052.

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Summary Fréchet mean and variance provide a way of obtaining a mean and variance for metric space-valued random variables, and can be used for statistical analysis of data objects that lie in abstract spaces devoid of algebraic structure and operations. Examples of such data objects include covariance matrices, graph Laplacians of networks and univariate probability distribution functions. We derive a central limit theorem for the Fréchet variance under mild regularity conditions, using empirical process theory, and also provide a consistent estimator of the asymptotic variance. These results lead to a test for comparing $k$ populations of metric space-valued data objects in terms of Fréchet means and variances. We examine the finite-sample performance of this novel inference procedure through simulation studies on several special cases that include probability distributions and graph Laplacians, leading to a test for comparing populations of networks. The proposed approach has good finite-sample performance in simulations for different kinds of random objects. We illustrate the proposed methods by analysing data on mortality profiles of various countries and resting-state functional magnetic resonance imaging data.

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Ozturk, Mustafa C., Dongming Xu, and José C. Príncipe. "Analysis and Design of Echo State Networks." Neural Computation 19, no. 1 (January 2007): 111–38. http://dx.doi.org/10.1162/neco.2007.19.1.111.

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The design of echo state network (ESN) parameters relies on the selection of the maximum eigenvalue of the linearized system around zero (spectral radius). However, this procedure does not quantify in a systematic manner the performance of the ESN in terms of approximation error. This article presents a functional space approximation framework to better understand the operation of ESNs and proposes an information-theoretic metric, the average entropy of echo states, to assess the richness of the ESN dynamics. Furthermore, it provides an interpretation of the ESN dynamics rooted in system theory as families of coupled linearized systems whose poles move according to the input signal dynamics. With this interpretation, a design methodology for functional approximation is put forward where ESNs are designed with uniform pole distributions covering the frequency spectrum to abide by the richness metric, irrespective of the spectral radius. A single bias parameter at the ESN input, adapted with the modeling error, configures the ESN spectral radius to the input-output joint space. Function approximation examples compare the proposed design methodology versus the conventional design.

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Arenas-Gullo, A., F. Martínez-Manzano, and A. Fernández-Nieves. "Vortex flow, a couple important theorems, and an introduction to distributions." European Journal of Physics 43, no. 6 (September 15, 2022): 065802. http://dx.doi.org/10.1088/1361-6404/ac8706.

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Abstract We study vortex flow and perform a number of textbook calculations to highlight inconsistencies between results when using familiar, and widely important, mathematical theorems; these include Stokes’ theorem and a theorem that often enables interchanging field notions like irrotational and conservative, and their connection to scalar potentials and their associated exact differentials. The purpose is to use the familiar setting of a fluid vortex to go beyond conventional functional analysis and introduce students to the theory of distributions. After briefly doing this, we revisit vortex flow using a distributional approach to show how all prior inconsistencies disappear, emphasizing the significance of distributions in physics.

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Ning, Si-Yuan, Jing-Wen Cao, Xiao-Yan Liu, Hao-Jian Wu, Xiao-Qing Yuan, Xiao-Tong Dong, Yi-Ning Li, Yan Jiang, and Peng Zhang. "Computational Analysis of Hydrogen Bond Vibrations of Ice III in the Far-Infrared Band." Crystals 12, no. 7 (June 26, 2022): 910. http://dx.doi.org/10.3390/cryst12070910.

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The hydrogen-disordered structure of ice III makes it difficult to analyze its vibrational spectrum theoretically. To clarify the contribution of hydrogen bonds (HBs), we constructed a 24-molecule supercell to mimic the real structure and performed first-principles density functional theory calculations. The calculated curve of phonon density of states showed good correspondence with the experimental data. Based on the theory of two kinds of HB vibrational modes, we analyzed the distributions of two-bond modes and four-bond modes. The energy splitting of these modes results in a flat vibrational band, which is a common phenomenon in high-pressure ice phases. These findings verified the general rule that there are two types of HB vibrations in ice, thereby furthering our understanding of HB interactions in water ice and their broad role in nature.

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Silva, Luís M., J. Marques de Sá, and Luís A. Alexandre. "The MEE Principle in Data Classification: A Perceptron-Based Analysis." Neural Computation 22, no. 10 (October 2010): 2698–728. http://dx.doi.org/10.1162/neco_a_00013.

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This letter focuses on the issue of whether risk functionals derived from information-theoretic principles, such as Shannon or Rényi's entropies, are able to cope with the data classification problem in both the sense of attaining the risk functional minimum and implying the minimum probability of error allowed by the family of functions implemented by the classifier, here denoted by min Pe. The analysis of this so-called minimization of error entropy (MEE) principle is carried out in a single perceptron with continuous activation functions, yielding continuous error distributions. In spite of the fact that the analysis is restricted to single perceptrons, it reveals a large spectrum of behaviors that MEE can be expected to exhibit in both theory and practice. In what concerns the theoretical MEE, our study clarifies the role of the parameters controlling the perceptron activation function (of the squashing type) in often reaching the minimum probability of error. Our study also clarifies the role of the kernel density estimator of the error density in achieving the minimum probability of error in practice.

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Jia, Haikun, Shi Bin Wang, Nobumichi Tamura, and Philippe Goudeau. "Stress Relaxation Related to Spontaneous Thin Film Buckling: Correlation between Finite Element Calculations and Micro Diffraction Analysis." Quantum Beam Science 3, no. 1 (December 20, 2018): 1. http://dx.doi.org/10.3390/qubs3010001.

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Compressive residual stresses generated during thin film deposition may lead to undesirable film damage, such as delamination, buckling, and flaking, ultimately leading to the failure of the device employing the film. Understanding the residual stress generation and role in these damage mechanisms is necessary to preserve thin film integrity and optimize its functional properties. Thin shell theory has been used for decades to predict buckling but the results have not yet been correlated with experimental data since the techniques used to measure stress in metallic films were not able to do so at the required micron scale until recently. Micro scanning X-ray diffraction now enables the direct mapping of the local stress of metallic films. In this paper, finite element method based on thin shell theory and synchrotron X-ray micro diffraction have been used to determine stress maps of thin film buckling patterns. Calculations of the stress distribution in the metallic films have been performed taking into account the buckling geometry determined from optical measurements. Stress distributions over gold blisters and tungsten wrinkles obtained with the two techniques are in fair agreement and allow for the accurate determination of the stress relaxation profile from the bottom to the top of the buckling, validating the thin shell theory model.

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Ningyi, Lan. "Analysis of the Thematic Structure and Thematic Progression Patterns of the Queen’s 2020 National Speech." English Literature and Language Review, no. 68 (October 17, 2020): 147–52. http://dx.doi.org/10.32861/ellr.68.147.152.

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Under the guidance of the theory of theme and rheme as well as thematic progression patterns, two significant components in Systemic Functional Linguistics, this paper discusses the thematic structure and thematic progression patterns of the Queen’s national speech “We will meet again!” which was delivered on April 5, 2020, when both England and the rest of the world were in the throes of the growing pandemic. With the use of quantitative and qualitative research methods, their distributions and the reasons are explored to figure out the thematic features, the effects, or the functions that have been achieved in Queen’s speech.

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Vologzhanina, Anna V., Svitlana V. Kats, Larisa V. Penkova, Vadim A. Pavlenko, Nikolay N. Efimov, Vadim V. Minin, and Igor L. Eremenko. "Combined analysis of chemical bonding in a CuIIdimer using QTAIM, Voronoi tessellation and Hirshfeld surface approaches." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 71, no. 5 (September 30, 2015): 543–54. http://dx.doi.org/10.1107/s2052520615015279.

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Interaction of 1-(1H-pyrazol-5-yl)ethanone oxime (H2PzOx) with copper(II) chloride in the presence of pyridine afforded a binuclear discrete [Cu2(HPzOx)2Cl2py2] complex, which was characterized by Fourier transform–IR and electron paramagnetic resonance (EPR) spectra, magnetochemistry and high-resolution X-ray diffraction experiments. Multipole refinement of X-ray diffraction data and density-functional theory (DFT) calculations of an isolated molecule allowed charge and spin distributions to be obtained for this compound. Magnetochemistry data, EPR spectra and DFT calculations of an isolated molecule show antiferromagnetic coupling between copper(II) ions. The spin distribution suggests an exchange pathwayviathe bridging pyrazole ring in the equatorial plane of the CuN4Cl coordination polyhedron, thus providing support for the classical superexchange mechanism; the calculated value of the magnetic coupling constant −2Jis equal to 220 cm−1, which compares well with the experimental value of 203 ± 2 cm−1. Chemical connectivity was derived by Bader's `quantum theory of atoms in molecules' and compared with Voronoi tessellation and Hirshfeld surface representations of crystal space. All methodologies gave a similar qualitative and semi-quantitative description of intra- and intermolecular connectivity.

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Morachkovska, Iryna, Lidiya Kurpa, Anna Linnik, Galina Timchenko, and Tetyana Shmatko. "Dynamic analysis of functional gradient porous sigmoidal sandwich plates." Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines, no. 1 (December 21, 2023): 39–44. http://dx.doi.org/10.20998/2078-9130.2023.1.281191.

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Analysis of free vibrations of functionally graded (FG) porous sigmoid sandwich plates, is considered in this paper. The plate can have a complex geometric shape and various types of fastening. To solve the problem, we used the variational-structural method (RFM), which combines the theory of R-functions and variational method of Rayleigh-Ritz. The mathematical statement of the problem is carried out within the framework of the deformation theory of plates of the first order (FSDT). Plates are considered, the outer layers of which are made of functionally graded materials (FGM), and the core is isotropic. For different models of porosity distribution (sigmoid uniform and nonuniform), analytical expressions were obtained to calculate the effective properties of FGM. For rectangular plates, a comparison of the obtained results with known results obtained using other approaches is shown. Calculations for plates with a complex shape are presented in the form of tables and graphs. The influence of the volume fraction of ceramics, the different types Of FGM and the coefficient of porosity on the natural frequencies of the plate is analyzed.

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Bock, Hans, Sven Holl, and Volker Krenzel. "Wechselwirkungen in Molekülkristallen, 166 [1, 2]. Polyiod-Moleküle I2C=CI2, (IC)4S, (IC)4NH, (IC)4N-CH3 und HCI3: Strukturbestimmung nach Kristallzüchtung oder durch Dichtefunktionaltheorie-Berechnung / Interaction in Molecular Crystals, 166 [1, 2], Polyiodo Molecules I2C=CI2, (IC)4S, (IC)4 NH, (IC)4N-CH and HCI3: Structure Determination Following Crystallization or by Density Functional Theory Calculation." Zeitschrift für Naturforschung B 56, no. 1 (January 1, 2001): 13–24. http://dx.doi.org/10.1515/znb-2001-0104.

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Abstract The structures of tri-and tetraiodo-substituted carbon compounds are determined either experimentally by X-Ray Structure Analysis or, because crystallization of tetraiodothiophene could not be achieved, approximated by Density Functional Theory optimization of structural data from a donor/acceptor complex. The structures show noteworthy details such as a second polymorph of tetraiodoethene crystallized by sublimation or herringbone crystal packing patterns of tetraiodopyrrole derivatives. All molecular geometries are discussed and compared based on relativistic density functional theory calculations with 6 -31G* basis sets including iodine pseudopotentials. They reproduce even finer structural details due to van der Waals repulsion of the bulky iodo substituents. Natural Bond Orbital (NBO) charge distributions suggest positive partial charges at all iodine centers with the strongest polarization Cδ㊀ → Iδ㊉ in HCI3, which contains well over 97% iodine.

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Galvani, Marta, Chiara Bardelli, Silvia Figini, and Pietro Muliere. "A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap." Algorithms 14, no. 1 (January 3, 2021): 11. http://dx.doi.org/10.3390/a14010011.

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Bootstrap resampling techniques, introduced by Efron and Rubin, can be presented in a general Bayesian framework, approximating the statistical distribution of a statistical functional ϕ(F), where F is a random distribution function. Efron’s and Rubin’s bootstrap procedures can be extended, introducing an informative prior through the Proper Bayesian bootstrap. In this paper different bootstrap techniques are used and compared in predictive classification and regression models based on ensemble approaches, i.e., bagging models involving decision trees. Proper Bayesian bootstrap, proposed by Muliere and Secchi, is used to sample the posterior distribution over trees, introducing prior distributions on the covariates and the target variable. The results obtained are compared with respect to other competitive procedures employing different bootstrap techniques. The empirical analysis reports the results obtained on simulated and real data.

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Ayad, Somia, Ali Laksaci, Saâdia Rahmani, and Rachida Rouane. "LOCAL LINEAR MODELLING OF THE CONDITIONAL DISTRIBUTION FUNCTION FOR FUNCTIONAL ERGODIC DATA." Mathematical Modelling and Analysis 27, no. 3 (August 12, 2022): 360–82. http://dx.doi.org/10.3846/mma.2022.14909.

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The focus of functional data analysis has been mostly on independent functional observations. It is therefore hoped that the present contribution will provide an informative account of a useful approach that merges the ideas of the ergodic theory and the functional data analysis by using the local linear approach. More precisely, we aim, in this paper, to estimate the conditional distribution function (CDF) of a scalar response variable given a random variable taking values in a semimetric space. Under the ergodicity assumption, we study the uniform almost complete convergence (with a rate), as well as the asymptotic normality of the constructed estimator. The relevance of the proposed estimator is verified through a simulation study.

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Kocot, Antoni, Barbara Loska, Yuki Arakawa, Georg H. Mehl, and Katarzyna Merkel. "Study of the Experimental and Simulated Vibrational Spectra Together with Conformational Analysis of Thioether Cyanobiphenyl-Based Liquid Crystal Dimers." International Journal of Molecular Sciences 23, no. 14 (July 20, 2022): 8005. http://dx.doi.org/10.3390/ijms23148005.

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Infrared spectroscopy (IR) and quantum chemistry calculations that are based on the density functional theory (DFT) have been used to study the structure and molecular interactions of the nematic and twist-bend phases of thioether-linked dimers. Infrared absorbance measurements were conducted in a polarized beam for a homogeneously aligned sample in order to obtain more details about the orientation of the vibrational transition dipole moments. The distributions to investigate the structure and conformation of the molecule dihedral angle were calculated. The calculated spectrum was compared with the experimental infrared spectra and as a result, detailed vibrational assignments are reported.

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Sato, Jun. "Modern Analysis for Characterization of Pore Size Distribution by Non–Local Density Functional Theory." membrane 41, no. 1 (2016): 16–21. http://dx.doi.org/10.5360/membrane.41.16.

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Nitanda, Atsushi, Denny Wu, and Taiji Suzuki. "Particle dual averaging: optimization of mean field neural network with global convergence rate analysis*." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 11 (November 1, 2022): 114010. http://dx.doi.org/10.1088/1742-5468/ac98a8.

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Abstract We propose the particle dual averaging (PDA) method, which generalizes the dual averaging method in convex optimization to the optimization over probability distributions with quantitative runtime guarantee. The algorithm consists of an inner loop and outer loop: the inner loop utilizes the Langevin algorithm to approximately solve for a stationary distribution, which is then optimized in the outer loop. The method can thus be interpreted as an extension of the Langevin algorithm to naturally handle nonlinear functional on the probability space. An important application of the proposed method is the optimization of neural network in the mean field regime, which is theoretically attractive due to the presence of nonlinear feature learning, but quantitative convergence rate can be challenging to obtain. By adapting finite-dimensional convex optimization theory into the space of measures, we analyze PDA in regularized empirical/expected risk minimization, and establish quantitative global convergence in learning two-layer mean field neural networks under more general settings. Our theoretical results are supported by numerical simulations on neural networks with reasonable size.

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Kumawat, Nitesh, Andrejs Tucs, Soumen Bera, Gennady N. Chuev, Marat Valiev, Marina V. Fedotova, Sergey E. Kruchinin, Koji Tsuda, Adnan Sljoka, and Amit Chakraborty. "Site Density Functional Theory and Structural Bioinformatics Analysis of the SARS-CoV Spike Protein and hACE2 Complex." Molecules 27, no. 3 (January 26, 2022): 799. http://dx.doi.org/10.3390/molecules27030799.

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The entry of the SARS-CoV-2, a causative agent of COVID-19, into human host cells is mediated by the SARS-CoV-2 spike (S) glycoprotein, which critically depends on the formation of complexes involving the spike protein receptor-binding domain (RBD) and the human cellular membrane receptor angiotensin-converting enzyme 2 (hACE2). Using classical site density functional theory (SDFT) and structural bioinformatics methods, we investigate binding and conformational properties of these complexes and study the overlooked role of water-mediated interactions. Analysis of the three-dimensional reference interaction site model (3DRISM) of SDFT indicates that water mediated interactions in the form of additional water bridges strongly increases the binding between SARS-CoV-2 spike protein and hACE2 compared to SARS-CoV-1-hACE2 complex. By analyzing structures of SARS-CoV-2 and SARS-CoV-1, we find that the homotrimer SARS-CoV-2 S receptor-binding domain (RBD) has expanded in size, indicating large conformational change relative to SARS-CoV-1 S protein. Protomer with the up-conformational form of RBD, which binds with hACE2, exhibits stronger intermolecular interactions at the RBD-ACE2 interface, with differential distributions and the inclusion of specific H-bonds in the CoV-2 complex. Further interface analysis has shown that interfacial water promotes and stabilizes the formation of CoV-2/hACE2 complex. This interaction causes a significant structural rigidification of the spike protein, favoring proteolytic processing of the S protein for the fusion of the viral and cellular membrane. Moreover, conformational dynamics simulations of RBD motions in SARS-CoV-2 and SARS-CoV-1 point to the role in modification of the RBD dynamics and their impact on infectivity.

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Dadda, Noureddine, Amani Direm, Benoit Guillot, Christian Jelsch, and Nourredine Bnelai-cherif. "Charge-density analysis and electrostatic properties of a new hybrid compound." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C285. http://dx.doi.org/10.1107/s2053273314097149.

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2-carboxy-4-methylaniline is a biologically active molecule serving as a pharmaceutical intermediate [1]. We've synthesized, studied and refined the crystal structure of its derivative 2-carboxy-4-methylanilinium chloride monohydrate using three different electron-density models. In the first model, the ELMAM2 multipolar electron-density database [2] was transferred to the molecule. Theoretical structure factors were also computed from periodic density functional theory calculations [3] and yielded, after multipolar-atoms refinement, the second charge-density model. An alternative electron-density modelling, based on spherical atoms and additional charges on the covalent bonds and electron lone-pair sites, was used in the third model in the refinement versus the theoretical data. The crystallographic refinements, structural properties, electron-density distributions and molecular electrostatic potentials obtained from the different charge-density models were compared.

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Joshi, Bhawani Datt, Ghanshyam Thakur, and Manoj Kumar Chaudhary. "Molecular Structure, Homo-Lumo and Vibrational Analysis Of Ergoline By Density Functional Theory." Scientific World 14, no. 14 (February 15, 2021): 21–30. http://dx.doi.org/10.3126/sw.v14i14.34978.

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In this work, quantum chemical study on a natural product ergoline has been presented using density functional theory (DFT) employing 6-311++G(d,p) basis set. A complete vibrational assignment has been performed for the theoretical FT-IR and Raman wavenumbers along with the potential energy distribution (PED) with the result of quantum chemical calculations. The structure–activity relationship has been interpreted by mapping electrostatic potential surface (MEP). Graphical representation of frontier molecular orbitals with their energy gap have been analyzed theoretically for both the gaseous and solvent environment employing time dependent density functional theory (TDDFT) employing 6-31G basis set.

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Rafik, Abdellatif, Hafid Zouihri, and Taoufiq Guedira. "Investigation of Hybrid Organic-Inorganic Dihydrogen Phosphate by Hirshfeld Surface Analysis and Quantum Chemical Analysis." Chemistry & Chemical Technology 17, no. 2 (June 1, 2023): 244–52. http://dx.doi.org/10.23939/chcht17.02.244.

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This present work undertakes the study of organic-inorganic hybrid material, which has been obtained successfully by an acid-base reaction at room tem-perature and structurally studied by the single crystal X-ray diffraction method. N-(Dicyclopropylmethylamino)-4,5-dihydro-1,3-oxazolium dihydrogenphosphate [10-CN@DP] crystallizes in the triclinic system with the space group P-1. The X-ray structural analysis supported by a Hirshfeld surface analysis of the crystal structure indicates that the most significant contributions to the crystal packing are from H…H (63.3%), H…O/O…H (32.2%) and H…C/C…H (2.5%) contacts. Density functional theory geometry-optimized calculations were compared to the experimentally determined structure. Using the same level of theory to imagine the chemical reactivity and charge distribution on the molecule, used to determine the HOMO-LUMO energy gap and density of state (DOS) range, the molecular electrostatic potential (MEP) image was drawn. Keywords: HOMO–LUMO, density of state, Hirshfeld surface analysis, electrostatic potential surface.

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Mardiono, Mardiono. "TRANSITIVITY ANALYSIS OF KEYNOTE SPEECH OF JOKO WIDODO AT WEF EA 2015." Jurnal Pendidikan Bahasa Inggris Proficiency 3, no. 2 (July 31, 2021): 31. http://dx.doi.org/10.32503/proficiency.v3i2.1918.

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International political speeches have played an extremely important role in political environment and take broader public attention due to their political, economy, and cultural values manifested through the language used. Systemic–Functional Grammar introduced and developed by Halliday (1967) sets out that with languages there are ideational meta-function, interpersonal meta-function, and textual meta-function. Hiring the theory of transitivity from Halliday’s Systemic Functional Linguistics, this study focuses on analysing Joko Widodo’s keynote speech. The aim is to figure out the deeper meaning of the speech through the distributions and so the dominations of the transitivity processes along with their participants. At the same time this study tries to find out the hidden information by analysing the functions of the transitivity processes and the main participants. The qualitative method is employed for the transitivity analysis while the quantitative method is taken to provide the statistic description on the distributions of the types of the process and the participants found. The analysis generates two major findings: First, there are five types of process: material, relational, verbal, mental, existential and the participants found, and no single behavioural process and its participants occurred. Among them, the material process and relational process along with their participants dominate the speech, which makes it well-delivered, more powerful, objective, and convincing. Second, the pronouns ‘we, our, and us’ are found as the main participants in Joko Widodo’s keynote speech that indicate his efforts to draw a close relation between him and his audience so his addressing has succeeded.

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Zou, Jingjing, Richard A. Davis, and Gennady Samorodnitsky. "EXTREME VALUE ANALYSIS WITHOUT THE LARGEST VALUES: WHAT CAN BE DONE?" Probability in the Engineering and Informational Sciences 34, no. 2 (January 30, 2019): 200–220. http://dx.doi.org/10.1017/s0269964818000542.

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AbstractIn this paper, we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree distributions of such networks tend to have power law behavior in the tails. We focus on the Hill estimator, which plays a starring role in heavy-tailed modeling. The Hill estimator for these data exhibited a smooth and increasing “sample path” as a function of the number of upper order statistics used in constructing the estimator. This behavior became more apparent as we artificially removed more of the upper order statistics. Building on this observation we introduce a new version of the Hill estimator. It is a function of the number of the upper order statistics used in the estimation, but also depends on the number of unavailable extreme values. We establish functional convergence of the normalized Hill estimator to a Gaussian process. An estimation procedure is developed based on the limit theory to estimate the number of missing extremes and extreme value parameters including the tail index and the bias of Hill's estimator. We illustrate how this approach works in both simulations and real data examples.

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Mughal, Ehsan Ullah, Masoud Mirzaei, Amina Sadiq, Sana Fatima, Ayesha Naseem, Nafeesa Naeem, Nighat Fatima, et al. "Terpyridine-metal complexes: effects of different substituents on their physico-chemical properties and density functional theory studies." Royal Society Open Science 7, no. 11 (November 2020): 201208. http://dx.doi.org/10.1098/rsos.201208.

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A series of different substituted terpyridine (tpy)-based ligands have been synthesized by Kröhnke method. Their binding behaviour was evaluated by complexing them with Co(II), Fe(II) and Zn(II) ions, which resulted in interesting coordination compounds with formulae, [Zn(tpy) 2 ]PF 6 , [Co(tpy) 2 ](PF 6 ) 2 , [Fe(tpy) 2 ](PF 6 ) 2 and interesting spectroscopic properties. Their absorption and emission behaviours in dilute solutions were investigated in order to explain structure–property associations and demonstrate the impact of different aryl substituents on the terpyridine scaffold as well as the role of the metal on the complexes. Photo-luminescence analysis of the complexes in acetonitrile solution revealed a transition from hypsochromic to bathochromic shift. All the compounds displayed remarkable photo-luminescent properties and various maximum emission peaks owing to the different nature of the functional groups. Furthermore, the anti-microbial potential of ligands and complexes was evaluated with docking analyses carried out to investigate the binding affinity of terpyridine-based ligands along with corresponding proteins (shikimate dehydrogenase and penicillin-binding protein) binding sites. To obtain further insight into molecular orbital distributions and spectroscopic properties, density functional theory calculations were performed for representative complexes. The photophysical activity and interactions between chromophore structure and properties were both investigated experimentally as well as theoretically.

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Chernozhukov, Victor, Iván Fernández-Val, Whitney Newey, Sami Stouli, and Francis Vella. "Semiparametric estimation of structural functions in nonseparable triangular models." Quantitative Economics 11, no. 2 (2020): 503–33. http://dx.doi.org/10.3982/qe1239.

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Triangular systems with nonadditively separable unobserved heterogeneity provide a theoretically appealing framework for the modeling of complex structural relationships. However, they are not commonly used in practice due to the need for exogenous variables with large support for identification, the curse of dimensionality in estimation, and the lack of inferential tools. This paper introduces two classes of semiparametric nonseparable triangular models that address these limitations. They are based on distribution and quantile regression modeling of the reduced form conditional distributions of the endogenous variables. We show that average, distribution, and quantile structural functions are identified in these systems through a control function approach that does not require a large support condition. We propose a computationally attractive three‐stage procedure to estimate the structural functions where the first two stages consist of quantile or distribution regressions. We provide asymptotic theory and uniform inference methods for each stage. In particular, we derive functional central limit theorems and bootstrap functional central limit theorems for the distribution regression estimators of the structural functions. These results establish the validity of the bootstrap for three‐stage estimators of structural functions, and lead to simple inference algorithms. We illustrate the implementation and applicability of all our methods with numerical simulations and an empirical application to demand analysis.

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Pei, Zhenxing. "Free vibration Analysis of Beams with Functional Gradient Materials with Cracks." Academic Journal of Science and Technology 11, no. 1 (May 21, 2024): 265–69. http://dx.doi.org/10.54097/eawe6q56.

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The article presents the development of a dynamic model for a functionally graded material (FGM) beam incorporating cracks. Initially, it assumes an exponential distribution of material properties along the thickness direction of the beam and simulates the opening crack using a zero-mass rotational spring model. This approach enables the calculation of bending stiffness and local flexibility at the cracked section. Subsequently, drawing upon Timoshenko beam theory and von Kármán geometric nonlinear theory, the study formulates the energy equation of the beam and establishes the partial differential control equations for the cracked FGM using Hamilton's principle. The method of separation of variables is employed to discretize the partial differential motion equations into ordinary differential motion equations. Beam functions serve as mode functions, whose unknown coefficients are determined according to the boundary and continuity conditions, thereby yielding the natural frequencies and mode shapes of the cracked FGM beam. Numerical analysis is conducted to evaluate the impact of boundary conditions, the relative position of cracks, and the length-to-thickness ratio on the natural frequencies of the cracked FGM beam.

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Aydogdu, Immihan Sezen, Ilkay Gumus, and Hakan Arslan. "Hirshfeld surface and theoretical studies of 2,2,2-trichloro-N,N-bis(2-(2,2,2-trichloroacetamido)phenyl)acetamide compound." European Journal of Chemistry 10, no. 4 (December 31, 2019): 323–35. http://dx.doi.org/10.5155/eurjchem.10.4.323-335.1920.

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The vibrational frequencies, atomic charges and the related properties of the 2,2,2-trichloro-N,N-bis(2-(2,2,2-trichloroacetamido)phenyl)acetamide (H2LNNN) were investi-gated by Ab-initio Hartree-Fock (HF) and Density Functional Theory (DFT) methods such as BLYP, B3LYP, B3PW91 and mPW1PW91 functionals with 6-31G(d,p) and 6-311G(d,p) basis sets. The experimentally determined parameters were compared with those calculated theoretically and they were found to complement each other with a very good correlation. The theoretical vibrational spectrum of H2LNNN molecule was interpreted by means of potential energy distributions using the SQM 2.0 program. The Hirshfeld surface analysis was carried out to discuss the role of the hydrogen bonds and other intermolecular contacts in crystal lattice. Hirshfeld surface analysis revealed the occurrence of Cl⋯H, Cl⋯Cl, Cl⋯C, H···H, O⋯H, C···H and Cl···π interactions that display an important role on the crystal packing stabilization of the compound.

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Papanyan, Zakar Kh, and Liana S. Gabrielyan. "PREDICTION OF DIPROPYL SULFONE PROPERTIES BY DENSITY FUNCTIONAL THEORY METHODS: CONFORMATIONAL ANALYSIS AND SIMULATED IR SPECTRUM." Proceedings of the YSU B: Chemical and Biological Sciences 56, no. 3 (259) (December 1, 2022): 185–202. http://dx.doi.org/10.46991/pysu:b/2022.56.3.185.

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In this work, the conformational and vibrational analysis of dipropyl sulfone in its isolated gaseous state with identification of all stable conformers, their energy and degeneracy, relative population determined by Boltzmann distribution, as well as IR spectra have been performed by density functional theory (DFT) methods. Several DFT methods and basis sets were tested. It was demonstrated that the various local and hybrid DFT functionals such as well-known B3LYP, regardless of the size of basis sets, completely fail in the prediction of correct molecular structures, let alone the IR spectra. It was found that only long-range corrected hybrid density functionals, combined with decently sized basis sets are capable to predict correct values of dihedral angles between non-bonded atomic groups: the most important coordinates in conformational analysis. Thus, wB97XD/6-311++G(2df,2pd) method/basis set combination appears to be the best method for the titled system both in terms of geometry and IR spectra prediction. A detailed analysis of the potential energy surface revealed the existence of 28 distinct conformers with various populations at 298 K, which have significant impact in the simulated IR spectra. The linear scaling equation (LSE) fitting methodology was successfully adopted for the calibration of wavenumbers and achievement of the best match between theoretical and experimental absorption regions of functional groups in sulfones. Moreover, in the construction of the simulated IR spectra, the Lorentzian broadening of each calculated mode with different full widths at half maximum was considered to obtain extinction coefficients, thus more realistic ε(ν) dependency, that is directly comparable with experimental spectra. The authenticity of the results obtained have been verified by comparison with existing experimental literature data on sulfones.

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Huang, Chao, Jianquan Liu, Lihan Hai, Zenghao Dong, and Xinyi Niu. "Symmetric Heat Transfer Pattern of Fuel Assembly Subchannels in a Sodium-Cooled Fast Reactor." Symmetry 14, no. 11 (November 16, 2022): 2423. http://dx.doi.org/10.3390/sym14112423.

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The method outlined in this paper is convenient and effective for studying the thermal performance of fuel assemblies cooled with sodium fast reactors using the subchannel procedure. To initially study an optimization model for a symmetric single fuel assembly heat transfer pattern analysis in a fast sodium-cooled reactor based on subchannel calculations, this paper innovatively proposes a subchannel heat transfer analysis method with the entransy dissipation theory, which can solve the limitations and inaccuracies of the traditional entropy method such as poor applicability for heat transfer processes without functional conversion and the paradox of entropy production of heat exchangers. The symmetric distributions of the thermal-hydraulic parameters such as coolant flow rate, coolant temperature, cladding temperature, and fuel pellet temperature were calculated, and the entransy dissipation calculation method corresponding to the fuel assembly subchannels was derived based on the entransy theory. The effect of subchannel differences on the thermal-hydraulic parameters and the symmetric distribution pattern of entransy dissipation during the cooling process of the fuel assembly was analyzed and compared from the symmetrical arrangement of subchannels in the axial and radial directions.

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Kolokoltsov, Vassili N. "The Rates of Convergence for Functional Limit Theorems with Stable Subordinators and for CTRW Approximations to Fractional Evolutions." Fractal and Fractional 7, no. 4 (April 17, 2023): 335. http://dx.doi.org/10.3390/fractalfract7040335.

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From the initial development of probability theory to the present days, the convergence of various discrete processes to simpler continuous distributions remains at the heart of stochastic analysis. Many efforts have been devoted to functional central limit theorems (also referred to as the invariance principle), dealing with the convergence of random walks to Brownian motion. Though quite a lot of work has been conducted on the rates of convergence of the weighted sums of independent and identically distributed random variables to stable laws, the present paper is the first to supply the rates of convergence in the functional limit theorem for stable subordinators. On the other hand, there is a lot of activity on the convergence of CTRWs (continuous time random walks) to processes with memory (subordinated Markov process) described by fractional PDEs. Our second main result is the first one yielding rates of convergence in such a setting. Since CTRW approximations may be used for numeric solutions of fractional equations, we obtain, as a direct consequence of our results, the estimates for error terms in such numeric schemes.

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Ahmed, N. U. "Generalized functionals of Brownian motion." Journal of Applied Mathematics and Stochastic Analysis 7, no. 3 (January 1, 1994): 247–67. http://dx.doi.org/10.1155/s1048953394000250.

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In this paper we discuss some recent developments in the theory of generalized functionals of Brownian motion. First we give a brief summary of the Wiener-Ito multiple Integrals. We discuss some of their basic properties, and related functional analysis on Wiener measure space. then we discuss the generalized functionals constructed by Hida. The generalized functionals of Hida are based on L2-Sobolev spaces, thereby, admitting only Hs, s∈R valued kernels in the multiple stochastic integrals. These functionals are much more general than the classical Wiener-Ito class. The more recent development, due to the author, introduces a much more broad class of generalized functionals which are based on Lp-Sobolev spaces admitting kernels from the spaces 𝒲p,s, s∈R. This allows analysis of a very broad class of nonlinear functionals of Brownian motion, which can not be handled by either the Wiener-Ito class or the Hida class. For s≤0, they represent generalized functionals on the Wiener measure space like Schwarz distributions on finite dimensional spaces. In this paper we also introduce some further generalizations, and construct a locally convex topological vector space of generalized functionals. We also present some discussion on the applications of these results.

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TAFERGUENNIT, Manel, Noura KICHOU, and Zakia HANK. "Comparative Experimental and Theoretical Study on the Structure of Potassium 2,4-Hexadienoate: Structure-Activity Relationship." Eurasia Proceedings of Science Technology Engineering and Mathematics 23 (October 16, 2023): 69–84. http://dx.doi.org/10.55549/epstem.1361714.

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For the first time, a density functional theory (DFT) study was conducted on the structure of a well-known antibacterial agent namely potassium 2,4-Hexadienoate, in order to elucidate its vibrational, electronic and reactivity proprieties. Structure optimization was performed using three common hybrid functionals (DFT/ B3LYP-D3; DFT/ M05-2X and DFT/M06-2X) to identify the suitable functional. Geometric parameters, IR and UV-vis spectra were well reproduced when using DFT/M06-2X with 6-311(d)G+ basis set (R2 = 0.99913). The assimilation of IR frequencies has been achieved using potential energy distribution (PED)analysis at M06-2X/6-311(d) G + level. Time-dependent density functional theory (TD-DFT) and natural bond orbital (NBO) analysis were realized to identify the excited states of 2,4-Hexadienoate anion in the liquid phase, using the solute electron density solvation model (SMD). Moreover, reactive sites in the molecule were localized by molecular electrostatic potential (MEP) analysis. Highest Occupied Molecular Orbitals (HOMO), lowest Unoccupied Molecular Orbitals (LUMO) and energy gap (HOMO-LUMO gap), were used to calculate global reactivity descriptors (GRDs), according to the frontier molecular orbitals (FMO) theory, the resulting values were analyzed to explore the chemical reactivity of the molecule and elucidate the structure-activity relationship.

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Zhabanov, Yuriy A., Igor V. Ryzhov, Ilya A. Kuzmin, Alexey V. Eroshin, and Pavel A. Stuzhin. "DFT Study of Molecular and Electronic Structure of Y, La and Lu Complexes with Porphyrazine and Tetrakis(1,2,5-thiadiazole)porphyrazine." Molecules 26, no. 1 (December 29, 2020): 113. http://dx.doi.org/10.3390/molecules26010113.

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Electronic and geometric structures of Y, La and Lu complexes with porphyrazine (Pz) and tetrakis(1,2,5-thiadiazole)porphyrazine (TTDPz) were investigated by density functional theory (DFT) calculations and compared. The nature of the bonds between metal atoms and nitrogen atoms has been described using the analysis of the electron density distribution in the frame of Bader’s quantum theory of atoms in molecule (QTAIM). Simulation and interpretation of electronic spectra were performed with use of time-dependent density functional theory (TDDFT) calculations. Description of calculated IR spectra was carried out based on the analysis of the distribution of the potential energy of normal vibrations by natural vibrational coordinates.

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

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