Groups definable in linear o-minimal structures: the non-compact case

2010 ◽  
Vol 75 (1) ◽  
pp. 208-220 ◽  
Author(s):  
Pantelis E. Eleftheriou
Keyword(s):  
Quotient Group ◽  
Ordered Group ◽  
Compact Part ◽  
Dimensional Group ◽  
Compact Case

AbstractLet = ⟨M, +, <, 0, S⟩ be a linear o-minimal expansion of an ordered group, and G = ⟨G, ⊕,eG) an n-dimensional group definable in . We show that if G is definably connected with respect to the t-topology, then it is definably isomorphic to a definable quotient group U/L. for some convex ∨-definable subgroup U of ⟨Mn, +⟩ and a lattice L of rank equal to the dimension of the ‘compact part’ of G.

Groups definable in ordered vector spaces over ordered division rings

2007 ◽  
Vol 72 (4) ◽  
pp. 1108-1140 ◽  
Author(s):  
Pantelis E. Eleftheriou ◽  
Sergei Starchenko
Keyword(s):  
Fundamental Group ◽  
Vector Space ◽  
Division Ring ◽  
Quotient Group ◽  
Vector Spaces ◽  
Division Rings ◽  
Ordered Vector Space ◽  
Dimensional Group ◽  
Ordered Vector Spaces

AbstractLet M = 〈M, +, <, 0, {λ}λЄD〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a ‘definable quotient group’ U/L, for some convex V-definable subgroup U of 〈Mn, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's conjecture for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L.

The four-dimensional group velocity

1978 ◽  
Vol 125 (7) ◽  
pp. 549-565 ◽  
Author(s):  
V.G. Polevoi ◽  
S.M. Rytov
Keyword(s):  
Group Velocity ◽  
Dimensional Group

scholarly journals New Visualization Models of Designation Pathway and Group Categorization of Device–Drug and Device–Biologic Combination Products Classification in the United States: Analysis of FDA Capsular Decisions

2021 ◽  
Author(s):  
Nobuo Uemura ◽  
Hiroshi Kasanuki ◽  
Mitsuo Umezu
Keyword(s):  
The United States ◽  
New Combination ◽  
Biological Product ◽  
Regulatory Scheme ◽  
Early Access ◽  
Dimensional Group ◽  
Device Component ◽  
Intended Use ◽  
Component Function

Abstract Objective The developer and sponsor of new combination products in US needs to forecast which classification and designation to the regulatory scheme of drug, biological product, or device would be required for the new products by the Food and Drug Administration (FDA). To improve the predictability and acceptability of the designation of new combination products for innovators, developers, and sponsors, and to encourage the development and early access of new combination products, we proposed new visualization models of the designation pathway and group categorization. Method We searched the website of the FDA on 15 November, 2020 to identify the regulatory scheme of the FDA’s 129 capsular decision cases of device–drug and device–biologics combination products and other publicly available cases the FDA designated to the drug/biologic or device regulatory scheme. Results By introducing a new definition for primary intended use (PIU) by developers and sponsors extracted from the classification factors of primary mode of action (PMOA), we developed new visualization models of the designation pathway and two-dimensional group categorization. And applying these models to the cases the FDA designated, we proposed a new group categorization of combination products while focusing on the device component function. Conclusions The new visualization models with PIU and PMOA and the new group categorization focusing on the device component function proposed in this study may increase predictability and acceptability of the classification of newly developed combination products into the regulatory scheme of drug, biological product, and device, for innovators, developers, and sponsors.

scholarly journals Symmetry group analysis and invariant solutions of hydrodynamic-type systems

2004 ◽  
Vol 2004 (10) ◽  
pp. 487-534 ◽  
Author(s):  
M. B. Sheftel
Keyword(s):  
Group Analysis ◽  
Type Systems ◽  
Hydrodynamic Type ◽  
Recursion Operators ◽  
Higher Symmetries ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Component Systems ◽  
Two Component Systems ◽  
Existence Conditions

We study point and higher symmetries of systems of the hydrodynamic type with and without an explicit dependence ont,x. We consider such systems which satisfy the existence conditions for an infinite-dimensional group of hydrodynamic symmetries which implies linearizing transformations for these systems. Under additional restrictions on the systems, we obtain recursion operators for symmetries and use them to construct infinite discrete sets of exact solutions of the studied equations. We find the interrelation between higher symmetries and recursion operators. Two-component systems are studied in more detail thann-component systems. As a special case, we consider Hamiltonian and semi-Hamiltonian systems of Tsarëv.

Electronic, Elastic and Piezoelectric Properties of Two-Dimensional Group-IV Buckled Monolayers

2017 ◽  
Vol 34 (8) ◽  
pp. 087701 ◽  
Author(s):  
Jing Shi ◽  
Yong Gao ◽  
Xiao-Li Wang ◽  
Si-Ning Yun
Keyword(s):  
Piezoelectric Properties ◽  
Group Iv ◽  
Two Dimensional ◽  
Dimensional Group
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