05868nam 2200577 450 99650355230331620230512152002.03-031-05480-6(MiAaPQ)EBC7151651(Au-PeEL)EBL7151651(CKB)25554151000041(EXLCZ)992555415100004120230404d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierDeterminants, Gröbner bases and cohomology /Winfried Bruns [and three others]Cham, Switzerland :Springer,[2022]©20221 online resource (514 pages)Springer monographs in mathematicsPrint version: Bruns, Winfried Determinants, Gröbner Bases and Cohomology Cham : Springer International Publishing AG,c2023 9783031054792 Includes bibliographical references and index.Intro -- Preface -- Contents -- 1 Gröbner Bases, Initial Ideals and Initial Algebras -- 1.1 Monomial Orders -- 1.2 Gröbner Bases -- 1.3 Sagbi Bases -- 1.4 Initial Subspaces and Gradings -- 1.5 Initial Subspaces for Weights. Homogenization -- 1.6 Deformation to the Initial Object -- 2 More on Gröbner Deformations -- 2.1 Minimal and Associated Primes -- 2.2 Connectedness -- 2.3 Optimal Gröbner Deformations -- 2.4 Square-Free Gröbner Deformations -- 3 Determinantal Ideals and the Straightening Law -- 3.1 Minors and Determinantal Ideals -- 3.2 Standard Bitableaux and the Straightening Law -- 3.3 Refinement of the Straightening Law -- 3.4 Determinantal Rings -- 3.5 Powers and Products of Determinantal Ideals -- 3.6 Representation Theory -- 4 Gröbner Bases of Determinantal Ideals -- 4.1 An Instructive Case: the Ideal of 2-Minors -- 4.2 The Robinson-Schensted-Knuth Correspondence -- 4.3 RSK and Gröbner Bases of Ideals -- 4.4 Cohen-Macaulayness and Hilbert Series of Determinantal Rings -- 4.5 Gröbner Bases via Secants -- 4.6 Multigraded Structures and the Multidegree -- 5 Universal Gröbner Bases -- 5.1 Universal Gröbner Bases -- 5.2 Universal Gröbner Bases for Maximal Minors -- 5.3 Universal Gröbner Bases for 2-Minors -- 6 Algebras Defined by Minors -- 6.1 A Recap of Toric Algebra -- 6.2 Algebras Defined by Maximal Minors -- 6.3 Rees Algebras of Determinantal Ideals -- 6.4 The Algebra of Minors -- 6.5 Algebraic Relations between Minors -- 6.6 Exterior Powers of Linear Maps -- 6.7 Sagbi Deformations of Determinantal Rings -- 7 F-singularities of Determinantal Rings -- 7.1 F-purity -- 7.2 F-regularity -- 7.3 F-rationality and Gröbner Deformations -- 7.4 Equivariant Deformations -- 7.5 F-pure Thresholds -- 8 Castelnuovo-Mumford Regularity -- 8.1 Castelnuovo-Mumford Regularity over General Base Rings.8.2 Castelnuovo-Mumford Regularity and Multigraded Structures -- 8.3 Vanishing over Nonstandard Multigraded Rings -- 8.4 Regularity of Powers and Products of Ideals -- 8.5 Linear Powers and Linear Products -- 8.6 A Family of Determinantal Ideals with Linear Products -- 8.7 Maximal Minors of Matrices of Linear Forms and Linear Powers -- 9 Grassmannians, Flag Varieties, Schur Functors and Cohomology -- 9.1 Fundamental Multilinear Algebra Constructions -- 9.2 Affine and Projective Bundles, Grassmannians, Flag Varieties -- 9.3 Basic Calculus with Direct Images -- 9.4 The Kempf Vanishing Theorem -- 9.5 Characteristic-Free Vanishing for some Nondominant Weights -- 9.6 A Sharp Characteristic-Free Vanishing on Projective Bundles -- 9.7 Algebraic Groups and Representations -- 9.8 Schur Functors -- 9.9 Grothendieck Duality -- 9.10 Cohomology Vanishing on Grassmannians -- 10 Asymptotic Regularity for Symbolic Powers of Determinantal Ideals -- 10.1 Quotients of Ideals Defined by Shape -- 10.2 Filtrations Associated with Ideals Defined by Shape -- 10.3 An algorithm to Compute Z(Σ) -- 10.4 The Filtration for Symbolic Powers of Determinantal Ideals -- 10.5 Sheaves Defined by Shape and Their Quotients -- 10.6 A Geometric Realization of the Modules J(σ)l -- 10.7 Regularity of Symbolic Powers of Determinantal Ideals -- 10.8 Some Geometric Properties of Determinantal Varieties -- 11 Cohomology and Regularity in Characteristic Zero -- 11.1 The Borel-Weil-Bott Theorem -- 11.2 The Optimality of Theorem 9.5.1摥映數爠eflinkthm:charspsfreespsvanishing9.5.19 -- 11.3 Borel-Weil-Bott on Grassmannians -- 11.4 Effective Vanishing of Cohomology in Characteristic Zero -- 11.5 Cauchy's Formula Revisited -- 11.6 Explicit Description of `3́9`42`"̇613A``45`47`"603AExt Modules for J(σ)l -- 11.7 `3́9`42`"̇613A``45`47`"603AExt Modules for Symbolic Powers.11.8 The Basics on `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- 11.9 `3́9`42`"̇613A``45`47`"603AExt Modules for `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- 11.10 Local Cohomology with Determinantal Support -- 11.11 Syzygies of `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- Appendix List of Symbols -- References -- -- Index.Springer monographs in mathematics.Algebra, HomologicalAlgebraic geometryCommutative algebraÀlgebra homològicathubGeometria algebraicathubÀlgebra commutativathubLlibres electrònicsthubAlgebra, Homological.Algebraic geometry.Commutative algebra.Àlgebra homològicaGeometria algebraicaÀlgebra commutativa512.55Bruns Winfried56675MiAaPQMiAaPQMiAaPQBOOK996503552303316Determinants, Gröbner bases and cohomology3084265UNISA03123nam 2200469 450 991069822140332120230308050944.0(CKB)2430000000035959(NjHacI)992430000000035959(OCoLC)84734928(EXLCZ)99243000000003595920230308d2009 uy 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierInformation security guide for government executives /Pauline Bowen, Elizabeth Chew Bennett, Joan HashGaithersburg, Md. :National Institute of Standards and Technology,2009.1 online resource (14 pages)NISTIRTitle from title screen (viewed on Feb. 20, 2007)."January 2007."Information Security Guide for Government Executives provides a broad overview of information security program concepts to assist senior leaders in understanding how to oversee and support the development and implementation of information security programs. Management is responsible for: (1) Establishing the organization's information security program; (2) Setting program goals and priorities that support the mission of the organization; and (3) Making sure resources are available to support the security program and make it successful. Senior leadership commitment to security is more important now than ever before. Studies have shown that senior management's commitment to information security initiatives is the number one critical element that impacts an information security program's success. Meeting this need necessitates senior leadership to focus on effective information security governance and support which requires integration of security into the strategic and daily operations of an organization. When considering this challenge, five key security questions emerge for the executive: (1) What are the information security laws, regulations, standards, and guidance that I need to understand to build an effective security program? (2) What are the key activities to build an effective security program? (3) Why do I need to invest in security? (4) Where do I need to focus my attention in accomplishing critical security goals? (5) Where can I learn more to assist me in evaluating the effectiveness of my security program? This guide provides the answers to those questions.Government executivesInformation technologyComputer securityUnited StatesHandbooks and manuals.lcgftGovernment executives.Information technology.Computer security351.0074Bowen Pauline1351624Bennett Elizabeth Chew1922-Hash JoanNational Institute of Standards and Technology (U.S.)NjHacINjHaclBOOK9910698221403321Information security guide for government executives3152835UNINA01061nam0 22002771i 450 UON0005780320231205102254.7620020107d1979 |0itac50 bahinIN|||| 1||||Gandhi ki prasamghikataJayadeva SethiDilliRadhakrishna Prakashana1979200 p.21 cmGANDHIFILOSOFIA (1869-1948)UONC011110FIINNew DelhiUONL000110SI IV BSUBCONT. INDIANO - STORIA MODERNA (1526-1947)ASETHIJayadevaUONV036917654032Radhakrishna PrakashanaUONV249379650SETHI, JayadevSETHI, JayadevaUONV078127ITSOL20240220RICASIBA - SISTEMA BIBLIOTECARIO DI ATENEOUONSIUON00057803SIBA - SISTEMA BIBLIOTECARIO DI ATENEOSI SI IV B 429 SI SA 56144 5 429 Gandhi ki prasamghikata1169639UNIOR