Capability of Crossed Modules of Lie Algebras

In this paper, we introduce the concept of capability for crossed modules of Lie algebras, which is a generalization of capability in Lie algebras and groups. By using a special central ideal of a crossed module, we give a sufficient condition for the capability of a crossed module of Lie algebras. Also, we will extend the five-term exact sequence on homology of crossed modules of Lie algebras one term further and study the connection between the capability of crossed modules and this sequence. Finally, we study the relation between the capability and the center of a cover of a crossed module.     

A new infeasible interior-point method based on Darvay’s technique for symmetric optimization

We present a full Nesterov and Todd step primal-dual infeasible interior-point algorithm for symmetric optimization based on Darvay’s technique by using Euclidean Jordan algebras. The search directions are obtained by an equivalent algebraic transformation of the centering equation. The algorithm decreases the duality gap and the feasibility residuals at the same rate. During this algorithm we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Each main iteration of the algorithm consists of a feasibility step and some centering steps. The starting point in the first iteration of the algorithm depends on a positive number ξ and it is strictly feasible for a perturbed pair. The feasibility steps find strictly feasible iterates for the next perturbed pair. By using centering steps for the new perturbed pair, we obtain strictly feasible iterates close to the central path of the new perturbed pair. The algorithm finds an ?-optimal solution or detects infeasibility of the given problem. Moreover, we derive the currently best known iteration bound for infeasible interior-point methods.     

Carbon‐iodide bond activation by cyclometalated Pt (II) complexes bearing tricyclohexylphosphine ligand: A comparative kinetic study and theoretical elucidation

Cyclometalated Pt (II) complexes [PtMe(C^N)(L)], in which C^N = deprotonated 2,2′‐bipyridine N‐oxide (Obpy), 1 , deprotonated 2‐phenylpyridine (ppy), 2 , deprotonated benzo [h] quinolone (bzq), 3 , and L = tricyclohexylphosphine (PCy₃) were prepared and fully characterized. By treatment of 1–3 with excess MeI, the thermodynamically favored Pt (IV) complexes cis‐[PtMe₂I(C^N)(PCy₃)] (C^N = Obpy, 1a ; ppy, 2a ; and bzq, 3a ) were obtained as the major products in which the incoming methyl and iodine groups adopted cis positions relative to each other. All the complexes were characterized by means of NMR spectroscopy while the absolute configuration of 1a was further determined by X‐ray crystal structure analysis. The reaction of methyl iodide with 1–3 were kinetically explored using UV–vis spectroscopy. On the basis of the kinetic data together with the time‐resolved NMR investigation, it was established that the oxidative addition reaction occurred through the classical S_N2 attack of Pt (II) center on the MeI reagent. Moreover, comparative kinetic studies demonstrated that the electronic and steric nature of either the cyclometalating ligands or the phosphine ligand influence the rate of reaction. Surprisingly, by extending the oxidative addition reaction time, very stable iodine‐bridged Pt (IV)‐Pt (IV) complexes [Pt₂Me₄(C^N)₂(μ‐I)₂] (C^N = Obpy, 1b ; ppy, 2b ; and bzq, 3b ) were obtained and isolated. In order to find a reasonable explanation for the observation, a DFT (density functional theory) computational analysis was undertaken and it was found that the results were consistent with the experimental findings.     

Analyticity of free boundary in an optimal harvesting problem

Letters in Mathematical Physics - This note revisits an optimisation problem pertaining to the optimal harvesting of a marine species. The existence of solutions and the corresponding optimal...     

Copper-doped silica cuprous sulfate (CDSCS) as a highly efficient and new heterogeneous nano catalyst for [3+2] Huisgen cycloaddition

The synthesis and characterization of copper-doped silica cuprous sulfate (CDSCS) as a new and efficient heterogeneous nano catalyst are described. CDSCS has been fully characterized by different microscopic, spectroscopic and physical techniques, including scanning electron microscopy (SEM), transmission electron microscopy (TEM), atomic forced microscopy (AFM), X-ray diffraction (XRD), inductively coupled plasma (ICP) analysis, thermogravimetric analysis (TGA) and FT-IR. CDSCS is proved to be a useful heterogeneous nano catalyst in Cu(I)-catalyzed ‘Click’ cycloaddition of organic azides with terminal alkynes. CDSCS catalyzes the 1,3-dipolar cycloaddition reactions of β-azido alcohols and alkynes at room temperature, in THF/H₂O (1:1, v/v) solution. Using CDSCS, 1,4-disubstituted 1,2,3-triazole adducts are mainly obtained, in good to excellent yields and in short reaction times. These compounds have featural resemblance to β-adrenoceptor blocking agents. CDSCS was approved as a chemically and thermally stable nano catalyst that can be reused for many consecutive trials without a significant decline in its reactivity.     

Simplified infeasible interior-point algorithm for SDO using full Nesterov-Todd step

Interior-point methods for semidefinite optimization problems have been studied frequently, due to their polynomial complexity and practical implications. In this paper we propose a primal-dual infeasible interior-point algorithm that uses full Nesterov-Todd (NT) steps with a different feasibility step. We obtain the currently best known iteration bound for semidefinite optimization problems.     

A Novel Polymeric Lead(II)‐Azido Compound: Synthesis,Structural Characterization,and DFT Calculations of [Pb(dmp)(N3)2]n

A novel 1D Pb^II coordination polymer containing Pb₂‐(μ‐N₃)₂ unit [Pb(dmp)(N₃)₂]_n (dmp =  2,9‐dimethyl‐1,10‐phenanthroline) has been prepared and characterized. Single‐crystal X‐ray diffraction analyses show that the coordination number for Pb^II ions is six, PbN₆, with “stereochemically active” electron lone pairs and the coordination sphere being hemidirected. The single‐crystal X‐ray data show the chains interact with each other through the π–π stacking interactions, which create a 3D framework. The structure of title complex has been optimized by density functional theory. Structural parameters and IR spectra for the complex are in agreement with the crystal structure.     

Some notes on the second homology of Leibniz algebras

Some properties of the second homology and cover of Leibniz algebras are established. By constructing a stem cover, the second Leibniz homology and cover of abelian, Heisenberg Lie algebras and cyclic Leibniz algebras are described. Also, for the dimension of a non-cyclic nilpotent Leibniz algebra L, we obtain dim(HL₂(L))≥2.     

Engineering the nonlinear phase shift

We treat the nonlinear phase shift response in the weak perturbation limit as a linear digital filter that can be synthesized into the values of its poles and zeros and mapped onto an optical architecture. This procedure results in a significant enhancement in the nonlinear sensitivity with a response that is robust to frequency changes within the filter passband. A precompensation technique can be used to reduce distortions under strongly driven nonlinear operation to achieve a larger phase shift. We also show that nonlinear sensitivity improves with increasing filter group delay and can be increased within constant linear bandwidth by use of higher-order filters.