Estimation of a Piecewise Constant Function Using Reparameterized Level-Set Functions

2010 ◽  
pp. 733-737
Author(s):  
Inga Berre ◽  
Martha Lien ◽  
Trond Mannseth
Keyword(s):  
Level Set ◽  
Constant Function ◽  
Piecewise Constant Function ◽  
Piecewise Constant ◽  
Set Functions ◽  
Level Set Functions

scholarly journals Current-phase relation in layered superconducting structures of SIS’IS type

2021 ◽  
Vol 24 (2) ◽  
pp. 23701
Author(s):  
A. M. Shutovskyi ◽  
V. E. Sakhnyuk
Keyword(s):  
Phase Difference ◽  
Current Density ◽  
Phase Relation ◽  
Dielectric Layer ◽  
Intermediate Layer ◽  
Order Parameter ◽  
Constant Function ◽  
Piecewise Constant Function ◽  
Current Phase ◽  
Piecewise Constant

The dependence of the current density on the phase difference is investigated considering the layered superconducting structures of a SIS’IS type. To simplify the calculations, the quasiclassical equations for the Green’s functions in a t-representation are derived. An order parameter is considered as a piecewise constant function. To consider the general case, no restrictions on the dielectric layer transparency and the thickness of the intermediate layer are imposed. It was found that a new analytical expression for the current-phase relation can be used with the aim to obtain a number of previously known results arising in particular cases.

scholarly journals Continuous CM-regularity of semihomogeneous vector bundles

2020 ◽  
Vol 20 (3) ◽  
pp. 401-412
Author(s):  
Alex Küronya ◽  
Yusuf Mustopa
Keyword(s):  
Vector Bundle ◽  
Abelian Variety ◽  
Upper Bound ◽  
Vector Bundles ◽  
Projective Variety ◽  
Constant Function ◽  
Piecewise Constant Function ◽  
Piecewise Constant ◽  
Generic Vanishing

AbstractWe ask when the CM (Castelnuovo–Mumford) regularity of a vector bundle on a projective variety X is numerical, and address the case when X is an abelian variety. We show that the continuous CM-regularity of a semihomogeneous vector bundle on an abelian variety X is a piecewise-constant function of Chern data, and we also use generic vanishing theory to obtain a sharp upper bound for the continuous CM-regularity of any vector bundle on X. From these results we conclude that the continuous CM-regularity of many semihomogeneous bundles — including many Verlinde bundles when X is a Jacobian — is both numerical and extremal.

scholarly journals PERIODIC ORBITS OF SINGLE NEURON MODELS WITH INTERNAL DECAY RATE 0 < Β ≤ 1

2013 ◽  
Vol 18 (3) ◽  
pp. 325-345 ◽  
Author(s):  
Aija Anisimova ◽  
Maruta Avotina ◽  
Inese Bula
Keyword(s):  
Dynamical System ◽  
Decay Rate ◽  
Single Neuron ◽  
Discrete Dynamical System ◽  
Constant Function ◽  
Piecewise Constant Function ◽  
Sigmoid Function ◽  
Signal Function ◽  
Neuron Models ◽  
Piecewise Constant

In this paper we consider a discrete dynamical system x n+1=βx n – g(x n ), n=0,1,..., arising as a discrete-time network of a single neuron, where 0 &lt; β ≤ 1 is an internal decay rate, g is a signal function. A great deal of work has been done when the signal function is a sigmoid function. However, a signal function of McCulloch-Pitts nonlinearity described with a piecewise constant function is also useful in the modelling of neural networks. We investigate a more complicated step signal function (function that is similar to the sigmoid function) and we will prove some results about the periodicity of solutions of the considered difference equation. These results show the complexity of neurons behaviour.

High-order time-marching reinitialization for regional level-set functions

2018 ◽  
Vol 354 ◽  
pp. 311-319 ◽  
Author(s):  
Shucheng Pan ◽  
Xiuxiu Lyu ◽  
Xiangyu Y. Hu ◽  
Nikolaus A. Adams
Keyword(s):  
Level Set ◽  
High Order ◽  
Regional Level ◽  
Set Functions ◽  
Time Marching ◽  
High Order Time ◽  
Level Set Functions

scholarly journals The Kirchhoff Transformation and the Fick’s Second Law with Concentration-dependent Diffusion Coefficient

2021 ◽  
Vol 16 ◽  
pp. 59-67
Author(s):  
R. M. S. Gama ◽  
R. Pazetto S. Gama
Keyword(s):  
Diffusion Coefficient ◽  
Mathematical Structure ◽  
Constant Function ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Piecewise Constant Function ◽  
Second Law ◽  
Piecewise Constant ◽  
Numerical Examples ◽  
Kirchhoff Transformation

In this work it is considered the Fick’s second law in a context in which the diffusion coefficient depends on the concentration. It is employed the Kirchhoff transformation in order to simplify the mathematical structure of the Fick’s second law, giving rise to a more convenient description. In order to provide a general protocol, the diffusion coefficient will be assumed a piecewise constant function of the concentration. Exact formulas are presented for both the Kirchhoff transformation and its inverse, in such a way that there is no limit of accuracy. Some numerical examples are presented with the aid of a semi-implicit procedure associated with a finite difference approximation.

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