Fixed points of multivalued quasi-nonexpansive mappings using a faster iterative process

In this article, we prove some strong and weak convergence theorems for quasi-nonexpansive multivalued mappings in Banach spaces. The iterative process used is independent of Ishikawa iterative process and converges faster. Some examples are provided to validate our results. Our results extend and unify some results in the contemporary literature.     

Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings

The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappin...     

Synthesis and characterization of dimeric μ-oxidovanadium complexes as the functional model of vanadium bromoperoxidase

Two vanadium (IV) complexes [V^IVO(Haeae-sal)(MeOH)]⁺ ( 1 ) and [V^IVO(Haeae-hyap)(MeOH)]⁺ ( 2 ) were prepared by reacting [VO(acac)₂] with ligands [H₂aeae-sal] ( I ) and [H₂aeae-hyap] ( II ) respectively. Condensation of 2-(2-aminoethylamino)ethanol with salicylaldehyde and 2-hydroxyacetophenone produces the ligands ( I ) and ( II ) respectively. Both vanadium complexes 1 and 2 are sensitive towards aerial oxygen in solution and rapidly convert into vanadium(V) dioxido species. Vanadium(V) dioxido species crystalizes as the dimeric form in the solid-state. Single-crystal XRD analysis suggests octahedral geometry around each vanadium center in the solid-state. To access the benefits of heterogeneous catalysis, vanadium(V) dioxido complexes were anchored into the polymeric chain of chloromethylated polystyrene. All the synthesized neat and supported vanadium complexes have been studied by a number of techniques to confirm their structural and functional properties. Bromoperoxidase activity of the synthesized vanadium(V) dioxido complexes 3 and 4 was examined by carrying out oxidative bromination of salicylaldehyde and oxidation of thioanisole. In the presence of hydrogen peroxide, 3 shows 94.4% conversion ( TOF value of 2.739 × 10² h⁻¹) and 4 exhibits 79.0% conversion (TOF value of 2.403 × 10² h⁻¹) for the oxidative bromination of salicylaldehyde where 5-bromosalicylaldehyde appears as the major product. Catalysts 3 and 4 also efficiently catalyze the oxidation of thioanisole in the presence of hydrogen peroxide where sulfoxide is observed as the major product. Covalent attachment of neat catalysts 3 and 4 into the polymer chain enhances substrate conversion (%) and their catalytic efficiency increases many folds, both in the oxidative bromination and oxidation of thioether. Polymer supported catalysts 5 displayed 98.8% conversion with a TOF value of 1.127 × 10⁴ h⁻¹ whereas catalyst 6 showed 95.7% conversion with a TOF value of 4.675 × 10³ h⁻¹ for the oxidative bromination of salicylaldehyde. These TOF values are the highest among the supported vanadium catalysts available in the literature for the oxidative bromination of salicylaldehyde.     

Hybrid projection method for generalized mixed equilibrium problem and fixed point problem of infinite family of asymptotically quasi-?-nonexpansive mappings in Banach spaces

In this paper, we consider a hybrid projection method for finding a common element in the set of fixed points of a infinite family of asymptotically quasi-?-nonexpansive mappings and in the set of solutions of a generalized mixed equilibrium problem. Some strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. The results presented in the paper improve and extend some recent results.     

广义黏性逼近方法及其应用

黏性逼近方法在非扩张映射不动点问题的研究中扮演着重要的角色。提出了一类广义黏性逼近方法，在一定条件下，证明了该算法的收敛性.作为应用，将所得的收敛性结果应用于求解约束凸优化问题与双层优化问题。     

On geodesic mappings of equidistant generalized Riemannian spaces

In this paper geodesic mappings of equidistant generalized Riemannian spaces are discussed. It is proved that each equidistant generalized Riemannian space of basic type admits non-trivial geodesic mapping with preserved equidistant congruence. Especially, there exists non-trivial geodesic mapping of equidistant generalized Riemannian space onto equidistant Riemannian space. An example of geodesic mapping of an equidistant generalized Riemannian spaces is presented.     

Characterizing affinity epitopes between prion protein and β-amyloid using an epitope mapping immunoassay

Cellular prion protein, a membrane protein, is expressed in all mammals. Prion protein is also found in human blood as an anchorless protein, and this protein form is one of the many potential sources of misfolded prion protein replication during transmission. Many studies have suggested that β-amyloid_1–42 oligomer causes neurotoxicity associated with Alzheimer''s disease, which is mediated by the prion protein that acts as a receptor and regulates the hippocampal potentiation. The prevention of the binding of these proteins has been proposed as a possible preventative treatment for Alzheimer''s disease; therefore, a greater understanding of the binding hot-spots between the two molecules is necessary. In this study, the epitope mapping immunoassay was employed to characterize binding epitopes within the prion protein and complementary epitopes in β-amyloid. Residues 23–39 and 93–119 in the prion protein were involved in binding to β-amyloid_1–40 and _1–42, and monomers of this protein interacted with prion protein residues 93–113 and 123–166. Furthermore, β-amyloid antibodies against the C-terminus detected bound β-amyloid_1–42 at residues 23–40, 104–122 and 159–175. β-Amyloid epitopes necessary for the interaction with prion protein were not determined. In conclusion, charged clusters and hydrophobic regions of the prion protein were involved in binding to β-amyloid_1–40 and _1–42. The 3D structure appears to be necessary for β-amyloid to interact with prion protein. In the future, these binding sites may be utilized for 3D structure modeling, as well as for the pharmaceutical intervention of Alzheimer''s disease.     

Construction of conformal mappings by generalized polarization tensors

We present a new systematic method to compute the Riemann mapping from the outside of the unit disc to the outside of a simply connected domain. We derive explicit relations between the coefficients of the Riemann mapping and the generalized polarization tensors associated with the domain. Because the generalized polarization tensors can be computed numerically, we are able to compute the coefficients of the Riemann mapping using these relations. Effectiveness of the method is validated by numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of monoclonal antibody by a novel CE‐UV/MALDI‐MS interface

mAbs are highly complex proteins that present a wide range of microheterogeneity that requires multiple analytical methods for full structure assessment and quality control. As a consequence, the characterization of mAbs on different levels is particularly product‐ and time‐consuming. CE‐MS couplings, especially to MALDI, appear really attractive methods for the characterization of biological samples. In this work, we report the last instrumental development and performance of the first totally automated off‐line CE‐UV/MALDI‐MS/MS. This interface is based on the removal of the original UV cell of the CE apparatus, modification of the spotting device geometry, and creation of an integrated delivery matrix system. The performance of the method was evaluated with separation of five intact proteins and a tryptic digest mixture of nine proteins. Intact protein application shows the acquisition of electropherograms with high resolution and high repeatability. In the peptide mapping approach, a total number of 154 unique identified peptides were characterized using MS/MS spectra corresponding to average sequence coverage of 64.1%. Comparison with NanoLC/MALDI‐MS/MS showed complementarity at the peptide level with an increase of 42% when using CE/MALDI‐MS coupling. Finally, this work represents the first analysis of intact mAb charge variants by CZE using an MS detection. Moreover, using a peptide mapping approach CE‐UV/MALDI‐MS/MS fragmentation allowed 100% sequence coverage of the light chain and 92% of the heavy chain, and the separation of four major glycosylated peptides and their structural characterization.