Generalized (Jordan) left derivations on rings associated with an element of rings

In this paper, we introduce a new notion of generalized (Jordan) left derivation on rings as follows: let R be a ring, an additive mapping F : R → R is called a generalized (resp. Jordan) left derivation if there exists an element w ∈ R such that F(xy) = xF(y) + yF(x) + yxw (resp. F(x ²) = 2xF(x) + x ² w) for all x, y ∈ R. Then, some related properties and results on generalized (Jordan) left derivation of square closed Lie ideals are obtained.     

On using mesh-based and mesh-free methods in problems defined by Eringen’s non-local integral model: issues and remedies

With the recent success of nonlocal theories in modeling of engineering problems involving small intrinsic length scales, such as modeling of crack propagation, this paper addresses issues pertaining to cost-ineffectiveness of Eringen’s integral model. The cost effectiveness of the computation may be considered as a twofold issue; one pertaining to the non-local model and another pertaining to the numerical tool. First of all, we shall show that during the solution of problems with Eringen’s non-local integral model, there is no need to consider the integral model for the whole computational domain. In fact, the problems may be solved by just using the integral model close to the boundaries, i.e. a boundary layer effect, or around the points with singularities. In this paper we propose a partitioning strategy to remarkably reduce the computational cost. This may be considered as a gateway for solving some types of two-scale problems, e.g. those with macro/micro and nano scales, in which the small scale effects are localized just at parts of the domain. To demonstrate the efficiency of the numerical tools, we examine the performance of the finite element method (FEM), the element free Galerkin method (EFG) and the finite point method (FPM). This paves the way for using mesh-free methods in the solution of problems with non-local integral models. Examples with smooth and non-smooth solutions are considered for examining the efficiency of the methods. It will be shown that, by considering the boundary layer effect, the FEM and FPM will be efficient enough for being used in problems defined by Eringen’s non-local integral model.

     

Chemistry of Diruthenium and Dirhodium Analogues of Pentaborane(9): Synthesis and Characterization of Metal N,S‐Heterocyclic Carbene and B‐Agostic Complexes

Building upon our earlier results on the synthesis of electron‐precise transition‐metal–boron complexes, we continue to investigate the reactivity of pentaborane(9) and tetraborane(10) analogues of ruthenium and rhodium towards thiazolyl and oxazolyl ligands. Thus, mild thermolysis of nido‐[(Cp*RuH)₂B₃H₇] ( 1 ) with 2‐mercaptobenzothiazole (2‐mbtz) and 2‐mercaptobenzoxazole (2‐mboz) led to the isolation of Cp*‐based (Cp*=η⁵‐C₅Me₅) borate complexes 5 a , b [Cp*RuBH₃L] ( 5 a : L=C₇H₄NS₂; 5 b : L=C₇H₄NOS)) and agostic complexes 7 a , b [Cp*RuBH₂(L)₂], ( 7 a : L=C₇H₄NS₂; 7 b : L=C₇H₄NOS). In a similar fashion, a rhodium analogue of pentaborane(9), nido‐[(Cp*Rh)₂B₃H₇] ( 2 ) yielded rhodaboratrane [Cp*RhBH(L)₂], 10 (L=C₇H₄NS₂). Interestingly, when the reaction was performed with an excess of 2‐mbtz, it led to the formation of the first structurally characterized N,S‐heterocyclic rhodium‐carbene complex [(Cp*Rh)(L₂)(1‐benzothiazol‐2‐ylidene)] ( 11 ) (L=C₇H₄NS₂). Furthermore, to evaluate the scope of this new route, we extended this chemistry towards the diruthenium analogue of tetraborane(10), arachno‐[(Cp*RuCO)₂B₂H₆] ( 3 ), in which the metal center possesses different ancillary ligands.     

Electromagnetic field with induced massive term: Case with scalar field

We consider an interacting system of massless scalar and electromagnetic fields, with the Lagrangian explicitly depending on the electromagnetic potentials, i.e., interaction with broken gauge invariance. The Lagrangian for interaction is chosen in such a way that the electromagnetic field equation acquires an additional term, which in some cases is proportional to the vector potential of the electromagnetic field. This equation can be interpreted as the equation of motion of photon with induced nonzero rest-mass. This system of interacting fields is considered within the scope of Bianchi type-I (BI) cosmological model. It is shown that, as a result of interaction the isotropization process of the expansion takes place.     

One-Pot Stereoselective Synthesis of Alkyl Z-2-[2-Amino-4-oxo-1,3-selenazol-5(4H)-yliden] Acetates

Abstract

Selenourea reacts with dialkyl acetylenedicarboxylates in acetone to form 1:1 adducts, which undergo a cyclization reaction to produce alkyl Z-2-(2-amino-4-oxo-1,3-selenazol-5(4H)-yliden) acetates in fairly good yields. The reaction is completely stereoselective.     

Stereoselective Synthesis of Alkyl Z -2-(2-Amino-4-oxo-1,3-thiazol-5(4 H )-yliden)Acetates in Solventless Conditions

Tiourea reacts with dialkyl acetylenedicarboxylates in solventless conditions to form 1:1 adducts, which undergo a cyclization reaction to produce alkyl Z-2-(2-amino-4-oxo-1,3-thiazol-5(4H)-yliden)acetates in fairly good yields. The stereochemistry of the ethyl Z-2-(2-amino-4-oxo-1,3-thiazol-5(4H)-yliden)acetate was established by the use of X-ray single crystal structure analysis. The reaction is completely stereoselective.     

收缩喷嘴中的湍流Ⅰ——边界层解

应用边界层积分法,研究锥形喷嘴入口区域中湍动涡流的发展.球面坐标系中的控制方程,通过边界层的假定得到简化,并对边界层进行了积分.应用4阶Adams预测校正法求解该微分方程组.入口区域的切向和轴向速度,分别应用自由涡流和均匀速度分布来表示.由于缺乏收缩喷嘴中涡流的实验数据,需要用数值模拟对该发展模式进行逆向验证.数值模拟的结果证明,该解析模型在预测边界层参数中的能力,例如边界层的生长、剪切率和边界层厚度,以及不同锥度角时的涡流强度衰减率等.为所提出的方法引进一个简明而有效的程序,用以研究几何形状收缩设备内的边界层参数.     

Numerical investigation of turbulent free jet flows issuing from rectangular nozzles: the influence of small aspect ratio

In this research, the fluid and thermal characteristics of a rectangular turbulent jet flow is studied numerically. The results of three-dimensional jet issued from a rectangular nozzle are presented. A numerical method employing control volume approach with collocated grid arrangement was employed. Velocity and pressure fields are coupled with SIMPLEC algorithm. The turbulent stresses are approximated using k–e{\varepsilon} model with two different inlet conditions. The velocity and temperature fields are presented and the rates of their decay at the jet centerline are noted. The velocity vectors of the main flow and the secondary flow are illustrated. Also, effect of aspect ratio on mixing in rectangular cross-section jets is considered. The aspect ratios that were considered for this work were 1:1 to 1:4. The results showed that the jet entrains more with smaller AR. Special attention has been drawn to the influence of the Reynolds number (based on hydraulic diameter) as well as the inflow conditions on the evolution of the rectangular jet. An influence on the jet evolution is found for smaller Re, but the jet is close to a converged state for higher Reynolds numbers. The inflow conditions have considerable influence on the jet characteristics.