A non-abelian tensor product of precrossed modules in lie algebras

Abstract

In this paper, we introduce the non-abelian tensor square of precrossed modules in Lie algebras and investigate some of its properties. In particular, for an arbitrary Lie algebra L, we study the relation of the second homology of a precrossed L-module and the non-abelian exterior square. Also, we show how this non-abelian tensor product is related to the universal central extensions (with respect to the subcategory of crossed modules) of a precrossed module.     

Chiral bisoxazoline ligands with a biphenyl backbone: development and application in catalytic asymmetric allylic oxidation of cycloolefins

A simple and efficient method for the synthesis of chiral biphenylbisoxazoline ligands was developed. The bishydroxylamide precursors of ligands showed a dynamic atropselective resolution effect in the crystallization process. When biphenylbisoxazoline ligands were coordinated to tetrakis(acetonitrile)copper(I) hexafluorophosphate, it resulted in the formation of only a single diastereomer complex (S,aS,S), which behaved as a catalyst for the enantioselective allylic oxidation of cycloolefins. The enantioselectivity, yield, and rate of this reaction were optimized under different conditions, such as a change of solvents, temperature, and additives and also using various copper salts. The use of SBA-15 mesoporous silica as an additive played a crucial role in increasing the efficiency of the reaction.     

Scale directional distance function and its application to the measurement of eco-efficiency in the manufacturing sector

Directional distance function (DDF) is a recognized technique for measuring efficiency while incorporating undesirable outputs. This approach allows for desirable outputs to be expanded while undesirable outputs are contracted simultaneously. A drawback of the DDF approach is that the direction vector to the production boundary is fixed arbitrarily, which may not provide the best efficiency measure. Therefore, this study extends the previous framework of efficiency analysis to introduce a new slacks-based measure of efficiency called the scale directional distance function (SDDF) approach. This new approach determines the optimal direction to the frontier for each unit of analysis and provides dissimilar expansion and contraction factors to achieve a more reasonable eco-efficiency score. This new approach is employed to measure the eco-efficiency of the Malaysian manufacturing sector. In addition, the paper demonstrates the use of the new approach to establish target values for the reduction/expansion of outputs in order for the inefficient DMUs to achieve full eco-efficiency. The results indicate that Melaka, Pulau Pinang, Negeri Sembilan, Sabah, Sarawak and Labuan have attained full eco-efficiency while Terengganu is the least eco-efficient. The overall eco-efficiency of the manufacturing sector in Malaysia is 80.5 % with wide variations across the states.     

Character Connes-amenability of dual Banach algebras

The concept of left character Connes-amenability for a dual Banach algebra \({\mathcal {A}}\) is introduced. We obtain a cohomological characterization of left character Connes-amenability as well as the relation between left \(\varphi \)-Connes-amenability and existence of left \(\varphi \)-normal virtual diagonals for a \(\omega ^{*}\)-continuous character \(\varphi \). We prove that left character amenability of \({\mathcal {A}}\) is equivalent to left character Connes-amenability of \({\mathcal {A}}^{**}\) when \({\mathcal {A}}\) is Arens regular. Moreover for a locally compact group G, we show that M(G) is left character Connes-amenable. In addition by means of some examples we show that for the new notion, the corresponding class of dual Banach algebras is larger than Connes-amenable dual Banach algebras.     

Extension of Talenti’s Inequality and Maximum Values Relative to Rearrangement Classes

The article starts by revisiting and extending the Talenti’s inequality where the sharpness of the extended inequality is also addressed. The process leading to the extension comprises two steps. First, an observation that the Talenti’s inequality indeed can be formulated in terms of a rearrangement class. Second, proving that the inequality holds even when the rearrangement class is replaced by a much bigger (modulo trivial cases) set namely an appropriate closure of the class. The article then continues to introduce and explore a related maximization problem, associated to the classical Poisson equation, where the admissible set is the class of rearrangements of a given function. The article briefly explains the physical interest in this optimization problem. The existence of optimal solutions is proved and the optimality conditions they satisfy are explicitly derived. The particular case where the rearrangement class is built out of a characteristic function is also discussed.     

Sonochemical Synthesis of a Novel Nanoscale Lead(II) Coordination Polymer: Synthesis,Crystal Structure,Thermal Properties,and DFT Calculations of [Pb(dmp)(μ‐N3)(μ‐NO3)]n with the Novel Pb2(μ‐N3)2(μ‐NO3)2 Unit

A new nanostructured coordination polymer of divalent lead with the ligand 2,9‐dimethyl‐1,10‐phenanthroline (dmp), [Pb(dmp)(μ‐N₃)(μ‐NO₃)]_n ( 1 ), was synthesized by sonochemical methods. The polymer was characterized by scanning electron microscopy, X‐ray powder diffraction, IR, ¹H NMR, and ¹³C NMR spectroscopy, and elemental analyses. Compound 1 was structurally characterized by single‐crystal X‐ray diffraction. The single‐crystal analysis shows that the coordination number of Pb^II ions is seven, (PbN₄O₃) has a “stereo‐chemically active” electron lone pair, and the coordination sphere is hemidirected. The chains interact with each other through π–π stacking interactions to create a 3D framework. The structure of the title complex was optimized by density functional calculations. The calculated structural parameters and the IR spectrum of the title complex are in agreement with the crystal structure.     

Highly Efficient One-Pot Synthesis of N-Alkyl Sulfonamides from Alcohols Using N-(p-Toluenesulfonyl) Imidazole (Tsim)

Abstract

A facile and efficient method for one-pot synthesis of N-alkyl sulfonamides from alcohols using N-(p-toluenesulfonyl)imidazole (TsIm) is described. In this protocol, treatment of various potassium sulfonylamide salts and alcohols in the presence of TsIm and triethylamine in refluxing DMF furnishes the corresponding N-alkyl sulfonamides in good to excellent yields. This methodology is highly efficient for reaction of various structurally diverse primary and secondary alcohols as well as potassium sulfonylamides. Also, the density functional theoretical calculations are employed to mechanistically study this protocol.

[Supplementary materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements for the following free supplemental files: Additional text and figures.]     

catena‐Poly[[di‐μ2‐aqua‐hexaaquabis(μ3‐4‐oxidopyridine‐2,6‐dicarboxylato)trimanganese(II)] trihydrate]: a new one‐dimensional coordination polymer based on a trinuclear MnII complex of chelidamic acid

4‐Hydroxypyridine‐2,6‐dicarboxylic acid (chelidamic acid, hypydc_[H]H₂) reacts with MnCl₂·2H₂O in the presence of piperazine in water to afford the title complex, {[Mn₃(C₇H₂NO₅)₂(H₂O)₈]·3H₂O}_n or {[Mn₃(hypydc)₂(H₂O)₈]·3H₂O}_n. This compound is a one‐dimensional coordination polymer, with the twofold symmetric repeat unit containing three metal centres. Two different coordination geometries are observed for the two independent Mn^II metal centres, viz. a distorted pentagonal bipyramid and a distorted octahedron. The 4‐oxidopyridine‐2,6‐dicarboxylate anions and two of the water molecules act as bridging ligands. The zigzag‐like geometry of the coordination polymer is stabilized by hydrogen bonds. O—H...O and C—H...O hydrogen bonds and water clusters consolidate the three‐dimensional network structure.