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Books on the topic 'Functional expansion methods'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Marti, Kurt. Differentiation of probability functions: The transformation method. Neubiberg: Forschungsschwerpunkt Simulation und Optimierung Deterministischer und Stochastischer Dynamischer Systeme, Universität der Bundeswehr München, 1994.

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2

Gil, Amparo. Numerical methods for special functions. Philadelphia, Pa: Society for Industrial and Applied Mathematics, 2007.

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3

Patil, S. H. Asymptotic Methods in Quantum Mechanics: Application to Atoms, Molecules and Nuclei. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000.

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4

Michel, Volker. Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball. Boston: Birkhäuser Boston, 2013.

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5

ŁU, Novokshenov V. I., ed. The isomonodromic deformation method in the theory of Painleve equations. Berlin: Springer-Verlag, 1986.

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6

N.Y.) AMS Special Session in Memory of Daryl Geller Wavelet and Frame Theoretic Methods in Harmonic Analysis and Partial Differential Equations (2012 Rochester. Commutative and noncommutative harmonic analysis and applications: AMS Special Session in Memory of Daryl Geller on Wavelet and Frame Theoretic Methods in Harmonic Analysis and Partial Differential Equations, September 22-23, 2012, Rochester Institute of Technology, Rochester, NY. Edited by Mayeli, Azita, 1976- editor of compilation. Providence, Rhode Island: American Mathematical Society, 2013.

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7

Patil, S. H. Asymptotic methods in quantum mechanics: Application to atoms, molecules, and nuclei. Berlin: Springer, 2000.

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8

service), SpringerLink (Online, ed. Extremal Polynomials and Riemann Surfaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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9

Numerical Methods for Special Functions. Society for Industrial Mathematics, 2007.

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10

Budelmann, Felix, and Tom Phillips, eds. Textual Events. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805823.001.0001.

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Recent decades have seen a major expansion in our understanding of how early Greek lyric functioned in its social, political, and ritual contexts. The fundamental role song played in the day-to-day lives of communities, groups, and individuals has been the object of intense study. This volume places its focus elsewhere, and attempts to illuminate poetic effects that cannot be captured in functional terms. Employing a range of interpretative methods, it explores the idea of lyric performances as textual events. Several chapters investigate the pragmatic relationship between real performance contexts and imaginative settings. Others consider how lyric poems position themselves in relation to earlier texts and textual traditions, or discuss the distinctive encounters lyric poems create between listeners, authors, and performers. In addition to studies that analyse individual lyric texts and lyric authors (Sappho, Alcaeus, Pindar), the volume includes treatments of the relationship between lyric and the Homeric Hymns. Building on the renewed concern with the aesthetic in the study of Greek lyric and beyond, Textual Events re-examines the relationship between the poems’ formal features and their historical contexts. Lyric poems are a type of sociopolitical discourse, but they are also objects of attention in themselves. They enable reflection on social and ritual practices as much as they are embedded within them. As well as enacting cultural norms, lyric challenges listeners to think about and experience the world afresh.

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11

Fox, Raymond. The Use of Self. Oxford University Press, 2011. http://dx.doi.org/10.1093/oso/9780190616144.001.0001.

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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.

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12

Raff, Lionel, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam. Neural Networks in Chemical Reaction Dynamics. Oxford University Press, 2012. http://dx.doi.org/10.1093/oso/9780199765652.001.0001.

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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.

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13

Theodoulou, Stella Z., and Ravi K. Roy. 3. Progressive reform across the globe. Oxford University Press, 2016. http://dx.doi.org/10.1093/actrade/9780198724230.003.0003.

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Modern, rationally structured, hierarchical state administrative bureaucracies coincided with the centralization of government authority and expansion of European imperialist military systems in the 18th and 19th centuries. ‘Progressive reform across the globe’ explains that the characteristics and dimensions of the modern nation-state helped lay the foundations of modern public administration and social welfare systems in America and Western Europe. The American Progressive era and the progressive reforms that shaped European welfare states are discussed. Public administrators were compelled to adopt new bureaucratic methods and processes to carry out their functions and mandates. These new administrative processes were rooted in principles and methods associated with the Gilded Age and the Scientific Revolution.

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14

Novokshenov, Victor Y., and Alexander R. Its. Isomonodromic Deformation Method in the Theory of Painleve Equations. Springer London, Limited, 2006.

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15

Osman, Gamaleldin M., James J. Riviello, and Lawrence J. Hirsch. EEG in the Intensive Care Unit. Edited by Donald L. Schomer and Fernando H. Lopes da Silva. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780190228484.003.0022.

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The field of continuous electroencephalographic monitoring (cEEG) in the intensive care unit has dramatically expanded over the past two decades. Expansion of cEEG programs led to recognition of the frequent occurrence of electrographic seizures, and complex rhythmic and periodic patterns in various critically ill populations. The majority of electrographic seizures are of nonconvulsive nature, hence the need for cEEG for their identification. Guidelines on when and how to perform cEEG and standardized nomenclature for description of rhythmic and periodic patterns are now available. Quantitative EEG analysis methods depict EEG data in a compressed (hours on one screen) colorful graphical representation, facilitating early identification of key events, recognition of slow, long-term trends, and timely therapeutic intervention. Integration of EEG with other invasive and noninvasive modalities of monitoring brain function provides critical information about the development of secondary neuronal injury, providing a valuable window of opportunity for intervention before irreversible damage ensues.

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16

Baldwin, Eric. Religious Markets, Capital Markets, and Church Finances in Industrializing America. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198798071.003.0003.

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A number of scholars in recent years have turned to market models to describe religion in nineteenth-century America, arguing that competition among churches largely accounts for the nation’s relative religious vitality. However, a detailed examination of one religious ‘marketplace’—the city of Lowell, Massachusetts—demonstrates the limits of such interpretations. First, such scholars fail to capture the ways that Protestant churches functioned as an interdenominational de facto establishment, co-operating in the shared project of promoting the public good and defending moral norms. Also, to the extent that churches did compete, they competed for money, as much as for adherents. In doing so, they appropriated new methods accompanying the expansion of capitalism, competing for funds in nascent capital markets. Thus, churches appealed to individuals not primarily as consumers of religious goods, but as potential investors in religious institutions, and presented churches as both safe and profitable investments and bulwarks of social stability.

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17

Tang, K. T., and S. H. Patil. Asymptotic Methods in Quantum Mechanics: Applications to Atoms, Molecules, and Nuclei (Springer Series in Chemical Physics). Springer, 2000.

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18

Meola, David A., ed. A Cultural History Of Genocide in the Long Nineteenth Century. Bloomsbury Publishing Plc, 2021. http://dx.doi.org/10.5040/9781350034921.

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The long 19th century, approximately 1750 to 1918, was one of significant existential change for peoples across the globe. The beginning of this period saw the expansion of empires, and shortly thereafter, the EuroAmerican Enlightenment brought about calls for revolutions and the “rights of man”. The events and ideas made way for empire and the creation of the nation-state. European states primarily concentrated their aggressive colonization in the Global South, bringing mostly white metropolitans and settlers into intimate contact with diverse African, Asian, and American populations. The inherent violence of imperialism eventually ushered in flashpoints of conflict, as well as indentured servitude, racial segregation, ecological destruction, and genocide throughout Europe’s overseas empires. While communal destruction functioned as a central element of 19th-century genocides, colonial governments also used other methods to destroy indigenous life, such as forced assimilation, language adoption, religious instruction, and economic subjugation. Memories of these atrocities have since contributed both to systemic violence in subsequent decades, and to education about these events in the hope of genocide prevention. Yet for all of the violence, a spirit of humanitarianism developed alongside these vile actions that tried to reverse the policies of states and help the aggrieved.

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19

Bogatyrev, Andrei, and Nikolai Kruzhilin. Extremal Polynomials and Riemann Surfaces. Springer, 2014.

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