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Relevant bibliographies by topics / Convexity estimates

Academic literature on the topic 'Convexity estimates'

Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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Dissertations / Theses
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Journal articles on the topic "Convexity estimates"

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Shi, Shujun. "Convexity estimates for the Green’s function." Calculus of Variations and Partial Differential Equations 53, no. 3-4 (August 12, 2014): 675–88. http://dx.doi.org/10.1007/s00526-014-0763-4.

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Grunau, Hans-Christoph, and Stephan Lenor. "Uniform estimates and convexity in capillary surfaces." Nonlinear Analysis: Theory, Methods & Applications 97 (March 2014): 83–93. http://dx.doi.org/10.1016/j.na.2013.11.016.

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Almutairi, Ohud Bulayhan. "Quantum Estimates for Different Type Intequalities through Generalized Convexity." Entropy 24, no. 5 (May 20, 2022): 728. http://dx.doi.org/10.3390/e24050728.

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This article estimates several integral inequalities involving (h−m)-convexity via the quantum calculus, through which Important integral inequalities including Simpson-like, midpoint-like, averaged midpoint-trapezoid-like and trapezoid-like are extended. We generalized some quantum integral inequalities for q-differentiable (h−m)-convexity. Our results could serve as the refinement and the unification of some classical results existing in the literature by taking the limit q→1−.

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Fraser, Ailana. "Index estimates for minimal surfaces and $k$-convexity." Proceedings of the American Mathematical Society 135, no. 11 (November 1, 2007): 3733–45. http://dx.doi.org/10.1090/s0002-9939-07-08894-6.

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Andrews, Ben, Mat Langford, and James McCoy. "Convexity estimates for surfaces moving by curvature functions." Journal of Differential Geometry 99, no. 1 (January 2015): 47–75. http://dx.doi.org/10.4310/jdg/1418345537.

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Alessandroni, Roberta, and Carlo Sinestrari. "Convexity estimates for a nonhomogeneous mean curvature flow." Mathematische Zeitschrift 266, no. 1 (June 5, 2009): 65–82. http://dx.doi.org/10.1007/s00209-009-0554-3.

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Andrews, Ben, Mathew Langford, and James McCoy. "Convexity estimates for hypersurfaces moving by convex curvature functions." Analysis & PDE 7, no. 2 (May 30, 2014): 407–33. http://dx.doi.org/10.2140/apde.2014.7.407.

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Cao, Jia-Ding, and Heinz H. Gonska. "Pointwise estimates for higher order convexity preserving polynomial approximation." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 36, no. 2 (October 1994): 213–33. http://dx.doi.org/10.1017/s0334270000010365.

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AbstractDeVore-Gopengauz-type operators have attracted some interest over the recent years. Here we investigate their relationship to shape preservation. We construct certain positive convolution-type operators Hn, s, j which leave the cones of j-convex functions invariant and give Timan-type inequalities for these. We also consider Boolean sum modifications of the operators Hn, s, j show that they basically have the same shape preservation behavior while interpolating at the endpoints of [−1, 1], and also satisfy Telyakovskiῐ- and DeVore-Gopengauz-type inequalities involving the first and second order moduli of continuity, respectively. Our results thus generalize related results by Lorentz and Zeller, Shvedov, Beatson, DeVore, Yu and Leviatan.

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Garofalo, Nicola. "Geometric second derivative estimates in Carnot groups and convexity." manuscripta mathematica 126, no. 3 (March 26, 2008): 353–73. http://dx.doi.org/10.1007/s00229-008-0182-y.

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Edelen, Nick. "Convexity estimates for mean curvature flow with free boundary." Advances in Mathematics 294 (May 2016): 1–36. http://dx.doi.org/10.1016/j.aim.2016.02.026.

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Dissertations / Theses on the topic "Convexity estimates"

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Lynch, Stephen [Verfasser]. "Convexity and gradient estimates for fully nonlinear curvature flows / Stephen Lynch." Tübingen : Universitätsbibliothek Tübingen, 2020. http://d-nb.info/1222510812/34.

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Langford, Mat. "Motion of hypersurfaces by curvature." Phd thesis, 2014. http://hdl.handle.net/1885/14119.

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It is well-known that solutions of such flows necessarily suffer finite time singularities. On the other hand, under various natural conditions, singularities are characterised by a curvature blow-up. Our first main area of study concerns the asymptotic behaviour of the curvature at a singularity. We first prove a quantitative convexity estimate for positive solutions (that is, solutions moving with inward normal speed everywhere positive) under one of the following additional assumptions: either the evolving hypersurfaces are of dimension two, or the flow speed is a convex function of the curvature. Roughly speaking, the convexity estimate states that, for positive solutions, the normalised Weingarten curvature operator is asymptotically non-negative at a singularity. We then prove a family of cylindrical estimates for flows by convex speed functions. Roughly speaking, these estimates state that, for $(m+1)$-positive solutions (that is, solutions with $(m+1)$-positive Weing! arten curvature), the Weingarten curvature is asymptotically $m$-cylindrical at a singularity unless it becomes $m$-positive. The convexity and cylindrical estimates yield a detailed description of the possible singularities which may form under surface flows and flows by convex speeds. Moreover, they are uniform across the class of solutions with given dimension, flow speed, and initial volume, diameter and curvature hull, which should make them useful for applications such as the development of flows with surgeries. Our second main area of study concerns the development, in the fully non-linear setting, of the recently discovered {\it non-collapsing} phenomena for the mean curvature flow; namely, we prove that embedded solutions of flows by concave speeds are {\it interior non-collapsing}, whilst embedded solutions of flows by convex or inverse-concave speeds are {\it exterior non-collapsing}. The non-collapsing results complement the above curvature estimates by ruling out certain types of asymptotic behaviour which the curvature estimates do not. (This is mainly due to the non-local nature of the non-collapsing estimates.) As a particular application, we show how non-collapsing gives rise to a particularly efficient proof of the Andrews--Huisken theorem on the convergence of convex hypersurfaces to {\it round points} under such flows.

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Cooney, Hugh. "A Survey of Convexity Estimates and Singularities for Mean Curvature Flow with Surgery." Thesis, 2018. http://hdl.handle.net/1885/173631.

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In this survey we aim to introduce the basics of Mean Curvature Flow and detail the programme of Mean Curvature Flow with surgery developed by Huisken and Sinestrari over four seminal papers, [29],[28],[30] and [8]. We divide the survey into 3 chapters, the rst being an introduction to the Mean Curvature Flow. This is followed by the convexity estimates that were developed by Huisken and Sinestrari, which allow us to understand the singularities that form under Mean Curvature Flow. We also present an alternative proof of the convexity estimates for compact mean-convex Mean Curvature Flow that avoids the use of induction on symmetric functions and is based o the proof of Ben Andrews, James Mccoy and Mat Langford in [5]. In chapter 3 we use the convexity estimates for the 2-convex case to discuss the surgery procedure. We also compare and contrast aspects of the Ricci Flow and Hamilton's surgery programme for 4 dimensional manifolds with Positive Isotropic Curvature undergoing Ricci Flow which motivated Huisken and Sinestrari's surgery procedure. In this chapter we explain too the added technicality that was required to extend Mean Curvature Flow with surgery to dimension n = 2, achieved in [8], and we relate it to Perelman's surgery programme that extended Ricci Flow to 3-manifolds. Finally, we conclude with some topological applications and a discussion of further open problems.

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Book chapters on the topic "Convexity estimates"

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Ritoré, Manuel, and Carlo Sinestrari. "Convexity estimates." In Mean Curvature Flow and Isoperimetric Inequalities, 23–25. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0213-6_7.

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Nourdin, Ivan, and Giovanni Peccati. "Fourth Moments and Products: Unified Estimates." In Convexity and Concentration, 285–95. New York, NY: Springer New York, 2017. http://dx.doi.org/10.1007/978-1-4939-7005-6_10.

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Cifre, María A. Hernández, and David Alonso-Gutiérrez. "Estimates for the Integrals of Powered i-th Mean Curvatures." In Analytic Aspects of Convexity, 19–37. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71834-7_2.

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"Convexity estimates for mean convex surfaces." In Lectures on Mean Curvature Flows, 77–87. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/amsip/032/08.

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SINESTRARI, CARLO. "Convexity estimates for mean curvature flow of mean convex surfaces." In Equadiff 99, 572–74. World Scientific Publishing Company, 2000. http://dx.doi.org/10.1142/9789812792617_0115.

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Carter, Kelly E. "Corporate Bond Markets." In Debt Markets and Investments, 113–30. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780190877439.003.0007.

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This chapter covers the fundamentals of corporate bond markets. It begins by highlighting the size and importance of these markets, followed by a discussion of the major types of corporate bonds and the process of issuing bonds. Next, the chapter provides a discussion of important relationships between a bond’s price and market interest rates, including the key observation that bond prices move opposite market interest rates. The next topic focuses on duration and convexity, which are techniques to estimate the dollar and percent changes in bond prices for a given change in market interest rates, followed by a discussion of bond immunization, which is a technique used to protect the value of bond portfolios from adverse changes in market interest rates. The final topics covered concern yield curves, credit ratings, and the impact of the Dodd-Frank Wall Street Reform Act of 2010 on corporate bond markets.

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Conference papers on the topic "Convexity estimates"

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Yanagisawa, Hideyoshi, and Shuichi Fukuda. "Global Feature Based Interactive Reduct Evolutional Computation for Aesthetic Design." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57651.

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In this paper, we verify the enhancement of IREC, which is a computer algorithm for interactive design support system, to support global design features as design attributes. IREC (Interactive Reduct Evolutional Computation) is a method to evolve designs based on users’ personal preferences. The method works through an interaction between the user and a computer system. The computer system with IREC generates design samples consisting of random attributes and the user evaluates and scores each samples depending on his/her psychological preferences. The system estimates the design attributes that the user pays more attention to (favored features) with reduct in Rough set theory and reflects it to generate new design samples. This interaction continues until the samples converge to a satisfactory design. So far design parameters such as coordinate of nodes for spline curve have been regarded as design attributes. However, design attributes consist of not only detailed local parameters but also global features such as convexity, softness etc. In earlier design process, designers first drew a rough sketch to determine the outline of a design, and designed the details later. Therefore it is important to introduce global features to accelerate the convergence and to increase user friendliness. We develop G-IREC (Global feature based IREC) which allows to introduce global features in IREC. This method is applied to design an automobile side-view shape model. The effectiveness of the method is demonstrated by comparing the results of the experiments carried out.

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Barrett, Ronald M., and Ronald P. Barrett. "Thermally Adaptive Building Coverings: Theory and Application." In ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/smasis2016-9014.

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The paper begins with a brief overview of historical building coverings. Thermadapt™ thermally adaptive buildings are introduced as a completely new class of shingles, siding and roofing. These elements physically change shape in response to thermal loading. In hot weather with high solar loading, the panels curl up and away from the building. As the temperature cools and the sun sets, the Thermadapt™ elements lie close to the building. In cool temperatures, the elements lie flat agains the building transferring solar energy. In extremely cold temperatures, high convexity inherently forms in the elements, forming a pocket of trapped dead air which forms a highly effective layer of insulation. Thermadapt™ elements are analytically modeled using Classical Laminated Plate Theory (CLPT). Although Thermadapt™ elements may use materials like shape memory alloys, cost concerns drive the use of coefficient of thermal expansion mismatch as the basic driving mechanism. A series of experiments were performed on a variety of Thermadapt™ elements using high CTE mismatch pairs of structural materials including graphite-epoxy and aluminum and Invar and aluminum pairings. Analytical estimates are shown to predict the performance of the Thermadapt™ panels with great accuracy with curvature levels measured and predicted in excess of 5 deg/m/°C. Analytical predictions using CLPT employed a lateral constraint, driving lateral curvature, κy, to zero by the use of stiff lateral constraint mechanisms like edge rolls and lateral corrugations. This constraint was shown to increase deflections by roughly 33% over the unconstrained elements which were simply allowed to encounter equal curvatures in x and y directions, or “doming.”

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Hertlein, Nathan, Andrew Gillman, and Philip R. Buskohl. "Generative Adversarial Design Analysis of Non-Convexity in Topology Optimization." In ASME 2022 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/detc2022-89997.

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Abstract Material penalization and filtering schemes are key strategies applied to topology optimization (TO) to promote more discrete and manufacturable designs. However, these modifications introduce fluctuations in the design landscape that amplify non-convexity and influence the local minima identified by TO. Harnessing the machine learning approach of generative adversarial networks (GAN), we investigate the role of penalization and filtering by comparing the designs between TO and GAN-based TO surrogates. A total of 17 GANs were constructed to predict 2D minimum compliance topologies across a set of penalization factors and filters, each interpolating a design space of 270,000 boundary condition and loading scenarios. The prevalence of GAN-predicted topologies with better compliance than TO-calculated topologies was estimated via a random sampling of the design space. GAN ‘over-performance’ occurs across material penalization and filtering conditions, where the frequency tends to increase as penalization increases. Analysis of this test set is leveraged to highlight trends regarding the conditions under which this ‘over-performance’ occurs, and the geometric characteristics these designs exhibit. Collectively, this study presents an alternative method to characterize the effects of penalization and filtering on design outcomes and motivates the use of data-driven surrogates to augment traditional approaches.

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Yagola, Anatoly G., and Yury M. Korolev. "Error Estimations in Linear Inverse Problems With a Priori Information." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47799.

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We consider an inverse problem for an operator equation Az = u. The exact operator A and the exact right-hand side u are unknown. Only their upper and lower estimations are available. We provide techniques of calculating upper and lower estimations for the exact solution belonging to a compact set in this case, as well as a posteriori error estimations. We obtain approximate solutions with an optimal a posteriori error estimate. We also make use of a priori information about the exact solution, e.g. its monotonicity and convexity. The developed software package was applied to solving practical ill-posed problems.

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Huang, Feihu, Shangqian Gao, Songcan Chen, and Heng Huang. "Zeroth-Order Stochastic Alternating Direction Method of Multipliers for Nonconvex Nonsmooth Optimization." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/354.

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Alternating direction method of multipliers (ADMM) is a popular optimization tool for the composite and constrained problems in machine learning. However, in many machine learning problems such as black-box learning and bandit feedback, ADMM could fail because the explicit gradients of these problems are difficult or even infeasible to obtain. Zeroth-order (gradient-free) methods can effectively solve these problems due to that the objective function values are only required in the optimization. Recently, though there exist a few zeroth-order ADMM methods, they build on the convexity of objective function. Clearly, these existing zeroth-order methods are limited in many applications. In the paper, thus, we propose a class of fast zeroth-order stochastic ADMM methods (\emph{i.e.}, ZO-SVRG-ADMM and ZO-SAGA-ADMM) for solving nonconvex problems with multiple nonsmooth penalties, based on the coordinate smoothing gradient estimator. Moreover, we prove that both the ZO-SVRG-ADMM and ZO-SAGA-ADMM have convergence rate of $O(1/T)$, where $T$ denotes the number of iterations. In particular, our methods not only reach the best convergence rate of $O(1/T)$ for the nonconvex optimization, but also are able to effectively solve many complex machine learning problems with multiple regularized penalties and constraints. Finally, we conduct the experiments of black-box binary classification and structured adversarial attack on black-box deep neural network to validate the efficiency of our algorithms.

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