Relevant bibliographies by topics / Simplex (Mathematics)

Contents

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

Academic literature on the topic 'Simplex (Mathematics)'

Author: Grafiati
Published: 4 June 2021
Last updated: 17 February 2022

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Journal articles on the topic "Simplex (Mathematics)"

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Zeng, M., and W. Q. Tao. "A comparison study of the convergence characteristics and robustness for four variants of SIMPLE‐family at fine grids." Engineering Computations 20, no. 3 (May 1, 2003): 320–40. http://dx.doi.org/10.1108/02644400310467234.

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A comparative study is performed to reveal the convergence characteristics and the robustness of four variants in the semi‐implicit method for pressure‐linked equations (SIMPLE)‐family: SIMPLE, SIMPLE revised (SIMPLER), SIMPLE consistent (SIMPLEC), and SIMPLE extrapolation (SIMPLEX). The focus is concentrated in the solution at fine grid system. Four typical fluid flow and heat transfer problems are taken as the numerical examples (lid‐driven cavity flow, flow in an axisymmetric sudden expansion, flow in an annulus with inner surface rotating and the natural convection in a square enclosure). It is found that an appropriate convergence condition should include both mass conservation and momentum conservation requirements. For the four problems computed, the SIMPLEX always requires the largest computational time, the SIMPLER comes the next, and the computational time of SIMPLE and SIMPLEC are the least. As far as the robustness is concerned, the SIMPLE algorithm is the worst, the SIMPLER comes the next and the robustness of SIMPLEX and SIMPLEC are superior to the others. The SIMPLEC algorithm is then recommended, especially for the computation at a fine grid system. Brief discussion is provided to further reveal the reasons which may account for the difference of the four algorithms.
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Yeh, Wei-Chang, and H. W. Corley. "A simple direct cosine simplex algorithm." Applied Mathematics and Computation 214, no. 1 (August 2009): 178–86. http://dx.doi.org/10.1016/j.amc.2009.03.080.

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Kalai, Gil. "Linear programming, the simplex algorithm and simple polytopes." Mathematical Programming 79, no. 1-3 (October 1997): 217–33. http://dx.doi.org/10.1007/bf02614318.

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Neamtu, Marian. "Homogeneous simplex splines." Journal of Computational and Applied Mathematics 73, no. 1-2 (October 1996): 173–89. http://dx.doi.org/10.1016/0377-0427(96)00042-8.

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LE, HUILING, and DENNIS BARDEN. "ON SIMPLEX SHAPE SPACES." Journal of the London Mathematical Society 64, no. 2 (October 2001): 501–12. http://dx.doi.org/10.1112/s0024610701002332.

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The right-invariant Riemannian metric on simplex shape spaces in fact makes them particular Riemannian symmetric spaces of non-compact type. In the paper, the general properties of such symmetric spaces are made explicit for simplex shape spaces. In particular, a global matrix coordinate representation is suggested, with respect to which several geometric features, important for shape analysis, have simple and easily computable expressions. As a typical application, it is shown how to locate the Fréchet means of a class of probability measures on the simplex shape spaces, a result analogous to that for Kendall's shape spaces.
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Izumi, Shuzo. "Sufficiency of simplex inequalities." Proceedings of the American Mathematical Society 144, no. 3 (July 8, 2015): 1299–307. http://dx.doi.org/10.1090/proc12756.

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Nishiyama, Kenta. "Incomplete hypergeometric systems associated to $1$-simplex $\times $ $(n-1)$-simplex." Rocky Mountain Journal of Mathematics 49, no. 3 (June 2019): 913–28. http://dx.doi.org/10.1216/rmj-2019-49-3-913.

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MUBAYI, DHRUV, and RESHMA RAMADURAI. "Simplex Stability." Combinatorics, Probability and Computing 18, no. 3 (May 2009): 441–54. http://dx.doi.org/10.1017/s0963548309009705.

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A d-simplex is a collection of d + 1 sets such that every d of them has non-empty intersection and the intersection of all of them is empty. Fix k ≥ d + 2 ≥ 3 and let be a family of k-element subsets of an n-element set that contains no d-simplex. We prove that if $|\cG| \geq (1 - o(1))\binom{n-1 }{k-1}$, then there is a vertex x of such that the number of sets in omitting x is o(nk−1) (here o(1)→ 0 and n → ∞). A similar result when n/k is bounded from above was recently proved in [10].Our main result is actually stronger, and implies that if $|\cG| > (1 + \epsilon)\binom{n-1 }{ k-1}$ for any ϵ < 0 and n sufficiently large, then contains d + 2 sets A, A1, . . . ,Ad+1 such that the Ais form a d-simplex, and A contains an element of ∩j≠iAj for each i. This generalizes, in asymptotic form, a recent result of Vestraëte and the first author [18], who proved it for d = 1, ϵ = 0 and n ≥ 2k.
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Shiguo, Yang. "Geometric inequalities for a simplex." Mathematical Inequalities & Applications, no. 4 (2005): 727–33. http://dx.doi.org/10.7153/mia-08-67.

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Hu, Jian-Feng, and Ping-Qi Pan. "An efficient approach to updating simplex multipliers in the simplex algorithm." Mathematical Programming 114, no. 2 (February 15, 2007): 235–48. http://dx.doi.org/10.1007/s10107-007-0099-3.

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Dissertations / Theses on the topic "Simplex (Mathematics)"

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Alpert, Hannah (Hannah Chang). "Special gradient trajectories counted by simplex straightening." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104608.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 65-67).
We prove three theorems based on lemmas of Gromov involving the simplicial norm on stratified spaces. First, the Gromov singular fiber theorem (with proof originally sketched by Gromov) relates the simplicial norm to the number of maximum multiplicity critical points of a smooth map of manifolds that drops in dimension by 1. Second, the multitangent trajectory theorem (proved with Gabriel Katz) relates the simplicial norm to the number of maximum-multiplicity tangent trajectories of a nowhere-vanishing gradient-like vector field on a manifold with boundary. And third, the Morse broken trajectory theorem relates the simplicial volume to the number of maximally broken trajectories of the gradient flow of a Morse--Smale function. Corollary: a Morse function on a closed hyperbolic manifold must have a critical point of every Morse index.
by Hannah Alpert.
Ph. D.
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Webb, Simon Peter. "Central slices of the regular simplex." Thesis, University College London (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338771.

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Trevisan, Eberson Paulo. "O uso da programação linear na separação de pontos." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306659.

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Orientador: Valéria Abrão de Podestá
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-16T01:49:31Z (GMT). No. of bitstreams: 1 Trevisan_EbersonPaulo_M.pdf: 1587820 bytes, checksum: 334e76317d2424126dd4bb1fb621c7e4 (MD5) Previous issue date: 2010
Resumo: Neste trabalho são apresentados alguns assuntos iniciais da teoria de Programação Linear e o método Simplex. Mostramos também como a Programação Linear pode ser utilizada na separação de dois conjuntos de pontos (padrões), através de um modelo linear cuja solução é um hiperplano separador. Finalizamos o trabalho com a apresentação de alguns exemplos de aplicação da Programação Linear na separação de dois conjuntos linearmente separáveis e linearmente inseparáveis
Abstract: In this work we present some introductory issues from Linear Programming theory and the Simplex method. We also show how we can use Linear Programming in two patterns separation by constructing a linear model which solution is a separating hyperplane. Finaly, we also present some examples of Linear Programming application in the linear separability and inseparability of two patterns sets
Mestrado
Programação Linear
Mestre em Matemática
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Alajmi, Abdulrahman N. "On The Lattice Size With Respect To The Standard Simplex in 3D." Kent State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=kent1598893373379275.

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Passos, Adão Nascimento dos. "Estudos em programação linear." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306658.

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Orientador: Valeria Abrão de Podesta
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-14T16:33:59Z (GMT). No. of bitstreams: 1 Passos_AdaoNascimentodos_M.pdf: 1173380 bytes, checksum: 9650e6a87755fbc73407fcb71aed15c1 (MD5) Previous issue date: 2009
Resumo: Neste trabalho é feito um estudo sobre Programação Linear e um texto sobre alguns de seus assuntos básicos, construído com uma linguagem didática, visando sua utilização em sala de aula. São apresentados alguns problemas lineares, os fundamentos matemáticos da Programação Linear e o método Simplex, finalizando com um estudo do princípio da decomposição de Dantzig-Wolfe, que é um procedimento para a resolução de problemas lineares de grande porte e com estrutura especial.
Abstract: In this work we have done a study on Linear Programming and a text with some basic issues, using a didactic language, and aiming its utilization in the classroom. Some linear problems are shown here, the mathematical background of Linear Programming and the Simplex method. Finaly, we have also presented a study on the principle of Dantzig-Wolfe's decomposition, which is a procedure for solving large linear problems with special structure.
Mestrado
Programação Linear
Mestre em Matemática
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Tinaztepe, Ramazan. "Modulation spaces, BMO and the Zak transform, and minimizing IPH functions over the unit simplex." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34659.

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This thesis consists of two parts. In the first chapter, we give some results on modulation spaces. First the relationship between the classical spaces and the modulation spaces is established. It is proved that certain modulation spaces defined on R² lie in the BMO space. Another result is that the Zak transform, a discrete time-frequency transform, maps a modulation space into a higher dimensional modulation space. And by using these results, an uncertainty principle for Gabor frames via modulation spaces is obtained. In the second part, we deal with optimization of an increasing positively homogeneous functions on the unit simplex. The class of increasing positively homogeneous functions is one of the function classes obtained via min-type functions in the context of abstract convexity. The cutting angle method is used for the minimization of this type functions. The most important step of this method is the minimization of a function which is the maximum of a number of min-type functions on the unit simplex. We propose a numerical algorithm for the minimization of such functions on the unit simplex and we mathematically prove that this algorithm finds the exact solution of the minimization problem. Some experiments have been carried out and the results of the experiments have been presented.
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Linnell, Joshua Randall. "Multilattice Tilings and Coverings." BYU ScholarsArchive, 2021. https://scholarsarchive.byu.edu/etd/8911.

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Let L be a discrete subgroup of \mathbb{R}^n under addition. Let D be a finite set of points including the origin. These two sets will define a multilattice of \mathbb{R}^n. We explore how to generate a periodic covering of the space \mathbb{R}^n based on L and $D$. Additionally, we explore the problem of covering when we restrict ourselves to covering \mathbb{R}^n using only dilations of the right regular simplex in our covering. We show that using a set D= {0,d} to define our multilattice the minimum covering density is 5-\sqrt{13}. Furthermore, we show that when we allow for an arbitrary number of displacements, we may get arbitrarily close to a covering density of 1.
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Michel, Jean-Luc. "Polysimplices in euclidean spaces and the enumeration of domino tilings of rectangles." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209922.

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Nous étudions, dans la première partie de notre thèse, les polysimplexes d’un espace euclidien de dimension quelconque, c’est-à-dire les objets consistant en une juxtaposition de simplexes réguliers (de tétraèdres si la dimension est 3) accolés le long de leurs faces. Nous étudions principalement le groupe des symétries de ces polysimplexes. Nous présentons une façon de représenter un polysimplexe à l’aide d’un diagramme. Ceci fournit une classification complète des polysimplexes à similitude près. De plus, le groupe des symétries se déduit du groupe des automorphismes du diagramme. Il découle en particulier de notre étude qu’en dimension supérieure à 2, une telle structure ne possède jamais deux faces parallèles et ne contient jamais de circuit fermé de simplexes.

Dans la seconde partie de notre thèse, nous abordons un problème classique de combinatoire :l’énumération des pavages d’un rectangle mxn à l’aide de dominos. Klarner et Pollack ont montré qu’en fixant m la suite obtenue vérifie une relation de récurrence linéaire à coefficients constants. Nous établissons une nouvelle méthode nous permettant d’obtenir la fonction génératrice correspondante et la calculons pour m <= 16, alors qu’elle n’était connue que pour m <= 10.


Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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Talačkaitė, Simona. "Daugiamačių simpleksinių Lipšico algoritmų su nežinoma Lipšico konstanta ir įvairiais simplekso centrais kūrimas ir eksperimentinis tyrimas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20140724_105124-61903.

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Globaliojo optimizavimo metodai, pagrįsti Lipšico rėžių apskaičiavimu, yra plačiai taikomi įvairių optimizavimo uždavinių sprendimui. Tačiau Lipšico metodai dažniausiai remiasi prielaida, kad Lipšico konstanta žinoma iš anksto, o tai retas atvejis sprendžiant praktinius uždavinius. Todėl Simonos Talačkaitės magistro darbe yra toliau nagrinėjama aktuali ir svarbi problematika iškylanti realizuojant Lipšico metodus nesiremiančius jokiomis išankstinėmis prielaidomis apie Lipšico konstantą. Praktinio tiriamojo pobūdžio magistro darbe iškeliamas toks pagrindinis tikslas: ištirti daugiamačių simpleksinių globaliojo optimizavimo algoritmų su nežinoma Lipšico konstanta efektyvumą priklausomai nuo naudojamo simplekso centro. Šiam tikslui pasiekti buvo iškelti šie uždaviniai: apžvelgti naujausią literatūrą skirta Lipšico metodams su nežinoma Lipšico konstanta; matematiškai išnagrinėti įvairių daugiamačių simplekso centrų apskaičiavimus bendru atveju bei juos realizuoti Matlab aplinkoje; papildyti simpleksinį globaliojo optimizavimo DISIMPL algoritmą šių simpleksų centrų apskaičiavimo paprogramėmis; eksperimentiškai ištirti pasiūlytų rezultatų praktiškumą sprendžiant testinius optimizavimo uždavinius.
This work analyzes Global optimization objectives, the most important it will be algorithms with simplicial Lipšico constant. Also, this work analyzes multidi- mensional DIRECT algorithm. We will provide dividing in higher dimennsions DIRECT algorithm. Then analyzes two simplex and apply the solutions. The hand simplex to smallerpartitions. Perceive multidimensional DIRECT algorithm division rules. In this work wrote a lot about simplicial center about dividing of hyoer-cube. Finally, the experiment it will be about the best way, how we can …nd circle center ir diferent way. Simplex centers using 8 test funkcions , changing the number of iterations and mistakes number. Create tables and to analyzes them. The purpose of this paper work is to introduce the simplex algorithm for global optimization with unknown Lipšicas constant depending on the e¢ ciency of the division of the rules used in the simplex.
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Soares, Vanessa de Carvalho Alves. "Aplicações do problema de otimização de carteiras de investimento." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305876.

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Orientador: Luziane Ferreira de Mendonça
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-17T11:31:02Z (GMT). No. of bitstreams: 1 Soares_VanessadeCarvalhoAlves_M.pdf: 1540180 bytes, checksum: 198ad552da53ca9cbe2fd6bf7fc77c17 (MD5) Previous issue date: 2011
Resumo: Neste trabalho, propomos a determinação de uma carteira de investimento ótima via um método sem derivada. Para isso, utilizamos o modelo de média-variância proposto por Harry M. Markowitz. no qual o problema é formulado de modo a se minimizar o risco do portfolio para um dado nível de retorno esperado, ou maximizar o nível de retorno fixado do portfolio associado a um dado nível de risco e determinar todas as carteiras ótimas, no sentido risco e retorno, formando a Fronteira Eficiente. Nosso algoritmo é baseado no Método Nelder-Mead, destinado à resolução de problemas de programação não linear irrestritos. Assim, adequamos a formulação do portfolio, que depende de restrições, para a utilização do mesmo.
Abstract: In this work we perform a portfolio optimization by using a derivative-free method. For this, we use the Mean-Variance Analysis proposed by Harry M. Markowitz, in which the problem is formulated as one of minimizing portfolio risk subject to a targeted expected portfolio return. Or, for a particular level of risk, we can find a combination of assets that is going to give the highest expected return and determine all the optimal portfolios, towards risk and return, forming the Efficient Frontier. Our algorithm is based on Nelder-Mead method, for solving problems of unconstrained nonlinear programming. Therefore, the formulation of the portfolio, subject to constraints, was adapted for its use.
Mestrado
Mestre em Matemática
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Books on the topic "Simplex (Mathematics)"

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Linear optimization: The simplex workbook. New York: Springer, 2010.

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Maros, István. Computational Techniques of the Simplex Method. Boston, MA: Springer US, 2003.

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Reeb, J. E. Using the simplex method to solve linear programming maximization problems. Corvallis, Or: Oregon State University Extension Service, 1998.

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Monroe, Stuart, and Peckaitis Christine M, eds. Mathematics made simple. 5th ed. New York: Made Simple Books, 1991.

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Cusick, Thomas W. Mathematics made simple. 6th ed. New York: Broadway Books, 2003.

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Sperling, Abraham Paul. Mathematics made simple. 5th ed. New York: Broadway Books, 2001.

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Sankaracarya, Jayadguru. Vedic mathematics: Or sixteen simple mathematical formulae from the Vedas. 2nd ed. Delhi: Motilal Banarsidass, 1992.

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Murphy, Patrick. Additional mathematics made simple. London: Heinemann, 1985.

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Zingo, Laurie. Mathematics dictionary made simple. New York: Vantage, 1988.

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Cheung, Yun-Hsing. A simple mathematical model of lottery play. Perth, W.A: Edith Cowan University, Faculty of Business, School of Finance and Business Economics, 1996.

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Book chapters on the topic "Simplex (Mathematics)"

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Hurlbert, Glenn H. "The Simplex Algorithm." In Undergraduate Texts in Mathematics, 29–57. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-79148-7_2.

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Akin, Ethan. "Examples: Circles, simplex, and symbols." In Graduate Studies in Mathematics, 179–97. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/gsm/001/10.

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Dai, Feng, and Yuan Xu. "Harmonic Analysis on the Simplex." In Springer Monographs in Mathematics, 333–61. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6660-4_13.

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Altman, Eitan, Bruno Gaujal, and Arie Hordijk. "Part IV: 12 Simplex convexity." In Lecture Notes in Mathematics, 243–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-39705-2_13.

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Lee, S. L., and G. M. Phillips. "Interpolation on the Simplex by Homogeneous Polynomials." In Numerical Mathematics Singapore 1988, 295–305. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-6303-2_24.

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Hall, Julian, and Qi Huangfu. "A High Performance Dual Revised Simplex Solver." In Parallel Processing and Applied Mathematics, 143–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31464-3_15.

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Köhler, Günter. "An Algorithm for Listing Lattice Points in a Simplex." In Springer Monographs in Mathematics, 55–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-16152-0_4.

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Agarwal, Pankaj K. "Simplex Range Searching and Its Variants: A Review." In A Journey Through Discrete Mathematics, 1–30. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-44479-6_1.

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Mirzakhani, Maryam, and Jan Vondrák. "Sperner’s Colorings and Optimal Partitioning of the Simplex." In A Journey Through Discrete Mathematics, 615–31. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-44479-6_25.

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Panik, Michael J. "The Dual Simplex, Primal-Dual, and Complementary Pivot Methods." In Linear Programming: Mathematics, Theory and Algorithms, 251–88. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-3434-7_10.

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Conference papers on the topic "Simplex (Mathematics)"

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Шатиришвили, Медея, and Medeya Shatirishvili. "Comparison of the method to structural optimization and the simplex method." In Mathematics in Economics. AUS PUBLISHERS, 2018. http://dx.doi.org/10.26526/conferencearticle_5c24b1d3a1dd91.65715857.

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This article compares the structural optimization method and the simlex method used in solving linear programming problems. The characteristic of each method is given and the analysis of algorithm of the solution of problems by means of these techniques is carried out. The problem showing advantages of one of the methods is solved.
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Mukhamedov, Farrukh, Chin Hee Pah, and Azizi Rosli. "On orthogonality preserving cubic stochastic operator defined on 1-dimensional simplex." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH2018): Innovative Technologies for Mathematics & Mathematics for Technological Innovation. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5136362.

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Voskov, D. V., and H. A. Tchelepi. "Tie-simplex Based Framework for General Multi-phase Thermodynamic Equilibrium Computations." In 11th European Conference on the Mathematics of Oil Recovery. Netherlands: EAGE Publications BV, 2008. http://dx.doi.org/10.3997/2214-4609.20146434.

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Voskov, D. V., and H. A. Tchelepi. "Tie-simplex-based Nonlinear Solver for Mass-variables Compositional Formulation." In ECMOR XIII - 13th European Conference on the Mathematics of Oil Recovery. Netherlands: EAGE Publications BV, 2012. http://dx.doi.org/10.3997/2214-4609.20143218.

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Iranshahr, A., D. Voskov, and H. Tchelepi. "Continuation of the Tie-simplex Space for Three-phase Thermal-compositional Systems." In 12th European Conference on the Mathematics of Oil Recovery. Netherlands: EAGE Publications BV, 2010. http://dx.doi.org/10.3997/2214-4609.20144934.

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Zaydullin, R., D. V. Voskov, and H. A. Tchelepi. "Compositional Formulation Based on Piece-wise Linear Representation in Tie-simplex Space." In ECMOR XIII - 13th European Conference on the Mathematics of Oil Recovery. Netherlands: EAGE Publications BV, 2012. http://dx.doi.org/10.3997/2214-4609.20143219.

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Khait, M., D. Voskov, and G. Konidala. "Tie-Simplex Parametrization For Operator-Based Linearization For Non-Isothermal Multiphase Compositional Flow In Porous." In ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery. Netherlands: EAGE Publications BV, 2018. http://dx.doi.org/10.3997/2214-4609.201802183.

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Skala, Vaclav. "A new robust algorithm for computation of a triangle circumscribed sphere in E3 and a hypersphere simplex." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4952269.

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Fong, Wan Heng, Yee Siang Gan, Nor Haniza Sarmin, and Sherzod Turaev. "The generative capacity of weighted simple and semi-simple splicing systems." In ADVANCES IN INDUSTRIAL AND APPLIED MATHEMATICS: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23). Author(s), 2016. http://dx.doi.org/10.1063/1.4954601.

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NESIN, ALI. "SIMPLE MEMORIES FROM A SIMPLE MATHEMATICS LECTURER - LEELAVATI PRIZE LECTURE." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0013.

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Reports on the topic "Simplex (Mathematics)"

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Bhargava, Hemant K. Dimensional Analysis in Mathematical Modeling Systems: A Simple Numerical Method. Fort Belvoir, VA: Defense Technical Information Center, February 1991. http://dx.doi.org/10.21236/ada236904.

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Keith, B., A. Apostolatos, A. Kodakkal, R. Rossi, R. Tosi, B. Wohlmuth, and C. Soriano. D2.3. Adjoint-based error estimation routines. Scipedia, 2021. http://dx.doi.org/10.23967/exaqute.2021.2.022.

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This document presents a simple and ecient strategy for adaptive mesh renement (AMR) and a posteriori error estimation for the transient incompressible Navier{Stokes equations. This strategy is informed by the work of Prudhomme and Oden [22, 23] as well as modern goal-oriented methods such as [5]. The methods described in this document have been implemented in the Kratos Multiphysics software and uploaded to https://zenodo.org [27].1 This document includes: A review of the state-of-the-art in solution-oriented and goal-oriented AMR. The description of a 2D benchmark model problem of immediate relevance to the objectives of the ExaQUte project. The denition and a brief mathematical summary of the error estimator(s). The results obtained. A description of the API.
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Patel, Reena. Complex network analysis for early detection of failure mechanisms in resilient bio-structures. Engineer Research and Development Center (U.S.), June 2021. http://dx.doi.org/10.21079/11681/41042.

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Bio-structures owe their remarkable mechanical properties to their hierarchical geometrical arrangement as well as heterogeneous material properties. This dissertation presents an integrated, interdisciplinary approach that employs computational mechanics combined with flow network analysis to gain fundamental insights into the failure mechanisms of high performance, light-weight, structured composites by examining the stress flow patterns formed in the nascent stages of loading for the rostrum of the paddlefish. The data required for the flow network analysis was generated from the finite element analysis of the rostrum. The flow network was weighted based on the parameter of interest, which is stress in the current study. The changing kinematics of the structural system was provided as input to the algorithm that computes the minimum-cut of the flow network. The proposed approach was verified using two classical problems three- and four-point bending of a simply-supported concrete beam. The current study also addresses the methodology used to prepare data in an appropriate format for a seamless transition from finite element binary database files to the abstract mathematical domain needed for the network flow analysis. A robust, platform-independent procedure was developed that efficiently handles the large datasets produced by the finite element simulations. Results from computational mechanics using Abaqus and complex network analysis are presented.
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