Algebraic prime subalgebras in simple Artinian algebras

We prove a Wedderburn-Artin type theorem for algebraic prime subalgebras in simple Artinian algebras, giving a generalized version of Yahaghi’s theorem [B.R. Yahaghi, On F-algebras of algebraic matrices over a subfield F of the center of a division ring, Linear Algebra Appl. 418 (2006) 599-613]. We also show that every semiprime left algebraic subring in a semiprime right Goldie ring must be a semiprime Artinian ring.     

Multiplication operators on sobolev disk algebra

In this paper,we study the algebra consisting of analytic functions in the Sobolev space W~(2,2) (D) (D is the unit disk),called the Sobolev disk algebra,explore the properties of the multiplication operators M_f on it and give the characterization of the corn- mutant algebra A′(M_f) of M_f.We show that A′(M_f) is commutative if and only if M_f~* is a Cowen-Douglas operator of index 1.     

On Modules Over Group Rings

Let M be a right module over a ring R and let G be a group. The set MG of all formal finite sums of the form ∑? _g?∈?G m _g g where m _g ?∈?M becomes a right module over the group ring RG under addition and scalar multiplication similar to the addition and multiplication of a group ring. In this paper, we study basic properties of the RG-module MG, and characterize module properties of (MG) _RG in terms of properties of M _R and G. Particularly, we prove the module-theoretic versions of several well-known results on group rings, including Maschke’s Theorem and the classical characterizations of right self-injective group rings and of von Neumann regular group rings.     

Tail asymptotics of the waiting time and the busy period for the {{\varvec{M/G/1/K}}} queues with subexponential service times

We study the asymptotic behavior of the tail probabilities of the waiting time and the busy period for the $M/G/1/K$ queues with subexponential service times under three different service disciplines: FCFS, LCFS, and ROS. Under the FCFS discipline, the result on the waiting time is proved for the more general $GI/G/1/K$ queue with subexponential service times and lighter interarrival times. Using the well-known Laplace–Stieltjes transform (LST) expressions for the probability distribution of the busy period of the $M/G/1/K$ queue, we decompose the busy period into a sum of a random number of independent random variables. The result is used to obtain the tail asymptotics for the waiting time distributions under the LCFS and ROS disciplines.     

Low‐Dimensional Dion–Jacobson‐Phase Lead‐Free Perovskites for High‐Performance Photovoltaics with Improved Stability

1,4‐butanediamine (BEA) is incorporated into FASnI₃ (FA=formamidinium) to develop a series of lead‐free low‐dimensional Dion–Jacobson‐phase perovskites, (BEA)FA_n?1Sn_nI_3n+1. The broadness of the (BEA)FA₂Sn₃I₁₀ band gap appears to be influenced by the structural distortion owing to high symmetry. The introduction of BEA ligand stabilizes the low‐dimensional perovskite structure (formation energy ca. 10⁶ j mol^?1), which inhibits the oxidation of Sn²⁺. The compact (BEA)FA₂Sn₃I₁₀ dominated film enables a weakened carrier localization mechanism with a charge transfer time of only 0.36 ps among the quantum wells, resulting in a carrier diffusion length over 450 nm for electrons and 340 nm for holes, respectively. Solar cell fabrication with (BEA)FA₂Sn₃I₁₀ delivers a power conversion efficiency (PCE) of 6.43 % with negligible hysteresis. The devices can retain over 90 % of their initial PCE after 1000 h without encapsulation under N₂ environment.     

Brain metabolomics study for the protective effects of Rhodiola crenulata extract on Alzheimer's disease by HPLC coupled with Fourier transform‐ion cyclotron resonance mass spectrometry

In order to investigate the protective effects of Rhodiola crenulata extract on Alzheimer's disease, a brain metabolomics study in rats was conducted by high performance liquid chromatography coupled with Fourier transform ion cyclotron resonance mass spectrometry. Rat model was constructed by bilateral hippocampal injection of amyloid‐β peptide and immunohistochemistry was performed to evaluate the pharmacological effect of Rhodiola crenulata extract. Multivariate statistical analysis was used to discover potential biomarkers in rat brain and related metabolic pathways analysis was conducted to elucidate the action mechanism of Rhodiola crenulata extract. As a result, a total of 19 metabolites contributing to Alzheimer's disease progress were identified and nine of them were restored to the normal levels after drug administration. Pathway analysis revealed that the protective effects of Rhodiola crenulata extract are related to the regulation of glutathione metabolism and arachidonic acid metabolism in rat brain. In conclusion, this work demonstrates that the developed metabolomics method is useful to investigate the protective effects of Rhodiola crenulata extract against Alzheimer's disease. These outcomes may further provide reliable evidence to illuminate the intervention mechanism of other traditional Chinese medicines on Alzheimer's disease.     

Analysis of the GIX/M/c model

In this paper, the GI^X/M/c queueing model is analyzed. An explicit expression of the generating function of equilibrium probabilities of customer numbers in the system for the model is derived. Based on the generating function, it is proved that the equilibrium probabilities are given by a linear combination of some geometric terms. Due to this result, other interesting measures are also considered without difficulty. Examples and numerical results are given.     

Low-Dimensional Dion–Jacobson-Phase Lead-Free Perovskites for High-Performance Photovoltaics with Improved Stability

1,4-butanediamine (BEA) is incorporated into FASnI₃ (FA=formamidinium) to develop a series of lead-free low-dimensional Dion–Jacobson-phase perovskites, (BEA)FA_n−1Sn_nI_3n+1. The broadness of the (BEA)FA₂Sn₃I₁₀ band gap appears to be influenced by the structural distortion owing to high symmetry. The introduction of BEA ligand stabilizes the low-dimensional perovskite structure (formation energy ca. 10⁶ j mol⁻¹), which inhibits the oxidation of Sn²⁺. The compact (BEA)FA₂Sn₃I₁₀ dominated film enables a weakened carrier localization mechanism with a charge transfer time of only 0.36 ps among the quantum wells, resulting in a carrier diffusion length over 450 nm for electrons and 340 nm for holes, respectively. Solar cell fabrication with (BEA)FA₂Sn₃I₁₀ delivers a power conversion efficiency (PCE) of 6.43 % with negligible hysteresis. The devices can retain over 90 % of their initial PCE after 1000 h without encapsulation under N₂ environment.