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.

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.

scholarly journals A Production Inventory Model for deteriorating items with backlog-dependent demand

2019 ◽  
Author(s):  
Chayanika Rout ◽  
Debjani Chakraborty ◽  
Prof Adrijit Goswami
Keyword(s):  
Inventory Model ◽  
Constant Function ◽  
Deteriorating Items ◽  
Piecewise Constant Function ◽  
High Quality ◽  
Piecewise Constant ◽  
Production Inventory ◽  
Demand Rate ◽  
Theoretical Results ◽  
Dependent Demand

This paper investigates a production inventory model under classical EPQ framework with the assumption that the customer demand during the stock out period is affected by the accumulated back-orders. The backlog rate is not fixed; instead, the demand rate during stock-out is assumed to decrease proportionally to the existing backlog which is thereby approximated by a piecewise constant function. Deteriorating items are taken into consideration in this proposed work. For better illustration of the theoretical results and to highlight managerial insights, numerical examples arepresentedwhicharethencomparedtotheresultsobtainedbyconsideringanexact (non-approximated) backlogging rate (from literature). The comparisons indicate high quality results for the approximated model.

scholarly journals Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds

2018 ◽  
Vol 168 (1) ◽  
pp. 29-41 ◽  
Author(s):  
JOONAS ILMAVIRTA ◽  
JERE LEHTONEN ◽  
MIKKO SALO
Keyword(s):  
Higher Dimensions ◽  
Uniqueness Result ◽  
Constant Function ◽  
Piecewise Constant Function ◽  
Two Dimensional ◽  
Local Uniqueness ◽  
Piecewise Constant ◽  
Convex Boundary ◽  
X Ray ◽  
Strictly Convex

AbstractWe show that on a two-dimensional compact nontrapping manifold with strictly convex boundary, a piecewise constant function is determined by its integrals over geodesics. In higher dimensions, we obtain a similar result if the manifold satisfies a foliation condition. These theorems are based on iterating a local uniqueness result. Our proofs are elementary.

scholarly journals Existence and Uniqueness of Positive Solutions for a Fractional Switched System

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zhi-Wei Lv ◽  
Bao-Feng Chen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Constant Function ◽  
Switched System ◽  
Piecewise Constant Function ◽  
Piecewise Constant

We discuss the existence and uniqueness of positive solutions for the following fractional switched system: (Dc0+αu(t)+fσ(t)(t,u(t))+gσ(t)(t,u(t))=0,t∈J=[0,1]);(u(0)=u′′(0)=0,u(1)=∫01u(s) ds), whereDc0+αis the Caputo fractional derivative with2<α≤3,σ(t):J→{1,2,…,N}is a piecewise constant function depending ont, andℝ+=[0,+∞),  fi,gi∈C[J×ℝ+,ℝ+],i=1,2,…,N. Our results are based on a fixed point theorem of a sum operator and contraction mapping principle. Furthermore, two examples are also given to illustrate the results.

scholarly journals DEFINITION, PROPERTIES AND WAVELET ANALYSIS OF MULTISCALE FRACTIONAL BROWNIAN MOTION

Fractals ◽  
2007 ◽  
Vol 15 (01) ◽  
pp. 73-87 ◽  
Author(s):  
JEAN-MARC BARDET ◽  
PIERRE BERTRAND
Keyword(s):  
Brownian Motion ◽  
Wavelet Analysis ◽  
Fractional Brownian Motion ◽  
Long Memory ◽  
Constant Function ◽  
Piecewise Constant Function ◽  
Model Data ◽  
Fractional Brownian Motions ◽  
Piecewise Constant ◽  
Functional Central Limit

In some applications, for instance, finance, biomechanics, turbulence or internet traffic, it is relevant to model data with a generalization of a fractional Brownian motion for which the Hurst parameter H is dependent on the frequency. In this contribution, we describe the multiscale fractional Brownian motions which present a parameter H as a piecewise constant function of the frequency. We provide the main properties of these processes: long-memory and smoothness of the paths. Then we propose a statistical method based on wavelet analysis to estimate the different parameters and prove a functional Central Limit Theorem satisfied by the empirical variance of the wavelet coefficients.

scholarly journals Predictive Geometric Models for Heat-Insulation Properties of Semi-Finished Fur and Down Products

2021 ◽  
Author(s):  
Victor Yurkov ◽  
Elena Dolgova ◽  
Margarita Chizhik
Keyword(s):  
Predictive Models ◽  
Heat Insulation ◽  
Constant Function ◽  
Piecewise Constant Function ◽  
Light Industry ◽  
Piecewise Constant ◽  
Geometric Models ◽  
Input And Output ◽  
Component Systems ◽  
Geometric Simulation

This paper is devoted to geometric simulation of heat-insulation properties of fur and down products which are considered as multi-parameter and multi-component systems. We consider predictive models of heat resistance depended on physical characteristics of fur and pelt. There is a problem of construction co-ordinate geometric models on condition that the set of experimental data is limited. We solve the problem as a problem for static multi-component systems. The model is considered as a piecewise constant function in the space of input and output parameters. The paper proposes an algorithm of construction the clusters on the set of given experimental points. Moreover, we construct multidimensional convex covering on the set of the points. The covering is based on its two-dimensional projections. Results of the investigations allow us to substantiate producer’s choice of fur and down semi-finished products and its composition for manufacturing the product of special purpose. The method suggested in the paper may be one of geometric modulus of the software HYPER-DESCENT which has been developed formerly. Our geometric models together with software HYPER- DESCENT may be applied for simulation and prediction the properties of another multi- parametrical systems or technological processes of light industry.

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