New biphenantherene and nervogenic acid derivatives from Liparis regnieri Finet and their inhibitory activities against NF-κB activation

A phytochemical investigation of the whole plant of Liparis regnieri Finet led to the isolation of one new biphenantherene (1) and ten new nervogenic acid derivatives (2–11), together with nine known compounds. Their structures were elucidated mainly by extensive analyses of 1D and 2D NMR spectroscopic data and chemical reactions. Additionally, for the first time a previously unreported biphenantherene was discovered to effectively suppress TNF-α induced expression of NF-κB-Luc in Hela cells with the IC₅₀ value of 1.80 μM and the structure-activity relationshipwas also discussed.     

Synthesis of oxacalothrixin B and its analogues involving iodine/TBHP-mediated electrocyclization

The total synthesis of oxacalothrixins, an isostere of biologically important carbazoloquinone alkaloid, calothrixin B was achieved from 2-acetyl-3-methylbenzofuran. An iodine/TBHP-mediated oxidative cyclization of benzofuranyl-enamine has been employed as a key step to synthesize, the crucial intermediate 1-hydroxy dibenzofurancarbaldehyde. The latter upon reductive cyclization followed by PIDA-mediated oxidation furnished oxacalothrixin B and its analogues.     

Vulgarisins B–D,three novel diterpenoids with a rare skeleton isolated from Prunella vulgaris Linn

Three new diterpenoids, vulgarisins B–D (1–3), have been isolated from a medicinal plant Prunella vulgaris Linn. These diterpenoids contain a rare 5/6/4/5 fused tetracyclic ring skeleton. Their structures were determined through the analysis of spectroscopic data, and the absolute configuration were further confirmed by single crystal X-ray diffraction as well as CD analysis. All the compounds were evaluated for their cytotoxicity activity, vulgarisins B (1) and C (2) demonstrated modest cytotoxicity activity against human lung carcinoma A549 cell line.     

Homoleptic Zinc(II) Complexes Based on 4′‐(2‐Thienyl)‐terpyridine: Preparation,Structures, and Properties

The homoleptic complexes Zn^II(4′‐(2‐(5‐R‐thienyl))‐terpyridine)₂(ClO₄)₂ [R = hydrogen ( 1 ), bromo ( 2 ), methyl ( 3 ), and methoxy ( 4 )] were prepared. Their structures were determined by single‐crystal X‐ray diffraction analyses, and further characterized by high resolution mass, infrared spectra (IR), and elemental analyses. Single crystal X‐ray diffraction analysis showed that Zn^II ions in the complexes are both six‐coordinate with N₆ coordination sphere, displaying distorted octahedral arrangements. The absorption and emission spectra of the homoleptic Zn^II complexes were investigated and compared to those of the parent complex Zn^II(4′‐(2‐thienyl))‐terpyridine)₂(ClO₄)₂. The UV/Vis absorption spectra showed that the complexes all exhibit strong absorption component in UV region, moreover, complex 4 has an absorption component in the visible region. Thus, the photocatalytic activities of the complexes in degradation of organic dyes were investigated under UV and visible irradiation.     

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.     

Characterizations of the boundedness of generalized fractional maximal functions and related operators in Orlicz spaces

Given and a Young function η, we consider the generalized fractional maximal operator defined by where the supremum is taken over every ball B contained in . In this article, we give necessary and sufficient Dini type conditions on the functions , and η such that is bounded from the Orlicz space into the Orlicz space . We also present a version of this result for open subsets of with finite measure. Both results generalize those contained in 6 and 14 when , respectively. As a consequence, we obtain a characterization of the functions involved in the boundedness of the higher order commutators of the fractional integral operator with BMO symbols. Moreover, we give sufficient conditions that guarantee the continuity in Orlicz spaces of a large class of fractional integral operators of convolution type with less regular kernels and their commutators, which are controlled by .     

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.     

Summability in of a vector measure

We show a picture of the relations among different types of summability of series in the space  of integrable functions with respect to a vector measure m of relatively norm compact range. In order to do that, we study the class of the so‐called m‐1‐summing operators. We give several applications regarding the existence of copies of c ₀ in , as well as on m‐1‐summing operators which are weakly compact, Asplund or weakly precompact.