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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Chen, Lili, Shilei Lin, and Yanfeng Zhao. "Global Stability of a Lotka-Volterra Competition-Diffusion-Advection System with Different Positive Diffusion Distributions." Axioms 10, no. 3 (July 28, 2021): 166. http://dx.doi.org/10.3390/axioms10030166.

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In this paper, the problem of a Lotka–Volterra competition–diffusion–advection system between two competing biological organisms in a spatially heterogeneous environments is investigated. When two biological organisms are competing for different fundamental resources, and their advection and diffusion strategies follow different positive diffusion distributions, the functions of specific competition ability are variable. By virtue of the Lyapunov functional method, we discuss the global stability of a non-homogeneous steady-state. Furthermore, the global stability result is also obtained when one of the two organisms has no diffusion ability and is not affected by advection.

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Kang, Jianxiong, Yanni An, Jiwei Xue, Xiao Ma, Jiuzhou Li, Fanfan Chen, Sen Wang, He Wan, Chonghui Zhang, and Xianzhong Bu. "Density Functional Theory Study of the Electronic Structures of Galena." Processes 11, no. 2 (February 17, 2023): 619. http://dx.doi.org/10.3390/pr11020619.

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In this study, the electronic structure of the galena surface was investigated using the first-principle calculation. The results of band structure, density of states, Mulliken population distribution, and frontier orbital analysis showed that galena was the p-type semiconductor of the direct band gap. During the formation of galena crystals, the 3p orbital of the S and the 6p orbital of the Pb played a primary role. Additionally, S atoms in galena quickly lose electrons and are oxidized, while Pb readily reacts with anions. The results of surface structure and electronic properties, such as surface relaxation, surface state energy levels, electronic density of states, and atomic charge distribution showed that the electronics in the 6p orbital of the Pb are transferred to the 3p orbital of the S in galena crystal. They caused the change of atomic valence states in lattice surfaces. The total electron number of the outermost surface layer was also higher than the bulk, giving the galena surface the properties of electron enrichment. This research is of great significance for developing new galena flotation reagents and for further in-depth exploration of the adsorption of reagents on the galena surface.

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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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Marahatta, Anant Babu. "Chemical Energetics and Atomic Charges Distribution of Variably Sized Hydrated Sulfate Clusters in the light of Density Functional Theory." International Journal of Progressive Sciences and Technologies 25, no. 1 (February 28, 2021): 595. http://dx.doi.org/10.52155/ijpsat.v25.1.2690.

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Among the ions classified in the Hofmeister series, the firstly ranked divalent sulfate anion has the strongest hydrating and water-structure making propensity. This unique characteristic actually makes it kosmotropic which causes water molecules to interact each other and contributes to gain structural stability of its hydrated clusters [SO42−(H2O)n]n = 1−40. In this study, few variably sized microhydrated sulfate clusters [SO42−(H2O)n]n = 1−4, 16 are considered separately, and inquired their chemical energetics and atomic charge distributions through ab initio based theoretical model. The main objective of this insight is to specify and interpret their thermodynamic stabilities, binding energies, and specific bonding and electronic interactions quantum mechanically. An in-depth analysis of their change in relative ground state electronic energy with respect to hydration number indicates stronger affinity of the sulfate ion towards water molecules while attaining structural stability in any aqueous type solutions. The mathematically determined values of their binding energy (DE) almost holds up the same with this structural stability order: [SO42−(H2O)16] > [SO42−(H2O)4] > [SO42−(H2O)3] > [SO42−(H2O)2] > [SO42−(H2O)], as reliable as experimentally and molecular dynamics simulation predicted trend. Moreover, the Mulliken derived partial atomic charges feature qualitative charge distribution in them which not only depicts electronic interactions between the specific atoms but also exemplifies the involvement of central sulfate units in hydrogen bond formation with surrounding water molecules.

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Rekha, T. N., and Beulah J. M. Rajkumar. "Density functional theory study on silver clusters using dimers, trimers, and tetramers as building units." Canadian Journal of Physics 93, no. 3 (March 2015): 318–25. http://dx.doi.org/10.1139/cjp-2014-0256.

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We systematically investigate growth patterns of small silver clusters, Agn (n ≤ 10), using density functional theory (DFT) and time-dependent density functional theory (TDDFT), considering Ag2, Ag3, and Ag4 as basic building units. Nearest-neighbor distances increase gradually with increasing n. Compared with an earlier study, where the clusters were developed by adding one atom at a time, the clusters derived in this investigation had considerably higher computed binding energies, confirming increased stability and suggesting possible growth patterns using these basic units. We used TDDFT methods to simulate the ultraviolet–visible spectra of the silver clusters, which are in good agreement with the reported experimental absorption spectrum of Ag nanoparticles. Our study indicates that the clusters formed with units of Ag3 tend to form more reactive clusters, particularly if an odd number of atoms is involved. Further, the higher level of computations employed gives better insight into the process of particle growth. The disproportionation energies of clusters built using this scheme are compared with those built one atom at a time. Mulliken population analysis of the distributions indicates the presence of polarities among the atoms in some of the cluster isomers, suggesting sites of increased activity. In addition, patterns established for the highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), and HOMO–LUMO energy gaps may be used to model stable clusters with modified optoelectrical properties.

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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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Page, Katharine, Matthew W. Stoltzfus, Young-Il Kim, Thomas Proffen, Patrick M. Woodward, Anthony K. Cheetham, and Ram Seshadri. "Local Atomic Ordering in BaTaO2N Studied by Neutron Pair Distribution Function Analysis and Density Functional Theory." Chemistry of Materials 19, no. 16 (August 2007): 4037–42. http://dx.doi.org/10.1021/cm0709673.

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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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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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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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Paar, Nils, Goran Kružić, and Tomohiro Oishi. "Nuclear magnetic transitions in the relativistic energy density functional approach." EPJ Web of Conferences 252 (2021): 02002. http://dx.doi.org/10.1051/epjconf/202125202002.

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Recently a novel theory framework has been established for description of magnetic dipole (M1) transitions in finite nuclei, based on relativistic nuclear energy density functional with point coupling interactions. The properties of M1 transitions have been studied, including the sum rules, spin, orbital, isoscalar and isovector M1 transition strengths in magic and open shell nuclei. It is shown that pairing correlations and spinorbit interaction plays an important role in the description of M1 transition strength distributions. The analysis of the evolution of M1 transition properties in the isotope chain 100-140 Sn shows the interplay between single and double-peak structures, determined by the evolution of single-particle states, their occupations governed by the pairing correlations, and two-quasiparticle transitions involved. Comparison of the calculated B(M1) transition strength with recent data from inelastic proton scattering on 112-124 Sn, shows that quenching of the g factors geff/gfree =0.80-0.93 is required to reproduce the experimental data. Further experimental investigations are needed to determine accurately the quenching factor.

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Kalaycı, T., N. K. Kınaytürk, and B. Tunalı. "Experimental and theoretical investigations (FTIR, UV-VIS spectroscopy, HOMO-LUMO, NLO and MEP analysis) of aminothiophenol isomers." Bulletin of the Chemical Society of Ethiopia 35, no. 3 (January 31, 2022): 601–14. http://dx.doi.org/10.4314/bcse.v35i3.11.

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ABSTRACT. In this research, theoretical and experimental investigation was performed on the structural and spectral data of aminothiophenol isomers. The theoretical electronic structure analyses were performed by density functional theory at the B3LYP level with the LanL2DZ basis set in the gas phase of the isolated compounds at the ground state. Potential energy distribution analysis was performed to determine the assignments of the vibration bands. Experimental and theoretical spectroscopic data were compared. Energy gap, ionization potential, electron affinity, and electronegativity were obtained through frontier molecular orbitals. KEY WORDS: Aminothiophenols, Density functional theory, Polarizability, Vibrational assignments, Molecular electrostatic potential surface Bull. Chem. Soc. Ethiop. 2021, 35(3), 601-614. DOI: https://dx.doi.org/10.4314/bcse.v35i3.11

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

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