scholarly journals On absolutely continuous curves of probabilities on the line

2019 ◽  
Vol 39 (9) ◽  
pp. 5105-5124
Author(s):  
Adrian Tudorascu ◽  
Keyword(s):  
Absolutely Continuous ◽  
Continuous Curves

scholarly journals Absolutely continuous curves in extended Wasserstein−Orlicz spaces

2016 ◽  
Vol 22 (3) ◽  
pp. 670-687 ◽  
Author(s):  
Stefano Lisini
Keyword(s):  
Orlicz Spaces ◽  
Absolutely Continuous ◽  
Continuous Curves

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.

scholarly journals Fractional Order of Evolution Inclusion Coupled with a Time and State Dependent Maximal Monotone Operator

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1395
Author(s):  
Charles Castaing ◽  
Christiane Godet-Thobie ◽  
Le Xuan Truong
Keyword(s):  
Fractional Order ◽  
Monotone Operator ◽  
Maximal Monotone Operator ◽  
Separable Hilbert Space ◽  
Maximal Monotone ◽  
Fractional Flow ◽  
Order Problem ◽  
Absolutely Continuous ◽  
State Dependent ◽  
Fractional Differential

This paper is devoted to the study of evolution problems involving fractional flow and time and state dependent maximal monotone operator which is absolutely continuous in variation with respect to the Vladimirov’s pseudo distance. In a first part, we solve a second order problem and give an application to sweeping process. In a second part, we study a class of fractional order problem driven by a time and state dependent maximal monotone operator with a Lipschitz perturbation in a separable Hilbert space. In the last part, we establish a Filippov theorem and a relaxation variant for fractional differential inclusion in a separable Banach space. In every part, some variants and applications are presented.

On Finite Part Integrals and Hadamard-Type Fractional Derivatives

2018 ◽  
Vol 13 (9) ◽  
Author(s):  
Li Ma ◽  
Changpin Li
Keyword(s):  
Fractional Derivative ◽  
Singular Integral ◽  
Fractional Derivatives ◽  
Continuous Functions ◽  
Finite Part ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Fundamental Properties ◽  
Logarithmic Series ◽  
The Right

This paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense; that is to say, the Hadamard-type fractional derivative of a given function can be expressed by the finite part integral of a strongly singular integral, which actually does not exist. Besides, our results also cover some fundamental properties on absolutely continuous functions, and the logarithmic series expansion formulas at the right end point of interval for functions in certain absolutely continuous spaces.

scholarly journals A Lochs-Type Approach via Entropy in Comparing the Efficiency of Different Continued Fraction Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 255
Author(s):  
Dan Lascu ◽  
Gabriela Ileana Sebe
Keyword(s):  
Dynamical Systems ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Unit Interval ◽  
Probability Measures ◽  
Absolutely Continuous ◽  
Continued Fraction Expansions ◽  
Absolutely Continuous Invariant

We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aim to compare the efficiency by describing the rate at which the digits of one number-theoretic expansion determine those of another. We study Chan’s continued fractions, θ-expansions, N-continued fractions, and Rényi-type continued fractions. A central role in fulfilling our goal is played by the entropy of the absolutely continuous invariant probability measures of the associated dynamical systems.

Sign in / Sign up

Export Citation Format

Share Document