Second-Order Structured Deformations: Approximation Theorems and Energetics

2004 ◽  
pp. 177-202 ◽  
Author(s):  
Roberto Paroni
Keyword(s):  
Second Order ◽  
Approximation Theorems ◽  
Structured Deformations

scholarly journals Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-28
Author(s):  
Jiang Zhu ◽  
Dongmei Liu
Keyword(s):  
Time Scales ◽  
Initial Value Problems ◽  
Second Order ◽  
Dynamic Equations ◽  
Maximum Principles ◽  
Uniqueness Theorems ◽  
Initial Value ◽  
Approximation Theorems ◽  
Construction Techniques ◽  
Linear And Nonlinear

Some delta-nabla type maximum principles for second-order dynamic equations on time scales are proved. By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.

scholarly journals Integrated cosine functions

1996 ◽  
Vol 19 (3) ◽  
pp. 575-580 ◽  
Author(s):  
Quan Zheng
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Second Order ◽  
Basic Theory ◽  
Cosine Function ◽  
Integrated Semigroups ◽  
Approximation Theorems ◽  
The Relationship ◽  
Cosine Functions

In order to the second order Cauchy problem(CP2):x″(t)=Ax(t),x(0)=x∈D(An),x″(0)=y∈D(Am)on a Banach space, Arendt and Kellermann recently introduced the integrated cosine function. This paper is concerned with its basic theory, which contain some properties, perturbation and approximation theorems, the relationship to analytic integrated semigroups, interpolation and extrapolation theorems.

Second-Order Structured Deformations in the Space of Functions of Bounded Hessian

2019 ◽  
Vol 29 (6) ◽  
pp. 2699-2734 ◽  
Author(s):  
Irene Fonseca ◽  
Adrian Hagerty ◽  
Roberto Paroni
Keyword(s):  
Second Order ◽  
Structured Deformations ◽  
Functions Of Bounded Hessian

Direct and converse results for q-Bernstein operators

2009 ◽  
Vol 52 (2) ◽  
pp. 339-349 ◽  
Author(s):  
Zoltán Finta
Keyword(s):  
Bernstein Polynomials ◽  
Modulus Of Smoothness ◽  
Second Order ◽  
Bernstein Operators ◽  
Approximation Theorems ◽  
Converse Theorems ◽  
Direct And Converse Results ◽  
Direct Approximation ◽  
Converse Results

AbstractDirect and converse theorems are established for the q-Bernstein polynomials introduced by G. M. Phillips. The direct approximation theorems are given for the second-order Ditzian–Totik modulus of smoothness. The converse results are theorems of Berens–Lorentz type.

scholarly journals Second-Order Structured Deformations: Relaxation, Integral Representation and Applications

2017 ◽  
Vol 225 (3) ◽  
pp. 1025-1072 ◽  
Author(s):  
Ana Cristina Barroso ◽  
José Matias ◽  
Marco Morandotti ◽  
David R. Owen
Keyword(s):  
Integral Representation ◽  
Second Order ◽  
Structured Deformations

Second-Order Structured Deformations

2000 ◽  
Vol 155 (3) ◽  
pp. 215-235 ◽  
Author(s):  
David R. Owen ◽  
Roberto Paroni
Keyword(s):  
Second Order ◽  
Structured Deformations

scholarly journals Lp-Approximation (p≥1) by q-Kantorovich Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zoltán Finta
Keyword(s):  
Modulus Of Smoothness ◽  
Second Order ◽  
Approximation Theorems ◽  
Lp Approximation ◽  
Direct Approximation ◽  
Kantorovich Operators

For a new q-Kantorovich operator we establish direct approximation theorems in the space Lp[0,1],1≤p≤∞, via Ditzian-Totik modulus of smoothness of second order.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

Sign in / Sign up

Export Citation Format

Share Document