Academic literature on the topic 'Functions of several real vari'
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Journal articles on the topic "Functions of several real vari"
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Evans, Michael J., and Paul D. Humke. "Baire one, Gibson and weakly Gibson real functions of several real variables." Rendiconti del Circolo Matematico di Palermo 59, no. 1 (April 2010): 47–51. http://dx.doi.org/10.1007/s12215-010-0002-6.
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Carpintero, C., N. Rajesh, and E. Rosas. "On real valued ω-continuous functions." Acta Universitatis Sapientiae, Mathematica 10, no. 2 (December 1, 2018): 242–48. http://dx.doi.org/10.2478/ausm-2018-0019.
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Abstract The aim of this paper is to introduce and study upper and lower ω-continuous functions. Some characterizations and several properties concerning upper (resp. lower) ω-continuous functions are obtained.
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ALMIRA, J. M., and KH F. ABU-HELAIEL. "On Montel’s theorem in several variables." Carpathian Journal of Mathematics 31, no. 1 (2015): 1–10. http://dx.doi.org/10.37193/cjm.2015.01.01.
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Recently, the first author of this paper, used the structure of finite dimensional translation invariant subspaces of C(R, C) to give a new proof of classical Montel’s theorem, about continuous solutions of Frechet’s functional equation ∆m h f = 0, for real functions (and complex functions) of one real variable. In this paper we use similar ideas to prove a Montel’s type theorem for the case of complex valued functions defined over the discrete group Z d. Furthermore, we also state and demonstrate an improved version of Montel’s Theorem for complex functions of several real variables and complex functions of several complex variables.
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Evans, Michael J., and Paul D. Humke. "Generalizations of Young’s Theorem to real functions of several variables." Rendiconti del Circolo Matematico di Palermo 58, no. 2 (July 18, 2009): 287–96. http://dx.doi.org/10.1007/s12215-009-0023-1.
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Burke, Maxim R. "Approximation and Interpolation by Entire Functions of Several Variables." Canadian Mathematical Bulletin 53, no. 1 (March 1, 2010): 11–22. http://dx.doi.org/10.4153/cmb-2010-006-4.
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AbstractLet f : ℝn → ℝ be C∞ and let h: ℝn → ℝ be positive and continuous. For any unbounded nondecreasing sequence ﹛ck﹜ of nonnegative real numbers and for any sequence without accumulation points ﹛xm﹜ in ℝn, there exists an entire function g : ℂn → ℂ taking real values on ℝn such thatThis is a version for functions of several variables of the case n = 1 due to L. Hoischen.
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Sprecher, David. "On computational algorithms for real-valued continuous functions of several variables." Neural Networks 59 (November 2014): 16–22. http://dx.doi.org/10.1016/j.neunet.2014.05.015.
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Chen, So-Chin, and Cin-Chang Lu. "ON DOMINATING PHENOMENON FOR BOUNDED REAL HARMONIC FUNCTIONS IN SEVERAL VARIABLES." Taiwanese Journal of Mathematics 14, no. 2 (April 2010): 501–15. http://dx.doi.org/10.11650/twjm/1500405804.
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Domański, Paweł, and Michael Langenbruch. "Multiplier projections on spaces of real analytic functions in several variables." Complex Variables and Elliptic Equations 62, no. 2 (August 16, 2016): 241–68. http://dx.doi.org/10.1080/17476933.2016.1218854.
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Kraus, Christiane. "Bernstein–Walsh Type Theorems for Real Analytic Functions in Several Variables." Constructive Approximation 33, no. 2 (May 15, 2010): 191–217. http://dx.doi.org/10.1007/s00365-010-9097-4.
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Ciesielski, Krzysztof. "Topologizing Different Classes of Real Functions." Canadian Journal of Mathematics 46, no. 06 (December 1994): 1188–207. http://dx.doi.org/10.4153/cjm-1994-067-x.
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AbstractThe purpose of this paper is to examine which classesof functions fromcan be topologized in a sense that there exist topologies τ1and τ2onandrespectively, such thatis equal to the class C(τ1, τ2) of all continuous functions. We will show that the Generalized Continuum Hypothesis GCH implies the positive answer for this question for a large number of classes of functionsfor which the sets {x : f(x) = g(x)} are small in some sense for all f, g ∈f ≠ g. The topologies will be Hausdorff and connected. It will be also shown that in some model of set theory ZFC with GCH these topologies could be completely regular and Baire. One of the corollaries of this theorem is that GCH implies the existence of a connected Hausdorff topology T onsuch that the class L of all linear functions g(x) = ax + b coincides with. This gives an affirmative answer to a question of Sam Nadler. The above corollary remains true for the classof all polynomials, the classof all analytic functions and the class of all harmonic functions.We will also prove that several other classes of real functions cannot be topologized. This includes the classes of C∞functions, differentiable functions, Darboux functions and derivatives.
Dissertations / Theses on the topic "Functions of several real vari"
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Guimar?es, Bruce Franca. "Um estudo sobre fun??es de v?rias vari?veis." UFVJM, 2017. http://acervo.ufvjm.edu.br/jspui/handle/1/1639.
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Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES)
O foco do presente trabalho ? apresentar um estudo sobre fun??es reais de v?rias vari?veis reais, bem como, estudar as principais t?cnicas envolvendo esse tipo de fun??o. Conv?m destacar os conceitos de limites, derivadas parciais, m?ximos e m?nimos multiplicadores de Lagrange. Na parte final da disserta??o, apresentamos uma aplica??o na Engenharia.
Disserta??o (Mestrado Profissional) ? Programa de P?s-Gradua??o Matem?tica, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2017.
The focus of the present work is to present a study on the real functions of several real variables, as well as to study the main techniques involving this type of function. It is worth mentioning the concepts of limits, partial derivatives, maximum and minimum and Lagrange multipliers. In the final part of the dissertation, we present an application in Engineering.
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Huynh, Huy. "Estimating the maximum probability of categorical classes with applications to biological diversity measurements." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44868.
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The study of biological diversity has seen a tremendous growth over the past few decades. Among the commonly used indices capturing both the richness and evenness of a community, the Berger-Parker index, which relates to the maximum proportion of all species, is particularly effective. However, when the number of individuals and species grows without bound this index changes, and it is important to develop statistical tools to measure this change. In this thesis, we introduce two estimators for this maximum: the multinomial maximum and the length of the longest increasing subsequence. In both cases, the limiting distribution of the estimators, as the number of individuals and species simultaneously grows without bound, is obtained. Then, constructing the 95% confidence intervals for the maximum proportion helps improve the comparison of the Berger-Parker index among communities. Finally, we compare the two approaches by examining their associated bias corrected estimators and apply our results to environmental data.
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Porta, Leonardo Dalla. "Contribuições da engenharia didática para o ensino e aprendizagem de funções de várias variáveis reais." Universidade Franciscana, 2014. http://tede.universidadefranciscana.edu.br:8080/handle/UFN-BDTD/154.
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Previous issue date: 2014-02-26Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Esta pesquisa tem como objetivo analisar as contribuições da Engenharia Didática para a melhoria do ensino e da aprendizagem de funções de várias variáveis reais, com a utilização do software Maple. A pesquisa foi realizada com alunos do Curso de Licenciatura em Matemática matriculados na disciplina de Cálculo III do Centro Universitário Franciscano em Santa Maria, RS. Os estudos preliminares, com a aplicação de um teste diagnóstico, mostraram as dificuldades dos alunos na construção do conceito de função de uma variável real. A partir da análise preliminar foi elaborada uma sequência de ensino, baseada em 3 unidades didáticas que abordaram, respectivamente, a construção do conceito de função de uma variável real, a construção do conceito de funções de várias variáveis reais e a construção do conceito de funções de várias variáveis reais com a manipulação do software Maple. As unidades didáticas foram constituídas de questões com diferentes pontos de vista em relação a funções, tais como: pela descrição em palavras, numericamente através de uma tabela de valores, algebricamente por fórmulas explícitas e visualmente por gráficos. Os resultados da investigação demonstraram que a sequência de ensino proposta contribuiu para a compreensão do conceito de funções e a utilização do software Maple possibilitou que os alunos inferissem e comprovassem suas asserções construindo seus próprios exemplos e, assim, participando do processo de aprendizagem.
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Piasson, Diego. "Otimização de colunas de destilação : uma abordagem aplicada dos multiplicadores de Lagrange." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306533.
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Orientador: Sandra Augusta SantosDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Este trabalho aborda a otimizacao de um processo de destilacao de uma mistura binaria em uma coluna de pratos, motivado pela destilacao do metanol no processo de produção do biodiesel. Mais especificamente, considera a minimização de uma função custo energetico envolvendo o calor do refervedor e a temperatura fornecida a carga de alimentação sujeita a restrições de equilibrio e canalizações. Esse problema foi formulado baseado no artigo de More A collection of Nonlinear Model Problems. Para a solução foi utilizada a metodologia dos multiplicadores de Lagrange delineada no Teorema de Karush-Kuhn-Tucker para otimização de problemas com restrições mistas. Os softwares Maxima e MatLab foram utilizados para a investigação numerica da solução do problema. Uma explanação do funcionamento da coluna tambem e feita, bem como a apresentação dos principais resultados envolvendo otimização, desde problemas irrestritos ate problemas com varias restrições mistas
Abstract: This work tackles the optimization of a distillation process of a binary mixture in a column with plates, which came from the methanol distillation in the production process of the biodiesel. More specifically, it considers the minimization of a cost objective function that encompass the heat rate supplied to the reboiler and the feed temperature, subject to equilibrium constraints and simple bounds. This problem was formulated based on Mor'e¿s article A collection of Nonlinear Model Problems. The Lagrange multiplier methodology was used for solve it, outlined in the Karush-Kuhn-Tucker Theorem for optimization problems with mixed constraints. The softwares Maxima and MatLab were employed for the numerical investigation of the problem solution. An explanation about the operation of the column is also included, together with the presentation of the main results encompassing optimization, from unconstrained to mixed constrained problems
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Otimização
Mestre em Matemática
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Padua, Suzan Grazielle Benetti de. "Multiplicadores de Lagrange : aspectos geometricos e algebricos e uma aplicação em engenharia quimica na destilação do metanol." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306532.
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Orientador: Sandra Augusta SantosDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Este trabalho se inicia com um breve resgate histórico da abordagem de Fermat para encontrar máximos e mínimos sem o uso de derivadas. Em termos teóricos, trás uma discussão sobre máximos e mínimos de funções em Rn, com um estudo detalhado sobre a otimizacao sem restrições, destacando a regra de Fermat e a classificacao dos pontos críticos. Trata também da otimização com restrições, por meio dos Teoremas dos Mul-tiplicadores de Lagrange para restrições de igualdade e desigualdade, e para restrições mistas, o Teorema de Karush-Kuhn-Tucker (KKT). Do ponto de vista prático, apresenta uma aplicacao envolvendo uma coluna de destilacao do metanol vinculada 'a produção do biodiesel, com a otimização da proporção de metanol destilado
Abstract: This work begins with a brief historical overview of Fermat¿s method to find maxima and minima without derivatives. In theoretical terms, the elements concerning maximum and minimum of functions of n variables are discussed, together with a detailed study of unconstrained optimization, focusing on the Fermat¿s rule and the classification of critical points. Constrained optimization is also analyzed, by means of the Lagrange Multilplier Theorem for equality constrained problems, and the Karush-Kuhn-Tucker (KKT) Theorem for mixed constrained optimization. In practical terms, an application concerning a distillation column of methanol associated to the biodiesel production is presented, with the optimization of the proportion of methanol in the amount of material that is removed from the top of the column
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Otimização
Mestre em Matemática
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(8882636), Michael R. Pilla. "Spectra of Composition Operators on the Unit Ball in Two Complex Variables." Thesis, 2020.
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Let φ be a self-map of B2, the unit ball in C2. We investigate the equation Cφf=λf where we define Cφf : -f◦φ, with f a function in the Drury Arves on Space. After imposing conditions to keep Cφ bounded and well-behaved, we solve the equation Cφf - λf and determine the spectrum σ(Cφ) in the case where there is no interior fixed point and boundary fixed point without multiplicity. We then investigate the existence of one-parameter semigroups for such maps and discuss some generalizations.
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(9132815), Kuang-Ru Wu. "Hermitian-Yang-Mills Metrics on Hilbert Bundles and in the Space of Kahler Potentials." Thesis, 2020.
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The two main results in this thesis have a common point: Hermitian--Yang--Mills (HYM) metrics. In the first result, we address a Dirichlet problem for the HYM equations in bundles of infinite rank over Riemann surfaces. The solvability has been known since the work of Donaldson \cite{Donaldson92} and Coifman--Semmes \cite{CoifmanSemmes93}, but only for bundles of finite rank. So the novelty of our first result is to show how to deal with infinite rank bundles. The key is an a priori estimate obtained from special feature of the HYM equation.
In the second result, we take on the topic of the so-called ``geometric quantization." This is a vast subject. In one of its instances the aim is to approximate the space of K\"ahler potentials by a sequence of finite dimensional spaces. The approximation of a point or a geodesic in the space of K\"ahler potentials is well-known, and it has many applications in K\"ahler geometry. Our second result concerns the approximation of a Wess--Zumino--Witten type equation in the space of K\"ahler potentials via HYM equations, and it is an extension of the point/geodesic approximation.
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(6858680), Lida Ahmadi. "Asymptotic Analysis of the kth Subword Complexity." Thesis, 2019.
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The Subword Complexity of a character string refers to the number of distinct substrings of any length that occur as contiguous patterns in the string. The kth Subword Complexity in particular, refers to the number of distinct substrings of length k in a string of length n. In this work, we evaluate the expected value and the second factorial moment of the kth Subword Complexity for the binary strings over memory-less sources. We first take a combinatorial approach to derive a probability generating function for the number of occurrences of patterns in strings of finite length. This enables us to have an exact expression for the two moments in terms of patterns' auto-correlation and correlation polynomials. We then investigate the asymptotic behavior for values of k=a log n. In the proof, we compare the distribution of the kth Subword Complexity of binary strings to the distribution of distinct prefixes of independent strings stored in a trie.
The methodology that we use involves complex analysis, analytical poissonization and depoissonization, the Mellin transform, and saddle point analysis.
Books on the topic "Functions of several real vari"
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1941-, Haussmann W., Jetter K, and Reimer Manfred 1933-, eds. Advances in multivariate approximation: Proceedings of the 3rd International Conference on Multivariate Approximation Theory held at Witten-Bommerholz, Germany, September 27-October 2, 1998. Berlin: Wiley-VCH, 1999.
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Srivastava, Pramila. Functions of several variables. Allahabad, India: Allahabad Mathematical Society, 1990.
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Berkey, Dennis D. Calculus of several variables. 2nd ed. New York: Saunders College Pub., 1988.
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Hervé, Michel. Several complex variables, local theory. 2nd ed. Oxford: Published for the Tata Institute of Fundamental Research, Bombay [by the] Oxford University Press, 1987.
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D'Angelo, John P. Several complex variables and the geometry of real hypersurfaces. Boca Raton: CRC Press, 1993.
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Aczél, J. Functional equations in several variables. Cambridge [Cambridgeshire]: Cambridge University Press, 1989.
Find full textBook chapters on the topic "Functions of several real vari"
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Ziemer, William P. "Functions of Several Variables." In Modern Real Analysis, 335–74. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64629-9_11.
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Fonda, Alessandro. "Functions of Several Real Variables." In Compact Textbooks in Mathematics, 61–123. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95321-2_2.
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Eriksson, Kenneth, Claes Johnson, and Donald Estep. "Vector-Valued Functions of Several Real Variables." In Applied Mathematics: Body and Soul, 789–814. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05800-8_1.
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Chabrillac, Yves, and J. P. Crouzeix. "Continuity and differentiability properties of monotone real functions of several real variables." In Mathematical Programming Studies, 1–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0121151.
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Barthe, Gilles, Raphaëlle Crubillé, Ugo Dal Lago, and Francesco Gavazzo. "On the Versatility of Open Logical Relations." In Programming Languages and Systems, 56–83. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44914-8_3.
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AbstractLogical relations are one among the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be immediately proved by means of logical relations, for instance program continuity and differentiability in higher-order languages extended with real-valued functions. Informally, the problem stems from the fact that these properties are naturally expressed on terms of non-ground type (or, equivalently, on open terms of base type), and there is no apparent good definition for a base case (i.e. for closed terms of ground types). To overcome this issue, we study a generalization of the concept of a logical relation, called open logical relation, and prove that it can be fruitfully applied in several contexts in which the property of interest is about expressions of first-order type. Our setting is a simply-typed $$\lambda $$ λ -calculus enriched with real numbers and real-valued first-order functions from a given set, such as the one of continuous or differentiable functions. We first prove a containment theorem stating that for any collection of real-valued first-order functions including projection functions and closed under function composition, any well-typed term of first-order type denotes a function belonging to that collection. Then, we show by way of open logical relations the correctness of the core of a recently published algorithm for forward automatic differentiation. Finally, we define a refinement-based type system for local continuity in an extension of our calculus with conditionals, and prove the soundness of the type system using open logical relations.
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Cates, Dennis M. "DIFFERENTIALS OF ANY FUNCTION OF SEVERAL VARIABLES EACH OF WHICH IS IN ITS TURN A LINEAR FUNCTION OF OTHER SUPPOSED INDEPENDENT VARIABLES. DECOMPOSITION OF ENTIRE FUNCTIONS INTO REAL FACTORS OF FIRST OR OF SECOND DEGREE." In Cauchy's Calcul Infinitésimal, 91–96. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11036-9_18.
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Asami, Yasushi. "Introduction: City Planning and New Technology." In New Frontiers in Regional Science: Asian Perspectives, 261–65. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-15-8848-8_17.
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AbstractIn Part III, titled “City Planning and New Technology,” we discuss two topics, namely, compact cities and real estate technology in Japan.Promotion of compact cities is regarded as a high priority issue in urban policies in the era of population decrease. The Act on Special Measures concerning Urban Reconstruction in 2014 was revised to institutionalize the framework for the Location Normalization Plan, a plan for local governments to build compact cities to manage population decline and aging urban infrastructure while placing less burden on environment. Three chapters are devoted to issues related to this movement. In Chap.10.1007/978-981-15-8848-8_18, Ishikawa (2020) discusses how urban functions can be guided by residents’ perspectives. To build a compact city, various day-to-day services must be placed proximal to residential areas; however, some services must be placed at a certain distance from residences because of land use restrictions. Therefore, we must determine the uses allowed in residential areas. In Chap.10.1007/978-981-15-8848-8_19, Morimoto (2020) discusses the history of major contributions made by the development of transportation facilities to urban spread, the important role of traffic facilities to guide land use toward desirable purposes, and impact of self-driving vehicles on land use. In Chap.10.1007/978-981-15-8848-8_20, Ogushi (2020) explains how the Location Normalization Plan in Niigata City was formed in detail.Real estate technology refers to real estate business-related services that use new technology. Several new services based on new technology have been introduced in the field of real estate in Japan. Three chapters are devoted to issues related to real estate technology. In Chap.10.1007/978-981-15-8848-8_21, Narimoto (2020) explains the outline of real estate technology services in Japan and identifies legal problems associated with handling of information. In Chap.10.1007/978-981-15-8848-8_22, Nishio and Ito (2020) report on creating a sky view factor calculating system that uses Google Street View. Sky view factor is a term that refers to a configuration factor for the amount of sky in a hypothetical hemisphere. In Chap.10.1007/978-981-15-8848-8_23, Kiyota (2020) explains the transition of neural network research and characteristics of deep learning and introduces a system that detects category inconsistencies in real estate property photographs submitted by real estate companies by using deep learning and a system that detects indexes associated with ease of living based on property photographs.
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"- Functions of Several Variables." In Real Analysis and Foundations, 271–88. Chapman and Hall/CRC, 2016. http://dx.doi.org/10.1201/b15061-17.
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"Functions on Euclidean Spaces." In Functions of Several Real Variables, 61–102. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814299282_0002.
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"Differential Calculus in Several Variables." In Functions of Several Real Variables, 103–229. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814299282_0003.
Full textConference papers on the topic "Functions of several real vari"
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Liang, Yongtu, and Jing Gong. "Offtaking Scheduling Software for Multi-Product Pipeline." In 2006 International Pipeline Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/ipc2006-10062.
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The main objective of this work is to exhibit the functions of a software program that prepares offtaking schedules for multi-product pipelines. The software program is currently being used on two multi-product pipelines in China. In the paper, the pipeline system modeled in the software involves several offtaking stations, pump stations, and one multi-product pipeline connected to several depots that distribute large amounts of oil products to customer markets. The background for developing this software is presented and the mathematical model utilized in the software will be given. The software can track the interface positions on the basis that the liquid is incompressible and transported adiabatically in the pipeline — the density doesn’t vary with pressure and temperature. In the model, the author adopts the advantages of variable paces to speed the calculation in the Master-Clock Method and adds interfaces’ reaching stations to the set of control points, while honoring handling contamination only at terminal station and keeping turbulence flow all time. Finally, a real-world application on the Lan-Cheng-Yu Multi-product Pipeline (LCYPP) is introduced. This is the first real test on a multi-product pipeline in China. Through the application, the characteristics and functions of the software is reported. The software provides users with a diagram for batch movement, the interface timetable, the scheduling table, the interface size, and so on. The application shows that the software is successful.
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"Spaces of Differentiable Functions of Several Real Variables and Applications." In Proceedings of the 6th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812837332_others10.
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Pellegrini, Giovanni, Alessandro Tibo, Paolo Frasconi, Andrea Passerini, and Manfred Jaeger. "Learning Aggregation Functions." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/398.
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Learning on sets is increasingly gaining attention in the machine learning community, due to its widespread applicability. Typically, representations over sets are computed by using fixed aggregation functions such as sum or maximum. However, recent results showed that universal function representation by sum- (or max-) decomposition requires either highly discontinuous (and thus poorly learnable) mappings, or a latent dimension equal to the maximum number of elements in the set. To mitigate this problem, we introduce LAF (Learning Aggregation Function), a learnable aggregator for sets of arbitrary cardinality. LAF can approximate several extensively used aggregators (such as average, sum, maximum) as well as more complex functions (e.g. variance and skewness). We report experiments on semi-synthetic and real data showing that LAF outperforms state-of-the-art sum- (max-) decomposition architectures such as DeepSets and library-based architectures like Principal Neighborhood Aggregation, and can be effectively combined with attention-based architectures.
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Baptista, Renan Martins, Aline Barbosa Figueiredo, and Gustavo C. R. Bodstein. "On the Comparison of Different Multiphase Flow Kernels for Gas Pipeline Real Time Advanced Functions." In 2010 8th International Pipeline Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ipc2010-31589.
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The nature of real time advanced functions or systems for gas pipelines carrying two phase mixtures is complex, especially when the dominant phase is gaseous. In this case, the flow quite often requires periodic pig runs, among several other specific operational procedures. Thus, a robust, accurate, reliable and fast kernel is mandatory for good performance on leak detection, location and quantification, as well as any other real time function such as virtual instrumentation or inventory management and reconciliation. This work aims at comparing different transient two-phase one-dimensional kernels under the perspective highlighted above. Specifically, one may cite: (i) a two-fluid model, implemented in 20 years consolidated commercial flow simulator, bringing a kernel of first order in time and second-order in space, three continuity equations, and three momentum equations, where 2 different pressures are possible to be calculated; (ii) a simple two-fluid model to serve as the basis of a different way to approach the same problem. The main focus of this paper is on real time applications, then its main goal is to provide considerations and comparisons on accuracy, reliability and processing speed (CPU performance) coming from six different numerical methods and schemes. The commercial flow simulator is then being used as the basis of comparison, as it is considered highly reliable and robust by the market.
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Taher, Matt. "The Use of Departure Functions to Estimate Deviation of a Real Gas From the Ideal Gas Model." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-90112.
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Abstract In many practical applications of thermodynamics, the use of simplified relationships of the ideal-gas model over a more accurate but more complex real gas model, is a critical decision to make. Thermodynamic departure functions provide screening criteria to evaluate whether the ideal-gas model can accurately represent a gas behavior. This paper reports several departure functions to evaluate deviation of a real gas from the ideal-gas model. Included in this paper is the derivation of departure functions based on isothermal compressibility, isobaric expansivity, isochoric change of pressure with temperature, isochoric change of internal energy with pressure, sonic speed, and heat capacities difference. The description of each of these departure functions is accompanied by a numerical example. Departure functions defined in this paper have led to improved representation of deviation from the ideal-gas model across a range of ±2% deviation of the specific volume departure (also known as the compressibility factor, Z) for a typical gas mixture encountered in natural gas processing. The limitations involved in using the compressibility factor, Z, to evaluate departure from the ideal-gas model is highlighted. It is shown that even as the compressibility factor, Z, approaches unity at certain thermodynamic conditions, other departure functions exhibit considerable deviations from the ideal-gas model. It is concluded that the compressibility factor, Z, should not be used as “the only criterion” to evaluate conformance to the ideal-gas model. This paper also explains the physical significance of Schultz compressibility functions X, Y, and L [3] by introducing departure functions based on isothermal compressibility and isobaric expansivity.
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Houser, Donald R., Jonny Harianto, B. Chandrasekaran, John Josephson, and Naresh Iyer. "A Multi-Variable Approach to Determine the “Best” Gear Design." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/ptg-14362.
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Abstract Gear design requires the designer to compromise many design variables in order to determine the best performance of a gear set. Unfortunately the designer has a multiplicity of goals including keeping both bending and pitting stresses under an allowable value, minimizing scoring, achieving minimum efficiency and trying to minimize noise. This latter response variable is rarely considered in the initial gear design. In this work, noise is considered to be one of the more important design considerations. One approach to multi-variable gear design that has been tried is design optimization. Usually optimization techniques are limited in the number of variables that can be handled and with so many response variables, it is difficult to come up with an objective function that reflects the considerations of a real gear designer. In this paper we present a simulation-based approach to gear design that allows the designer to essentially “run all of the cases”. The simulation accounts for the true load distribution of the gears when computing response variables. Also, such factors as manufacturing tolerances may be included in the simulation so that truly robust designs may be obtained. Rather than using an objective function approach, designs are analyzed with a dominance filter that assesses each response variable in a manner that results in the “best” design. After these “best” designs are found, an interactive viewer allows the selection of those designs that best meet the designer’s goals with regard to all design variables. Several examples are presented in this paper. In each case, over 65,000 designs are evaluated and the dominance filter results in from 200 to 900 successful designs, depending on the tolerances that are applied. After sorting with the viewer the designer usually ends up with from 5 to 20 designs whose features may vary significantly, but have similar performances.
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Teng, Xin, WuLi Chu, HaoGuang Zhang, Kai Liu, and JinGe Li. "The Influence of Geometry Deformation on a Multistage Compressor." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-75935.
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Over the service time, the rotating parts of turbine engine vary in their geometry. When aircraft take off or fly through a volcanic ash cloud, the particles are sucked into the engine, impinge the blade and gradually erode the surface. The impinging between particles and blades is responsible for the increase of the surface roughness. Also, during the long-time operation, the function of the blade’s stacking law combined with the centrifugal force could cause deviation of the stagger angle. Moreover, blade tip clearance could vary because of the casing deformation. All the deformation of geometry could severely reduce the engine performance and thus engine life. The work presented in this paper focused on the influence of geometry deformation in a real low-pressure compressor. The investigation is more difficult than most of the previously published researches with a total of five stages being considered. Due to the irregularities in geometry, it is difficult to numerically assess the performance of the compressor. The aim of this study is to give an analysis method that allows an efficient and accurate estimation of the performance for multistage compressor with geometry deformation. In the first step, the geometry models with different deviation in tip clearance, roughness and stagger angle were established respectively. A CFD study was then applied to the compressor with RANS method to calculate the flow field with different types of deformation. The variation of overall performance due to the deformation was finally analyzed to identify the dominant factor on influencing the performance of the compressor among different types of geometry deformation. A method based on polytropic efficiency analysis and flow field analysis was also established to specifically analyze which stage is most sensitive to the geometry deformation. The results show a significant influence of geometric deformation on the efficiency, total pressure rise and flow range of the multistage compressor. The conclusions of this study would provide an important guidance for engine overhaul in the factory.
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Suffield, Sarah, and Amir Jokar. "Modeling the Flow of a Liquid Droplet Diffusing Into Various Porous Media for Inkjet Printing Applications." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-68151.
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Inkjet technology currently relies heavily upon the absorption of ink into porous media. Characterizing the absorption capacity of media as well as the absorption rate can be critical in understanding the entire drying process. Evaluating the absorption performance of a coated medium can particularly be important since the coating may be either semi-absorptive, or in some cases non-absorptive. The absorption performance can also vary among uncoated media. In order to better understand the absorption mechanism, the fluid flow of a water droplet impacting with and diffusing into several porous papers, each with a unique permeability, was analyzed numerically and experimentally in this study. The droplet impact was simulated by computational fluid dynamics techniques for a variety of conditions. The transient computational modeling predicted the shape of the droplet at different time intervals before and after the impact. It also predicted the volume of liquid that had diffused into the porous substrate over time. The results predicted by the computational modeling were then compared to experimental data, which was collected for a real system with the same configuration as in the computational modeling using a high speed digital video camera. The camera captured images of the droplet as it impacted with various coated and uncoated papers. Results showed a relatively good agreement between the computational modeling and experimentation at drop times greater than 0.1 seconds after the impact. A dimensional analysis was also performed on the most effective parameters of the flow process, and a correlation was developed to predict the aspect ratio of the droplet after the impact as a function of the other dimensionless parameters, such as Reynolds and Weber numbers. The results of this study can be useful for drying applications, such as inkjet printing, where absorption of a liquid into a porous medium is critical for the drying process.
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Tibbals, Thomas F., Theodore A. Bapty, and Ben A. Abbott. "CADDMAS: A Real-Time Parallel System for Dynamic Data Analysis." In ASME 1994 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/94-gt-194.
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Arnold Engineering Development Center (AEDC) has designed and built a high-speed data acquisition and processing system for real-time online dynamic data monitoring and analysis. The Computer Assisted Dynamic Data Monitoring and Analysis System (CADDMAS) provides 24 channels at high frequency and another 24 channels at low frequency for online real-time aeromechanical, vibration, and performance analysis of advanced turbo-engines and other systems. The system is primarily built around two different parallel processors and several PCs to demonstrate hardware independence and architecture scalability. These processors provide the computational power to display online and in real-time what can take from days to weeks using existing offline techniques. The CADDMAS provides online test direction and immediate hardcopy plots for critical parameters, all the while providing continuous health monitoring through parameter limit checking. Special in-house developed Front End Processors (FEP) sample the dynamic signals, perform anti-aliasing, signal transfer function correction, and bandlimit filtering to improve the accuracy of the time domain signal. A second in-house developed Numeric Processing Element (NPE) performs the FFT, threshold monitoring, and packetizes the data for rapid asynchronous access by the parallel network. Finally, the data are then formatted for display, hardcopy plotting, and cross-channel processing within the parallel network utilizing off-the-shelf hardware. The parallel network is a heterogeneous message-passing parallel pipeline configuration which permits easy scaling of the system. Advanced parallel processing scheduler/controller software has been adapted specifically for CADDMAS to allow quasi-dynamic instantiation of a variety of simultaneous data processing tasks concurrent with display and alarm monitoring functions without gapping the data. Although many applications of CADDMAS exist, this paper describes the features of CADDMAS, the development approach, and the application of CADDMAS for turbine engine aeromechanical testing.
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Ponti, Fabrizio, Vittorio Ravaglioli, and Matteo De Cesare. "Development of a Common Rail Diesel Engine Combustion Model for ROHR Real-Time Estimation." In ASME 2011 Internal Combustion Engine Division Fall Technical Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/icef2011-60153.
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Combustion control is a crucial aspect in modern Diesel engines control strategies, mainly due to the requests to increase efficiency and maintain pollutant emissions within the values bounded by standard regulations. In order to perform an accurate combustion control, modern “closed loop” control algorithms require the evaluation of a large number of quantities that provide information about combustion process effectiveness. This work presents a methodology that allows real-time estimation of energy released, during the combustion process, in a Common Rail Multi-Jet Diesel engine. This procedure can be divided in two main steps. The first step consists in the development of a zero-dimensional combustion model based on the linear combination of a proper number of Wiebe functions. In this case, a zero-dimensional approach has been chosen, because it is accurate enough for this analysis and requires low computational efforts. Once the combustion model has been developed, it can be used to determine Rate of Heat Release (RoHR) and the angular position in which 50% of fuel burned within an engine cycle is reached (MFB50). The second section of this work describes the relationships existing between injection parameters (such as Start of Injection, injected fuel quantities, rail pressure...) and the Wiebe parameters identified in the first step of the procedure. The above mentioned relationships have been used to set up correlations that allow estimating Wiebe parameters, therefore ROHR and MFB50, starting from injection parameters. The results obtained in MFB50 estimation are particularly emphasized, because real-time knowledge of this quantity is necessary to feedback a control algorithm for optimal combustion positioning. This work is based on several experimental tests performed on a 2.2 liters Common Rail Multi-Jet Diesel engine. First, experimental tests have been carried out to identify the combustion model and the correlations existing between Wiebe parameters and injection parameters. Then, in order to determine the accuracy of the approach, the complete estimation methodology has been applied to the engine under study. This work describes a methodology for real-time estimation of several quantities that provide important information about combustion process effectiveness (useful, for example, in modern low temperature combustion control systems). No extra cost is needed, because the methodology requires no additional sensor.
Reports on the topic "Functions of several real vari"
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Wilson, D., Vladimir Ostashev, and Chris Pettit. Distribution of the two-point product of complex amplitudes in the fully saturated scattering regime. Engineer Research and Development Center (U.S.), November 2020. http://dx.doi.org/10.21079/11681/38701.
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This Letter considers probability density functions (pdfs) involving products of the complex amplitudes observed at two points (which may, in general, involve separations in space, time, or frequency) in conditions of fully saturated scattering. First, the pdf is derived for the product of the complex amplitude at one point with the conjugate of the complex amplitude at another point. It is shown that the real and imaginary parts of this product each have a variance gamma pdf. Second, expressions are derived for several joint pdfs involving complex amplitude products and powers at two points.
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Rahmani, Mehran, and Manan Naik. Structural Identification and Damage Detection in Bridges using Wave Method and Uniform Shear Beam Models: A Feasibility Study. Mineta Transportation Institute, February 2021. http://dx.doi.org/10.31979/mti.2021.1934.
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This report presents a wave method to be used for the structural identification and damage detection of structural components in bridges, e.g., bridge piers. This method has proven to be promising when applied to real structures and large amplitude responses in buildings (e.g., mid-rise and high-rise buildings). This study is the first application of the method to damaged bridge structures. The bridge identification was performed using wave propagation in a simple uniform shear beam model. The method identifies a wave velocity for the structure by fitting an equivalent uniform shear beam model to the impulse response functions of the recorded earthquake response. The structural damage is detected by measuring changes in the identified velocities from one damaging event to another. The method uses the acceleration response recorded in the structure to detect damage. In this study, the acceleration response from a shake-table four-span bridge tested to failure was used. Pairs of sensors were identified to represent a specific wave passage in the bridge. Wave velocities were identified for several sensor pairs and various shaking intensities are reported; further, actual observed damage in the bridge was compared with the detected reductions in the identified velocities. The results show that the identified shear wave velocities presented a decreasing trend as the shaking intensity was increased, and the average percentage reduction in the velocities was consistent with the overall observed damage in the bridge. However, there was no clear correlation between a specific wave passage and the observed reduction in the velocities. This indicates that the uniform shear beam model was too simple to localize the damage in the bridge. Instead, it provides a proxy for the overall extent of change in the response due to damage.
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Financial Stability Report - Second Semester of 2020. Banco de la República de Colombia, March 2021. http://dx.doi.org/10.32468/rept-estab-fin.sem2.eng-2020.
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The Colombian financial system has not suffered major structural disruptions during these months of deep economic contraction and has continued to carry out its basic functions as usual, thus facilitating the economy's response to extreme conditions. This is the result of the soundness of financial institutions at the beginning of the crisis, which was reflected in high liquidity and capital adequacy indicators as well as in the timely response of various authorities. Banco de la República lowered its policy interest rates 250 points to 1.75%, the lowest level since the creation of the new independent bank in 1991, and provided ample temporary and permanent liquidity in both pesos and foreign currency. The Office of the Financial Superintendent of Colombia, in turn, adopted prudential measures to facilitate changes in the conditions for loans in effect and temporary rules for rating and loan-loss provisions. Finally, the national government expanded the transfers as well as the guaranteed credit programs for the economy. The supply of real credit (i.e. discounting inflation) in the economy is 4% higher today than it was 12 months ago with especially marked growth in the housing (5.6%) and commercial (4.7%) loan portfolios (2.3% in consumer and -0.1% in microloans), but there have been significant changes over time. During the first few months of the quarantine, firms increased their demands for liquidity sharply while consumers reduced theirs. Since then, the growth of credit to firms has tended to slow down, while consumer and housing credit has grown. The financial system has responded satisfactorily to the changes in the respective demands of each group or sector and loans may grow at high rates in 2021 if GDP grows at rates close to 4.6% as the technical staff at the Bank expects; but the forecasts are highly uncertain. After the strict quarantine implemented by authorities in Colombia, the turmoil seen in March and early April, which was evident in the sudden reddening of macroeconomic variables on the risk heatmap in Graph A,[1] and the drop in crude oil and coal prices (note the high volatility registered in market risk for the region on Graph A) the local financial markets stabilized relatively quickly. Banco de la República’s credible and sustained policy response played a decisive role in this stabilization in terms of liquidity provision through a sharp expansion of repo operations (and changes in amounts, terms, counterparties, and eligible instruments), the purchases of public and private debt, and the reduction in bank reserve requirements. In this respect, there is now abundant aggregate liquidity and significant improvements in the liquidity position of investment funds. In this context, the main vulnerability factor for financial stability in the short term is still the high degree of uncertainty surrounding loan quality. First, the future trajectory of the number of people infected and deceased by the virus and the possible need for additional health measures is uncertain. For that reason, there is also uncertainty about the path for economic recovery in the short and medium term. Second, the degree to which the current shock will be reflected in loan quality once the risk materializes in banks’ financial statements is uncertain. For the time being, the credit risk heatmap (Graph B) indicates that non-performing and risky loans have not shown major deterioration, but past experience indicates that periods of sharp economic slowdown eventually tend to coincide with rises in non-performing loans: the calculations included in this report suggest that the impact of the recession on credit quality could be significant in the short term. This is particularly worrying since the profitability of credit establishments has been declining in recent months, and this could affect their ability to provide credit to the real sector of the economy. In order to adopt a forward-looking approach to this vulnerability, this Report presents several stress tests that evaluate the resilience of the liquidity and capital adequacy of credit institutions and investment funds in the event of a hypothetical scenario that seeks to simulate an extreme version of current macroeconomic conditions. The results suggest that even though there could be strong impacts on the credit institutions’ volume of credit and profitability under such scenarios, aggregate indicators of total and core capital adequacy will probably remain at levels that are above the regulatory limits over the horizon of a year. At the same time, the exercises highlight the high capacity of the system's liquidity to face adverse scenarios. In compliance with its constitutional objectives and in coordination with the financial system's security network, Banco de la República will continue to closely monitor the outlook for financial stability at this juncture and will make the decisions that are necessary to ensure the proper functioning of the economy, facilitate the flow of sufficient credit and liquidity resources, and further the smooth operation of the payment systems. Juan José Echavarría Governor