scholarly journals The set of regular values (in the sense of Clarke) of a Lipschitz map. A sufficient condition for rectifiability of class $C^3$

2016 ◽  
pp. 1-16
Author(s):  
Silvano Delladio
Keyword(s):  
Sufficient Condition ◽  
Lipschitz Map ◽  
Class C

A Mountain Pass to the Jacobian Conjecture

1998 ◽  
Vol 41 (4) ◽  
pp. 442-451 ◽  
Author(s):  
Marc Chamberland ◽  
Gary Meisters
Keyword(s):  
Mountain Pass ◽  
Jacobian Conjecture ◽  
Mountain Pass Lemma ◽  
Sufficient Condition ◽  
Polynomial Maps ◽  
Class C ◽  
Open Question ◽  
Uniformly Bounded

AbstractThis paper presents an approach to injectivity theorems via the Mountain Pass Lemma and raises an open question. The main result of this paper (Theorem 1.1) is proved by means of the Mountain Pass Lemma and states that if the eigenvalues of are uniformly bounded away from zero for x ∊ Rn, where is a class C1 map, then F is injective. This was discovered in a joint attempt by the authors to prove a stronger result conjectured by the first author: Namely, that a sufficient condition for injectivity of class C1 maps F of Rn into itself is that all the eigenvalues of F′(x) are bounded away from zero on Rn. This is stated as Conjecture 2.1. If true, it would imply (via Reduction-of-Degree) injectivity of polynomial mapssatisfying the hypothesis, det F′(x) ≡ 1, of the celebrated Jacobian Conjecture (JC) of Ott-Heinrich Keller. The paper ends with several examples to illustrate a variety of cases and known counterexamples to some natural questions.

Ck centre unstable manifolds

1988 ◽  
Vol 108 (3-4) ◽  
pp. 303-320 ◽  
Author(s):  
Shui-Nee Chow ◽  
Ke ning Lu
Keyword(s):  
Unstable Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Infinite Dimensional ◽  
Lipschitz Map ◽  
Unstable Manifolds ◽  
Necessary And Sufficient

SynopsisWe consider the existence and smoothness of global centre unstable manifolds for finite and infinite dimensional flows or maps. We show that every global centre unstable manifold can be expressed as a graph of a Ck map, provided that the nonlinearities are Ck smooth. The proofs are based on a lemma by D. Henry on a necessary and sufficient condition for a Lipschitz map to be continuously differentiable.

The Current Situation in Chemical Stabilization of Biological Materials

1972 ◽  
Vol 30 ◽  
pp. 132-133
Author(s):  
John H. Luft
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Osmium Tetroxide ◽  
Molecular Level ◽  
Cross Linking ◽  
Chemical Stabilization ◽  
Specimen Preparation ◽  
Sufficient Condition ◽  
Radio Telescopes

With information processing devices such as radio telescopes, microscopes or hi-fi systems, the quality of the output often is limited by distortion or noise introduced at the input stage of the device. This analogy can be extended usefully to specimen preparation for the electron microscope; fixation, which initiates the processing sequence, is the single most important step and, unfortunately, is the least well understood. Although there is an abundance of fixation mixtures recommended in the light microscopy literature, osmium tetroxide and glutaraldehyde are favored for electron microscopy. These fixatives react vigorously with proteins at the molecular level. There is clear evidence for the cross-linking of proteins both by osmium tetroxide and glutaraldehyde and cross-linking may be a necessary if not sufficient condition to define fixatives as a class.

Surgical Management of Class C and D Glomus Jugulare Tumors: Fisch Infratemporal Fossa Type A Approach

2020 ◽  
Author(s):  
Yin Xia ◽  
Yubin Xue ◽  
Ting Ye ◽  
Xiaopeng Qu ◽  
Xukun Yan ◽  
...  
Keyword(s):  
Surgical Management ◽  
Infratemporal Fossa ◽  
Type A ◽  
Glomus Jugulare ◽  
Class C

A Constant-Current-Controlled Class-C Voltage-Controlled Oscillator using Self-Adjusting Replica Bias Circuit

2015 ◽  
Vol E98.C (6) ◽  
pp. 471-479
Author(s):  
Teerachot SIRIBURANON ◽  
Wei DENG ◽  
Kenichi OKADA ◽  
Akira MATSUZAWA
Keyword(s):  
Constant Current ◽  
Voltage Controlled Oscillator ◽  
Class C
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