Synthesis,spectral, DFT calculations and biological studies of solvatochromic copper(II)-ONS hydrazone derived from 2-aminochromone-3-carboxaldehyde

New ONS hydrazone ligand, 2-[(2-aminochromon-3-yl)methylidene]-N-phenylhydrazinecarbothioamide, HL , was synthesized and reacted with different salts of Cu (II) ion (OAc⁻, NO₃⁻, SO₄²⁻ and Cl⁻) in absence and presence of secondary ligands (L′); 8-hydroxyquinoline, 1,10-phenanthroline or SCN⁻; to form binary and ternary Cu(II)-chelates. The ligand and its Cu(II)-complexes were fully characterized by analytical, spectral, thermal, conductivity and magnetic susceptibility measurements. The metal chelates showed octahedral, square planar and /or distorted tetraherdal arrangements. Coats–Redfern equations used to calculate the kinetic parameters of the thermal decomposition stages (E_a, A, ΔH, ΔS and ΔG). The compounds exhibit luminescence property; promising interesting potential applications as photoactive materials. Lippert–Mataga, Bakhshiev, Kawski–Chamma–Viallet and microscopic solvent polarity parameter and E_T^N correlation methods were applied on the solvatochromic shifts of emission spectra to evaluate the ground (μ_g) and excited (μ_e) states dipole moments. Excited state dipole moment is larger than the ground state which may be attributed to π-π* transition. The coordinating anions play an important role on the position and intensity of emission band. The ligand and its metal complexes showed antimicrobial activity towards Gram–positive bacteria, Gram–negative bacteria, yeast and fungus. The molecular structural parameters of HL and its Cu(II)- complexes have been calculated on the basis of DFT engaged in the Gaussian 09 program at the B3LYP/6-31G(d,p) level; the theoretical data are correlated with the experimental data.     

Theoretical studies of the concentration dependences of d–d transition band,g factors,and local distortion for V4+ in Li2O–PbO–B2O3–P2O5 glasses

In this work, the g factors, d–d transition band, local distortion, and their concentration dependences for impurity V⁴⁺ in 20Li₂O–20PbO–45B₂O₃–(15 − x)P₂O₅:V₂O₅ (0 ≤ x ≤ 2.5 mol%) glasses are theoretically investigated by using perturbation formulas of g factors for a tetragonally compressed octahedral 3d¹ cluster. In the light of the cubic polynomial concentration functions for cubic field parameter D_q, covalency factor N, and relative tetragonal compression ratio ρ, the calculated concentration dependences of d–d transition band and g factors for V⁴⁺ show good agreement with the experimental data. With increasing x, N (≈0.7682–0.8165) displays the monotonously increasing trend, whereas ρ (≈6.5–4.2%) and D_q (≈1504.9–1481.1 cm⁻¹) exhibit the decreasing tendencies. The above concentration dependences can be ascribed to the modifications of the V⁴⁺–O²⁻ bonding and orbital admixtures around the impurity V⁴⁺ due to the effects of V₂O₅ doping on the stability of the glass network, the strength of local crystal fields, and the electron cloud distribution.     

A Lie theoretic categorification of the coloured Jones polynomial

We use the machinery of categorified Jones-Wenzl projectors to construct a categorification of a type A Reshetikhin-Turaev invariant of oriented framed tangles where each strand is labelled by an arbitrary finite-dimensional representation. As a special case, we obtain a categorification of the coloured Jones polynomial of links.     

Chemical investigation of metabolites produced by an endophytic Aspergillus sp. isolated from Limonia acidissima

Endophytic fungi are considered as a good source to produce important secondary metabolites with interesting bioactivities. In a continuation of our studies towards the search for environmentally friendly bioactive compounds from Sri Lankan flora, we investigated the secondary metabolites produced by the endophytic fungi Aspergillus sp. isolated from the seeds of the popular edible fruit Limonia acidissima L. of the family Rutaceae. The pure culture of the Aspergillus sp. was grown on potato dextrose broth media. After 4 weeks fermentation, fungal media were extracted with organic solvents. Chromatographic separation of the fungal extracts over silica gel, Sephadex LH-20 and RP-HPLC furnished flavasperone (1), rubrofusarin B (2), aurasperone A (3), fonsecinone D (4) and aurasperone B (5). Compounds 1–4 showed moderate activities in brine shrimp toxicity assay. This is the first report of the ¹³C NMR data of compounds 4 and 5.     

基于罗丹明B的激活型α-酮戊二酸荧光探针

α-酮戊二酸(α-KA)是人体三羧酸循环的一个重要代谢中间体,异柠檬酸脱氢酶-1(IDH1)及异柠檬酸脱氢酶-2(IDH2)的突变将导致α-KA转化为2-羟基戊二酸(2HG),该过程与急性骨髓性白血病(AML)密切相关,因此检测人体内α-KA的含量变化具有重要意义。本文以罗丹明B作为荧光基团,通过将罗丹明B与水合肼反应得到能够检测α-KA的荧光增强型探针RBN,并优化了检测温度、pH及响应时间等条件。研究表明,RBN对α-KA表现出很好的选择性,不受人体内常见氨基酸、化学结构类似的羰基化合物及活性氧化物(ROS)的影响,具有潜在的应用价值。     

Modules over quantaloids: Applications to the isomorphism problem in algebraic logic and π-institutions

We solve the isomorphism problem in the context of abstract algebraic logic and of π-institutions, namely the problem of when the notions of syntactic and semantic equivalence among logics coincide. The problem is solved in the general setting of categories of modules over quantaloids. We introduce closure operators on modules over quantaloids and their associated morphisms. We show that, up to isomorphism, epis are morphisms associated with closure operators. The notions of (semi-)interpretability and (semi-)representability are introduced and studied. We introduce cyclic modules, and provide a characterization for cyclic projective modules as those having a g-variable. Finally, we explain how every π-institution induces a module over a quantaloid, and thus the theory of modules over quantaloids can be considered as an abstraction of the theory of π-institutions.     

On exceptional groups of order p5

A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient.The smallest examples of exceptional p-groups have order $p^5$. For an odd prime p, we classify all pairs $(G,Q)$ where G has order $p^5$ and Q is a distinguished quotient. (The case $p=2$ has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order $p^5$ with at least one exceptional quotient tends to 1/2.     

On Lorentzian Ricci solitons on nilpotent Lie groups

The aim of this article is to exhibit the variety of different Ricci soliton structures that a nilpotent Lie group can support when one allows for the metric tensor to be Lorentzian. In stark contrast to the Riemannian case, we show that a nilpotent Lie group can support a number of non‐isometric Lorentzian Ricci soliton structures with decidedly different qualitative behaviors and that Lorentzian Ricci solitons need not be algebraic Ricci solitons. The analysis is carried out by classifying all left invariant Lorentzian metrics on the connected, simply‐connected five‐dimensional Lie group having a Lie algebra with basis vectors and and non‐trivial bracket relations and , investigating the various curvature properties of the resulting families of metrics, and classifying all Lorentzian Ricci soliton structures.     

Contractivity results in ordered spaces. Applications to relative operator bounds and projections with norm one

This paper provides various “contractivity” results for linear operators of the form where C are positive contractions on real ordered Banach spaces X . If A generates a positive contraction semigroup in Lebesgue spaces , we show (M. Pierre's result) that is a “contraction on the positive cone ”, i.e. for all provided that .  We show also that this result is not true for 1 ⩽ . We give an extension of M. Pierre's result to general ordered Banach spaces X under a suitable uniform monotony assumption on the duality map on the positive cone . We deduce from this result that, in such spaces, is a contraction on for any positive projection C with norm 1. We give also a direct proof (by E. Ricard) of this last result if additionally the norm is smooth on the positive cone. For any positive contraction C on base‐norm spaces X (e.g. in real spaces or in preduals of hermitian part of von Neumann algebras), we show that for all where N is the canonical half‐norm in X . For any positive contraction C on order‐unit spaces X (e.g. on the hermitian part of a algebra), we show that is a contraction on . Applications to relative operator bounds, ergodic projections and conditional expectations are given.     

Volumes of unit balls of mixed sequence spaces

The volume of the unit ball of the Lebesgue sequence space is very well known since the times of Dirichlet. We calculate the volume of the unit ball of the mixed norm , whose special cases are nowadays popular in machine learning under the name of group Lasso. We give two proofs of the main results, one in the spirit of Dirichlet, the other one using polarization identities. The result is given by a closed formula involving the gamma function, only slightly more complicated than the one of Dirichlet. We consider the real as well as the complex case. We also consider the anisotropic unit balls. We close by an overview of open problems.