Дисертації з теми "Concave and convex functions"
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Ghadiri, Hamid Reza. "Convex Functions." Thesis, Karlstads universitet, Fakulteten för teknik- och naturvetenskap, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-7473.
Повний текст джерелаZagar, Susanna Maria. "Convex functions." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/986.
Повний текст джерелаMa, Jie. "Heterogeneous nucleation on convex and concave spherical surfaces." Thesis, University of Portsmouth, 2008. http://eprints.port.ac.uk/15503/.
Повний текст джерелаChoe, Byung-Tae. "Essays on concave and homothetic utility functions." Uppsala : Stockholm, Sweden : s.n. ; Distributor, Almqvist & Wiksell International, 1991. http://catalog.hathitrust.org/api/volumes/oclc/27108685.html.
Повний текст джерелаBrennan, Derek. "Convex functions, majorization properties and the convex conjugate transform." Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=81603.
Повний текст джерелаThen we have Kw ≤ Kv ↔01 1wq +l dtheta ≥ 01 1vq+l dtheta ∀ lambda ≥ 0.
We present two similar proofs of this result, which are analogous to the well-known majorization theorem: Let v, w ≥ 0 be decreasing functions, and suppose 01 w(theta)dtheta = 01 v(theta)dtheta.
Then Fw ≤ Fv ↔01 (w(theta) - x)+ dtheta ≥ 01 (v(theta) - x)+ dtheta ∀ x ≥ 0, where F w(t) = t1 w(theta)dtheta. Since our proofs of this result rely mainly on the convex conjugate transform, or Legendre transform, we include an exposition of convex functions and convex conjugate transforms.
Caglar, Umut. "Divergence And Entropy Inequalities For Log Concave Functions." Case Western Reserve University School of Graduate Studies / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=case1400598757.
Повний текст джерелаSaysupan, Sutthilak. "Design and Fabrication of convex and concave Lenses made of Transparent Liquids." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-295596.
Повний текст джерелаUndersökning gällande optiska linser konvexa och konkava, bestående av flytande material. Designförslag av linser och skall, samt tillverkningsmetod har undersökts. De teoretiska förväntningarna validerades genom simulering och experimentella resultat. Metoden visas har både fördelar och nackdelar. Material i de linserna som vi har undersökt är vatten, sockerlösning, bensylbensoat och Bromonaftalen.
Kandidatexjobb i elektroteknik 2020, KTH, Stockholm
Morales, J. M. "Structured sparsity with convex penalty functions." Thesis, University College London (University of London), 2012. http://discovery.ucl.ac.uk/1355964/.
Повний текст джерелаEdwards, Teresa Dawn. "The box method for minimizing strictly convex functions over convex sets." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/30690.
Повний текст джерелаSemu, Mitiku Kassa. "On minimal pairs of compact convex sets and of convex functions /." [S.l. : s.n.], 2002. http://www.gbv.de/dms/zbw/36225754X.pdf.
Повний текст джерелаWang, Yanhui. "Affine scaling algorithms for linear programs and linearly constrained convex and concave programs." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/24919.
Повний текст джерелаEl-Ashwah, R. M. "On Bazilevic and close-to-convex functions." Thesis, Swansea University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636777.
Повний текст джерелаNekooie, Batool. "Convex optimization involving matrix inequalities." Diss., Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/13880.
Повний текст джерелаBurton, Andrew P. "Isoperimetric inequalities and applications of convex integral functions." Thesis, Keele University, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.277183.
Повний текст джерелаFontaine, Xavier. "Sequential learning and stochastic optimization of convex functions." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASM024.
Повний текст джерелаIn this thesis we study several machine learning problems that are all linked with the minimization of a noisy function, which will often be convex.Inspired by real-life applications we focus on sequential learning problems which consist in treating the data ``on the fly'', or in an online manner.The first part of this thesis is thus devoted to the study of three different sequential learning problems which all face the classical ``exploration vs. exploitation'' trade-off.Each of these problems consists in a situation where a decision maker has to take actions in order to maximize a reward or to evaluate a parameter under uncertainty, meaning that the rewards or the feedback of the possible actions are unknown and noisy.We demonstrate that all of these problems can be studied under the scope of stochastic convex optimization, and we propose and analyze algorithms to solve them.In the second part of this thesis we focus on the analysis of the Stochastic Gradient Descent algorithm, which is likely one of the most used stochastic optimization algorithms in machine learning.We provide an exhaustive analysis in the convex setting and in some non-convex situations by studying the associated continuous-time model, and obtain new optimal convergence results
Lin, Chin-Yee. "Interior point methods for convex optimization." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/15044.
Повний текст джерелаJunike, Gero Quintus Rudolf. "Advanced stock price models, concave distortion functions and liquidity risk in finance." Doctoral thesis, Universitat Autònoma de Barcelona, 2019. http://hdl.handle.net/10803/667194.
Повний текст джерелаThis thesis consists of three essays. In the first essay, we test empirically the pricing performance of several advanced financial models. We calibrate six advanced stock price models to a time series of real market data of European options on the DAX, a German blue chip index. Via a Monte Carlo simulation, we price barrier down-and-out call options for all models and compare the modelled prices to given real market data of the barrier options. The Bates model reproduces barrier option prices well. The BNS model overvalues and Lévy models with stochastic time-change and leverage undervalue the exotic options. A heuristic analysis suggests that the different degree of fluctuation of the random paths of the models are responsible of producing different prices for the barrier options. The second essay of this thesis discusses the relationship between coherent risk measures and concave distortion functions. A family of concave distortion functions is a set of concave and increasing functions, mapping the unity interval onto itself. Distortion functions play an important role defining coherent risk measures. We prove that any family of distortion functions which fulfils a certain translation equation, can be represented by a distribution function. An application can be found in actuarial science: moment based premium principles are easy to understand but in general are not monotone and cannot be used to compare the riskiness of different insurance contracts with each other. Our representation theorem makes it possible to compare two insurance risks with each other consistent with a moment based premium principle by defining an appropriate coherent risk measure. In the last essay of this thesis, we investigate financial markets with frictions, where bid and ask prices of financial intruments are described by sublinear pricing functionals. Such functionals can be defined recursively using coherent risk measures. We prove the convergence of bid and ask prices for various European and American possible path-dependent options, in particular plain vanilla, Asian, lookback and barrier options in a binomial model in the presence of transaction costs. We perform several numerical experiments to confirm the theoretical findings. We apply the results to real market data of European and American plain vanilla options and compute an implied liquidity to describe the bid-ask spread. This method describes liquidity over time very well, compared to the classical approach of describing the bid-ask spread by quoting bid and ask implied volatilities.
Trienis, Michael Joseph. "Computational convex analysis : from continuous deformation to finite convex integration." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/2799.
Повний текст джерелаLan, Guanghui. "Convex optimization under inexact first-order information." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29732.
Повний текст джерелаCommittee Chair: Arkadi Nemirovski; Committee Co-Chair: Alexander Shapiro; Committee Co-Chair: Renato D. C. Monteiro; Committee Member: Anatoli Jouditski; Committee Member: Shabbir Ahmed. Part of the SMARTech Electronic Thesis and Dissertation Collection.
Potaptchik, Marina. "Portfolio Selection Under Nonsmooth Convex Transaction Costs." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2940.
Повний текст джерелаDue to the special structure, this problem can be replaced by an equivalent differentiable problem in a higher dimension. It's main drawback is efficiency since the higher dimensional problem is computationally expensive to solve.
We propose several alternative ways to solve this problem which do not require introducing new variables or constraints. We derive the optimality conditions for this problem using subdifferentials. First, we generalize an active set method to this class of problems. We solve the problem by considering a sequence of equality constrained subproblems, each subproblem having a twice differentiable objective function. Information gathered at each step is used to construct the subproblem for the next step. We also show how the nonsmoothness can be handled efficiently by using spline approximations. The problem is then solved using a primal-dual interior-point method.
If a higher accuracy is needed, we do a crossover to an active set method. Our numerical tests show that we can solve large scale problems efficiently and accurately.
Wattanataweekul, Hathaikarn. "Convex analysis and flows in infinite networks." Diss., Mississippi State : Mississippi State University, 2006. http://sun.library.msstate.edu/ETD-db/ETD-browse/browse.
Повний текст джерелаSAMPAIO, RAIMUNDO JOSE B. DE. "A CONTRIBUITION TO THE STUDY OF D.C.: DIFFERENCE OF TWO CONVEX FUNCTIONS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1990. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=8617@1.
Повний текст джерелаUNIVERSIDADE FEDERAL DO PARANÁ
Este trabalho está dividido em duas partes. A primeira parte trata das relações entre o problema de otimização d.c. (diferença de duas funções convexas) e o problema de otimização d.c. regularizado por inf-convolução, com núcleo (2 lambda)-1 l l . l l 2 , lambda > 0. Neste sentido se generaliza a relação de TOLAND (1979): inf { g(x) - h(x) } = inf { h(asterístico (y) - g (asterístico(y) }, H H E a relação de GABAY (1982): inf { g(x) - h(x) } = inf { g lambda (x) - h lambda (x) } H H Onde g, h , são funções convexas próprias e semicontínuas inferiormente, g(asterístico), h(asterístico), são conjugadas de g e h, respectivamente, H é um espaço de Hilbert real, e g (lambda), h lambda , são as funções regularizadas respectivas de g e h, por inf-convolução com núcleo (2 lambda)-1 l l . l l 2 , lambda > 0. A segunda parte deste trabalho apresenta um algoritmo novo para tratar com o problema de otimização d.c.. Trata-se de um método de descida do tipo proximal, onde se leva em consideração separadamente as propriedades de convexidade das duas funções convexas.
The work is divided in two parts. The first part is concerned with the relationship between the d.c. optimization problem. In this sence we geralize the TOLAND´s relation (1979): inf { g(x) - h(x) } = inf { h(asteristic)(y) - g (asteristic)(y) }, H H And the GABAY´s relation (1982): inf { g(x) - h(x) } = inf { g lambda (x) - h lambda (x) } H H Where g, h, are l.s.c. convex functions, g(asteristic) and h(asteristic) are their conjugates, H is a real Hilbert space, and g lambda, h lambda, are the inf-convolution of g and h respectively, with the núcleos 8( . ) = (2 lambda)- 1 l l . l l 2 , lambda > 0. In the second part we present a new algorithm for dealing with d.c. functions. It is a descent method of proximal kind which takes in consideration the convex properties of the two convex functions separately
LIFSCHITZ, SERGIO. "AN ALGORITHM FOR THE COMPUTATION OF SOME DISTANCE FUNCTIONS BETWEEN CONVEX POLYGONS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1990. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=9412@1.
Повний текст джерелаApresenta-se nesta dissertação um novo algoritmo para o cálculo de algumas funções distância entre polígonos convexos, no caso geral em que os polígonos podem se interseptar, cuja complexidade linear de pior caso é melhor do que a dos algoritmos até então conhecidos na literatura. O algoritmo é baseado em um algoritmo de complexidade linear originalmente proposto para determinação da distância de Hausdorff entre polígonos convexos disjuntos e utiliza como sua principal componente um algoritmo linear para o cálculo da interseção entre polígonos convexos. A motivação para o estudo de algoritmos eficientes para este problema de cálculo de distâncias decorre de aplicações em reconhecimento de formas e superposição ótima de contornos. Resultados computacionais também são apresentados.
We present in this dissertation a new algorithm for the computation of some distance functions between convex polygons, in the general case where they can intersect, whose worst case time complexity is better than of the previously known algorithms. The algorthm is based on an algorithm originally proposed for the computation of the Hausdorff distance between disjoint polygons and uses as its main component a linear time algorithm for finding the intersection of convex polygons. The motivation for the study of efficient algorithms for this distance computation problem comes from applications in pattern recognition and contour fitting. Computatioal results are also presented.
Rodriguez-Mancilla, Jose Ramon. "Investment under risk tolerance constraints and non-concave utility functions: implicit risks, incentives and optimal strategies." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/31468.
Повний текст джерелаBusiness, Sauder School of
Graduate
Hodrea, Ioan Bogdan. "Farkas - type results for convex and non - convex inequality systems." Doctoral thesis, [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800075.
Повний текст джерелаSchlee, Glen A. (Glen Alan). "Borel sets with convex sections and extreme point selectors." Thesis, University of North Texas, 1991. https://digital.library.unt.edu/ark:/67531/metadc332694/.
Повний текст джерелаCox, Bruce. "Applications of accuracy certificates for problems with convex structure." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39489.
Повний текст джерелаBacklund, Ulf. "Envelopes of holomorphy for bounded holomorphic functions." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 1992. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-141155.
Повний текст джерелаdigitalisering@umu.se
Hefer, Torsten. "Regularität von Randwerten der kanonischen Lösung der [mean partial differential operative]-Gleichung auf streng pseudokonkaven Gebieten." Bonn [Germany] : Rheinische Friedrich-Wilhelms-Universität, 1999. http://catalog.hathitrust.org/api/volumes/oclc/45761314.html.
Повний текст джерелаKnörr, Jonas [Verfasser], Andreas [Gutachter] Bernig, Raman [Gutachter] Sanyal, and Andrea [Gutachter] Colesanti. "Smooth valuations on convex functions / Jonas Knörr ; Gutachter: Andreas Bernig, Raman Sanyal, Andrea Colesanti." Frankfurt am Main : Universitätsbibliothek Johann Christian Senckenberg, 2021. http://d-nb.info/1228432546/34.
Повний текст джерелаVargyas, Emese Tünde. "Duality for convex composed programming problems." Doctoral thesis, Universitätsbibliothek Chemnitz, 2004. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200401793.
Повний текст джерелаIn dieser Arbeit wird, anhand der sogenannten konjugierten Dualitätstheorie, ein allgemeines Dualitätsverfahren für die Untersuchung verschiedener Optimierungsaufgaben dargestellt. Um dieses Ziel zu erreichen wird zuerst eine allgemeine Optimierungsaufgabe betrachtet, wobei sowohl die Zielfunktion als auch die Nebenbedingungen zusammengesetzte Funktionen sind. Mit Hilfe der konjugierten Dualitätstheorie, die auf der sogenannten Störungstheorie basiert, werden für die primale Aufgabe drei verschiedene duale Aufgaben konstruiert und weiterhin die Beziehungen zwischen deren optimalen Zielfunktionswerten untersucht. Unter geeigneten Konvexitäts- und Monotonievoraussetzungen wird die Gleichheit dieser optimalen Zielfunktionswerte und zusätzlich die Existenz der starken Dualität zwischen der primalen und den entsprechenden dualen Aufgaben bewiesen. In Zusammenhang mit der starken Dualität werden Optimalitätsbedingungen hergeleitet. Die Ergebnisse werden abgerundet durch die Betrachtung zweier Spezialfälle, nämlich die klassische restringierte bzw. unrestringierte Optimierungsaufgabe, für welche sich die aus der Literatur bekannten Dualitätsergebnisse ergeben. Der zweite Teil der Arbeit ist der Dualität bei Standortproblemen gewidmet. Dazu wird ein sehr allgemeines Standortproblem mit konvexer zusammengesetzter Zielfunktion in Form eines Gauges formuliert, für das die entsprechenden Dualitätsaussagen abgeleitet werden. Als Spezialfälle werden Optimierungsaufgaben mit monotonen Normen betrachtet. Insbesondere lassen sich Dualitätsaussagen und Optimalitätsbedingungen für das klassische Weber und Minmax Standortproblem mit Gauges als Zielfunktion herleiten. Das letzte Kapitel verallgemeinert die Dualitätsaussagen, die im zweiten Kapitel erhalten wurden, auf multikriterielle Optimierungsprobleme. Mit Hilfe geeigneter Skalarisierungen betrachten wir zuerst ein zu der multikriteriellen Optimierungsaufgabe zugeordnetes skalares Problem. Anhand der in diesem Fall erhaltenen Optimalitätsbedingungen formulieren wir das multikriterielle Dualproblem. Weiterhin beweisen wir die schwache und, unter bestimmten Annahmen, die starke Dualität. Durch Spezialisierung der Zielfunktionen bzw. Nebenbedingungen resultieren die klassischen konvexen Mehrzielprobleme mit Ungleichungs- und Mengenrestriktionen. Als weitere Anwendungen werden vektorielle Standortprobleme betrachtet, zu denen wir entsprechende duale Aufgaben formulieren
Gu, Guohua. "Distance-two constrained labellings of graphs and related problems." HKBU Institutional Repository, 2005. http://repository.hkbu.edu.hk/etd_ra/590.
Повний текст джерелаGoebel, Rafal. "Convexity, convergence and feedback in optimal control /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/5792.
Повний текст джерелаWhite, Edward C. Jr. "Polar - legendre duality in convex geometry and geometric flows." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24689.
Повний текст джерелаChiou, Ing-Jang, and 邱英璋. "Concave-convex functions and Lie groups." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/27090919040418382430.
Повний текст джерела國立交通大學
應用數學系
87
Let V be an n-dimensional vector space, equipped with a non-degenerate symmetic bilinear form. Let G be the group of all linear mappings on V which preserves this bilinear form. In this thesis, we study the topological properties of G and its orbits, as well as the Lie algebra of G.
Wang, Hung-Ta, and 王鴻達. "A note on integral inequalities of Hadamard type for log-convex and log-concave functions." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/y5mnn7.
Повний текст джерелаBourn, Stephen. "Probabilistic shoot-look-shoot combat models." Thesis, 2012. http://hdl.handle.net/2440/73043.
Повний текст джерелаThesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2012
Pivovarov, Peter. "Volume distribution and the geometry of high-dimensional random polytopes." Phd thesis, 2010. http://hdl.handle.net/10048/1170.
Повний текст джерелаTitle from pdf file main screen (viewed on July 13, 2010). A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, Department of Mathematical and Statistical Sciences, University of Alberta. Includes bibliographical references.
Carretero, G. Juan Antonio. "Distance determination algorithms for convex and concave objects." Thesis, 2001. https://dspace.library.uvic.ca//handle/1828/10297.
Повний текст джерелаGraduate
Ferland, Alane Susan. "Isoperimetric inequalities and concave functions." 1999. https://scholarworks.umass.edu/dissertations/AAI9932309.
Повний текст джерелаJian-Da, Huang. "On Generalized Convex Functions." 2000. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0009-0112200611284837.
Повний текст джерелаHuang, Jian-Da, and 黃建達. "On Generalized Convex Functions." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/05369104825051284346.
Повний текст джерела元智大學
工業工程研究所
88
A class of functions called weakly convex and weakly quasiconvex functions is introduced by relaxing the definitions of convex and quasiconvex functions. Necessary and sufficient conditions, under which a lower semi-continuous function on a nonempty closed convex subsets of the n-dimensional Euclidean space is convex or quasiconvex are established. Another class of functions, called $-convex and $-B-vex, is defined. Some properties for these functions are presented.
Lin, Wen-Hua, and 林文化. "(a,b)-Convex Functions." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/15757279667918426000.
Повний текст джерела中原大學
應用數學研究所
96
Abstract The theory of (a,b)-convex functions was introduced by Norber Kuhn in 1987【1】.Kuhn focused mainly on the structure and the properties of (a,b)-convex functions.And we generalize a result raised by Zygfryd Kominek in 1992【2】.He would like to know on what conditions under which an (a,b)-convex function is a constant function. Given a function f:I→[-∞ , ∞),we define the following three sets: (Ⅰ) K’(f)=﹛(a,b)€(0,1)×(0,1) | f is an (a,b)-convex function﹜ (Ⅱ) K(f)=﹛a€(0,1) | f is an a-convex function﹜ (Ⅲ) A’(f)=﹛(a,b)€(0,1)×(0,1) | f is an (a,b)-affine function﹜ We proceed to discuss the properties of these sets K’(f)、K(f) and A’(f).Then we show that,if f:I→[-∞ , ∞)is a continuous (a,b)-convex function,f is a convex function. Finally we prove that,if (a,b)€K’(f),a≠b and a€Q ,then f is a constant function.
"Coordinate ascent for maximizing nondifferentiable concave functions." Massachusetts Institute of Technology, Laboratory for Information and Decision Systems], 1988. http://hdl.handle.net/1721.1/3107.
Повний текст джерелаCover title.
Includes bibliographical references.
Partially supported by the U.S. Army Research Office (Center for Intelligent Control Systems) DAAL03-86-K-0171 Partially supported by the National Science Foundation. NSF-ECS-8519058
Yang, Yuan-Ju, and 楊媛茹. "Study on the Convex- and Concave-Type Parallax-Barrier Autostereoscopic Displays." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/61211650459918354219.
Повний текст джерела國立臺灣大學
光電工程學研究所
104
Among the 3D imaging technology, the auto-stereoscopic 3D display technology has generally accepted because of its advantages about no need to wear glasses and various use. In recent years, the rise of flexible display make wearable displays and curved displays spring up, such as smart watch and curved smart phone and the research of the curved display is more important. Based on the bending direction, Curved displays are divided into concave-type displays and convex-type displays and provide the more natural and comfortable visual experience. The concave-type displays provide the effect of Panorama image and the convex-type provide the effect of Surrounding image. Therefore, the curved auto-stereoscopic display is highly expected in the future. For an auto-stereoscopic display, viewing position and the movable range for observers strongly affect image quality. Viewing zone describes the range that an observer could move while experiencing 3D images in front of the display. Regarding a curved auto-stereoscopic display, radius of curvature and width of the screen determine the relative degree of bending, by which the spacial light distribution is determined. In addition, this is a key factor influencing image quality, especially for the display which directs the views for left and right eyes based on binocular parallax. In this thesis, we investigate the effect of viewing zones with concave-type and convex-type in small size displays(such as mobile devices), medium size displays(such as desktop monitors) and large size displays(such as televisions) by modulating the radius of curvature. According to the results, both concave-type and convex-type can be applied for small size displays and medium size displays by different use, and the concave-type is better than convex-type for large size displays. Meanwhile, the limitation factors of the concave-type and convex-type are studied in this thesis. The purpose of this thesis is to provide a reference for designing the parameters of curved auto-stereoscopic displays in the future.
Shu-Chi, Hsu, and 許淑琪. "On (a,b)-convex functions." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/49436620216066290040.
Повний текст джерела中原大學
數學系
88
This thesis discusses so-called (a, b)-convex functions which was first raised by Norbert Kuhn in 1987 (see[1]). Generally speaking, "good"(a, b)-convex functions are almost constant. On the other hand, it is difficult to construct a "sickly" (a, b)-convex function. For a function f:I to [-\infty, \infty), we define the sets K'(f),K(f) and A'(f) as follows : K'(f)={(a,b) in (0,1)*(0,1): f is an (a,b)-convex function} K(f)={a in (0,1) : f is an a-convex function} A'(f)={(a,b) in (0,1)*(0,1):f is an (a,b)-affine function} First, we will discuss the structure of these sets K'(f) and A'(f), and give some suitable conditions under which an (a,b)-convex function is a constant.Also the structure of a (a, b)- convex function will be understood by means of K'(f) and A'(f). We present a result which was raised by Norbert Kuhn in 1987, he used the result concerning (a,b)-affine functions to investigate (a,b)-convex functions. And prove a result : "under some suitable conditions, K'(f) is almost a field ". We generalize a result raised by Zygfrvd Kominek in 1992 : " If (a, b) in K'(f), a not equal b and a in Q then f is a constant function " .We will have the same result if we change rational number into algebraic number and b is not algebraic number. Furthermore, we will consider the set Omega_{a, b}={f:I to [-infty, infty) :f is (a, b)-convex function }. We discuss the structure of this set.In the previous sections, the function f was given and then consider the set K'(f) consisting of all ordered pairs (a, b) which makes f (a, b)-convex. Conversely, we fix (a, b) and consider the set Omega_{a, b} consisting of all (a, b) functions on I.We find Omega_{a, b} is a convex cone. And Omega_{a, b}=Omega_{1-a, 1-b}. If a function f:I to [-infty, infty) is an (a,b)-convex function, (a, b) in K'(f), a not equal b and f is a continuous function then f is a constant function.In other words, if we want to find an example of an (a, b)-convex function then f must be discontinuous in Int I.
Tseng, Kuei-Lin, and 曾貴麟. "On Inequalities Concern Convex Functions." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/26389526707935709103.
Повний текст джерела淡江大學
數學學系
88
This dissertation consists of three chapters. The first chapter, we introduce some definitions and some foundational theorems which will be used thereafter. In the second chapter, we classify inequalities of means in discrete form derived by Ky Fan, Wang-Wang, Wang-Yang, Chong, Mitrinovic-Pečarić, Slater and Alzer into two forms. That is Form1: If M is a real linear space, U a nonempty convex set in M, ■is a real-valued function with ■ (J is an interval in R) and ■is a continuous strictly increasing function such that■is convex, then ■, (1) where ■, ■■with■. Form2: Let ■ be defined as in Form 1, and let M=R, U be an interval in R. Suppose ■ is differentiable on U with ■. Then ■ (2) We construct a continuous increasing convex function F on [0,1] in Form 1 such that ■ (3) and we also construct a continuous increasing convex function E on [0,1] in Form 2 such that ■. (4) Hence the inequalities (3) and (4) refine (1) and (2), respectively. Under different special M, U, J, f, g, (3) and (4) can refine and generalize some inequalities which found by Ky Fan, Wang-Wang, Wang-Yang, Chong, Mitrinovic-Pečarić, Slater and Alzer, respectively. In chapter 3, we investigate the inequalities of means in integral form. We start with Hermite-Hadamard inequalities and Fejér inequalities; i.e. ■ (5) and ■ (6) where■is a convex function and■is nonnegative integrable function such that g is symmetric to■. Some refinements and generalizations of (5) and (6) are found by Brenner-Alzer, Dragomir, Yang-Hong and Yang- Wang, respectively. Now we define P, Q on [0,1] such that ■ ■. (7) The inequalities (7) refine the inequalities (6) and the inequalities (5). Also, the inequalities (7) generalize some results established by Brenner-Alzer, Dragomir, Yang-Hong and Yang- Wang, respectively. 摘要 і 摘要(英文) ііі PartⅠ中文 第一章 定義與前言 1 §1‧1 加權與非加權平均數 1 §1‧2 單變數之凸函數 3 §1‧3 實線性空間上之凸函數 6 第二章 有關平均數之不等式 9 §2‧1 Ky Fan與Wang-Wang不等式 9 §2‧2 與平均數相關之不等式 14 §2‧3 有關Ky Fan與Wang-Wang不等式的一般化與細分 16 第三章 有關Hermite-Hadamard不等式之積分型態不等式 34 §3‧1 Hermite-Hadamard不等式與其細分 34 §3‧2 Hermite-Hadamard不等式之進一步細分 36 §3‧3 有關重積分的Hermite-Hadamard不等式 43 參考文獻為 47 PartⅡ英文 Contents Chapter 1. Definitions and Preliminaries 51 §1.1. Weighted and Unweighted Means 51 §1.2. One-Variable Convex Functions 53 §1.3. Convex Functions on a Normed Linear Space 56 Chapter 2. Inequalities Related To Means 59 §2.1. Ky Fan and Wang-Wang’s Inequalities 59 §2.2. Some Inequalities Related To Means 65 §2.3. Generalization and Refinement of Ky Fan and Wang-Wang’s Inequalities 67 Chapter 3. On Certain Integral Inequalities Related to Hermite- Hadamard’s Inequalities 85 §3.1. Hermite-Hadamard’s Inequalities and Their Refinements 85 §3.2. Further Refinements of Hermite-Hadamard’s Inequalities 87 §3.3. Hermite-Hadamard’s Inequalities for Multiple Integrals 95 References 99
LIN, LAI-JU, and 林來居. "Optimization for convex set functions." Thesis, 1987. http://ndltd.ncl.edu.tw/handle/02933557435255019699.
Повний текст джерелаHuang, Hung-Yi, and 黃弘毅. "Some Inequalities For Convex Functions." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/99108769118578037817.
Повний текст джерела淡江大學
中等學校教師在職進修數學教學碩士學位班
102
Hermite-Hadamard’s inequality(or Hadamard’s inequality).Since it’s discovery in 1883,Hadamard’s inequality [3] has proven to be one of the most useful inequality in mathematical analysis. A number of papers have been written on this inequality providing new proofs, noteworthy generalizations and numerous application, see [1-4] and the references cited there in. The main purpose of this paper is to establish some generalizations of Theorem P.
YU, CHUN HSIUNG, and 游俊雄. "Some Inequalities For Convex Functions." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/17797741379061409536.
Повний текст джерела