Relevant bibliographies by topics / Functionsof real variables

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  1. Dissertations / Theses
  2. Books
  3. Book chapters
  4. Conference papers
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Academic literature on the topic 'Functionsof real variables'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Dissertations / Theses on the topic "Functionsof real variables"

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Balli, Umut. "Utility Accrual Real-Time Scheduling Under Variable Cost Functions." Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/34358.

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We present a utility accrual real-time scheduling algorithm called CIC-VCUA, for tasks whose execution times are functions of their starting times. We model such variable execution times employing variable cost functions (or VCFs). The algorithm considers application activities that are subject to time/utility function time constraints (or TUFs), execution times de- scribed using VCFs, and concurrent, mutually exclusive sharing of non-CPU resources. We consider the multi-criteria scheduling objective of (1) assuring that the maximum interval between any two consecutive, successful completions of jobs of a task must not exceed a specified upper bound, and (2) maximizing the system's total accrued utility, while satis- fying mutual exclusion resource constraints. Since the scheduling problem is intractable, CIC-VCUA statically computes worst-case sojourn times of tasks, selects tasks for execution based on their potential utility density, and completes them at specific times, in polynomial- time. We establish that CIC-VCUA achieves optimal timeliness during under-loads. Further, we identify the conditions under which timeliness assurances hold. Our simulation experi- ments illustrate CIC-VCUA's effectiveness and superiority.
Master of Science
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Zagar, Susanna Maria. "Convex functions." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/986.

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Ko, Hong Fu. "Marcinkiewicz's theorem and its generalizations /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?MATH%202004%20KO.

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Płotka, Krzysztof. "Set-theoretic and algebraic properties of certain families of real functions." Morgantown, W. Va. : [West Virginia University Libraries], 2001. http://etd.wvu.edu/templates/showETD.cfm?recnum=2013.

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Thesis (Ph. D.)--West Virginia University, 2001.
Title from document title page. Document formatted into pages; contains iv, 60 p. Includes abstract. Includes bibliographical references (p. 64-66).
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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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Singh, Shiu Raj. "Dynamics of macroeconomic variables in Fiji : a cointegrated VAR analysis." Diss., Lincoln University, 2008. http://hdl.handle.net/10182/774.

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Abstract of thesis submitted in partial fulfilment of the requirements for the Degree of Master of Commerce and Management Dynamics of macroeconomic variables in Fiji : a cointegrated VAR analysis By Shiu Raj Singh The objective of this study is to examine how macroeconomic variables of Fiji inter-relate with aggregate demand and co-determine one another using a vector autoregression (VAR) approach. This study did not use a prior theoretical framework but instead used economic justification for selection of variables. It was found that fiscal policy, which is generally used as a stabilisation tool, did not have a positive effect on real Gross Domestic Product (GDP) growth in the short term. Effects on GDP growth were positive over the long term but not statistically significant. Furthermore, expansionary fiscal policy caused inflationary pressures. Fiji has a fixed exchange rate regime, therefore, it was expected that the focus of monetary policy would be the maintenance of foreign reserves. It was, however, found that monetary expansion in the short term resulted in positive effects on real GDP growth and resulted in inflation. The long term effects of monetary policy on real GDP growth were negative, which are explained by the fixed exchange rate regime, endogenous determination of money supply by the central bank, an unsophisticated financial market and, perhaps, an incomplete transmission of the policy. Both merchandise trade and visitor arrivals growth were found to positively contribute to short term and long term economic growth. Political instability was found not to have significant direct effects on real GDP growth but caused a significant decline in visitor arrivals which then negatively affected economic growth in the short term.
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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 Santos
Dissertação (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
Mestrado
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 Santos
Dissertação (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
Mestrado
Otimização
Mestre em Matemática
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Imafuku, Roberto Seidi. "Sobre a passagem do estudo de função de uma variável real para o caso de duas variáveis." Pontifícia Universidade Católica de São Paulo, 2008. https://tede2.pucsp.br/handle/handle/11354.

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Secretaria da Educação do Estado de São Paulo
This research was developed with the goal of verifying the difficulties and the knowledge shown by students related to the transition of the study of functions of one variable to the case of two variables, regarding dependent and independent variables well as the interdependence between them, to the dominion and the graphic, to the relation between the graphic of the dominion of the function and also which manifestations are revealed in the study of the partial derivatives of the first order. In order to do so we developed two questionnaires based upon the Theory of the Registers of Semiotic Representation of Raymond Duval, the questionnaires having been answered by students of the fourth and fifth term of the course of Mathematics of a private university in the greater São Paulo area. The first questionnaire was applied to students of the fourth term and it made possible to verify not only one first analysis of their difficulties, but also how pertinent the questions were, as well as how fitting the wording was. It has been found that some of the questions needed rephrasing, and also that the addition of new questions was necessary, which contributed to the making of a new questionnaire, which was answered by students of the fifth term. This research revealed some difficulties that students show when studying functions of two variables, such as the comprehension of the system of the 3D axis, the lack of clarity when determining and representing the dominium of the function, difficulty when performing the conversion from the representation of the natural language to the algebric language in contextualised situations, the confusion between the graphic representation of the dominion and the function, and the obstacles for the interpretation of the graphic of a function of two variables, difficulties that have negative effect on the study of partial derivatives. The registers of semiotic representation proved themselves an efficient tool for the explanation of the knowledge and the complexity that the study of functions with two variables represent for students
Esta pesquisa foi desenvolvida com o objetivo de verificar as dificuldades e saberes manifestados por estudantes relativos à transição do estudo das funções de uma variável para o caso de duas, no que diz respeito às variáveis dependentes e independentes e à interdependência entre elas, ao domínio e o gráfico, à relação entre o gráfico do domínio e o gráfico da função e, também quais manifestações são reveladas no estudo das derivadas parciais de primeira ordem. Para isso, elaboramos dois questionários fundamentados na Teoria dos Registros de Representação Semiótica de Raymond Duval, os quais foram aplicados a estudantes do quarto e quinto semestre de um curso de Licenciatura em Matemática de uma universidade particular da grande São Paulo. O primeiro questionário foi aplicado a alunos do quarto semestre e possibilitou, além de uma primeira análise das dificuldades, verificar a pertinência das questões, bem como a adequação dos enunciados. Foi constatado que algumas questões necessitavam de uma reestruturação e, também, que era necessário o acréscimo de novas questões, o que contribuiu na elaboração do questionário definitivo, que foi aplicado a estudantes do quinto semestre. Esta pesquisa revelou algumas dificuldades que os alunos apresentam quando estudam as funções de duas variáveis, como: a não compreensão do sistema de eixos 3D, a falta de clareza na determinação e representação do domínio da função, a dificuldade em realizar a conversão do registro da língua natural para o algébrico em situações contextualizadas, a confusão entre o registro gráfico do domínio e da função, e os obstáculos para a interpretação do gráfico de uma função de duas variáveis, dificuldades estas que se refletem negativamente no estudo das derivadas parciais. Os registros de representação semiótica se mostraram uma eficaz ferramenta para a explicitação dos saberes e da complexidade que o estudo de funções de duas variáveis representa para os alunos
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Signorelli, Shirley Ferreira. "Um ambiente virtual para o ensino semipresencial de funções de uma variável real: design e análise." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11284.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The purpose of this investigation was the elaboration and implementation of a virtual environment for a part time distance course for students of the Computer Science and Systems of Information. The students failed in a former discipline that approaches topics of elementary Mathematics. It happened in a particular university in the city of São Paulo. Our focus was on analyzing this environment, the tools and interactions that happened on distance mode, about the content of real function of one variable. The methodology used, design-based research, favored proposing and analyzing the activities about this topic, as well as their reorganization and, the re design of the environment. The Blackboard platform and the used tools were analyzed based on Chaves (2000) criteria, and it seemed efficient as a virtual environment for the learning in our course. However, we leaved some critical and suggestions for future works, mainly about the role of the tools for communication within part time distance courses. The analysis of the students and teacher speeches' was based on the Model of Argumentative Strategy (CASTRO et al, 2004) and allowed to raise some aspects on the understanding of Real Functions of one variable, as they were privileged in the different interactive spaces such as forum, chat, email and daily log. Aspects like the meaning production in Mathematics can be produced due to the authority of a teacher or of another student who is considered good by the classroom peers, or based on everyday language usage or on cultural characteristics. Moreover, we found that besides the students lack of prerequisite elementary mathematics, there is a lack of a culture for on-line courses
Nesta pesquisa objetivamos a elaboração e implementação de um ambiente virtual para um curso semipresencial, para estudantes dos cursos de Bacharelado em Ciência da Computação e Sistemas de Informação de uma instituição particular na cidade de São Paulo, dependentes na disciplina que aborda tópicos de pré-calculo. Nosso foco recaiu na análise do ambiente, da viabilidade das ferramentas e das interações que ocorreram a distância, no que tange o conteúdo de Funções de uma Variável Real. A metodologia utilizada, design research, permitiu propor e analisar as atividades sobre este tópico, incluindo a reestruturação e complementação deste ambiente. A plataforma Blackboard e as ferramentas foram analisadas segundo critérios definidos por Chaves (2000) e se mostraram eficazes como ambiente virtual de aprendizagem atendendo, para nosso curso, os critérios necessários. Entretanto, deixamos algumas críticas e sugestões para trabalhos futuros, principalmente quanto o papel do uso de ferramentas de comunicação em cursos semipresenciais. A análise dos discursos dos alunos e docente baseados no Modelo de Estratégia Argumentativa (CASTRO et al, 2004) permitiu levantar alguns aspectos sobre a compreensão de Funções de uma Variável Real que foram privilegiados nos diferentes espaços interativos como fórum, chat, e-mail e diário de rotina, tais como o fato de que a produção de significados em Matemática pode estar apoiada na autoridade do professor ou alunos bem vistos pela classe, na linguagem cotidiana e no aspecto cultural. Observamos ainda que além da falta de pré-requisitos de matemática básica, ainda há falta de cultura de trabalhos on-line
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Books on the topic "Functionsof real variables"

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Torchinsky, Alberto. Real variables. Redwood City, Calif: Addison-Wesley Pub. Co., Advanced Book Program, 1988.

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Real functions. Berlin: Springer-Verlag, 1985.

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Webb, J. R. L. Functions of several real variables. New York: E. Horwood, 1991.

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Srivastava, Pramila. Functions of several variables. Allahabad, India: Allahabad Mathematical Society, 1990.

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Medvedev, F. A. Scenes from the history of real functions. Basel: Birkhäuser Verlag, 1991.

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Ene, Vasile. Real functions: Contemporary aspects. New York: Springer-Verlag, 1995.

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Real functions: Current topics. Berlin: Springer, 1995.

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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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Association, Research and Education, ed. The ESSENTIALS of real variables. Piscataway, N.J: Research & Education Association, 1994.

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Nicolas Bourbaki. Functions of a real variable: Elementary theory. Berlin: Springer, 2004.

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Book chapters on the topic "Functionsof real variables"

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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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Krantz, Steven G. "Some Special Functions." In A Handbook of Real Variables, 113–38. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8128-9_9.

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Krantz, Steven G. "Sequences and Series of Functions." In A Handbook of Real Variables, 103–12. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8128-9_8.

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DiBenedetto, Emmanuele. "Topics on Measurable Functions of Real Variables." In Real Analysis, 193–245. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4939-4005-9_5.

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DiBenedetto, Emmanuele. "Topics on Integrable Functions of Real Variables." In Real Analysis, 431–89. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4939-4005-9_9.

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DiBenedetto, Emmanuele. "Topics on Measurable Functions of Real Variables." In Real Analysis, 171–219. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0117-5_5.

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DiBenedetto, Emmanuele. "Topics on Integrable Functions of Real Variables." In Real Analysis, 375–422. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0117-5_9.

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Krantz, Steven G. "Limits and the Continuity of Functions." In A Handbook of Real Variables, 53–69. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8128-9_5.

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Pugh, Charles C. "Functions of a Real Variable." In Real Mathematical Analysis, 149–210. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17771-7_3.

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Pugh, Charles Chapman. "Functions of a Real Variable." In Real Mathematical Analysis, 139–200. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-0-387-21684-3_3.

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Conference papers on the topic "Functionsof real variables"

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Marinov, S. M., George Venkov, Ralitza Kovacheva, and Vesela Pasheva. "On Analytic Functions of Four Cyclic Real Variables." In 35TH INTERNATIONAL CONFERENCE “APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS”: AMEE-2009. AIP, 2009. http://dx.doi.org/10.1063/1.3271618.

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Kong, Kyoungchul, Kiyonori Inaba, and Masayoshi Tomizuka. "Real-Time Nonlinear Programming by Amplitude Modulation." In ASME 2008 Dynamic Systems and Control Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/dscc2008-2160.

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Nonlinear Programming (NLP) is for optimization of nonlinear cost functions. In applications of NLP for real-time optimization, however, the estimation of the gradient of the cost function remains as a challenge. On the other hand, the Extremum-Seeking Control (ESC) optimizes the cost function in real-time, but it involves a complicated design of filters in multi-dimensional cases. In this paper, a new method that optimizes an arbitrary multi-variable cost function in real-time is proposed. In the proposed method, the variables are updated as in NLP while the gradient of the cost function is continuously estimated by the amplitude modulation as in ESC. The proposed method does not require design of any complicated filters. The performance is verified by simulations on time-varying and noisy cost functions as well as automatic controller tuning applications.
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Lee, Yu-Tai. "Mysterious Behavior of Optimization Calculation With MOGA." In ASME 2013 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/fedsm2013-16505.

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Multi-Objective Generic Algorithm (MOGA) is a popular and viable optimization calculation scheme for many practical engineering problems. This is because MOGA provides reliable search results covering wide and multi-variable design spaces. Most importantly when an optimization problem involves using mixed design variables, i.e. continuous and discrete variables, MOGA is still applicable. However, in such a condition MOGA needs to be programmed in a binary mode, which requires a minimum number of bits to represent each real and integer design variable. The accuracy of the prediction of the optimization calculation is expected to depend on the number of bits used. This paper introduces such a problem based on a general turbomachinery design problem. The design variables of the centrifugal impeller design consist of discrete and continuous variables. Some puzzling behavior occurred when the optimization calculation was carried out, related to the prediction accuracy when applying different number of bits to represent the continuous and discrete design variables. It is found that the accuracy is independent of the number of binary bits used. Detailed analyses were performed using simplified analytic formulations for the objective functions to determine why the calculated results show such a behavior. In addition, objective functions are developed and verified that do not show this behavior.
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Daxberger, Erik, Anastasia Makarova, Matteo Turchetta, and Andreas Krause. "Mixed-Variable Bayesian Optimization." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/365.

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The optimization of expensive to evaluate, black-box, mixed-variable functions, i.e. functions that have continuous and discrete inputs, is a difficult and yet pervasive problem in science and engineering. In Bayesian optimization (BO), special cases of this problem that consider fully continuous or fully discrete domains have been widely studied. However, few methods exist for mixed-variable domains and none of them can handle discrete constraints that arise in many real-world applications. In this paper, we introduce MiVaBo, a novel BO algorithm for the efficient optimization of mixed-variable functions combining a linear surrogate model based on expressive feature representations with Thompson sampling. We propose an effective method to optimize its acquisition function, a challenging problem for mixed-variable domains, making MiVaBo the first BO method that can handle complex constraints over the discrete variables. Moreover, we provide the first convergence analysis of a mixed-variable BO algorithm. Finally, we show that MiVaBo is significantly more sample efficient than state-of-the-art mixed-variable BO algorithms on several hyperparameter tuning tasks, including the tuning of deep generative models.
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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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Saczalski, Kenneth J., Sriringham Kumaresan, Anthony Sances, Joseph Lawson Burton, and Paul R. Lewis. "An Experimental Method for Multi-Variable Analysis of Vehicle Safety Systems and Application to Front Seats and Rear Occupant Interaction in Rear Impacts." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60785.

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This study presents a combined experimental-analytical method for test efficient, and cost effective, multi-variable analysis of safety system performance related to occupant injury potential analyzed over wide parameter ranges. Experimental techniques such as the “two-level factorial” method, in combination with sled-buck test set-ups (that match vehicle crash characteristics), are applied to demonstrate the technique for front seat performance as it relates to injury potential of the front occupant and rear seated children during rear impacts. The surrogate data from the above test method is combined into a “polynomial response function,” such as HIC, which is developed as a function of the many variables, and allows for analytical “interpolation and extrapolation” at variable combinations not tested. A minimum of 4 test combinations are used to establish the “polynomial injury curves” as functions of two variables (i.e. impact severity and front occupant weight) for a given seat type. Inclusion of a third variable for evaluation of “seat strength effects” can be accomplished with a minimum of 8 test combinations for the factorial method. Both front adult and rear child interactions are studied. Three year-old H-III surrogates are used for the study of rear child passengers. Plots of test generated “polynomial” multi-variable HIC level curves for the front adult and rear child surrogates are presented as functions of impact severity and front occupant weight, for various seat types. Accident case head injury data of rear-seated children is used to verify the experimental-analytical method.
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Nelatury, Sudarshan R., Charles W. Nelatury, and Charles F. Nelatury. "Use of formal derivative for extremizing real-valued functions of complex variables." In SPIE Defense, Security, and Sensing, edited by Alex A. Kazemi, Bernard C. Kress, and Simon Thibault. SPIE, 2013. http://dx.doi.org/10.1117/12.2016270.

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Mohd Zulkefli, Mohd Azrin, and Zongxuan Sun. "Real-Time Powertrain Optimization Strategy for Connected Hybrid Electrical Vehicle." In ASME 2016 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/dscc2016-9727.

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Connected Vehicle (CV) technology, which allows traffic information sharing, and Hybrid Electrical Vehicles (HEV) can be combined to improve vehicle fuel efficiency. However, transient traffic information in CV environment necessitates a fast HEV powertrain optimization for real-time implementation. Model Predictive Control (MPC) with Linearization is proposed, but the computational effort is still prohibitive. The Equivalent Consumption Minimization Strategy (ECMS) and Adaptive-ECMS are proposed to minimize computation time, but unable to guarantee charge-sustaining-operation (CS). Fast analytical result from Pontryagin’s Minimum Principles (PMP) is possible but the input has to be unconstrained. Numerical solutions with Linear Programming (LP) are proposed, but over-simplifications of the cost and constraint functions limit the performance of such methods. In this paper, a nonlinear CS constraint is transformed into linear form with input variable change. With linear input and CS constraints, the problem is solved with Separable Programming by approximating the nonlinear cost with accurate linear piecewise functions which are convex. The piecewise-linear functions introduce new dimensionless variables which are solved as a large-dimension constrained linear problem with efficient LP solvers. Comparable fuel economy with Dynamic Programming (DP) is shown, with maximum fuel savings of 7% and 21.4% over PMP and Rule-Based (RB) optimizations. Simulations with different levels of vehicle speed prediction uncertainties to emulate CV settings are presented.
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Turner, Cameron J., and Richard H. Crawford. "Modeling Design Spaces With Discontinuous Variables Using NURBs HyPerModels." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99643.

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The vast majority of metamodeling demonstrations focuses on problems composed of continuous variables. However, important engineering design problems often include one or more discontinuous variables that require special attention. Previous work demonstrated the ability of Non-Uniform Rational B-spline HyPerModels to represent highly nonlinear functions composed of continuous variables. With minor modifications those capabilities can be extended to include functions defined by combinations of discontinuous input and output variables of different types, including discrete integer variables, feasibility variables and membership functions. Examples are used to demonstrate these modeling capabilities including applications developed from real engineering design problems such as the optimal positioning of a construction site crane and the optimal lay-up of a composite material I-beam.
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A., Endang Cahya M. "Completeness properties of R × R and real valued functions of two variables under lexicographic order." In PROCEEDINGS OF INTERNATIONAL SEMINAR ON MATHEMATICS, SCIENCE, AND COMPUTER SCIENCE EDUCATION (MSCEIS 2015). AIP Publishing LLC, 2016. http://dx.doi.org/10.1063/1.4941164.

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Reports on the topic "Functionsof real variables"

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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
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