scholarly journals ON THE STABILITY OF THE PEXIDER EQUATION IN SCHWARTZ DISTRIBUTIONS VIA HEAT KERNEL

2011 ◽  
Vol 33 (4) ◽  
pp. 467-485
Author(s):  
Jae-Young Chung ◽  
Jeong-Wook Chang
Keyword(s):  
Heat Kernel ◽  
Schwartz Distributions ◽  
Pexider Equation ◽  
The Stability

scholarly journals On the Stability of Trigonometric Functional Equations in Distributions and Hyperfunctions

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jaeyoung Chung ◽  
Jeongwook Chang
Keyword(s):  
Functional Equations ◽  
Generalized Functions ◽  
Ulam Stability ◽  
Schwartz Distributions ◽  
The Stability

We consider the Hyers-Ulam stability for a class of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions and Gelfand hyperfunctions.

scholarly journals The stability of Cauchy equations in the space of Schwartz distributions

2004 ◽  
Vol 295 (1) ◽  
pp. 107-114 ◽  
Author(s):  
Jaeyoung Chung ◽  
Soon-Yeong Chung ◽  
Dohan Kim
Keyword(s):  
Schwartz Distributions ◽  
The Stability

scholarly journals Connections Between the Completion of Normed Spaces Over Non-Archimedean Fields and the Stability of the Cauchy Equation

2020 ◽  
Vol 34 (1) ◽  
pp. 151-163
Author(s):  
Jens Schwaiger
Keyword(s):  
Banach Spaces ◽  
Normed Space ◽  
Close Connection ◽  
Normed Spaces ◽  
Cauchy Equation ◽  
Absolute Value ◽  
Pexider Equation ◽  
Adic Valuation ◽  
The Stability ◽  
Stability Results

AbstractIn [12] a close connection between stability results for the Cauchy equation and the completion of a normed space over the rationals endowed with the usual absolute value has been investigated. Here similar results are presented when the valuation of the rationals is a p-adic valuation. Moreover a result by Zygfryd Kominek ([5]) on the stability of the Pexider equation is formulated and proved in the context of Banach spaces over the field of p-adic numbers.

scholarly journals On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Jae-Young Chung
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Classical Sense ◽  
Schwartz Distributions ◽  
The Stability ◽  
Logarithmic Type ◽  
Logarithmic Functional Equation

We prove the Hyers-Ulam stability of the logarithmic functional equation of Heuvers and Kannappanf(x+y)-g(xy)-h(1/x+1/y)=0,  x,y>0, in both classical and distributional senses. As a classical sense, the Hyers-Ulam stability of the inequality|f(x+y)-g(xy)-h(1/x+1/y)|≤ϵ,  x,y>0will be proved, wheref,g,h:ℝ+→ℂ. As a distributional analogue of the above inequality, the stability of inequality∥u∘(x+y)-v∘(xy)-w∘(1/x+1/y)∥≤ϵwill be proved, whereu,v,w∈𝒟'(ℝ+)and∘denotes the pullback of distributions.

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.

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