scholarly journals On the Stability of Convex-valued Mappings and Their Relative Boundary and Extreme Points Set Mappings

2006 ◽  
Vol 17 (1) ◽  
pp. 147-158 ◽  
Author(s):  
Miguel A. Goberna ◽  
Maxim I. Todorov ◽  
Virginia N. Vera de Serio
Keyword(s):  
Extreme Points ◽  
Relative Boundary ◽  
The Stability ◽  
Set Mappings

scholarly journals Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels

2009 ◽  
Vol 4 (3) ◽  
Author(s):  
Eric A. Butcher ◽  
Oleg A. Bobrenkov ◽  
Ed Bueler ◽  
Praveen Nindujarla
Keyword(s):  
Cutting Force ◽  
Extreme Points ◽  
Period Doubling ◽  
Milling Process ◽  
Depth Of Cut ◽  
Approximation Technique ◽  
The Stability ◽  
Delay Differential ◽  
High Degree ◽  
Period Doubling Bifurcations

In this paper the dynamic stability of the milling process is investigated through a single degree-of-freedom model by determining the regions where chatter (unstable) vibrations occur in the two-parameter space of spindle speed and depth of cut. Dynamic systems such as milling are modeled by delay-differential equations with time-periodic coefficients. A new approximation technique for studying the stability properties of such systems is presented. The approach is based on the properties of Chebyshev polynomials and a collocation expansion of the solution. The collocation points are the extreme points of a Chebyshev polynomial of high degree. Specific cutting force profiles and stability charts are presented for the up- and down-milling cases of one or two cutting teeth and various immersion levels with linear and nonlinear regenerative cutting forces. The unstable regions due to both secondary Hopf and flip (period-doubling) bifurcations are found, and an in-depth investigation of the optimal stable immersion levels for down-milling in the vicinity of where the average cutting force changes sign is presented.

scholarly journals The stability of pure weights under conditioning

1974 ◽  
Vol 15 (1) ◽  
pp. 5-12 ◽  
Author(s):  
D. J. Foulis ◽  
C. H. Randall
Keyword(s):  
Weight Function ◽  
Stochastic Models ◽  
Convex Set ◽  
Extreme Points ◽  
Weight Functions ◽  
The Stability ◽  
Universe Of Discourse

In [1], we showed how a collection of physical operations or experiments could be represented by a nonempty set of nonempty sets satisfying certain conditions (irredundancy and coherence) and we called such sets . We also introduced “complete stochastic models” for the empirical universe of discourse represented by such a manual , namely, the so-called weight functions for . These weight functions form a convex set the extreme points of which are called pure weights. We also showed that there is a so-called logic ∏() affiliated with a manual and that each weight function for induces a state on this logic.

Open discussion

1982 ◽  
Vol 99 ◽  
pp. 605-613
Author(s):  
P. S. Conti
Keyword(s):  
Buenos Aires ◽  
Large Mass ◽  
List Type ◽  
Common Phenomenon ◽  
Open Discussion ◽  
The Stability ◽  
Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

Uniformity of Magnification from Different Electron Microscopes

1967 ◽  
Vol 25 ◽  
pp. 32-33
Author(s):  
Godfrey C. Hoskins ◽  
V. Williams ◽  
V. Allison
Keyword(s):  
Diffraction Grating ◽  
The Other ◽  
Carbon Replica ◽  
Electron Microscopes ◽  
The Stability

The method demonstrated is an adaptation of a proven procedure for accurately determining the magnification of light photomicrographs. Because of the stability of modern electrical lenses, the method is shown to be directly applicable for providing precise reproducibility of magnification in various models of electron microscopes.A readily recognizable area of a carbon replica of a crossed-line diffraction grating is used as a standard. The same area of the standard was photographed in Phillips EM 200, Hitachi HU-11B2, and RCA EMU 3F electron microscopes at taps representative of the range of magnification of each. Negatives from one microscope were selected as guides and printed at convenient magnifications; then negatives from each of the other microscopes were projected to register with these prints. By deferring measurement to the print rather than comparing negatives, correspondence of magnification of the specimen in the three microscopes could be brought to within 2%.

Effect of Improved ThO2 Particle Dispersion in Nickel on High-Temperature Strength

1970 ◽  
Vol 28 ◽  
pp. 444-445
Author(s):  
E. R. Kimmel ◽  
H. L. Anthony ◽  
W. Scheithauer
Keyword(s):  
High Temperature ◽  
Metal Matrix ◽  
Oxide Particle ◽  
Oxide Phase ◽  
Dislocation Motion ◽  
Particle Dispersion ◽  
High Temperature Strength ◽  
Strengthening Effect ◽  
Oxide Particles ◽  
The Stability

The strengthening effect at high temperature produced by a dispersed oxide phase in a metal matrix is seemingly dependent on at least two major contributors: oxide particle size and spatial distribution, and stability of the worked microstructure. These two are strongly interrelated. The stability of the microstructure is produced by polygonization of the worked structure forming low angle cell boundaries which become anchored by the dispersed oxide particles. The effect of the particles on strength is therefore twofold, in that they stabilize the worked microstructure and also hinder dislocation motion during loading.

An Analysis of Dissociation of Molecules in a High Resolution Electron Microscope

1973 ◽  
Vol 31 ◽  
pp. 486-487
Author(s):  
Mihir Parikh
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
Cross Sections ◽  
Resolving Power ◽  
Peak Intensity ◽  
Molecular Film ◽  
Resolution Electron ◽  
Dissociation Cross Section ◽  
High Resolution Electron Microscope ◽  
The Stability

It is well known that the resolution of bio-molecules in a high resolution electron microscope depends not just on the physical resolving power of the instrument, but also on the stability of these molecules under the electron beam. Experimentally, the damage to the bio-molecules is commo ly monitored by the decrease in the intensity of the diffraction pattern, or more quantitatively by the decrease in the peaks of an energy loss spectrum. In the latter case the exposure, EC, to decrease the peak intensity from IO to I’O can be related to the molecular dissociation cross-section, σD, by EC = ℓn(IO /I’O) /ℓD. Qu ntitative data on damage cross-sections are just being reported, However, the microscopist needs to know the explicit dependence of damage on: (1) the molecular properties, (2) the density and characteristics of the molecular film and that of the support film, if any, (3) the temperature of the molecular film and (4) certain characteristics of the electron microscope used

Formation and Structure of Casein Micelles in Lactating Mammary Tissue

1970 ◽  
Vol 28 ◽  
pp. 150-151
Author(s):  
Robert J. Carroll ◽  
Marvin P. Thompson ◽  
Harold M. Farrell
Keyword(s):  
Size Distribution ◽  
G Protein ◽  
Milk Proteins ◽  
Mammary Tissue ◽  
Colloidal System ◽  
Casein Micelles ◽  
The Stability

Milk is an unusually stable colloidal system; the stability of this system is due primarily to the formation of micelles by the major milk proteins, the caseins. Numerous models for the structure of casein micelles have been proposed; these models have been formulated on the basis of in vitro studies. Synthetic casein micelles (i.e., those formed by mixing the purified αsl- and k-caseins with Ca2+ in appropriate ratios) are dissimilar to those from freshly-drawn milks in (i) size distribution, (ii) ratio of Ca/P, and (iii) solvation (g. water/g. protein). Evidently, in vivo organization of the caseins into the micellar form occurs in-a manner which is not identical to the in vitro mode of formation.

TEM Analysis of Long-Period Polytypes in SiC—S

1976 ◽  
Vol 34 ◽  
pp. 630-631
Author(s):  
S. Shinozaki ◽  
J. W. Sprys
Keyword(s):  
Electron Diffraction ◽  
Isothermal Annealing ◽  
Tem Analysis ◽  
Long Period ◽  
Transmission Electron ◽  
Average Grain Size ◽  
High Resolution Tem ◽  
Structural Lattice ◽  
The Stability ◽  
Continuous Curves

In reaction sintered SiC (∽ 5um average grain size), about 15% of the grains were found to have long-period structures, which were identifiable by transmission electron microscopy (TEM). In order to investigate the stability of the long-period polytypes at high temperature, crystal structures as well as microstructural changes in the long-period polytypes were analyzed as a function of time in isothermal annealing.Each polytype was analyzed by two methods: (1) Electron diffraction, and (2) Electron micrograph analysis. Fig. 1 shows microdensitometer traces of ED patterns (continuous curves) and calculated intensities (vertical lines) along 10.l row for 6H and 84R (Ramsdell notation). Intensity distributions were calculated based on the Zhdanov notation of (33) for 6H and [ (33)3 (32)2 ]3 for 84R. Because of the dynamical effect in electron diffraction, the observed intensities do not exactly coincide with those intensities obtained by structure factor calculations. Fig. 2 shows the high resolution TEM micrographs, where the striped patterns correspond to direct resolution of the structural lattice periodicities of 6H and 84R structures and the spacings shown in the figures are as expected for those structures.

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