THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

nAbstract Let p 0 and μ be a normal function on [0, 1), ν(r) =(1-r~2)~(1+(n/p)) μ(r) for r ∈ [0, 1). In this article, the bounded or compact weighted composition operator T_φ,ψfrom the μ-Bergman space A~p(μ) to the normal weight Bloch type space β_ν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator C_φis compact from A~p(μ) to β_ν is given. At the same time, the authors give the briefly sufficient and necessary condition that C_φis compact on β_μ for a 1.     

Renormalized solutions of elliptic equations with Robin boundary conditions

In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the type{-div(B(x, u)▽u) = f in ?,u = 0 on Γ_0,B(x, u)▽u·n→+γ(x)h(u) =g on Γ_1,where f and g are the element of L~1(?) and L~1(Γ_1), respectively. We define a notion of renormalized solution and we prove the existence of a solution. Under additional assumptions on the matrix field B we show that the renormalized solution is unique.     

Enantioselective preparation of C-ring fragment of cotylenin A via catalytic asymmetric intramolecular cyclopropanation of α-diazo β-keto ester

A synthetic pathway to the C-ring fragment of cotylenin A which emerged from our retrosynthetic analysis of cotylenin A is described. The catalytic asymmetric intramolecular cyclopropanation (CAIMCP) of the α-diazo-β-keto ester bearing 2,4,6-trimethylphenyl group as the ester part has been found to afford the crystalline product with high ee, which allowed to establish the approach to the C-ring fragment which required ten-pot operations. The developed approach would be beneficial to a large scale synthesis of the C-ring fragment for the total synthesis of cotylenin A.     

Photo-induced synthesis and in vitro biological activity of a Sansalvamide A analog

Photoinduced single electron transfer (SET) cyclization processes for synthesis of a Sansalvamide A analog containing double pharmacophores (cyclicpeptides and O-phthalimide moiety) is described to develop novel antitumor cyclopeptide drug. The resultant compound is active in drug-sensitive HeLa, HepG-2 and MCF-7 cell lines. Specifically, the title compound was found to inhibit MCF-7 cells with an IC₅₀ value of 15 μM (13.4 μg/mL), which may serve as a potential candidate for antitumor drug development.     

“On water” ultrasound-assisted one pot efficient synthesis of functionalized 2-oxo-benzo[1,4]oxazines: First application to the synthesis of anticancer indole alkaloid,Cephalandole A

For the first time, an efficient, simple, synthetic green protocol for the one-pot synthesis of functionalized 2-oxo-benzo[1,4]oxazines 24–29 in water under ultrasound irradiation is presented. As compared to conventional methods, the present protocol avoids traditional chromatography and purification steps and furnished the target molecules in excellent yields (upto 98%) with no side products. The methodology was also demonstrated on gram scale synthesis. Moreover, functionalized 2-oxo-quinoxaline analogues 31–33, another class of bio-active heterocyclic scaffolds, were also prepared using this method. For the first time, this protocol was successfully applied in the synthesis of the anticancer indole alkaloid, Cephalandole A 35.     

Unique cascade ring-opening/cyclization reaction of azlactones and DBU or DBN: Synthesis of new pyrrolam A analogues

1-Azabicyclo[3.3.0]oct-3-en-2-one derivatives were synthesized efficiently through the facile cascade reaction of 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) or 1,5-diazabicyclo[4.3.0]non-5-ene (DBN) with arylidene azlactones. This research provides a straightforward procedure for the synthesis of a novel class of multicyclic semi-alkaloids which shows good antimicrobial activity. Under catalyst-free, mild, and solventless condition, a wide range of fused tricyclic derivatives was obtained in high yields.     

Synthesis of a secretoglobin 3A2 type C (98–139) fragment by Dawson’s native chemical ligation

A secretoglobin 3A2 type C (98–139) peptide was synthesized by native chemical ligation between ¹¹⁵Ile and ¹¹⁶Cys residues using Dawson’s linker. The peptide-N-acyl-benzimidazolinone-glycine amide, a C-terminal thioesters precursor, was provided from 3-amino-4-(methylamino)benzoic acid. In addition, an N-terminal cysteine fragment, the (116–139) peptide, was prepared by ordinary Fmoc-solid phase peptide synthesis. Native chemical ligation of the (98–115) fragment with the Dawson’s linker and the (116–139) peptide smoothly proceeded to give SCGB3A2 type C (98–139) peptide.     

Anti-inflammatory chromone alkaloids and glycoside from Dysoxylum binectariferum

Herein we report isolation of a new chromone alkaloid chrotacumine K (12) from fruits and a chromone glycoside schumaniofioside A (13) from leaves of Dysoxylum binectariferum Hook f. Schumaniofioside A is reported for the first time from Meliaceae family. Other known alkaloids isolated include rohitukine (1) and chrotacumine E (6). The structure of new alkaloid 12 was elucidated on the basis of extensive 1D and 2D NMR analysis, synthesis and chemical hydrolysis. Chemically, chrotacumine K (12) is a 3′-O-acetyl rohitukine which on chemical or enzymatic hydrolysis produces rohitukine. The new alkaloid 12 is also present in seeds and stem-barks of this plant. The glycoside schumaniofioside A (13) is present only in leaves, and in abundance (～1% w/w of dried leaves). The isolated compounds and extracts were evaluated for in vitro effect on the proinflammatory cytokines (TNF-α and IL-6) in human monocytic THP-1 cells. The alkaloid 12 displayed potent inhibition (57%) of TNF-α at 0.3 µM, and was non-toxic to THP-1 cells up to 40 µM, indicating its excellent therapeutic window. Furthermore, a nitrobenzoyl ester analog 15e showed better inhibition of IL-6 than parent natural product chrotacumine K.     

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 Cartan's theorem for linear operators

In this paper, we describe a second main theorem of holomorphic curves in , of hyper‐order strictly less than 1, that involves a general linear operator . As an application, we derive a truncated second main theorem of degenerate holomorphic curves of hyper‐order strictly less than 1 using Nochka weights.