LEADER 07558nam 22008415 450 001 9910768478203321 005 20251116234206.0 010 $a3-540-45624-4 024 7 $a10.1007/3-540-45624-4 035 $a(CKB)1000000000211623 035 $a(SSID)ssj0000321339 035 $a(PQKBManifestationID)11247382 035 $a(PQKBTitleCode)TC0000321339 035 $a(PQKBWorkID)10263539 035 $a(PQKB)10180723 035 $a(DE-He213)978-3-540-45624-7 035 $a(MiAaPQ)EBC3072785 035 $a(PPN)155199668 035 $a(EXLCZ)991000000000211623 100 $a20121227d2001 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aApplied Algebra, Algebraic Algorithms and Error-Correcting Codes $e14th International Symposium, AAECC-14, Melbourne, Australia, November 26-30, 2001. Proceedings /$fedited by Serdar Boztas, Igor E. Shparlinski 205 $a1st ed. 2001. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2001. 215 $a1 online resource (XII, 404 p.) 225 1 $aLecture Notes in Computer Science,$x0302-9743 ;$v2227 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-42911-5 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aInvited Contributions -- The Ubiquity of Reed-Muller Codes -- Self-dual Codes-Theme and Variations -- Design of Differential Space-Time Codes Using Group Theory -- Ideal Error-Correcting Codes: Unifying Algebraic and Number-Theoretic Algorithms -- Block Codes -- Self-dual Codes Using Image Restoration Techniques -- Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance -- F q -Linear Cyclic Codes over F q m: DFT Characterization -- Code Constructions -- Cyclic Projective Reed-Muller Codes -- Codes Identifying Sets of Vertices -- Duality and Greedy Weights of Linear Codes and Projective Multisets -- Codes and Algebra:Rings and Fields -- Type II Codes over IF2r -- On Senary Simplex Codes -- Optimal Double Circulant Z4-Codes -- Constructions of Codes from Number Fields -- On Generalized Hamming Weights for Codes over Finite Chain Rings -- Information Rates and Weights of Codes in Structural Matrix Rings -- Codes and Algebra:Algebraic Geometry Codes -- On Hyperbolic Codes -- On Fast Interpolation Method for Guruswami-Sudan List Decoding of One-Point Algebraic-Geometry Codes -- Computing the Genus of a Class of Curves -- Sequences -- Iterations of Multivariate Polynomials and Discrepancy of Pseudorandom Numbers -- Even Length Binary Sequence Families with Low Negaperiodic Autocorrelation -- On the Non-existence of (Almost-)Perfect Quaternary Sequences -- Maximal Periods of x2 + c in Fq -- On the Aperiodic Correlation Function of Galois Ring m-Sequences -- Euclidean Modules and Multisequence Synthesis -- Cryptography -- On Homogeneous Bent Functions -- Partially Identifying Codes for Copyright Protection -- On the Generalised Hidden Number Problem and Bit Security of XTR -- CRYPTIM: Graphs as Tools for Symmetric Encryption -- Algorithms -- An Algorithm for Computing Cocyclic Matrices Developed over Some Semidirect Products -- Algorithms for Large Integer Matrix Problems -- On the Identification of Vertices and Edges Using Cycles -- Algorithms:Decoding -- On Algebraic Soft Decision Decoding of Cyclic Binary Codes -- Lifting Decoding Schemes over a Galois Ring -- Sufficient Conditions on Most Likely Local Sub-codewords in Recursive Maximum Likelihood Decoding Algorithms -- A Unifying System-Theoretic Framework for Errors-and-Erasures Reed-Solomon Decoding -- An Algorithm for Computing Rejection Probability of MLD with Threshold Test over BSC -- Algebraic Constructions -- Cartan?s Characters and Stairs of Characteristic Sets -- On the Invariants of the Quotients of the Jacobian of a Curve of Genus 2 -- Algebraic Constructions for PSK Space-Time Coded Modulation. 330 $aThe AAECC Symposia Series was started in 1983 by Alain Poli (Toulouse), who, together with R. Desq, D. Lazard, and P. Camion, organized the ?rst conference. Originally the acronym AAECC meant ?Applied Algebra and Error-Correcting Codes?. Over the years its meaning has shifted to ?Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes?, re?ecting the growing importance of complexity in both decoding algorithms and computational algebra. AAECC aims to encourage cross-fertilization between algebraic methods and their applications in computing and communications. The algebraic orientation is towards ?nite ?elds, complexity, polynomials, and graphs. The applications orientation is towards both theoretical and practical error-correction coding, and, since AAECC 13 (Hawaii, 1999), towards cryptography. AAECC was the ?rst symposium with papers connecting Gr¨obner bases with E-C codes. The balance between theoretical and practical is intended to shift regularly; at AAECC-14 the focus was on the theoretical side. The main subjects covered were: ? Codes: iterative decoding, decoding methods, block codes, code construction. ? Codes and algebra: algebraic curves, Gr¨obner bases, and AG codes. ? Algebra: rings and ?elds, polynomials. ? Codes and combinatorics: graphs and matrices, designs, arithmetic. ? Cryptography. ? Computational algebra: algebraic algorithms. ? Sequences for communications. 410 0$aLecture Notes in Computer Science,$x0302-9743 ;$v2227 606 $aAlgebra 606 $aCoding theory 606 $aInformation theory 606 $aComputer science?Mathematics 606 $aData encryption (Computer science) 606 $aAlgorithms 606 $aComputer science$xMathematics 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aCoding and Information Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/I15041 606 $aSymbolic and Algebraic Manipulation$3https://scigraph.springernature.com/ontologies/product-market-codes/I17052 606 $aCryptology$3https://scigraph.springernature.com/ontologies/product-market-codes/I28020 606 $aAlgorithm Analysis and Problem Complexity$3https://scigraph.springernature.com/ontologies/product-market-codes/I16021 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 608 $aOnline resources.$2local 615 0$aAlgebra. 615 0$aCoding theory. 615 0$aInformation theory. 615 0$aComputer science?Mathematics. 615 0$aData encryption (Computer science) 615 0$aAlgorithms. 615 0$aComputer science$xMathematics. 615 14$aAlgebra. 615 24$aCoding and Information Theory. 615 24$aSymbolic and Algebraic Manipulation. 615 24$aCryptology. 615 24$aAlgorithm Analysis and Problem Complexity. 615 24$aComputational Mathematics and Numerical Analysis. 676 $a005.7/2 702 $aBoztas?$b Serdar$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aShparlinski$b Igor E.$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910768478203321 996 $aApplied Algebra, Algebraic Algorithms and Error-Correcting Codes$9772419 997 $aUNINA LEADER 04914nam 22005895 450 001 9910558492603321 005 20260605205333.0 010 $a9783030981914$b(electronic bk.) 024 7 $a10.1007/978-3-030-98191-4 035 $a(MiAaPQ)EBC6944417 035 $a(Au-PeEL)EBL6944417 035 $a(CKB)21459774800041 035 $a(PPN)261520202 035 $a(OCoLC)1309070124 035 $a(DE-He213)978-3-030-98191-4 035 $a(EXLCZ)9921459774800041 100 $a20220331d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOptimal Design of Multi-Phase Materials $eWith a Cost Functional That Depends Nonlinearly on The Gradient /$fby Juan Casado-Díaz 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (119 pages) 225 1 $aSpringerBriefs in Mathematics,$x2191-8201 311 08$aPrint version: Casado-Díaz, Juan Optimal Design of Multi-Phase Materials Cham : Springer International Publishing AG,c2022 9783030981907 320 $aIncludes bibliographical references. 327 $aChapter 1. Homogenization of Elliptic PDE with Varying Coefficients -- Chapter 2. The Relaxed Formulation of an Optimal Design Problem via Homogenization Theory -- Chapter 3. Optimality Conditions and Numerical Resolution -- Chapter 4. Some Extesions: Multi-State and Evolutive Problems. 330 $aThis book aims the optimal design of a material (thermic or electrical) obtained as the mixture of a finite number of original materials, not necessarily isotropic. The problem is to place these materials in such a way that the solution of the corresponding state equation minimizes a certain functional that can depend nonlinearly on the gradient of the state function. This is the main novelty in the book. It is well known that this type of problems has no solution in general and therefore that it is needed to work with a relaxed formulation. The main results in the book refer to how to obtain such formulation, the optimality conditions, and the numerical computation of the solutions. In the case of functionals that do not depend on the gradient of the state equation, it is known that a relaxed formulation consists of replacing the original materials with more general materials obtained via homogenization. This includes materials with different properties of the originals but whose behavior can be approximated by microscopic mixtures of them. In the case of a cost functional depending nonlinearly on the gradient, it is also necessary to extend the cost functional to the set of these more general materials. In general, we do not dispose of an explicit representation, and then, to numerically solve the problem, it is necessary to design strategies that allow the functional to be replaced by upper or lower approximations. The book is divided in four chapters. The first is devoted to recalling some classical results related to the homogenization of a sequence of linear elliptic partial differential problems. In the second one, we define the control problem that we are mainly interested in solving in the book. We obtain a relaxed formulation and their main properties, including an explicit representation of the new cost functional, at least in the boundary of its domain. In the third chapter, we study the optimality conditions of therelaxed problem, and we describe some algorithms to numerically solve the problem. We also provide some numerical experiments carried out using such algorithms. Finally, the fourth chapter is devoted to briefly describe some extensions of the results obtained in Chapters 2 and 3 to the case of dealing with several state equations and the case of evolutive problems. The problems covered in the book are interesting for mathematicians and engineers whose work is related to mathematical modeling and the numerical resolution of optimal design problems in material sciences. The contents extend some previous results obtained by the author in collaboration with other colleagues. 410 0$aSpringerBriefs in Mathematics,$x2191-8201 606 $aMathematical analysis 606 $aMathematics 606 $aAnalysis 606 $aApplications of Mathematics 606 $aEquacions en derivades parcials$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematical analysis. 615 0$aMathematics. 615 14$aAnalysis. 615 24$aApplications of Mathematics. 615 7$aEquacions en derivades parcials 676 $a515.35 676 $a620.118 700 $aCasado-Di?az$b Juan$01220448 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910558492603321 996 $aOptimal Design of Multi-Phase Materials$92824627 997 $aUNINA