Abstract:
Using -strongly accretive and -strictly pseudocontractive mapping, we introduce a general iterative method for finding a common fixed point of a semigroup of non-expansive mappings in a Hilbert space, with respect to a sequence of left regular means defined on an appropriate space of bounded real-valued functions of the semigroup. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality.

Abstract:
Using the fixed point method, we prove the generalized Hyers-Ulam stability of ？-algebra homomorphisms and of generalized derivations on ？-algebras for the following functional equation of Apollonius type _=1_(_)=_(1/)___1_<__(

Abstract:
Introduction:. With regard to the interactions between brain and spleen, in this research, the effect of splenectomy on PTZ-induced epilepsy in Wistar rats was studied Methods:. In this study, 48 male and female wistar rats were used in 3 groups. Experimental groups for each of the two sexes included the negative control, positive control and splenectomy. Negative controls did not undergo surgery. The incision was created in the positive control group, but the spleen was not removed. The spleen was removed in splenectomy group. After seven days, PTZ was injected and the initiation time of different convulsive stages in terms of seconds and score of seizures in the three groups with the same gender were compared using one-way ANOVA. Results:. Second stage of convulsive seizures in the splenectomy group of male rats in comparison with control groups decreased significantly. Fourth stage of seizure in female splenectomized rats in comparison with negative control group decreased significantly. Also score terms of seizures in both male and female rats were not significantly different in the three groups.. Conclusion: Splenectomy intensifies PTZ-induced seizures in Wistar rats.

Abstract:
We consider weighted composition operators on spaces of analytic functions on the unit disc, which take values in some complex Banach space. We provide necessary and sufficient conditions for the boundedness and (weak) compactness of weighted composition operators on general function spaces, and in particular on weak vector-valued spaces. As an application, we characterize the weak compactness of these operators between two different vector-valued Bloch-type spaces. This result appears to be new also in the scalar-valued case.

Abstract:
The current study was an attempt to investigate the similarities and differences in using the speech act of refusing between Persian learners of English as a foreign language with some Persian native speakers in Iran. The data of this study was gathered from thirty students in Iran by discourse completion questionnaire, usual interaction, and role play. On the whole, the research findings revealed that Persian native speakers’ refusals were as formulaic in pragmatic structures. These participants were not economical at making excuses and tended to offer different indirect reasons in refusal to avoid annoyance. On the other hand, Iranian EFL learners are more frank and are more likely to refuse their friends’ requests, suggestions, and invitations. Moreover, social distance and power play a vital role in production of refusal among Persian native speakers. More detailed findings and implications are discussed in the paper. Key words: Speech Act; Refusal; Speech Act Of Refusal; Discourse Completion Test (DCT); Persian Native Speakers; Iranian EFL Learners Resumé: La présente étude a tenté d'étudier les similitudes et les différences dans l'utilisation de l'acte de discours de refus entre les persans qui apprennent l'anglais comme une langue étrangère et certains locuteurs natifs persans en Iran. Les données de cette étude ont été recueillies à partir d'une trentaine d'étudiants en Iran en utilisant le questionnaire de complétion de discours, l'interaction habituelle, et le jeu de r le. Dans l'ensemble, les résultats de recherche ont révélé que les refus des locuteurs natifs persans étaient formalisés dans les structures pragmatiques. Ces participants ne sont pas laconiques à faire des excuses et ont tendance à offrir de différentes raisons indirectes comme refus afin d'éviter des désagréments. D'autre part, les apprenants ALE iraniens sont plus francs et plus susceptibles de refuser les demandes, les suggestions et des invitations de leurs amis. Par ailleurs, la distance sociale et le pouvoir jouent un r le vital dans la fabrication de refus chez les locuteurs natifs persans. Des résultats plus détaillés et des implications sont discutées dans l'article. Mots-clés: Acte De Discours; Refus; Acte De Discours De Refus; Test De CompléTion De Discours (TCD); Locuteurs Natifs Persans; Apprenants ALE Iraniens

Abstract:
In this paper, we introduce a two-dimensional fractional topological superconductor (FTSC) as a strongly correlated topological state which can be achieved by inducing superconductivity into an Abelian fractional quantum Hall state, through the proximity effect. When the proximity coupling is weak, the FTSC has the same topological order as its parent state and is thus Abelian. However, upon increasing the proximity coupling, the bulk gap of such an Abelian FTSC closes and reopens resulting in a new topological order: a non-Abelian FTSC. Using several arguments we will conjecture that the conformal field theory (CFT) that describes the edge state of the non-Abelian FTSC is $U(1)/Z_2$ orbifold theory and use this to write down the ground-state wave function. Further, we predict FTSC based on the Laughlin state at $\nu=1/m$ filling to host fractionalized Majorana zero modes bound to superconducting vortices. These zero modes are non-Abelian quasiparticles which is evident in their quantum dimension of $d_m=\sqrt{2m}$. Using the multi-quasi-particle wave function based on the edge CFT, we derive the projective braid matrix for the zero modes. Finally, the connection between the non-Abelian FTSCs and the $Z_{2m}$ rotor model with a similar topological order is illustrated.

Abstract:
We generalize the Kitaev's spin-1/2 model on the honeycomb by introducing a two-dimensional $Z_3$ clock model on the triangular lattice with three body interaction. We discuss various properties of this model and show that the low energy theory of the $Z_3$ generalized Kitaev model (GKM) is described by a single $Z_3$ parafermion per lattice site coupled to a $Z_3$ gauge field. We also introduce a slave-fermion approach for this GKM, treat the resulting fermionic Hamiltonian at the mean-field level, solve the mean field parameters self-consistently, and obtain the low energy effective Chern-Simons (CS) gauge theory. The resulting CS gauge theory is identical to that of a (221) fractional quantum Hall state. We then go beyond the mean-field approximation and demonstrate that fluctuations generate a uniform interlayer pairing for the dual (221) bilayer state. We argue that this perturbed system can undergo a phase transition to the Fibonacci phase by tuning the interlayer pairing strength.

Abstract:
In this paper, I study the oxygen isotope effect (OIE) in cuprates. I introduce a simple model that can explain experiments both qualitatively and quantitatively. In this theory, isotope substitution only affects the superfluid density, but not the pseudo-gap. Within the spin-charge separation picture, I argue that the spinon-phonon interaction is in the adiabatic limit, and therefore within the Migdal-Eliashberg theory, there is no isotope effect in the spinon mass renormalization. On the other hand, I show that the holon-phonon interaction is in the non-adiabatic limit. Therefore, the small polaron picture is applicable and there is a large mass enhancement in an isotope-dependent way. Our theory explains why upon $^{16}$O/$^{18}$O substitution, the superconducting transition temperature changes only in underdoped cuprates, while there is no considerable OIE at the optimal doped as well as the overdoped cuprates. Additionally, in contrast to the conventional superconductors, we obtain OIE on the superfluid density for whole superconducting region in agreement with the experimental observations.