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Weakly one-based geometric theories

Alexander Berenstein, Evgueni Vassiliev
2012 Journal of Symbolic Logic (JSL)  
We also show that the lovely pair expansion of a non-trivial weakly one-based ω-categorical geometric theory interprets an infinite vector space over a finite field.  ...  We study the class of weakly locally modular geometric theories introduced in [4], a common generalization of the classes of linear SU-rank 1 and linear o-minimal theories.  ...  one-based geometric theory.  ... 
doi:10.2178/jsl/1333566629 fatcat:75rkdyzb4bbbrpw37m2jd6c72i

Book Review: Vertex algebras and algebraic curves

Yi-Zhi Huang
2002 Bulletin of the American Mathematical Society  
Frenkel, Lepowsky and Meurman based on their earlier construction of and their results on the moonshine module.  ...  This superb book contains the first published systematic exposition of the algebro-geometric approach to vertex algebras and its relation with the algebraic approach.  ...  To construct the algebro-geometric portions of general weakly conformal field theories, one first has to formulate these algebro-geometric portions in general.  ... 
doi:10.1090/s0273-0979-02-00955-2 fatcat:lrutac4r6rc2jefhy7luzukfbi

Page 6267 of Mathematical Reviews Vol. , Issue 99i [page]

1999 Mathematical Reviews  
In geometrical terms, the evolution equations in mechanics are described by a vector field on the phase space.  ...  Multisymplectic geometry provides a nice geometric framework for classical field theories which is very close to the symplectic formal- ism for mechanics.  ... 

Geometric duality and parametric duality for multiple objective linear programs are equivalent [article]

Daniel Dörfler, Andreas Löhne
2018 arXiv   pre-print
We show the converse statement: parametric duality can be derived from geometric duality. We point out that an easy geometric transformation embodies the relationship between both duality theories.  ...  The advantages of each theory are discussed.  ...  The theories we consider in this paper are geometric duality by Heyde and Löhne [3] and parametric duality as introduced by Luc in [8, Section 4] .  ... 
arXiv:1803.05546v2 fatcat:6ccz4voqejflri4sedrpatxzpa

New Z-Eigenvalue Localization Set for Tensor and Its Application in Entanglement of Multipartite Quantum States

Liang Xiong, Zhanfeng Jiang, Jianzhou Liu, Qi Qin
2022 Mathematics  
On the other hand, we present theoretical bounds of the geometric measure of entanglement for a weakly symmetric multipartite quantum state with non-negative amplitudes by virtue of different distance  ...  This study focuses on tensor Z-eigenvalue localization and its application in the geometric measure of entanglement for multipartite quantum states.  ...  As applications, we are devoted to the geometric measure of entanglement on the ground of tensor Z-eigenvalue theory.  ... 
doi:10.3390/math10152624 fatcat:zhvpcivt2rgrxgunanznglo7ey

Page 1217 of Mathematical Reviews Vol. 43, Issue 5 [page]

1972 Mathematical Reviews  
D. 6704 Geometric theory of Banach spaces. I. Theory of basic and minimal systems. (Russian) Uspehi Mat. Nauk 25 (1970), no. 3 (153), 113-174.  ...  In this paper the authors now | succeed in giving an affirmative answer to this question, solving one of the fundamental problems of basis theory.  ... 

Page 1778 of Mathematical Reviews Vol. , Issue 91C [page]

1991 Mathematical Reviews  
(D-FRNK) On the connectedness of the set of weakly efficient points of a vector optimization problem in locally convex spaces. J. Optim. Theory Appl. 65 (1990), no. 2, 257-270.  ...  Previous results on the connectedness of weakly efficient sets are extended to the infinite case.  ... 

On the relation between continuous and combinatorial

F. Marmolejo, M. Menni
2016 Journal of Homotopy and Related Structures  
Also, given a geometric morphism g : F → E between pre-cohesive toposes F and E (over the same base), we define what it means for g to preserve pieces.  ...  We introduce weakly Kan objects in a pre-cohesive topos.  ...  In Sect. 8 we show that if g : F → E (over the same base) preserves pieces then the direct image g * : F → E preserves weakly Kan objects.  ... 
doi:10.1007/s40062-016-0131-5 fatcat:prcbtoalvvbotayvzqwkoolzeu

Weak One-Basedness

Gareth Boxall, David Bradley-Williams, Charlotte Kestner, Alexandra Omar Aziz, Davide Penazzi
2013 Notre Dame Journal of Formal Logic  
Our main results are that this notion characterises linearity in the setting of geometric þ-rank 1 structures and that lovely pairs of weakly one-based geometric þ-rank 1 structures are weakly one-based  ...  We study the notion of weak one-basedness introduced in recent work of Berenstein and Vassiliev.  ...  We prove in §4 that if M is geometric with þ-rank 1 and (M, | acl ) is weakly one-based then | þ in a sufficiently saturated model of the corresponding theory of lovely pairs will also be weakly one-based  ... 
doi:10.1215/00294527-2143934 fatcat:j2opkh3imbahbmxzc5yli7akeu

Classifying topoi and the axiom of infinity

Andreas Blass
1989 Algebra Universalis  
In the known constructions [1, 4, 6] of classifying topoi for geometric theories, it is always assumed that the base topos fie satisfies the axiom of infinity.  ...  Let T be the one-sorted geometric theory having one constant symbol o, one unary function symbol ~, no other non-logical symbols, and no axioms.  ... 
doi:10.1007/bf01211840 fatcat:nbwueiqid5fihkge7di5iiihky

Emergent Strings, Duality and Weak Coupling Limits for Two-Form Fields [article]

Seung-Joo Lee, Wolfgang Lerche, Timo Weigand
2019 arXiv   pre-print
Concretely we first consider weakly coupled tensor fields in six-dimensional compactifications of F-theory, where the arising tensionless strings play the role of dual weakly coupled heterotic strings.  ...  IIB strings, again on K3 surfaces.  ...  Six-dimensional Type IIA compactifications on K3 surfaces do not have 2-forms which can become weakly coupled in the geometric moduli space.  ... 
arXiv:1904.06344v2 fatcat:cnnfdkplajebfde3japvjrefri

High‐frequency nonlinear acoustic beams and wave packets

Andrew N. Norris
1992 Journal of the Acoustical Society of America  
The theory of weakly nonlinear high-frequency waves is extended in this paper to allow for complex phase solutions.  ...  Geometrical singularities due to caustics and loci do not occur, and the only singularities in the theory are purely nonlinear.  ...  waves, 9 and also to the linear theory of geometrical optics. m-12 The effects of refraction enter the weakly nonlinear theories through the rays of geometrical optics while nonlinear effects enter via  ... 
doi:10.1121/1.405213 fatcat:zgpo6hvcpnexflcc3txcix2hai

Impact of nonlinear hydrodynamic modelling on geometric optimisation of a spherical heaving point absorber

Bingyong Guo, Qusai Elmoosa, Christian Windt, John V. Ringwood
2021 Zenodo  
In order to focus on the essential issues, this study takes the simplest possible device for optimisation, a heaving sphere (with just one free parameter), but one which exhibits nonlinear hydrodynamic  ...  Due to the amount of iterative computation involved, researchers involved in geometric optimisation of wave energy devices typically employ linear hydrodynamic models.  ...  energy based on those principles.  ... 
doi:10.5281/zenodo.5503857 fatcat:762q24agzratjbkx7hpjhepzfu

Page 2715 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
of the field theory based on the canonical field 2-form.  ...  On account of the fact that the geometrical objects associated to *gi;(x,y) are generally found to be complicated, the authors choose particular values of a,b and B; and consider the special form of the  ... 

Page 6620 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
More generally, given a cost function f on the unit d-sphere Uz, we can define an elliptic distribution based on the second moments of f.  ...  (If “induced” is replaced by “finite induced”, we get weakly compat- ible.) A weakly compatible topology on the vertex set completely determines the graph structure.  ... 
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