Influence of deformation path on the forming effect in a multistep flexible rolling process

The flexible rolling process(FRP) is a novel three-dimensional(3 D) forming process that combines the multipoint and traditional rolling forming. The principle of FRP is based on thickness thinning, so the deformation path significantly impacts the forming effect. In this study, the multistep forming process with different deformation paths was introduced to improve the forming effect of FRP. For instance, with the convex surface part, three finite element models of multistep FRP(MSFRP) were established. The corresponding numerical simulations and forming experiments performed among different deformation paths showed the surface part with a longer effective forming region was obtained and the forming regions with more steps in MSFRP were smoother. Thus, the sheet-metal utilization rate was greatly improved. Moreover, the MSFRP can improve the longitudinal bending effect dramatically and thereby endowing the forming part with a better forming effect. Therefore, MSFRP is a prospective method for broad applications.

Multistep hepatocarcinogenesis from a dysplastic nodule to well-differentiated hepatocellular carcinoma in a patient with alcohol-related liver cirrhosis

We describe a rare case of the transformation of a dysplastic nodule into well-differentiated hepato- cellular carcinoma (HCC) in a 56-year-old man with alcoholrelated liver cirrhosis. Ultrasound (US) disclosed a 10 mm hypoechoic nodule and contrast enhanced US revealed a hypovascular nodule, both in segment seven. US-guided biopsy revealed a high-grade dysplastic nodule characterized by enhanced cellularity with a high N/C ratio, increased cytoplasmic eosinophilia, and slight cell atypia. One year later, the US pattern of the nodule changed from hypoechoic to hyperechoic without any change in size or hypovascularity. US-guided biopsy revealed well-differentiated HCC of the same features as shown in the first biopsy, but with additional pseudoglandular formation and moderate cell atypia. Moreover, immunohistochemical staining of cyclase- associated protein 2, a new molecular marker of well- differentiated HCC, turned positive. This is the first case of multistep hepatocarcinogenesis from a dysplastic nodule to well-differentiated HCC within one year in alcohol-related liver cirrhosis.

Delay-dependent stability of linear multistep methods for differential systems with distributed delays

This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.

NGP_G-STABILITY OF LINEAR MULTISTEP METHODS FOR SYSTEMS OF GENERALIZED NEUTRAL DELAY DIFFERENTIAL EQUATIONS

The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.

Generalized Square Conservative Multistep Finite Difference Scheme Incorporating Historical Observations

In this paper,a multistep finite difference scheme has been proposed,whose coefficients are determined taking into consideration compatibility and generalized quadratic conservation,as well as incorporating historical observation data.The schemes have three advantages:high-order accuracy in time,generalized square conservation,and smart use of historical observations.Numerical tests based on the one-dimensional linear advection equations suggest that reasonable consideration of accuracy,square conservation,and inclusion of historical observations is critical for good performance of a finite difference scheme.

Multistep-ahead River Flow Prediction using LS-SVR at Daily Scale

In this study, potential of Least Square-Support Vector Regression (LS-SVR) approach is utilized to model the daily variation of river flow. Inherent complexity, unavailability of reasonably long data set and heterogeneous catchment response are the couple of issues that hinder the generalization of relationship between previous and forthcoming river flow magnitudes. The problem complexity may get enhanced with the influence of upstream dam releases. These issues are investigated by exploiting the capability of LS-SVR–an approach that considers Structural Risk Minimization (SRM) against the Empirical Risk Minimization (ERM)–used by other learning approaches, such as, Artificial Neural Network (ANN). This study is conducted in upper Narmada river basin in India having Bargi dam in its catchment, constructed in 1989. The river gauging station–Sandia is located few hundred kilometer downstream of Bargi dam. The model development is carried out with pre-construction flow regime and its performance is checked for both pre- and post-construction of the dam for any perceivable difference. It is found that the performances are similar for both the flow regimes, which indicates that the releases from the dam at daily scale for this gauging site may be ignored. In order to investigate the temporal horizon over which the prediction performance may be relied upon, a multistep-ahead prediction is carried out and the model performance is found to be reasonably good up to 5-day-ahead predictions though the performance is decreasing with the increase in lead-time. Skills of both LS-SVR and ANN are reported and it is found that the former performs better than the latter for all the lead-times in general, and shorter lead times in particular.

ALTERNATING-DIRECTION MULTISTEP PRECONDITIONED ITERATIVE METHODS FOR SEMICONDUCTOR PROBLEM WITH HEAT-CONDUCTION

The model of transient behavior of semiconductor with heat-conduction is an initial and boundary problem. Alternating-direction multistep preconditioned iterative methods and theory analyses are given in this paper. Electric potential equation is approximated by mixed finite element method, concentration and heat-conduction equations are approximated by Galerkin alternating-direction multistep methods. Error estimates of optimal order in L2 are demonstrated.

IMPLICIT-EXPLICIT MULTISTEP FINITE ELEMENT-MIXED FINITE ELEMENT METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived.

Stability of linear multistep methods for delay differential equations in the light of Kreiss resolvent condition

This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classical scalar test problem of the form y′(t)=λy(t)+μy(t-τ) with τ>0 and λ,μ are complex, by using (vartiant to) the resolvent condition of Kreiss. We prove that for A stable LM methods the upper bound for the norm of the n th power of square matrix grows linearly with the order of the matrix.

Geometric representation for numerical stability region of linear multistep methods

Studies the numerical stability region of linear multistep(LM) methods applied to linear test equation of the form y′(t)=ay(t)+by(t-1), t>0, y(t)=g(t)-1≤t≤0, a,b∈R, proves through delay dependent stability analysis that the intersection of stability regions of the equation and the method is not empty, in addition to approaches to the boundary of the delay differential equation(DDEs) in the limiting case of step size boundary of the stability region of linear multistep methods.

Algebraic Stability of Multistep Runge-Kutta Methods

A series of sufficient and necessary conditions for the algebraic stability of multistepRunge-Kutta methods is obtained, most of which can be regarded as extension of the relevant results available for Runge-Kutta methods, especially, for Radau Ⅰ A, Radau Ⅱ A and Gaussian Runge-Kutta methods.

Numerical Integration of Forced and Damped Oscillators through a New Multistep Method

Forced and damped oscillators appear in the mathematical modelling of many problems in pure and applied sciences such as physics, engineering and celestial mechanics among others. Although the accuracy of the T-functions series method is high, the calculus of their coefficients needs specific recurrences in each case. To avoid this inconvenience, the T-functions series method is transformed into a multistep method whose coefficients are calculated using recurrence procedures. These methods are convergent and have the same properties to the T-functions series method. Numerical examples already used by other authors are presented, such as a stiff problem, a Duffing oscillator and an equatorial satellite problem when the perturbation comes from zonal harmonics J2.

Stability analysis of linear multistep methods for neutral delay differential equations

The stability analysis of linear multistep (LM) methods is carried out under Kreiss resolvent condition when they are applied to neutral delay differential equations of the form y′(t)=ay(t)+by(t-τ)+ cy′(t- τ) y(t)=g(t) -τ≤t≤0 with τ>0 and a, b and c∈, and it is proved that the ‖B n‖ is suitably bounded, where B is the companion matrix.

High Order Semi-implicit Multistep Methods for Time-Dependent Partial Differential Equations

We consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where the separation of scales in additive form,typically used in implicit-explicit(IMEX)methods,is not possible.As shown in Boscarino et al.(J.Sci.Comput.68:975-1001,2016)for Runge-Kutta methods,these semi-implicit techniques give a great flexibility,and allow,in many cases,the construction of simple linearly implicit schemes with no need of iterative solvers.In this work,we develop a general setting for the construction of high order semi-implicit linear multistep methods and analyze their stability properties for a prototype lineal'advection-diffusion equation and in the setting of strong stability preserving(SSP)methods.Our findings are demonstrated on several examples,including nonlinear reaction-diffusion and convection-diffusion problems.

THE APPLICATION OF MICROELECTRODE TO THE STUDY OF MULTISTEP ELECTRODE PROCESSES UNDER STEADY STATE CONDITIONS PART I EE MECHANISM

Under steady-state conditions, the general currents of EE reactions at disk,hemispherical and spherical microelectrodes are derived.From these equations, some electrode reaction parameters can be very simply obtained.

Dissipativity of Multistep Runge-Kutta Methods for Nonlinear Neutral Delay-Integro-Differential Equations with Constrained Grid

This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear neutral delay-integro-differential equations.We investigate the dissipativity properties of-algebraically stable multistep Runge-Kutta methods with constrained grid.The finite-dimensional and infinite-dimensional dissipativity results of-algebraically stable multistep Runge-Kutta methods are obtained.

Progress on Studies of Quantum Multistep Theory

After considering the transitions from P to Q chains,a new formula for the multistepcompound reaction double differential cross-section is given.The new formula includes theMSC’s and CN’s contributions.The n-step(n】1)multistep direct reaction double differentialcross section is expressed by two one-step double differential cross-sections.

The Equivalence of Ishikawa-Mann and Multistep Iterations in Banach Space

Let E be a real Banach space and T be a continuous Φ-strongly accretive operator. By using a new analytical method, it is proved that the convergence of Mann, Ishikawa and three-step iterations are equivalent to the convergence of multistep iteration. The results of this paper extend the results of Rhoades and Soltuz in some aspects.

Multistep Desolvation as a Fundamental Principle Governing Peptide Self-Assembly Through Liquid-Liquid Phase Separation

Biomolecular self-assembly based on peptides and proteins is a general phenomenon encountered in natural and synthetic systems.Liquid–liquid phase separation(LLPS)is intimately involved in biomolecular self-assembly,yet the key factors at a molecular scale activating or modulating such a process remain largely elusive.Herein,we discovered in our experiments that multistep desolvation is fundamental to the formation and evolution of peptide-rich droplets:The first step was partial desolvation of peptides to form peptide clusters,and the second step was selective desolvation of hydrophobic groups within clusters to trigger LLPS and the formation of peptiderich droplets,followed by complete desolvation of droplets,initiating the nucleation of peptide selfassembly.Manipulation of the degree of desolvation at different stages was an effective strategy to control the self-assembly pathways and polymorphisms.This study sheds light on the molecular origin of LLPS-mediated self-assembly distinct from classical one-step self-assembly and paves the way for the precise control of supramolecular self-assembly.

STABILITY AND CONVERGENCE OF STEPSIZE-DEPENDENT LINEAR MULTISTEP METHODS FOR NONLINEAR DISSIPATIVE EVOLUTION EQUATIONS IN BANACH SPACE

Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by ω-dissipative vector fields in Banach space.To break through the order barrier p≤1 of unconditionally contractive linear multistep methods for dissipative systems,strongly dissipative systems are introduced.By employing the error growth function of the methods,new contractivity and convergence results of stepsize-dependent linear multistep methods on infinite integration intervals are provided for strictly dissipative systems(ω<0)and strongly dissipative systems.Some applications of the main results to several linear multistep methods,including the trapezoidal rule,are supplied.The theoretical results are also illustrated by a set of numerical experiments.