Quotient probabilistic normed spaces and completeness results

We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.     

Effects of mussel-inspired co-deposition of 2-hydroxymethyl methacrylate and poly (2-methoxyethyl acrylate) on the hydrophilicity and binding tendency of common hemodialysis membranes: Molecular dynamics simulations and molecular docking studies

Despite advances in the field, hemoincompatibility remains a critical issue for hemodialysis (HD) as interactions between various human blood constituents and the polymeric structure of HD membranes results in complications such as activation of immune system cascades. Adding hydrophilic polymer structures to the membranes is one modification approach that can decrease the extent of protein adsorption. This study conducted molecular dynamics (MD) simulations to understand the interactions between three human serum proteins (fibrinogen [FB], human serum albumin, and transferrin) and common HD membranes in untreated and modified forms. Poly(aryl ether sulfone) (PAES) and cellulose triacetate were used as the common dialyzer polymers, and membrane modifications were performed with 2-hydroxymethyl methacrylate (HEMA) and poly (2-methoxyethyl acrylate) (PMEA), using polydopamine-assisted co-deposition. The MD simulations were used as the framework for binding energy simulations, and molecular docking simulations were also performed to conduct molecular-level investigations between the two modifying polymers (HEMA and PMEA) and FB. Each of the three proteins acted differently with the membranes due to their unique nature and surface chemistry. The simulations show PMEA binds less intensively to FB with a higher number of hydrogen bonds, which reflects PMEA's superior performance compared to HEMA. The simulations suggest PAES membranes could be used in modified forms for blood-contact applications as they reflect the lowest binding energy to blood proteins.     

An optode membrane for determination of gold using a simple light-emitting diode-based device

Abstract  

A selective optode based on immobilization of 5-(p-dimethylaminobenzylidene)rhodanine on a triacetylcellulose membrane was developed for quantitative determination of Au(III). The determination procedure was performed using a simple light-emitting diode (LED)-based device as a new effort to overcome low reproducibility and repeatability problems which usually accompany optode-based determinations. The results obtained were compared with those of conventional spectrophotometric methods. The response characteristics of the sensor including dynamic range, reproducibility, response time, and lifetime are discussed in detail. This sensor was used for the determination of Au(III) in ore and electroplating liquid effluent samples with satisfactory results in comparison with flame atomic absorption spectroscopy as standard method. Under the optimum conditions, the calibration plot was linear in the concentration range of 0.3–6.0 μg cm⁻³. The relative standard deviations for five replicate determinations of 1.0 μg cm⁻³ Au(III) and the corresponding limits of detection were 1.76% and 0.12 μg cm⁻³, respectively.     

Some results on the ℒ-fuzzy topological isomorphism

In this paper, we define ℒ-fuzzy boundedness for linear operators and we prove that every finite dimensional ℒ-fuzzy normed space is complete.     

Strong ergodic theorem for commutative semigroup of non-Lipschitzian mappings in multi-Banach space

Let C be a bounded closed convex subset of a uniformly convex multi-Banach space X and let \({\mathfrak {I}}_{j} = \{T_j(t) : t\in G\}\) be a commutative semigroup of asymptotically nonexpansive in the intermediate mapping from C into itself. In this paper, we prove the strong mean ergodic convergence theorem for the almost-orbit of \(\mathfrak {I}\). Our results extend and unify many previously known results especially (Dong et al. On the strong ergodic theorem for commutative semigroup of non-Lipschitzian mappings in Banach space, preprint).     

The stability of an additive functional equation in menger probabilistic <Emphasis Type="Italic">φ</Emphasis>-normed spaces

We establish a stability result concerning the functional equation:

$\sum\limits_{i = 1}^m {f\left( {mx_i + \sum\limits_{j = 1,j \ne i}^m {x_j } } \right) + f\left( {\sum\limits_{i = 1}^m {x_i } } \right) = 2f\left( {\sum\limits_{i = 1}^m {mx_i } } \right)} $

in a large class of complete probabilistic normed spaces, via fixed point theory.

     

Solvent‐free synthesis of new 2,4,6‐triarylpyridines catalyzed by a Brønsted acidic ionic liquid as a green and reusable catalyst

Some new 4‐(aryl)‐2,6‐di‐2‐naphthylpyridines and 4‐(aryl)‐2,6‐di‐2‐thienylpyridines have been prepared through three‐component condensation of 2‐acetylnaphthalene or 2‐acetylthiophene, aromatic aldehydes, and ammonium acetate in presence of 1‐(4‐sulfonylbutyl) pyridinium hydrogensulfate [(CH₂)₄SO₃HPy][HSO₄], a Brønsted acidic ionic liquid as a green and reusable catalyst in solvent‐free conditions. Also some new 4,4'‐(1,4‐phenylene)‐bis‐(2,6‐di‐aryl pyridine) was prepared. J. Heterocyclic Chem., (2011).     

Creation of atomic W state in a cavity by adiabatic passage

We propose two relatively robust schemes to generate controllable (deterministic) atomic W states of three Λ-like atoms interacting with an optical cavity and a laser beam. Losses due to atomic spontaneous emissions and to cavity decay are efficiently suppressed by employing adiabatic passage technique and appropriately designed atom-field couplings. In these schemes the three atoms traverse the cavity-mode and the laser beam and become entangled in the free space outside the cavity.     

直观Menger内积空间及其在积分方程中的应用

首先引出和定义了直观的Menger内积空间的概念,然后在完备的直观的Menger内积空间中得出了一个新的不动点定理.作为应用,利用文中所得的结果,研究了线性Volterra积分方程解的存在性和唯一性.     

Quicksort algorithm: Application of a fixed point theorem in intuitionistic fuzzy quasi-metric spaces at a domain of words

In this paper, we apply an intuitionistic fuzzy quasi-metric version of a fixed point theorem, to obtain the existence of solution for a recurrence equation associated with the analysis of Quicksort algorithms.