Topology and smooth structure revisited

2008 ◽  
pp. 243-270
Author(s):  
Anatole Katok ◽  
Vaughn Climenhaga
Keyword(s):  
Smooth Structure

scholarly journals Flows of measures generated by vector fields

2018 ◽  
Vol 148 (4) ◽  
pp. 773-818
Author(s):  
Emanuele Paolini ◽  
Eugene Stepanov
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Borel Measure ◽  
Weak Sense ◽  
Positive Borel Measure ◽  
Smooth Structure ◽  
Smooth Vector ◽  
Integral Curves ◽  
The Given ◽  
Measurable Vector

The scope of the paper is twofold. We show that for a large class of measurable vector fields in the sense of Weaver (i.e. derivations over the algebra of Lipschitz functions), called in the paper laminated, the notion of integral curves may be naturally defined and characterized (when appropriate) by an ordinary differential equation. We further show that for such vector fields the notion of a flow of the given positive Borel measure similar to the classical one generated by a smooth vector field (in a space with smooth structure) may be defined in a reasonable way, so that the measure ‘flows along’ the appropriately understood integral curves of the given vector field and the classical continuity equation is satisfied in the weak sense.

EFFECT OF BORATES AND SILICATES ON WEARING PROPERTIES OF MAO COATINGS

2016 ◽  
Vol 24 (05) ◽  
pp. 1750061
Author(s):  
Yu ZHANG ◽  
YAN-WEI ZHAO ◽  
NAN XIANG ◽  
REN-GUO SONG
Keyword(s):  
Mechanical Properties ◽  
Aluminum Alloy ◽  
Treatment Time ◽  
Microarc Oxidation ◽  
Smooth Structure ◽  
Electrolytic Bath ◽  
Optimum Treatment ◽  
The One ◽  
Wear Tests

In the present study, microarc oxidation (MAO) coatings were formed on ZL101A aluminum alloy in an electrolytic bath containing 3[Formula: see text]g/L KOH [Formula: see text] 2[Formula: see text]g/L Na2WO[Formula: see text] 4[Formula: see text]g/L KF. The morphology and wearing behavior were investigated. In both electrolytes, the additives were borates (Na2B4O718[Formula: see text]g/L) and silicates (Na2SiO3 18[Formula: see text]g/L), respectively. It was found that the coating formed in borates-containing electrolyte was of compact and smooth structure than that of the one formed in silicates-containing electrolyte at the optimum treatment time. It was found that all the coatings were composed of á-Al2O3 and ã-Al2O3. The microhardness and wear tests proved that the coating formed in borates-containing electrolyte was having better mechanical properties than those of the coating formed in silicates-containing electrolyte.

scholarly journals The Geometric Theory of the Fundamental Germ

2008 ◽  
Vol 190 ◽  
pp. 1-34 ◽  
Author(s):  
T. M. Gendron
Keyword(s):  
Group Actions ◽  
Geometric Theory ◽  
Universal Cover ◽  
Closed Surface ◽  
Topological Invariant ◽  
Hyperbolic Type ◽  
Smooth Structure

The fundamental germ is a generalization of π1, first defined for laminations which arise through group actions [4]. In this paper, the fundamental germ is extended to any lamination having a dense leaf admitting a smooth structure. In addition, an amplification of the fundamental germ called the mother germ is constructed, which is, unlike the fundamental germ, a topological invariant. The fundamental germs of the antenna lamination and the PSL(2,ℤ) lamination are calculated, laminations for which the definition in [4] was not available. The mother germ is used to give a new proof of a Nielsen theorem for the algebraic universal cover of a closed surface of hyperbolic type.

scholarly journals Smooth structures and Einstein metrics on

2009 ◽  
Vol 147 (2) ◽  
pp. 409-417 ◽  
Author(s):  
RAREŞ RǍSDEACONU ◽  
IOANA ŞUVAINA
Keyword(s):  
Scalar Curvature ◽  
Einstein Metrics ◽  
Einstein Metric ◽  
Smooth Structure ◽  
Smooth Structures ◽  
Higher Dimensional

AbstractWe show that each of the topological 4-manifolds $\bcp^2\# k\overline{\bcp^2}$, for k = 5, 6, 7, 8 admits a smooth structure which has an Einstein metric of scalar curvature s > 0, a smooth structure which carries an Einstein metric with s < 0 and infinitely many non-diffeomorphic smooth structures which do not admit Einstein metrics. We also exhibit new examples of higher dimensional manifolds carrying Einstein metrics of both positive and negative scalar curvature.

AFM and Ellipsometry Studies of Ultra Thin Ti Film Deposited on a Silicon Wafer

2013 ◽  
Vol 773-774 ◽  
pp. 616-625 ◽  
Author(s):  
Bing Jing Lin ◽  
Hong Tao Zhu ◽  
A. Kiet Tieu ◽  
Gerry Triani
Keyword(s):  
Silicon Wafer ◽  
Smooth Structure ◽  
Force Microscopy ◽  
System A ◽  
Atomic Force ◽  
Combined Use ◽  
Height Step ◽  
Deposited Film ◽  
Arc Deposition ◽  
Coated Area

An ultra- thin Ti film with a thickness of less than 30 nm was deposited on the surface of a silicon wafer by the filtered arc deposition system. A novel technique was adopted to create a height step between the coated area and non-coated area (silicon wafer) during deposition. The surface morphology and thickness of the film was detected by atomic force microscopy (AFM). The AFM results showed that the deposited film formed a smooth structure on the silicon wafer and the height step between the coating and silicon wafer was clear enough to give the thickness of the deposited film. The composition of the deposited film was detected by a combined use of Ellipsometry and AFM. Natural oxidisation of Ti (TiO2) was found on the top of the Ti film after deposition, and the thickness of TiO2 was determined by ellipsometry to be about 0.6 nm.

scholarly journals The smooth structure of the moduli space of a weighted series-parallel graph

2014 ◽  
Vol 164 ◽  
pp. 242-247
Author(s):  
James Cruickshank ◽  
Jonathan McLaughlin
Keyword(s):  
Moduli Space ◽  
Smooth Structure ◽  
Parallel Graph

Friction and wear properties of semimetallic friction composites with bionic non-smooth structure

2014 ◽  
Vol 18 (sup2) ◽  
pp. S2-387-S2-392
Author(s):  
Y. H. Ma ◽  
Y. C. Liu ◽  
J. Peng ◽  
S. S. Ma ◽  
L. Guo ◽  
...  
Keyword(s):  
Friction And Wear ◽  
Smooth Structure ◽  
Wear Properties ◽  
Friction And Wear Properties

scholarly journals Smooth Decomposition of Generalized Fatou Set Explains Smooth Structure in Generalized Mandelbrot Set

1988 ◽  
Vol 43 (1) ◽  
pp. 14-16 ◽  
Author(s):  
J. Peinke ◽  
J. Parisi ◽  
B. Röhricht ◽  
O. E. Rössler ◽  
W. Metzler
Keyword(s):  
Parameter Space ◽  
Initial Conditions ◽  
Logistic Map ◽  
Mandelbrot Set ◽  
Fatou Set ◽  
Smooth Structure ◽  
Mandelbrot Sets ◽  
Generalized Mandelbrot Sets

Abstract Generalized Mandelbrot sets arise in perturbed (non-analytic) versions of the complex logistic map. Numerically, it contains smooth portions as shown previously. To exclude that this result is specific to particular initial conditions only, the structure of the analogue to the Fatou set is looked at in the region in question. The set of non-divergent points is being "eaten up" by a smooth invading boundary. Therefore, the same type of decomposition applies independent of position in parameter space, in the region in question.

scholarly journals Equivariant smoothing of piecewise linear manifolds

2017 ◽  
Vol 164 (2) ◽  
pp. 369-380
Author(s):  
CHRISTIAN LANGE
Keyword(s):  
Finite Group ◽  
Piecewise Linear ◽  
Linear Manifold ◽  
Smooth Structure ◽  
A Finite Group ◽  
Piecewise Linear Manifold

AbstractWe prove that every piecewise linear manifold of dimension up to four on which a finite group acts by piecewise linear homeomorphisms admits a compatible smooth structure with respect to which the group acts smoothly.

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