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標(biāo)題: Titlebook: A Course in Real Algebraic Geometry; Positivity and Sums Claus Scheiderer Textbook 2024 The Editor(s) (if applicable) and The Author(s), u [打印本頁]

作者: commotion    時間: 2025-3-21 19:34
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作者: anticipate    時間: 2025-3-21 22:23
0072-5285 ing and polynomial optimization, including recent research on semidefinite representation of convex sets...Written by a leading expert and based on courses taught for several years, the book assumes familiarity978-3-031-69213-0Series ISSN 0072-5285 Series E-ISSN 2197-5612
作者: 要控制    時間: 2025-3-22 03:14

作者: Anticlimax    時間: 2025-3-22 05:35
The Growth of Synthetic and Imitation Gems,Chapter 2 introduces Newton polytopes and Gram matrices of polynomials. After a proof of the Fejér–Riesz theorem, the main topics are Hilbert’s 1888 theorems on the (non-)existence of sum of squares representations of non-negative polynomials.
作者: PHAG    時間: 2025-3-22 10:55
https://doi.org/10.1007/978-3-642-67467-9The central object in Chapter 3 is the real spectrum of a ring. The topology of the real spectrum is discussed in some detail, and various stellens?tze (of Krivine–Stengle type) are presented, both in an abstract and in a geometric setting.
作者: condone    時間: 2025-3-22 15:19

作者: STENT    時間: 2025-3-22 19:19

作者: 與野獸博斗者    時間: 2025-3-22 22:12

作者: 分期付款    時間: 2025-3-23 05:00

作者: 頌揚本人    時間: 2025-3-23 06:22
Semialgebraic Geometry,Chapter 4 contains an introduction to central concepts from semialgebraic geometry, such as connected components, dimension or semialgebraic paths. Among the main results are the finiteness theorem and cylindrical algebraic decomposition of semialgebraic sets. Usefulness of the real spectrum is emphasized throughout.
作者: ANT    時間: 2025-3-23 12:11

作者: 舊病復(fù)發(fā)    時間: 2025-3-23 16:46

作者: Awning    時間: 2025-3-23 19:51

作者: CYN    時間: 2025-3-24 01:04

作者: 信徒    時間: 2025-3-24 04:27

作者: pulmonary-edema    時間: 2025-3-24 07:49

作者: BROOK    時間: 2025-3-24 10:49

作者: decipher    時間: 2025-3-24 17:43
The Role of the European Union,s are given to polynomials that are strictly positive on some domain, such as the positivstellens?tze of Schmüdgen and Putinar. An optional alternative approach is offered, which uses pure states for convex cones and leads to the Archimedean local-global principle.
作者: 食料    時間: 2025-3-24 22:02
https://doi.org/10.1007/978-1-349-20902-6local-global principle, which is given an independent second proof. Combining this result with an analysis of (weighted) sums of squares in local rings, a series of existence and non-existence results is obtained for sums of squares representations of non-negative polynomials.
作者: Banquet    時間: 2025-3-25 00:11
https://doi.org/10.1007/978-1-349-20902-6ariety . has minimal degree if, and only if, every non-negative quadratic form on . is a sum of squares of linear forms. Quantitative refinements are given as well. These results encompass several major classical theorems, among them the Hilbert 1888 theorems that were discussed in Chapter 2.
作者: 改正    時間: 2025-3-25 06:29

作者: 范圍廣    時間: 2025-3-25 11:14

作者: Conjuction    時間: 2025-3-25 11:47
The Role of the European Union,s are given to polynomials that are strictly positive on some domain, such as the positivstellens?tze of Schmüdgen and Putinar. An optional alternative approach is offered, which uses pure states for convex cones and leads to the Archimedean local-global principle.
作者: Vertical    時間: 2025-3-25 18:08

作者: 過分自信    時間: 2025-3-25 21:06
https://doi.org/10.1007/978-1-349-20902-6ariety . has minimal degree if, and only if, every non-negative quadratic form on . is a sum of squares of linear forms. Quantitative refinements are given as well. These results encompass several major classical theorems, among them the Hilbert 1888 theorems that were discussed in Chapter 2.
作者: 慷慨不好    時間: 2025-3-26 00:37

作者: 單挑    時間: 2025-3-26 06:02
Positive Polynomials with Zeros,local-global principle, which is given an independent second proof. Combining this result with an analysis of (weighted) sums of squares in local rings, a series of existence and non-existence results is obtained for sums of squares representations of non-negative polynomials.
作者: 玷污    時間: 2025-3-26 08:48
Sums of Squares on Projective Varieties,ariety . has minimal degree if, and only if, every non-negative quadratic form on . is a sum of squares of linear forms. Quantitative refinements are given as well. These results encompass several major classical theorems, among them the Hilbert 1888 theorems that were discussed in Chapter 2.
作者: Autobiography    時間: 2025-3-26 12:57

作者: 輕率的你    時間: 2025-3-26 18:22

作者: deciduous    時間: 2025-3-26 23:06
Textbook 2024ynomials...The first half of the book features a thorough introduction to ordered fields and real closed fields, including the Tarski–Seidenberg projection theorem and transfer principle. Classical results such as Artin‘s solution to Hilbert‘s 17th problem and Hilbert‘s theorems on sums of squares o
作者: Leaven    時間: 2025-3-27 01:54
6.4.2 Different growth techniques,rantee the existence of semidefinite representations under fairly general conditions. Constructions due to the author show, on the other hand, that prominent convex sets do not allow such a representation.
作者: indigenous    時間: 2025-3-27 08:51

作者: 高原    時間: 2025-3-27 09:28
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