An implicit Landweber method for nonlinear ill-posed operator equations

In this paper, we are interested in the solution of nonlinear inverse problems of the form F(x)=y. We propose an implicit Landweber method, which is similar to the third-order midpoint Newton method in form, and consider the convergence behavior of the implicit Landweber method. Using the discrepancy principle as a stopping criterion, we obtain a regularization method for ill-posed problems. We conclude with numerical examples confirming the theoretical results, including comparisons with the classical Landweber iteration and presented modified Landweber methods.     

Study of early stages of amyloid Aβ13-23 formation using molecular dynamics simulation in implicit environments

β-amyloid aggregation and formation of senile plaques is one of the hallmarks of Alzheimer’s disease (AD). It leads to degeneration of neurons and decline of cognitive functions. The most aggregative and toxic form of β-amyloid is Aβ_1-42 but in experiments, the shorter forms able to form aggregates are also used. The early stages of amyloid formation are of special interest due to the influence of this peptide on progression of AD. Here, we employed nine helices of undecapeptide Aβ_13-23 and studied progress of amyloid formation using 500 ns molecular dynamics simulation and implicit membrane environment. The small β-sheets emerged very early during simulation as separated two-strand structures and a presence of the membrane facilitated this process. Later, the larger β-sheets were formed. However, the ninth helix which did not form paired structure stayed unchanged till the end of MD simulation. Paired helix–helix interactions seemed to be a driving force of β-sheet formation at early stages of amyloid formation. Contrary, the specific interactions between α-helix and β-sheet can be very stable and be stabilized by the membrane.     

The implicit standard material theory for modelling the nonassociative behaviour of metals

Summary  Modelling the elastoplastic or elastoviscoplastic behaviour of metallic materials exhibiting strain hardening and damage leads to complex nonassociative constitutive equations, sources of many theoretical and numerical troubles. The usual modelling of a nonassociative constitutive equation leads to the loss of the interesting and very useful properties of generalised standard materials deriving from the key concepts of convexity and normality. The argument that will be developed is that the bipotential concept is an appropriate answer. In the first part, after introducing the state variables generally used to describe the behaviour of metallic materials, the constitutive equations subjected to the principles of thermodynamics are derived from two potentials. The state potential gives the state laws, and the bipotential of dissipation delivers the evolution laws for state variables, through the implicit normality assumption. The second part is devoted to several particular applications to metal elastoplasticity and elastoviscoplasticity models. Received 29 March 2000; accepted for publication 26 September 2000     

A uniformly computable Implicit Function Theorem

We prove uniformly computable versions of the Implicit Function Theorem in its differentiable and non‐differentiable forms. We show that the resulting operators are not computable if information about some of the partial derivatives of the implicitly defining function is omitted. Finally, as a corollary, we obtain a uniformly computable Inverse Function Theorem, first proven by M. Ziegler (2006). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Implicit Multifunction Theorems

We give implicit multifunction results generalizing to multifunctions the Robinson’s implicit function theorem (Robinson, Math Oper Res 16(2):292–309, 1991). To this end, we use parametric error bounds estimates for a suitable function refining the one given in Azé and Corvellec (ESAIM Control Optim Calc Var 10:409–425, 2004). Sharp approximations of the implicit multifunctions are given extending the results of Nachi and Penot (Control Cybernet 35:871–901, 2005). Dedicated to Boris Mordukhovich in honour of his 60th birthday.     

Implicit representation of generalized variable upper bounds in linear programming

In certain linear programs, especially those derived from integer programs, large numbers of constraints may have very simple form. Examples are:x _ij 1 (simple upper bounds [SUB]), _i x _ij = 1 (generalized upper bounds [GUB]) andx _ij y _i (variable upper bounds [VUB]). A class of constraints called generalized VUB [GVUB] is introduced which includes GUB and VUB as special cases. Also introduced is a method for representing GVUB constraints implicitly within the mechanics of the simplex method.Research supported in part by the Mobil Oil Corporation.     

Weak solutions in nonlinear poroelasticity with incompressible constituents

We consider quasi-static nonlinear poroelastic systems with applications in biomechanics and, in particular, tissue perfusion. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid pressure are considered. The system under consideration represents a nonlinear, implicit, degenerate evolution problem, which falls outside of the well-known implicit semigroup monotone theory. Previous literature related to proving existence of weak solutions for these systems is based on constructing solutions as limits of approximations, and energy estimates are obtained only for the constructed solutions. In comparison, in this treatment we provide for the first time a direct, fixed point strategy for proving the existence of weak solutions, which is made possible by a novel result on the uniqueness of weak solutions of the associated linear system (where the permeability is given as a function of space and time). The uniqueness proof for the associated linear problem is based on novel energy estimates for arbitrary weak solutions, rather than just for constructed solutions. The results of this work provide a foundation for addressing strong solutions, as well as uniqueness of weak solutions for nonlinear poroelastic systems.     

隐式Euler法关于Volterra延迟积分方程的数值稳定性

本文涉及隐式Euler法应用于非线性Volterra型延迟积分方程的稳定性,其探讨了基于非经典Lipschitz条件,其方法的整体与渐近稳定性结果被获得。     

Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions

In this paper, we present two optimized eight-step symmetric implicit methods with phase-lag order ten and infinite (phase-fitted). The methods are constructed to solve numerically the radial time-independent Schr?dinger equation with the use of the Woods–Saxon potential. They can also be used to integrate related IVPs with oscillating solutions such as orbital problems. We compare the two new methods to some recently constructed optimized methods from the literature. We measure the efficiency of the methods and conclude that the new method with infinite order of phase-lag is the most efficient of all the compared methods and for all the problems solved. T. E. Simos—Highly Cited Researcher, Active Member of the European Academy of Sciences and Arts.     

COMPUTATION OF NONEQUILIBRIUM HYPERSONIC FLOW OVER CONCAVE CORNERS

1. IntroductionWe consider steady inviscid hyPersonic flow of air about a concave corner including chendcalreaction effects. Computation of nonequllibrium flow is duncult because of the steep gradielltsbehind the shock and an entroPy layer near the body For many cases the time scale of theChemical reactions is 1arger than, or close to, the time scale of the origina1 meChanical problemand the equllibrium chendstry mode1 is not realistic. Therefore, it is necessary to eva1uate thekinetics of c…