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.     

A wide neighborhood interior-point algorithm for linear optimization based on a specific kernel function

This paper presents an interior point algorithm for solving linear optimization problems in a wide neighborhood of the central path introduced by Ai and Zhang (SIAM J Optim 16:400–417, 2005). In each iteration, the algorithm computes the new search directions by using a specific kernel function. The convergence of the algorithm is shown and it is proved that the algorithm has the same iteration bound as the best short-step algorithms. We demonstrate the computational efficiency of the proposed algorithm by testing some Netlib problems in standard form. To best our knowledge, this is the first wide neighborhood path-following interior-point method with the same complexity as the best small neighborhood path-following interior-point methods that uses the kernel function.

     

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.     

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.     

Efficient access to novel tetra- and pentacyclic dihydroquinolin-2-ones by catalyst-free domino Knöevenagel hetero-Diels–Alder reactions from <Emphasis Type="Italic">N</Emphasis>-(2-formylphenyl)-<Emphasis Type="Italic">N</Emphasis>-methylcinnamamides and cyclic 1,3-dicarbonyls in water

An efficient catalyst-free synthesis of novel annulated hybrid derivatives of two known scaffolds, dihydroquinolinone and pyranopyranone, pyranopyrimidinedione, pyranocoumarin or chromenone is described. N-(2-Formylphenyl)-N-methylcinnamamides underwent a one-pot domino Knöevenagel hetero-Diels–Alder reaction with dimedone, N,N-dimethylbarbituric acid, 1,3-indanedione, 4-hydroxycoumarins and 4-hydroxy-6-methyl-2H-pyran-2-one in water, affording the desired tetra and pentacyclic pyranoquinolinones in excellent yields.     

Chromium(III), manganese(II) and iron(III) complexes based on hydrazone Schiff-base and azide ligands: synthesis,crystal structure and antimicrobial activity

A tridentate NNO donor hydrazine Schiff base, HL, was obtained from condensation of pyridine 2-carbaldehyde and 4-hydroxy benzohydrazide. HL and azide ligands with Cr(III), Mn(II) and Fe(III) have been used to synthesize [Cr(L)(N₃)(OCH₃)]₂ (1), [Mn(HL)₂(N₃)₂] (2), and [Fe(L)(N₃)(OCH₃)]₂·H₂O (3). HL is quite diverse in its chelating ability and can be a neutral or monoanionic ligand as a tridentate unit. In this paper, we report structures showing different denticities of the ligand having different charges. The ligand 1–3 was characterized by elemental analysis, FT-IR, and UV–vis spectral studies and solid-state structures were determined by single-crystal X-ray diffraction analysis, revealing that 1 and 3 are binuclear, while 2 is mononuclear. The efficiencies of the ligand and the three complexes were evaluated for antimicrobial activity; MIC data revealed that HL 1–3 are not strongly active in comparison to standard drugs.     

Condensation of an ideal gas with intermediate statistics on the horizon

We consider a boson gas on the stretched horizon of the Schwartzschild and Kerr black holes. It is shown that the gas is in a Bose?CEinstein condensed state with the Hawking temperature T _c =T _H if the particle number of the system be equal to the number of quantum bits of space-time $N \simeq{A}/{l_{p}^{2}}$ . Entropy of the gas is proportional to the area of the horizon (A) by construction. For a more realistic model of quantum degrees of freedom on the horizon, we should presumably consider interacting bosons (gravitons). An ideal gas with intermediate statistics could be considered as an effective theory for interacting bosons. This analysis shows that we may obtain a correct entropy just by a suitable choice of parameter in the intermediate statistics.     

Calculation of on-state I–V characteristics of LDMOSFETs based on an accurate LDD resistance modeling

In this paper, we present an I–V model for LDMOSFETs. It is based on modeling the Lightly-Doped Drain (LDD) region of the device as voltage-controlled resistors where velocity saturation effect is also taken into account. Using the LDD region model along with a model for the channel region of the device, the on-state I–V characteristic of the transistor is accurately calculated. The models for the LDD region resistors can be incorporated into a circuit simulator such as HSPICE which has an accurate model for the channel region of the transistor. The accuracy of the models is verified by comparing its results with those of a device simulator. The results show a maximum error of 1% for a wide range of voltages and overlapped LDD region lengths.     

Primal-dual interior-point algorithm for semidefinite optimization based on a new kernel function with trigonometric barrier term

In this paper we propose primal-dual interior-point algorithms for semidefinite optimization problems based on a new kernel function with a trigonometric barrier term. We show that the iteration bounds are $O(\sqrt{n}\log(\frac{n}{\epsilon}))$ for small-update methods and $O(n^{\frac{3}{4}}\log(\frac{n}{\epsilon}))$ for large-update, respectively. The resulting bound is better than the classical kernel function. For small-update, the iteration complexity is the best known bound for such methods.     

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.