Four Mappings Satisfying Ψ-Contractive Type Condition and Having Unique Common Fixed Point on 2-Metric Spaces

In this paper, we introduce a class Ψ of real functions defined on the set of non-negative real numbers, and obtain a new unique common fixed point theorem for four mappings satisfying Ψ-contractive condition on a non-complete 2-metric space and give the versions of the corresponding result for two and three mappings.

Improving Electrochemical Performance of Cellulose Fiber-based Supercapacitor Electrode Using Polypyrrole-wrapped Iron Oxyhydroxide

Polypyrrole(PPy)@cellulose fiber-based composites have been widely investigated as electrode materials for use in flexible supercapacitors.However,they cannot readily provide high specific capacitance and cyclic stability owing to their inherent drawbacks,such as high resistance,Weber impedance,and volume expansion or collapse during charging/discharging.In this study,iron oxyhydroxide(FeOOH)is incorporated in the abovementioned composite to decrease the equivalent series resistance,charge transfer resistance,and Weber impedance,thereby enhancing electron transfer and ion diffusion,which results in superior electrochemical performance.The PPy-wrapped FeOOH@cellulose fiber-based composite electrode with the molar ratio of FeSO_(4) to NaBH4 of 1∶1 exhibits a high specific capacitance of 513.8 F/g at a current density of 0.2 A/g,as well as an excellent capacitance retention of 89.4% after 1000 cycles.

Fixed Points and Common Fixed Points of Quasi-Contractive Mappings on Partially Ordered-Cone Metric Spaces

In this paper, we use the mappings with quasi-contractive conditions, defined on a partially ordered set with cone metric structure, to construct convergent sequences and prove that the limits of the constructed sequences are the unique (common) fixed point of the mappings, and give their corollaries. The obtained results improve and generalize the corresponding conclusions in references.

The p.q.-Baer Property of Skew Group Rings under Finite Group Action

In this paper, Let R is a ring, G be a finite group of ring automorphisms of R. R*G denote the skew group ring of R under G. We investigate the right p.q.-Baer property of skew group rings under finite group action, Assume that R is a semiprime ring with a finite group G of X-outer ring automorphisms of R, then 1) R*G is p.q.-Baer if and only if R is G-p.q.-Baer;2) if R is p.q.-Baer, then R*G is p.q.-Baer.

The p.q.-Baer Property of Fixed Rings under Finite Group Action

A ring R is called right principally quasi-Baer (simply, right p.q.-Baer) if the right annihilator of every principal right ideal of R is generated by an idempotent. For a ring R, let G be a finite group of ring automorphisms of R. We denote the fixed ring of R under G by RG. In this work, we investigated the right p.q.-Baer property of fixed rings under finite group action. Assume that R is a semiprime ring with a finite group G of X-outer ring automorphisms of R. Then we show that: 1) If R is G-p.q.-Baer, then RG is p.q.-Baer;2) If R is p.q.-Baer, then RG are p.q.-Baer.

The (Quasi-)Baerness of Skew Group Ring and Fixed Ring

In this paper, the (quasi-)Baerness of skew group ring and fixed ring is investigated. The following two results are obtained: if R is a simple ring with identity and G an outer automorphism group, then R G is a Baer ring;if R is an Artinian simple ring with identity and G an outer automorphism group, then RG is a Baer ring. Moreover, by decomposing Morita Context ring and Morita Context Theory, we provided several conditions of Morita Context ring, which is formed of skew group ring and fixed ring, to be (quasi-)Baer ring.

The Some Properties of Skew Polynomial Rings

This paper mainly studies some properties of skew polynomial ring related to Morita invariance, Armendariz and (quasi)-Baer. First, we show that skew polynomial ring has no Morita invariance by the counterexample. Then we prove a necessary condition that skew polynomial ring constitutes Armendariz ring. We lastly investigate that condition of skew polynomial ring is a (quasi)-Baer ring, and verify that the conditions is necessary, but not sufficient by example and counterexample.

Performance of automated CT ASPECTS in comparison to physicians at different levels on evaluating acute ischemic stroke at a single institution in China

Background:Our aim was to evaluate the sensitivity and specificity of the automated computer-based Alberta Stroke Program Early CT Score(e-ASPECTS)for acute stroke patients and compare the result with physicians at different levels.Methods:In our center,e-ASPECTS and 9 physicians at different levels retrospectively and blindly assessed baseline computed tomography(CT)images of 55 patients.Sensitivity,specificity,receiver-operating characteristic curves,Bland–Altman plots with mean score error,and Matthews correlation coefficients were calculated.Comparisons were made between the scores by physicians and e-ASPECTS with diffusion-weighted imaging(DWI)being the ground truth.Two methods for clustered data were used to estimate sensitivity and specificity in the region-based analysis.Results:In total,1100(55 patients×20 regions per patient)ASPECTS regions were scored.In the region-based analysis,sensitivity of e-ASPECTS was better than junior doctors and residents(0.576 vs 0.165 and 0.111,p<0.05)but inferior to senior doctors(0.576 vs 0.617).Specificity was lower than junior doctors and residents(0.883 vs 0.971 and 0.914)but higher than senior doctors(0.883 vs 0.809,p<0.05).E-ASPECTS had the best Matthews correlation coefficient of 0.529,compared to senior doctors,junior doctors,and residents(0.463,0.251,and 0.087,respectively).Conclusions:e-ASPECTS showed a similar performance to that of senior physicians in the assessment of brain CT of acute ischemic stroke patients with the Alberta Stroke Program Early CT score method.

Remarks on Centers of Rings

It is proved that for matrices A,B in the n by n upper triangular matrix ring T_(n)(R)over a domain R,if AB is nonzero and central in T_(n)(R)then AB=BA.The n by n full matrix rings over right Noetherian domains are also shown to have this property.In this article we treat a ring property that is a generalization of this result,and a ring with such a property is said to be weakly reversible-over-center.The class of weakly reversible-over-center rings contains both full matrix rings over right Noetherian domains and upper triangular matrix rings over domains.The structure of various sorts of weakly reversible-over-center rings is studied in relation to the questions raised in the process naturally.We also consider the connection between the property of being weakly reversible-over-center and the related ring properties.

A Property Satisfying Reducedness over Centers

This article concerns a ring property called pseudo-reduced-over-center that is satisfied by free algebras over commutative reduced rings.The properties of radicals of pseudo-reduced-over-center rings are investigated,especially related to polynomial rings.It is proved that for pseudo-reduced-over-center rings of nonzero characteristic,the centers and the pseudo-reduced-over-center property are preserved through factor rings modulo nil ideals.For a locally finite ring R,it is proved that if R is pseudo-reduced-over-center,then R is commutative and R/J(R)is a commutative regular ring with J(R)nil,where J(R)is the Jacobson radical of R.