Inertial subgradient extragradient algorithms with line-search process for solving variational inequality problems and fixed point problems

Numerical Algorithms - In this paper, basing on the subgradient extragradient method and inertial method with line-search process, we introduce two new algorithms for finding a common element of...     

Some extragradient-viscosity algorithms for solving variational inequality problems and fixed point problems

Numerical Algorithms - The purpose of this paper is to study and analyze two different kinds of extragradient-viscosity-type iterative methods for finding a common element of the set of solutions...     

Amyloid peptide Aβ40 inhibits aggregation of Aβ42: evidence from molecular dynamics simulations

Effects of amyloid beta (Aβ) peptide Aβ(40) on secondary structures of Aβ(42) are studied by all-atom simulations using the GROMOS96 43a1 force field with explicit water. It is shown that in the presence of Aβ(40) the beta-content of monomer Aβ(42) is reduced. Since the fibril-prone conformation N? of full-length Aβ peptides has the shape of beta strand-loop-beta strand this result suggests that Aβ(40) decreases the probability of observing N? of Aβ(42) in monomer state. Based on this and the hypothesis that the higher is the population of N? the higher fibril formation rates, one can expect that, in agreement with the recent experiment, Aβ(40) inhibit fibril formation of Aβ(42). It is shown that the presence of Aβ(40) makes the salt bridge D23-K28 and fragment 18-33 of Aβ(42) more flexible providing additional support for this experimental fact. Our estimation of the binding free energy by the molecular mechanics-Poisson-Boltzmann surface area method reveals the inhibition mechanism that Aβ(40) binds to Aβ(42) modifying its morphology.     

Singular integrals with mixed homogeneity in Triebel-Lizorkin spaces

In this paper, we study the singular integral

     

Modified subgradient extragradient algorithms for variational inequality problems and fixed point problems

The subgradient extragradient method can be considered as an improvement of the extragradient method for variational inequality problems for the class of monotone and Lipschitz continuous mappings. In this paper, we propose two new algorithms as combination between the subgradient extragradient method and Mann-like method for finding a common element of the solution set of a variational inequality and the fixed point set of a demicontractive mapping.     

Discrete internal space and its visibility

In this paper we consider a version of extended space-time with the internal space of two discrete points. A complex metric structure for the internal space is suggested in order to use a common generalized differential calculus and a common wedge product for both gravity and the Standard Model. In this extended space-time there are some testable predictions near the electroweak energy scale: the Higgs mass of 350 GeV and the existence of a scalar particle from the gravity sector with mass of 440 GeV.     

Preinjective modules over pure semisimple rings

For a left pure semisimple ring R, it is shown that the local duality establishes a bijection between the preinjective left R-modules and the preprojective right R-modules, and any preinjective left R-module is the source of a left almost split morphism. Moreover, if there are no nonzero homomorphisms from preinjective modules to non-preinjective indecomposable modules in R-mod, the direct sum of all non-preinjective indecomposable direct summands of products of preinjective left R-modules is a finitely generated product-complete module. This generalizes a recent theorem of Angeleri Hügel [L. Angeleri Hügel, A key module over pure-semisimple hereditary rings, J. Algebra 307 (2007) 361-376] for hereditary rings.