scholarly journals Extended gradient systems: Dimension one

2000 ◽  
Vol 6 (3) ◽  
pp. 503-518 ◽  
Author(s):  
Siniša Slijepčević
Keyword(s):  
Gradient Systems ◽  
Dimension One

scholarly journals Exact solutions for the total variation denoising problem of piecewise constant images in dimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Riccardo Cristoferi
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Total Variation ◽  
Piecewise Constant ◽  
Geometrical Properties ◽  
Total Variation Denoising ◽  
Fidelity Term ◽  
Dimension One

AbstractA method for obtaining the exact solution for the total variation denoising problem of piecewise constant images in dimension one is presented. The validity of the algorithm relies on some results concerning the behavior of the solution when the parameter λ in front of the fidelity term varies. Albeit some of them are well-known in the community, here they are proved with simple techniques based on qualitative geometrical properties of the solutions.

scholarly journals Nonlinear Conditions for Ultradifferentiability

2021 ◽  
Author(s):  
David Nicolas Nenning ◽  
Armin Rainer ◽  
Gerhard Schindl
Keyword(s):  
General Validity ◽  
Dimension One ◽  
Analogous Theorem

AbstractA remarkable theorem of Joris states that a function f is $$C^\infty $$ C ∞ if two relatively prime powers of f are $$C^\infty $$ C ∞ . Recently, Thilliez showed that an analogous theorem holds in Denjoy–Carleman classes of Roumieu type. We prove that a division property, equivalent to Joris’s result, is valid in a wide variety of ultradifferentiable classes. Generally speaking, it holds in all dimensions for non-quasianalytic classes. In the quasianalytic case we have general validity in dimension one, but we also get validity in all dimensions for certain quasianalytic classes.

STARCH GEL ELECTROPHORESIS OF MYOGEN FROM CHICKEN BREAST MUSCLE IN CONSTANT AND GRADIENT BUFFER SYSTEMS

1963 ◽  
Vol 41 (1) ◽  
pp. 369-387 ◽  
Author(s):  
J. M. Neelin
Keyword(s):  
Gel Electrophoresis ◽  
Protein Concentration ◽  
Breast Muscle ◽  
Chicken Breast ◽  
Starch Gel Electrophoresis ◽  
Two Dimensional ◽  
Sodium Cacodylate ◽  
Gradient Systems ◽  
Optimal Separation ◽  
Starch Gel

By varying conditions of starch gel electrophoresis, factors contributing to the resolution of myogen proteins from chicken breast muscle have been studied. Variables examined included composition of the myogen extractant, protein concentration, ionic strength of electrophoretic media, pH of gel media, plane and direction of electrophoresis, and the nature of cations and anions in gel media and bridge solutions. The significance of anions was more closely studied with constant buffer systems, and gradient systems in which bridge electrolyte differed from, and gradually altered, the gel medium. Optimal separation was obtained in gradient systems with 0.10 M sodium chloride bridge solutions, and gel media of sodium cacodylate, pH 6.9, μ 0.010, which resolved 12 cationic zones, and sodium veronal, pH 7.4, μ 0.010, which resolved 10 anionic zones. These buffers in two-dimensional sequence revealed a total of about 24 components in this myogen.

Reference-free, depth-dependent characterization of nanolayers and gradient systems with advanced grazing incidence X-ray fluorescence analysis

2015 ◽  
Vol 212 (3) ◽  
pp. 523-528 ◽  
Author(s):  
Philipp Hönicke ◽  
Blanka Detlefs ◽  
Matthias Müller ◽  
Erik Darlatt ◽  
Emmanuel Nolot ◽  
...  
Keyword(s):  
Fluorescence Analysis ◽  
Grazing Incidence ◽  
X Ray ◽  
Gradient Systems

Improving the extraction of tetrachloroethylene from soil columns using surfactant gradient systems

2004 ◽  
Vol 71 (1-4) ◽  
pp. 27-45 ◽  
Author(s):  
Jeffrey D Childs ◽  
Edgar Acosta ◽  
Robert Knox ◽  
Jeffrey H Harwell ◽  
David A Sabatini
Keyword(s):  
Soil Columns ◽  
Gradient Systems

scholarly journals From non-local Eringen’s model to fractional elasticity

2018 ◽  
Vol 24 (6) ◽  
pp. 1935-1953 ◽  
Author(s):  
Anton Evgrafov ◽  
José C. Bellido
Keyword(s):  
Riesz Potential ◽  
Heterogeneous Material ◽  
Research Literature ◽  
Stress Concentrations ◽  
Uniqueness Of Solutions ◽  
Numerical Studies ◽  
Smooth Kernels ◽  
Ill Posed ◽  
Non Local ◽  
Dimension One

Eringen’s model is one of the most popular theories in non-local elasticity. It has been applied to many practical situations with the objective of removing anomalous stress concentrations around geometric shape singularities, which appear when local modelling is used. Despite the great popularity of Eringen’s model within the mechanical engineering community, even the most basic questions such as the existence and uniqueness of solutions have been rarely considered in research literature for this model. In this work we focus on precisely these questions, proving that the model is in general ill-posed in the case of smooth kernels, the case which appears rather often in numerical studies. We also consider the case of singular, non-smooth kernels and for the paradigmatic case of Riesz potential we establish the well-posedness of the model in fractional Sobolev spaces. For such a kernel, in dimension one the model reduces to the well-known fractional Laplacian. Finally, we discuss possible extensions of Eringen’s model to spatially heterogeneous material distributions.

Sign in / Sign up

Export Citation Format

Share Document