Relevant bibliographies by topics / Function extrema

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Function extrema'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 February 2022

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Journal articles on the topic "Function extrema"

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Rieger, J. H. "Hypersurfaces of extremal slope." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 133, no. 2 (April 2003): 449–65. http://dx.doi.org/10.1017/s030821050000247x.

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The hypersurface of extremal slope consists of extrema of the gradient magnitude along integral curves of the gradient vector field of a smooth function. We study the singularities, and other geometric features, of hypersurfaces of extremal slope associated with generic functions and with one-parameter families of functions representing generic solutions to the heat equation.
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Hirschhorn, Michael D. "91.35 Extrema of a symmetric function." Mathematical Gazette 91, no. 521 (July 2007): 264–67. http://dx.doi.org/10.1017/s0025557200181653.

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Beaulieu, N. C. "Extrema of sin x/x function." Electronics Letters 31, no. 15 (July 20, 1995): 1215. http://dx.doi.org/10.1049/el:19950850.

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Dorosiewicz, Slawomir. "On the extrema of integrable functions." International Journal of Mathematics and Mathematical Sciences 27, no. 9 (2001): 547–53. http://dx.doi.org/10.1155/s0161171201005488.

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This paper contains the definition of the extremum of integrable functions (e.g., the mode of density function). It seems to be a generalization of well-known standard definition and can be applied in estimation theory to extend the maximum likelihood method.
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El-Khoury, M., O. D. Crisalle, and R. Longchamp. "Discrete Transfer-function Zeros and Step-response Extrema." IFAC Proceedings Volumes 26, no. 2 (July 1993): 537–42. http://dx.doi.org/10.1016/s1474-6670(17)49000-8.

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Galkin, O. E., and S. Yu Galkina. "Global extrema of the Delange function, bounds for digital sums and concave functions." Sbornik: Mathematics 211, no. 3 (March 2020): 336–72. http://dx.doi.org/10.1070/sm9143.

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Guilloux, Antonin, and Julien Marché. "Volume function and Mahler measure of exact polynomials." Compositio Mathematica 157, no. 4 (April 2021): 809–34. http://dx.doi.org/10.1112/s0010437x21007016.

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We study a class of two-variable polynomials called exact polynomials which contains $A$ -polynomials of knot complements. The Mahler measure of these polynomials can be computed in terms of a volume function defined on the vanishing set of the polynomial. We prove that the local extrema of the volume function are on the two-dimensional torus and give a closed formula for the Mahler measure in terms of these extremal values. This formula shows that the Mahler measure of an irreducible and exact polynomial divided by $\pi$ is greater than the amplitude of the volume function. We also prove a K-theoretic criterion for a polynomial to be a factor of an $A$ -polynomial and give a topological interpretation of its Mahler measure.
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Fernando, José F. "On the set of local extrema of a subanalytic function." Collectanea Mathematica 71, no. 1 (February 22, 2019): 1–24. http://dx.doi.org/10.1007/s13348-019-00245-6.

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Cvetkovic, Dragos, Pierre Hansen, and Vera Kovacevic-Vujcic. "On some interconnections between combinatorial optimization and extremal graph theory." Yugoslav Journal of Operations Research 14, no. 2 (2004): 147–54. http://dx.doi.org/10.2298/yjor0402147c.

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The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set. While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various graph invariants under some constraints and with constructing extremal graphs. We analyze by examples some interconnections and interactions of the two theories and propose some conclusions.
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Veroy, Boris S. "An optimal algorithm for search of extrema of a bimodal function." Journal of Complexity 2, no. 4 (December 1986): 323–32. http://dx.doi.org/10.1016/0885-064x(86)90010-5.

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Dissertations / Theses on the topic "Function extrema"

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Huggins, Mark C. (Mark Christopher). "A Continuous, Nowhere-Differentiable Function with a Dense Set of Proper Local Extrema." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc500353/.

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In this paper, we use the following scheme to construct a continuous, nowhere-differentiable function 𝑓 which is the uniform limit of a sequence of sawtooth functions 𝑓ₙ : [0, 1] → [0, 1] with increasingly sharp teeth. Let 𝑋 = [0, 1] x [0, 1] and 𝐹(𝑋) be the Hausdorff metric space determined by 𝑋. We define contraction maps 𝑤₁ , 𝑤₂ , 𝑤₃ on 𝑋. These maps define a contraction map 𝑤 on 𝐹(𝑋) via 𝑤(𝐴) = 𝑤₁(𝐴) ⋃ 𝑤₂(𝐴) ⋃ 𝑤₃(𝐴). The iteration under 𝑤 of the diagonal in 𝑋 defines a sequence of graphs of continuous functions 𝑓ₙ. Since 𝑤 is a contraction map in the compact metric space 𝐹(𝑋), 𝑤 has a unique fixed point. Hence, these iterations converge to the fixed point-which turns out to be the graph of our continuous, nowhere-differentiable function 𝑓. Chapter 2 contains the background we will need to engage our task. Chapter 3 includes two results from the Baire Category Theorem. The first is the well known fact that the set of continuous, nowhere-differentiable functions on [0,1] is a residual set in 𝐶[0,1]. The second fact is that the set of continuous functions on [0,1] which have a dense set of proper local extrema is residual in 𝐶[0,1]. In the fourth and last chapter we actually construct our function and prove it is continuous, nowhere-differentiable and has a dense set of proper local extrema. Lastly we iterate the set {(0,0), (1,1)} under 𝑤 and plot its points. Any terms not defined in Chapters 2 through 4 may be found in [2,4]. The same applies to the basic properties of metric spaces which have not been explicitly stated. Throughout, we will let 𝒩 and 𝕽 denote the natural numbers and the real numbers, respectively.
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Hanzlíček, Tomáš. "Matematické modely produkce." Master's thesis, Vysoké učení technické v Brně. Fakulta podnikatelská, 2011. http://www.nusl.cz/ntk/nusl-222811.

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The thesis deals with the mathematical modelling of economic processes, particulary production. Basic approach, models and methods of modelling concerning the mentioned area are described. Further, specific characterizations are investigated. Application of selected methods to typical examples is presented. In the final part models on concrete data are constructed.
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Scarpa, Paulo Cesar Almeida. "Transgressão, mercado e distinção : a violencia extrema no cinema /." oai:ufpr.br:234707, 2007. http://200.17.209.5:8000/cgi-bin/gw_42_13/chameleon.42.13a?host=localhost%201111%20DEFAULT&sessionid=VTLS&function=CARDSCR&search=KEYWORD&pos=1&u1=12101&t1=234707.

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Orientador: Rodolfo Bode de Moraes
Dissertaçao (mestrado) - Universidade Federal do Paraná, Setor de Ciencias Humanas, Letras e Artes, Programa de Pós-Graduaçao em Sociologia. Defesa: Curitiba, 2007
Inclui bibliografia
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Johansson, Johannes, and André Åberg. "Motiv och motivation bakom volontärism i extrema situationer. : En kvalitativ studie om Volunteer Function Inventory och dess behållning som analysverktyg." Thesis, Högskolan för lärande och kommunikation, Högskolan i Jönköping, HLK, Globala studier, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-27190.

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This study is based on the notion that the most widely cited and used instrument for assessing volunteer motivations, the Volunteer Function Inventory (VFI), might not be sufficient in its aspiration to aid, streamline and benefit the recruitment and retention process within volunteer organizations. Understanding volunteers’ motivation is a crucial component in the process of securing future volunteer engagement in a world where their efforts are desperately needed. This study aims to explain motives and motivation behind volunteer efforts in extreme situations as well as to examine the dependability of the theoretical framework in relation to the forthcoming result, based on the following research questions: What motivated Swedish medical personnel to volunteer during the 2014 Ebola outbreak in West Africa? How could the motives and motivation of Swedish medical personnel be categorized in accordance with the Volunteer Function Inventory (VFI)? Is the Volunteer Function Inventory (VFI) a sufficient tool for analyzing the motives and motivation of Swedish medical personnel in the given case? The presented research questions will be answer through a qualitative theory-consuming study, based mainly on interviews. The interviews are, however, complimented by various written sources in the field of research. The result and subsequent analysis confirms the authors’ notion on the VFI and highlights certain deficits in the tool’s execution and its succeeding result. The result of the study shows that the respondents were motivated by a great variety of motivational elements, a variety that the VFI cannot properly account for. Essential information is therefore left unexposed by the VFI, leaving the volunteer organizations in an undesirable situation where they, in their pursuit to recruit and retain the volunteers, are forced to evaluate and accommodate candidates without knowing their complete motivational process. Therefore, the authors deem the tool as applicable but not sufficient. Concludingly, the authors call for additional and more distinct functions in the VFI; an instrument for assessing if the volunteers are intrinsically or extrinsically motivated as well as a sub-section within the tool for determining the presence and character of inhibiting factors affecting the volunteers motivation.
Att fastställa och möta en volontärarbetares motiv och motivation är en avgörande del i arbetet med att säkerställa ett framtida engagemang. I en värld med återkommande naturkatastrofer, väpnade konflikter och epidemier är betydelsen av volontärinsatser större än någonsin. Studien ämnar således undersöka om Volunteer Function Inventory (VFI) – det mest citerade och använda verktyget inom forskningsområdet för att undersöka och fastställa volontärarbetares motiv och motivation – är tillräckligt tillförlitligt i dess strävan att underlätta, effektivisera och gynna rekryterings- och retentionsprocessen inom volontärorganisationer. Undersökningen bygger på en kvalitativ teorikonsumerande studie vilken baseras på djupintervjuer med svensk sjukvårdspersonal kring deras volontärinsatser under ebolautbrottet i Västafrika 2014. Studiens resultat och efterföljande analys påvisar att VFI som verktyg uppvisar vissa brister i dess nuvarande utformning och i den data som genereras. Studien visar att respondenterna motiverades av en stor variation motivationsdrivande element som VFI inte kan redogöra för tillräckligt väl. Detta lämnar volontärorganisationer i en oönskad situation där de i sin strävan att rekrytera och behålla volontärarbetare tvingas utvärdera personer utan att känna till deras fullständiga motivationsbild. Sammanfattningsvis efterfrågar författarna fler och mer distinkta funktioner i VFI; ett instrument för att avgöra om volontärerna drivs av inre eller yttre motivation samt ett tillägg för att kunna fastställa förekomsten, och således karaktären, av motivationshämmande faktorer hos en volontärarbetare.
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Brymer, George Eric. "Extreme dude! a phenomenological perspective on the extreme sport experience /." Access electronically, 2005. http://www.library.uow.edu.au/adt-NWU/public/adt-NWU20060508.145406/index.html.

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Song, Zixia. "Extremal Functions for Contractions of Graphs." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/6425.

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In this dissertation, a problem related to Hadwiger's conjecture has been studied. We first proved a conjecture of Jakobsen from 1983 which states that every simple graphs on $n$ vertices and at least (11n-35)/2 edges either has a minor isomorphic to K_8 with one edge deleted or is isomorphic to a graph obtained from disjoint copies of K_{1, 2, 2, 2, 2} and/or K_7 by identifying cliques of size five. We then studied the extremal functions for complete minors. We proved that every simple graph on nge9 vertices and at least 7n-27 edges either has a minor, or is isomorphic to K_{2, 2, 2, 3, 3}, or is isomorphic to a graph obtained from disjoint copies of K_{1, 2, 2, 2, 2, 2} by identifying cliques of size six. This result extends Mader's theorem on the extremal function for K_p minors, where ple7. We discussed the possibilities of extending our methods to K_{10} and K_{11} minors. We have also found the extremal function for K_7 plus a vertex minor.
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Ngo, Tri Minh. "On the Behavior of the Gamma Function on the Negative Side." ScholarWorks@UNO, 2012. http://scholarworks.uno.edu/honors_theses/25.

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In this paper we analyze the behavior of the Gamma function at its critical points and points of discontinuity on the negative side of the x-axis. We will also explain the bluntness of the gamma function on this negative side.
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Goodey, G. C. "P2X receptor function in an extreme ionic environment." Thesis, University College London (University of London), 2013. http://discovery.ucl.ac.uk/1399846/.

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ATP activates P2X receptors in the apical surface of kidney epithelial cells. However, tubular fluid is unusual - with low sodium levels, high calcium levels and acidic in nature. This study investigated how P2X receptors operate in extreme ionic environments. Xenopus oocytes easily tolerated extreme ionic environments. Their membrane properties and pharmacological profile were examined under normal and extreme ionic conditions. It was confirmed that oocytes lack endogenous P2X receptors, and were unaffected by P2X receptor antagonists and allosteric modulators. Also, oocytes lacked muscarinic receptors. The pharmacological profile of P2X2 and P2X4 receptors expressed in oocytes were examined under normal and extreme ionic conditions. Each P2X subtype was activated by ATP and CTP and this activity was affected by extracellular ions. At rat P2X2, reduced extracellular sodium had an inhibitory effect on ATP signalling, which was reversed by acidifying of the medium or intensified by adding calcium to the medium. At rat P2X4, reduced extracellular sodium had a biphasic action (potentiation, then inhibition) on ATP signalling, which was insensitive to acidification but was intensified by adding calcium. A unique electrophysiological property of P2X2-expressing oocytes was used to investigate an ATP-releasing mechanism. An inward current (Ix) was identified and this current was blocked by the P2 receptor antagonist, suramin, and inhibited by the ATP-degrading enzyme, apyrase. The amplitude of IX was affected by the flow rate of the superfusate, confirming that ATP was released by a mechanosensory process. The present results show that ATP may activate P2X receptors present in the kidney, even in the extreme ionic environment of the distal nephron. Salt and water reclamation in the kidney may depend on flow rate, since a common mechanosensory mechanism can release enough ATP to activate those P2X receptors regulating ENaC and AQP2 channel function in the distal nephron.
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Geneson, Jesse (Jesse T. ). "Bounds on extremal functions of forbidden patterns." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/99069.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 63-66).
Extremal functions of forbidden sequences and 0 - 1 matrices have applications to many problems in discrete geometry and enumerative combinatorics. We present a new computational method for deriving upper bounds on extremal functions of forbidden sequences. Then we use this method to prove tight bounds on the extremal functions of sequences of the form (12 ... 1)t for 1 >/= 2 and t >/= 1, abc(acb)t for t >/= 0, and avav'a, such that a is a letter, v is a nonempty sequence excluding a with no repeated letters and v' is obtained from v by only moving the first letter of v to another place in v. We also prove the existence of infinitely many forbidden 0 - 1 matrices P with non-linear extremal functions for which every strict submatrix of P has a linear extremal function. Then we show that for every d-dimensional permutation matrix P with k ones, the maximum number of ones in a d-dimensional matrix of sidelength n that avoids P is 20(k) nd-1
by Jesse Geneson.
Ph. D.
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Meinke, Alexander. "Applications of the Extremal Functional Bootstrap." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-26112018-120129/.

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The study of conformal symmetry is motivated through an example in statistical mechanics and then rigorously developed in quantum field theories in general spatial dimensions. In particular, primary fields are introduced as the fundamental objects of such theories and then studied in the formalism of radial quantization. The implications of conformal invariance on the functional form of correlation functions are studied in detail. Conformal blocks are defined and various approaches to their analytical and numerical calculation are presented with a special emphasis on the one-dimensional case. Building on these preliminaries, a modern formulation of the conformal bootstrap program and its various extensions are discussed. Examples are given in which bounds on the scaling dimensions in a one-dimensional theory are derived numerically. Using these results I motivate the technique of using the extremal functional bootstrap which I then develop in more detail. Many technical details are discussed and examples shown. After a brief discussion of conformal field theories with a boundary I apply numerical methods to find constraints on the spectrum of the 3D Ising model. Another application is presented in which I study the 4-point function on the boundary of a particular theory in Anti-de-Sitter space in order to approximate the mass spectrum of the theory.
O estudo da simetria conforme é motivado através de um exemplo em mecânica estatística e em seguida rigorosamente desenvolvido em teorias de campos quânticos em dimensões espaciais gerais. Em particular, os campos primários são introduzidos como os objetos fundamentais de tais teorias e então estudados através do formalismo de quantização radial. As implicações da invariância conforme na forma funcional das funções de correlação são estudadas em detalhe. Blocos conformes são definidos e várias abordagens para seu cálculo analítico e numérico são apresentadas com uma ênfase especial no caso unidimensional. Com base nessas preliminares, uma formulação moderna do programa de bootstrap conforme e suas várias extensões são discutidas. Exemplos são dados em que limites nas dimensões de escala em uma teoria unidimensional são derivados numericamente. Usando esses resultados, motivei a técnica de usar o bootstrap funcional extremo, que depois desenvolvo em mais detalhes. Diversos detalhes técnicos são discutidos e exemplos são apresentados. Após uma breve discussão das teorias de campo conformes com fronteiras, eu aplico métodos numéricos para encontrar restrições no espectro do modelo de Ising em 3D. Outra aplicação é apresentada em que eu estudo a função de 4 pontos na fronteira de uma teoria particular no espaço Anti-de-Sitter, a fim de aproximar o espectro de massa da teoria.
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Books on the topic "Function extrema"

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El-Hodiri, Mohamed Ali. Extrema of Smooth Functions. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76793-7.

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Kislyakov, Sergey. Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals. Basel: Springer Basel, 2013.

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Taniguchi, Yoshihiro. Biological Systems Under Extreme Conditions: Structure and Function. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002.

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Extrema of smooth functions: With examples from economic theory. Berlin: Springer-Verlag, 1991.

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Shor, Naum Zuselevich. Kvadratichnye ėkstremalʹnye zadachi i nedifferent͡s︡iruemai͡a︡ optimizat͡s︡ii͡a︡. Kiev: Nauk. dumka, 1989.

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Beirlant, Jan. Practical analysis of extreme values. Leuven, Belgium: Leuven University Press, 1996.

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Kamenskiĭ, G. A. Extrema of nonlocal functionals and boundary value problems for functional differential equations. Hauppauge, N.Y: Nova Science Publishers, 2007.

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I͡A, Khavinson S., ed. Two papers on extremal problems in complex analysis. Providence, R.I: American Mathematical Society, 1986.

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Abramov, A. P. Connectedness and necessary conditions for an extremum. Dordrecht: Kluwer Academic Publishers, 1998.

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

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Book chapters on the topic "Function extrema"

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Sahiner, Ahmet, Shehab A. Ibrahem, and Nurullah Yilmaz. "Increasing the Effects of Auxiliary Function by Multiple Extrema in Global Optimization." In Nonlinear Systems and Complexity, 125–43. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37141-8_7.

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Hoeffding, Wassily. "The Extrema of the Expected Value of a Function of Independent Random Variables." In Springer Series in Statistics, 311–18. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-0865-5_18.

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Reid, James C., Sarah J. Brookes, Denis J. Evans, and Debra J. Searles. "The Dissipation Function: Its Relationship to Entropy Production, Theorems for Nonequilibrium Systems and Observations on Its Extrema." In Understanding Complex Systems, 31–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-40154-1_2.

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Górecki, Henryk. "Unconstrained Extrema of Functions." In Optimization and Control of Dynamic Systems, 185–235. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-62646-8_5.

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Blanchard, Philippe, and Erwin Brüning. "Extrema of Differentiable Functions." In Variational Methods in Mathematical Physics, 54–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-82698-6_4.

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Deimling, Klaus. "Extremal Problems." In Nonlinear Functional Analysis, 319–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-00547-7_9.

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Kuriata, Andrzej, and Ramesh G. Illikkal. "Predictable Performance for QoS-Sensitive, Scalable, Multi-tenant Function-as-a-Service Deployments." In Agile Processes in Software Engineering and Extreme Programming – Workshops, 133–40. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58858-8_14.

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Abstract In this paper we present the results of our studies focused on enabling predictable performance for functions executing in scalable, multi-tenant Function-as-a-Service environments. We start by analyzing QoS and performance requirements and use cases from the point of view of End-Users, Developers and Infrastructure Owners. Then we take a closer look at functions’ resource utilization patterns and investigate functions’ sensitivity to those resources. We specifically focus on the CPU microarchitecture resources as they have significant impact on functions’ overall performance. As part of our studies we have conducted experiments to research the effect of co-locating different functions on the compute nodes. We discuss the results and provide an overview of how we have further modified the scheduling logic of our containers orchestrator (Kubernetes), and how that impacted functions’ execution times and performance variation. We have specifically leveraged the low-level telemetry data, mostly exposed by the Intel® Resource Director Technology (Intel® RDT) [1]. Finally, we provide an overview of our future studies, which will be centered around node-level resource allocations, further improving a function’s performance, and conclude with key takeaways.
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El-Hodiri, Mohamed Ali. "No Major Constraints." In Extrema of Smooth Functions, 3–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76793-7_1.

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El-Hodiri, Mohamed Ali. "Equality Constraints." In Extrema of Smooth Functions, 23–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76793-7_2.

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El-Hodiri, Mohamed Ali. "Inequalities as Added Constraints." In Extrema of Smooth Functions, 47–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76793-7_3.

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Conference papers on the topic "Function extrema"

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Luo, Yuancheng, Dmitry N. Zotkin, Hal Daume, and Ramani Duraiswami. "Kernel regression for Head-Related Transfer Function interpolation and spectral extrema extraction." In ICASSP 2013 - 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2013. http://dx.doi.org/10.1109/icassp.2013.6637648.

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Nawara, Mariusz. "Optimizing neural network for searching of function extrema in the Remez algorithm." In 2008 International Conference on Signals and Electronic Systems. IEEE, 2008. http://dx.doi.org/10.1109/icses.2008.4673419.

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Bunce, Nicholas A., Bryan D. Quay, and Domenic A. Santavicca. "Interaction Between Swirl Number Fluctuations and Vortex Shedding in a Single-Nozzle, Turbulent, Swirling, Fully-Premixed Combustor." In ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-95812.

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Flame response to imposed velocity fluctuations is experimentally measured in a single-nozzle, turbulent, swirling, fully-premixed combustor. The flame transfer function is used to quantify the flame’s response to imposed velocity fluctuations. Both the gain and phase of the flame transfer function are qualitatively similar for all operating conditions tested. Flame transfer function gain exhibits alternating regions of decreasing gain with increasing forcing frequency followed by regions of increasing gain with increasing forcing frequency. This alternating behavior gives rise to gain extrema. Flame transfer function phase magnitude increases quasi-linearly with increasing forcing frequency. Deviations from the linear behavior occur in the form of inflection points. Within the field, the current understanding is that the flame transfer function gain extrema are caused by the constructive/destructive interference of swirl number fluctuations and vortex shedding. Phase-synchronized images of forced flames are acquired to investigate the presence/importance of swirl number fluctuations, which manifest as fluctuations in mean flame position, and vortex shedding in this combustor. Analysis of phase-synchronized flame images reveals that mean flame position fluctuations are present at forcing frequencies corresponding to flame transfer function gain minima but not at forcing frequencies corresponding to flame transfer function gain maxima. This observation contradicts the understanding that flame transfer function gain maxima are caused by the constructive interference of mean flame position fluctuations and vortex shedding since mean flame position fluctuations are shown not to exist at flame transfer function gain maxima. Further analysis of phase-synchronized flame images shows that the variation of mean flame position fluctuation magnitude with forcing frequency follows an inverse trend to the variation of flame transfer function gain with forcing frequency, i.e. when mean flame position fluctuation magnitude increases flame transfer function gain decreases and vice versa. Based on these observations it is concluded that mean flame position fluctuations are a subtractive effect. The physical mechanism through which mean flame position fluctuations decrease flame response is through the interaction of the flame with the Kelvin-Helmholtz instability of the mixing layer in the combustor. When mean flame position fluctuations are large the flame moves closer to the mixing layer and damps the Kelvin-Helmholtz instability due to the increased kinematic viscosity, fluid dilatation, and baroclinic production of vorticity with opposite sign associated with the high temperature reaction zone.
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De Rosa, Alexander J., Stephen J. Peluso, Bryan D. Quay, and Domenic A. Santavicca. "The Effect of Confinement on the Structure and Dynamic Response of Lean-Premixed, Swirl-Stabilized Flames." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-42178.

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The effect of flame-wall interaction on the forced response of a lean-premixed, swirl-stabilized flame is experimentally investigated by examining flames in a series of three combustors, each with a different diameter and therefore a different degree of lateral confinement. The confinement ratios tested are 0.5, 0.37 and 0.29 when calculated using the diameter of the nozzle relative to the combustor diameter. Using both flame images and measured flame transfer functions, the effect of confinement is investigated and generalized across a broad range of operating conditions. The major effect of confinement is shown to be a change in flame structure in both the forced and unforced cases. This effect is captured using the parameter Lf,CoHR/Dcomb, which describes the changing degree of flame-wall interaction in each combustor size. The measured flame transfer function data, as a function of confinement, is then generalized by Strouhal number. Data from the two larger combustors is collapsed by multiplying the Strouhal number by the confinement ratio to account for the flow expansion ratio and change in convective velocity within the combustor. Trends at the transfer function extrema are also assessed by examining them in the context of confinement and by using flame images. A change in the fluctuating structure of the flame is also seen to result from an increase in confinement.
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Kim, Kyu Hong, and Jung Ho Park. "Assessment of Enhanced Multi-Dimensional Limiting Process for Multi-Dimensional Flows." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-01001.

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In this paper, a new limiting process based on the Multi-dimensional Limiting Process, called enhanced Multi-dimensional Limiting Process is developed and tested with several cases. The enhanced Multi-dimensional Limiting Process, e-MLP has a number of useful features of MLP limiter such as multi-dimensional monotonicity and straightforward extensionality to higher order interpolation. It is applicable to local extrema and prevents excessive damping in a linear discontinuous region through application of appropriate limiting criteria. It is efficient because a limiting function is applied only to a discontinuous region. In addition, it is robust against shock instability due to the strict distinction of the computational domain and the use of regional information in a flux scheme as well as a high order interpolation scheme. The new limiting process was applied to numerous test cases. Through these tests, we could confirm that e-MLP enhances the accuracy and efficiency with both continuous and discontinuous multidimensional flows.
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Kano, Hiroyuki, Hiroyuki Fujioka, and Clyde F. Martin. "Extrema Detection of Bivariate Spline Functions." In 2007 American Control Conference. IEEE, 2007. http://dx.doi.org/10.1109/acc.2007.4282607.

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Sproson, Richard A. "Extreme Values of Total Water Level and Total Water Velocity in the Arabian Gulf." In ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/omae2008-57152.

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PERGOS hindcast model data from the north-east coast of Qatar has been analysed in order to estimate extreme values of total water level (crest height + surge height) and total water velocity (wave orbital velocity + in-line current velocity) based on analysis of 103 storms that occurred between 1961 and 2002. The PERGOS hindcast includes significant wave height, peak period, mean wave direction, surge height, depth-mean current speed and depth-mean current direction. Crest height has been derived from the source parameters using Fugro GEOS’ proprietary EXWAN program. Wave orbital velocity has been derived using stream function theory. Extreme values of total water level and total water velocity were estimated by: (i) univariate extremal analysis of the structure variable components, (ii) univariate extremal analysis of the structure variable, and (iii) bivariate extremal analysis of the structure variable components using Fugro GEOS’ proprietary GTMFIT program. The effect of the lag between the peak wave, current and surge events on extreme values of total water level and total water velocity has also been assessed. A reduction in the 10,000-year extreme water velocity of 14–21% and a reduction in the 10,000-year extreme water level of 3–14% have been achieved using the structure variable methods.
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Chen, Cheng-Yo, and Trevor Mills. "On Weibull Extreme Response of Offshore Structures." In ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-20476.

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This paper investigates the so-called two-parameter and three-parameter Weibull distribution functions with regard to their technical formulation and application to prediction of extreme responses of offshore structures. The validity of predicted Weibull extreme responses is evaluated using time-history responses of two floating structures (a Spar and a Truss Semi) and a fixed-base compliant tower platform. All these structures were previously designed for harsh environments in deepwater beyond 1,700 ft. in the Gulf of Mexico. The evaluation results indicate that the maximum responses predicted by both two-parameter and three-parameter Weibull distribution functions with a single 3-hr simulation agree well with those obtained from a more lengthy and rigorous process with numerous 3-hr time-history responses. It also shows that the predicted maxima from the two-parameter Weibull distribution function are more reliable and have less statistical variability than those from the three-parameter Weibull distribution function, particularly for highly nonlinear wide-banded non-Gaussian responses such as minimum air gaps at the cellar deck of the topsides of the floating structures. The approach using the two-parameter Weibull function as presented in this paper is thus an appealing tool in predicting maximum responses and will greatly improve the process in the early design stage of a fast track project.
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Bilchenko, Grigory, and Natalya Bilchenko. "Functional extreme values range." In 2016 International Conference "Stability and Oscillations of Nonlinear Control Systems" (Pyatnitskiy's Conference) (STAB). IEEE, 2016. http://dx.doi.org/10.1109/stab.2016.7541166.

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Huynh, Hieu Trung, and Yonggwan Won. "Extreme Learning Machine with Fuzzy Activation Function." In 2009 Fifth International Joint Conference on INC, IMS and IDC. IEEE, 2009. http://dx.doi.org/10.1109/ncm.2009.206.

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Reports on the topic "Function extrema"

1

Haerdle, Wolfgang. Nonparametric Sequential Estimation of Zeros and Extrema of Regression Functions. Fort Belvoir, VA: Defense Technical Information Center, January 1986. http://dx.doi.org/10.21236/ada169958.

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Jafari, Farhad, and Mihai Putinar. Extremal Positive Pluriharmonic Functions on Euclidean Balls (PREPRINT). Fort Belvoir, VA: Defense Technical Information Center, November 2007. http://dx.doi.org/10.21236/ada478575.

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Yoo, Choong-Shik. Novel Functional Extended Solids at Extreme Conditions. Fort Belvoir, VA: Defense Technical Information Center, February 2013. http://dx.doi.org/10.21236/ada578712.

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Dongarra, Jack J., and George Bosilca. Minimizing System Noise Effects For Extreme-Scale Scientific Simulation Through Function Delegation. Office of Scientific and Technical Information (OSTI), June 2013. http://dx.doi.org/10.2172/1083067.

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Krim, Jacqueline. Multi-functional Extreme Environment Surfaces: Nanotribology for Air and Space. Fort Belvoir, VA: Defense Technical Information Center, September 2010. http://dx.doi.org/10.21236/ada547360.

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Lumsdaine, Andrew. Award ER25844: Minimizing System Noise Effects for Extreme-Scale Scientific Simulation Through Function Delegation. Office of Scientific and Technical Information (OSTI), November 2012. http://dx.doi.org/10.2172/1082306.

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Baczewski, Andrew David, Luke Shulenburger, Michael Paul Desjarlais, and Rudolph J. Magyar. Numerical implementation of time-dependent density functional theory for extended systems in extreme environments. Office of Scientific and Technical Information (OSTI), February 2014. http://dx.doi.org/10.2172/1204090.

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Rosenberg, Michael L. Can Degradation of Performance by Fatigue be Predicted by Mechanical Tasks Involving Pupil, Somatic, and Extra-Ocular Muscle Function. Fort Belvoir, VA: Defense Technical Information Center, April 2004. http://dx.doi.org/10.21236/ada440264.

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Perdigão, Rui A. P., and Julia Hall. Spatiotemporal Causality and Predictability Beyond Recurrence Collapse in Complex Coevolutionary Systems. Meteoceanics, November 2020. http://dx.doi.org/10.46337/201111.

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Causality and Predictability of Complex Systems pose fundamental challenges even under well-defined structural stochastic-dynamic conditions where the laws of motion and system symmetries are known. However, the edifice of complexity can be profoundly transformed by structural-functional coevolution and non-recurrent elusive mechanisms changing the very same invariants of motion that had been taken for granted. This leads to recurrence collapse and memory loss, precluding the ability of traditional stochastic-dynamic and information-theoretic metrics to provide reliable information about the non-recurrent emergence of fundamental new properties absent from the a priori kinematic geometric and statistical features. Unveiling causal mechanisms and eliciting system dynamic predictability under such challenging conditions is not only a fundamental problem in mathematical and statistical physics, but also one of critical importance to dynamic modelling, risk assessment and decision support e.g. regarding non-recurrent critical transitions and extreme events. In order to address these challenges, generalized metrics in non-ergodic information physics are hereby introduced for unveiling elusive dynamics, causality and predictability of complex dynamical systems undergoing far-from-equilibrium structural-functional coevolution. With these methodological developments at hand, hidden dynamic information is hereby brought out and explicitly quantified even beyond post-critical regime collapse, long after statistical information is lost. The added causal insights and operational predictive value are further highlighted by evaluating the new information metrics among statistically independent variables, where traditional techniques therefore find no information links. Notwithstanding the factorability of the distributions associated to the aforementioned independent variables, synergistic and redundant information are found to emerge from microphysical, event-scale codependencies in far-from-equilibrium nonlinear statistical mechanics. The findings are illustrated to shed light onto fundamental causal mechanisms and unveil elusive dynamic predictability of non-recurrent critical transitions and extreme events across multiscale hydro-climatic problems.
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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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