Tsukuba Repository  (Tulips-R)

Noshiro Koji

Hasebe Koji

English

Counterexamples and amendments to the termination and optimality of ADOPT-based algorithms

沖中 美世乃

和田 恒彦

Japanese

<報告>視覚特別支援学校理療科生徒の指導のための坐骨神経パルスの刺入点およびその決定手順に関する文献調査

NISHIMURA Hirokazu

Yuan, Allen
The sphere of semiadditive height 1. (English)
  Zbl 07795395
Int. Math. Res. Not. 2024, No. 1, 675-697 (2024)
Let A be an abelian group with an action of a finite group G. Then there is a canonical map
NmG : AG → AG
given by the formula
[a] 7→
∑
g∈G
ga
The map being an isomorphism for Q-vector spaces is among the simplest examples of what has been
dubbed ambidexterity. Building on [M. Hovey and H. Sadofsky, Proc. Am. Math. Soc. 124, No. 11, 3579–
3585 (1996; Zbl 0866.55011); J. P. C. Greenlees and H. Sadofsky, Math. Z. 222, No. 3, 391–405 (1996;
Zbl 0849.55005)], N. J. Kuhn [Invent. Math. 157, No. 2, 345–370 (2004; Zbl 1069.55007)] has established
the following theorem.
Theorem. Let be a T (n)-local spectrum with the action of a finite group G. Then the canonical map
NmG : LT (n)XhG → XhG
is an equivalence.
Hopkins and Lurie [https://people.math.harvard.edu/\protect~\relaxlurie/papers/Ambidexterity.
pdf] interpreted this result as asserting that the ∞-category SpT (n) abides by a higher categoriccal ana-
logue of semiadditivity. S. Carmeli et al. [Invent. Math. 228, No. 3, 1145–1254 (2022; Zbl 1496.55010),
Theorem A] established the following theorem.
Theorem. The ∞-category SpT (n) is ∞-semiadditive.
They have shown also that
Theorem. For n ≥ 0, there exists an idempotent commutative algebra yn in the∞-category of presentable
∞-categories such that a presentable ∞-category C is stable, p-local, and ∞-semiadditive of height n iff
C admits a (necessarily unique) structure of a module over yn.
Since yn is in particular initial among presentable stable p-local symmetric monoidal ∞-categories that
are ∞-semiadditive of height n, it fits into a diagram of adjoint pairs
yn
Lyn ↗↙ Uyn U
y
T (n) ↖↘ L
y
T (n)
Sp
LT (n)−−−→←−−−
UT (n)
SpT (n)
with colimit preserving symmetric monoidal left adjoints displayed on top.
Carmeli, Schlank and Yanovski conjectured that the functor LyT (n) might be an equivalence for n > 0 as
well. This paper aims to give a counterexample to this conjecture in the case n = 1. The main result goes
as follows.
Theorem. Let Sp denote the p-completion of the sphere spectrum. Then there exists a commutative
algebra Sy1p ∈ CAlg (y1) together with a unique equivalence
Uy1
(
Sy1p
)
' Sp
of commutative algebras in spectra.
Reviewer: Hirokazu Nishimura (Tsukuba)
Edited by FIZ Karlsruhe, the European Mathematical Society and the Heidelberg Academy of Sciences and Humanities
© 2024 FIZ Karlsruhe GmbH Page 1
MSC:
18-XX Category theory; homological algebra
55-XX Algebraic topology
Keywords:
none
Full Text: DOI arXiv
Edited by FIZ Karlsruhe, the European Mathematical Society and the Heidelberg Academy of Sciences and Humanities
© 2024 FIZ Karlsruhe GmbH Page 2


a review of The sphere of semiadditive height 1 by Yuan Allen

篠塚 富士男

<論説>諸橋轍次東京文理科大学附属図書館長の図書館経営

筒井 弥生

<資料紹介>三浦周行が視察した海外アーカイブズ（下）

Pervova, Ekaterina
Finite-dimensional diffeological vector spaces being and not being coproducts. (English)  Zbl 07807747
Magnot, Jean-Pierre (ed.), Recent advances in diffeologies and their applications. AMS-EMS-SMF special
session, Université de Grenoble-Alpes, Grenoble, France, July 18–20, 2022. Providence, RI: American
Mathematical Society (AMS). Contemp. Math. 794, 129-138 (2024)
As far as topological vector spaces are concerned, it can occur that the coproduct of two spaces in
the category of vector spaces is not the coproduct of the same spacces in the category of topological
vector spaces. However, this can not occur for finite-dimensional spaces. In contrast, finite-dimensional
diffeological vector spaces easily admit of such a discrepancy.
This paper illustrates how even establishing a smoothness of a given direct sum decomposition of a
diffeological vector space could be tricky, considering the existence of non-complemented subspace and
that of finite-dimensional diffeological vector spaces that do not admit any smooth decomposition into a
direct sum.
For the entire collection see [Zbl 1531.53005].
Reviewer: Hirokazu Nishimura (Tsukuba)
MSC:
57N17 Topology of topological vector spaces
46Axx Topological linear spaces and related structures
Keywords:
diffeological vector spaces; coproducts
Full Text: DOI arXiv
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[12] D. Krepski, J. Watts, S. Wolbert, Sheaves, principal bundles, and Cech cohomology for diffeological spaces, arxiv:2111.01032
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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically
matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original
paper as accurately as possible without claiming the completeness or perfect precision of the matching.
Edited by FIZ Karlsruhe, the European Mathematical Society and the Heidelberg Academy of Sciences and Humanities
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a review of Finite-dimensional diffeological vector spaces being and not being coproducts by Pervova Ekaterina

Matono Gen

Nishio Mayuko

Component-level point cloud completion of bridge structures using deep learning

Maruyama Mina

Gao Yanlin

Okada Susumu

Metal–semiconductor transition in bilayer graphene by bowl inversion of monofluorosumanene

Theobald, Thorsten
Real algebraic geometry and optimization. (English)
  Zbl 07813233
Graduate Studies in Mathematics 241. Providence, RI: American Mathematical Society (AMS) (ISBN
978-1-4704-7431-7/hbk; 978-1-4704-7636-6/pbk; 978-1-4704-7635-9/ebook). xv, 293 p. (2024)
This book aims to provide comprehensive access to interacting and important ideas in the interplay of
real algebraic geometry and optimization.
The synopsis of the book goes as follows.
Chapter 1 is concerned with univariate real polynomials, which provides the background for the treatment of
real polynomials in several variables.
Chapter 2 starts from polytopes and polyhedra, then introducing the more general notion of a semialgebraic
set. Some basic properties of semialgebraic sets are addressed.
Chapter 3 discusses the fundamental Tarski-Seidenberg principle [A. Tarski, A decision method for elementary
algebra and geometry. Prepared for publication by J. C. C. McKinsey. Santa Monica, California:
The Rand Corporation (1948; Zbl 0035.00602); A. Seidenberg, Ann. Math. (2) 60, 365–374 (1954;
Zbl 0056.01804)], whose various consequences include that the class of semialgebraic sets in Rn is
closed under projections.
Chapter 4 is concerned with cylindrical algebraic decomposition (CAD) [G. E. Collins, in: Quantifier elimina-
tion and cylindrical algebraic decomposition. Proceedings of a symposium, Linz, Austria, October
6–8, 1993. Wien: Springer. 85–121 (1998; Zbl 0900.03055); G. E. Collins, Lect. Notes Comput. Sci.
33, 134–183 (1975; Zbl 0318.02051); G. E. Collins, Comput. Suppl. 4, 79–81 (1982; Zbl 0495.03016);
G. E. Collins, in: Quantifier elimination and cylindrical algebraic decomposition. Proceedings of a
symposium, Linz, Austria, October 6–8, 1993. Wien: Springer. 8–23 (1998; Zbl 0900.03053)], which
is better adapted to the structure of semialgebraic problems than proceeding within the proof of
the Tarski-Seidenberg principle.
Chapter 5 provides the foundations of linear, semidefinite, and conic optimization, giving the duality theory
of their programming. Semidefinite optimization can be viewed as linear optimization over the cone
of positive semidefinite matrices, being at the heart of a myriad optimization views of real algebraic
problems. Conic optimization copes with an even more versatile class allowing of replacing the
underlying cone by more general ones.
Chapter 6 begins with discussion on univariate positive polynomials [V. Powers and B. Reznick, Trans. Am.
Math. Soc. 352, No. 10, 4677–4692 (2000; Zbl 0957.26004)], then treating the connection between
positive polynomials and sums of squares. Some powerful representation theorems such as the Pos-
itivstellensatz of J. L. Krivine [J. Anal. Math. 12, 307–326 (1964; Zbl 0134.03902)] and G. Stengle
[Math. Ann. 207, 87–97 (1973; Zbl 0253.14001)] as well as the theorems of G. Pólya [Viertel-
jahrsschrift Zürich 73, 141–145 (1928; JFM 54.0138.01)], D. Handelman [Pac. J. Math. 132, No.
1, 35–62 (1988; Zbl 0659.52002)], M. Putinar [Indiana Univ. Math. J. 42, No. 3, 969–984 (1993;
Zbl 0796.12002)], K. Schmüdgen [Math. Ann. 289, No. 2, 203–206 (1991; Zbl 0744.44008)] and the
Artin-Schreier solution to Hilbert’s 17th problem [E. Artin and O. Schreier, Abh. Math. Semin.
Univ. Hamb. 5, 85–99 (1926; JFM 52.0120.05)] are presented.
Chapter 7 starts by discussing linear programming relaxations to polynomial optimizations based on Han-
delman’s theorem, which reveals the duality between positive polynomials and moments. A key
technique to approaching polynomial optimization rellies on sums of squares and semidefinite pro-
gramming. The main ideas of these methods for unconstrained and constrained optimization are
presented.
Chapter 8 is concerned with spectrahedra, which were defined in §2.3 and which arise as feasible sets of semidef-
inite programming. The author focuses on some concepts and results exhibiting fundamental con-
nections between real algebraic geometry and optimization.
Chapter 9 introduces and studies the classes of stable and hyperbolic polynomials.
Edited by FIZ Karlsruhe, the European Mathematical Society and the Heidelberg Academy of Sciences and Humanities
© 2024 FIZ Karlsruhe GmbH Page 1
Chapter 10 addresses the exponential cone and the relative entropy cone, which provide certificates of nonneg-
ativity based on the arithmetic-geometric mean inequality, both for polynomial optimization and
for the more general signomial optimization.
Appendix ls with algebra, convexity, positive semidefinite matrices, moments and complexity.
Reviewer: Hirokazu Nishimura (Tsukuba)
MSC:
14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry
90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research
and mathematical programming
14Pxx Real algebraic and real-analytic geometry
90C23 Polynomial optimization
Full Text: DOI
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© 2024 FIZ Karlsruhe GmbH Page 2


a review of Real algebraic geometry and optimization by Theobald Thorsten

Kazunori Sasaki

Aprill Kee Oliva

Hiroko Isoda

Hair Growth-Promoting effect of the coffee bean residue extract on hair follicle dermal papilla cells via the activation of autophagy

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