scholarly journals A uniform dichotomy for generic ${\rm SL}(2,{\mathbb{R}})$ cocycles over a minimal base

2007 ◽  
Vol 135 (3) ◽  
pp. 407-417 ◽  
Author(s):  
Artur Avila ◽  
Jairo Bochi
Keyword(s):  
Minimal Base ◽  
Uniform Dichotomy

scholarly journals The minimal base size for a $p$-solvable linear group

2015 ◽  
Vol 144 (8) ◽  
pp. 3231-3242 ◽  
Author(s):  
Zoltán Halasi ◽  
Attila Maróti
Keyword(s):  
Linear Group ◽  
Minimal Base ◽  
Base Size ◽  
Solvable Linear Group

Numerical and Experimental Studies on Extrusion of Fan-Shaped Shell of Magnesium Alloy

2012 ◽  
Vol 626 ◽  
pp. 381-385
Author(s):  
Bao Hong Zhang ◽  
Yao Jin Wu ◽  
Zhi Min Zhang
Keyword(s):  
Numerical Simulation ◽  
Magnesium Alloy ◽  
Experimental Studies ◽  
Extrusion Process ◽  
Base Thickness ◽  
Forming Process ◽  
Backward Extrusion ◽  
Minimal Base ◽  
Billet Shape

This paper presents a case study of optimizing the forming process for a fan-shaped shell component. Numerical simulation was used to study the backward extrusion process of a fan-shaped shell. The underfill defect produced at the opening of the extruded shell due to the billet shape was solved and the minimal base thickness required to avoid the presence of the underfill defect at the bottom corner of the component was defined through the numerical simulation. The extrusion drawing and forming process of the fan-shaped shell were designed on the basis of the results of the numerical simulation. Forming experiments had been performed on the fan-shaped shell at 380 °C and cracking was found on the outside wall in the center of the extruded shell. Choked groove on the inner wall of the die and reducing the lubrication had been used to avoid the presence of cracking. The fan-shaped shell of AZ31 magnesium alloy has been successfully formed by the three-stage forming process of hot upsetting, hot backward extrusion and cold sizing.

scholarly journals Homology Groups in Warped Product Submanifolds in Hyperbolic Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yanlin Li ◽  
Akram Ali ◽  
Fatemah Mofarreh ◽  
Nadia Alluhaibi
Keyword(s):  
Fundamental Group ◽  
Hyperbolic Space ◽  
Ricci Curvature ◽  
Warped Product ◽  
Hyperbolic Spaces ◽  
Warping Function ◽  
Base Manifold ◽  
Homology Groups ◽  
Minimal Base ◽  
Integral Currents

In this paper, we show that if the Laplacian and gradient of the warping function of a compact warped product submanifold Ω p + q in the hyperbolic space ℍ m − 1 satisfy various extrinsic restrictions, then Ω p + q has no stable integral currents, and its homology groups are trivial. Also, we prove that the fundamental group π 1 Ω p + q is trivial. The restrictions are also extended to the eigenvalues of the warped function, the integral Ricci curvature, and the Hessian tensor. The results obtained in the present paper can be considered as generalizations of the Fu–Xu theorem in the framework of the compact warped product submanifold which has the minimal base manifold in the corresponding ambient manifolds.

Minimal Base for Finite Topological Space by Matrix Method

2020 ◽  
Vol 174 (2) ◽  
pp. 167-183
Author(s):  
Yidong Lin ◽  
Jinjin Li ◽  
Liangxue Peng ◽  
Ziqin Feng
Keyword(s):  
Topological Space ◽  
Matrix Method ◽  
Minimal Base

scholarly journals Generalized bases of finite groups

2021 ◽  
Author(s):  
Benjamin Sambale
Keyword(s):  
Finite Group ◽  
Permutation Group ◽  
Finite Groups ◽  
Solvable Groups ◽  
Fusion Systems ◽  
Local Invariant ◽  
Minimal Base ◽  
A Finite Group

AbstractMotivated by recent results on the minimal base of a permutation group, we introduce a new local invariant attached to arbitrary finite groups. More precisely, a subset $$\Delta $$ Δ of a finite group G is called a p-base (where p is a prime) if $$\langle \Delta \rangle $$ ⟨ Δ ⟩ is a p-group and $$\mathrm {C}_G(\Delta )$$ C G ( Δ ) is p-nilpotent. Building on results of Halasi–Maróti, we prove that p-solvable groups possess p-bases of size 3 for every prime p. For other prominent groups, we exhibit p-bases of size 2. In fact, we conjecture the existence of p-bases of size 2 for every finite group. Finally, the notion of p-bases is generalized to blocks and fusion systems.

But who shall monitor the monitor?

PEDIATRICS ◽  
1978 ◽  
Vol 61 (4) ◽  
pp. 663-664
Author(s):  
Nicholas M. Nenson
Keyword(s):  
Task Force ◽  
Sudden Infant Death ◽  
Near Miss ◽  
Sudden Infant ◽  
Factual Knowledge ◽  
Upper Respiratory Tract ◽  
American Academy Of Pediatrics ◽  
Minimal Base ◽  
Upper Respiratory ◽  
A Minor

Three circumstances may (thinly) be argued to qualify the present writer as an "expert" commentator on the article by Kelly et al. in this issue of Pediatrics (p. 511): first (and nearly 20 years ago), that most humbling of all experiences for the pediatrician, the dismissal from one's office of an apparently healthy 2-month-old infant with a minor upper respiratory tract infection who is brought dead on arrival to one's own hospital not three hours later, the unavailability of any autopsy data (difficult to obtain from unsubsidized pathologists in small suburban hospitals ruled by the coroner system of forensic medicine) forcing the diagnosis of sudden infant death syndrome (SIDS) on bewildered parents and shaken physician; last, participation in a recent task force assembled by the American Academy of Pediatrics in an attempt to generate an omniscient statement to cover the optimal management of a dreaded condition ("near-miss SIDS") whose identification is by definition uncertain and concerning which a minimal base of factual knowledge is only now beginning to accrue.

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