Series and integral representations of the Taylor coefficients of the Weierstrass sigma-function

We provide two kinds of representations for the Taylor coefficients of the Weierstrass σ-function σ(?;Γ) associated to an arbitrary lattice Γ in the complex plane \(\mathbb{C}=\mathbb{R}^{2}\) , the first one in terms of the so-called Hermite–Gauss series over Γ and the second one in terms of Hermite–Gauss integrals over \(\mathbb{C}\) .     

Existence and Uniqueness of Renormalized Solution of Nonlinear Degenerated Elliptic Problems

In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β(u)-div(a(x, Du)+ F(u)) ■ f in Ω, where f ∈ L1 Ω. A vector field a(·,·) is a Carath′eodory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.     

Snail Hepatopancreatic Lipase: A New Member of Invertebrates Lipases' Group

Higher animal's lipases are well characterized; however, much less is known about lipases from mollusks. A lipolytic activity was located in the land snail (Eobania vermiculata) digestive glands (hepatopancreas), from which a snail digestive lipase (SnDL) was purified. Pure SnDL has a molecular mass of 60 kDa; it does not present the interfacial activation phenomenon. It was found to be more active on short-chain triacylglycerols than on long-chain triacylglycerols. The NH₂-terminal sequence of the SnDL shows 66% of identity with the 17 NH₂-terminal amino acids of a putative lipase from sea urchin (Strongylocentrotus purpuratus). No sequence identity was found with known lipases. Interestingly, neither colipase nor bile salts were detected in the snail hepatopancreas. This suggests that colipase evolved in vertebrates simultaneously with the appearance of an exocrine pancreas and a true liver which produces bile salts. Altogether, these results suggest that SnDL is a member of a new group of digestive lipases belonging to invertebrates.     

Utility of 4‐Benzylidene‐2‐phenyl‐5(4H)‐oxazolone in Synthesis of Triazine,Oxadiazole and Imidazole Derivatives of Anticipated Biological Activity

Treatment of oxazolone 1 with hydrazine hydrate at room temperature gave the (Z)‐configurated isomer hydrazide (Z)‐ 3 (high yield). However, refluxing 1 with hydrazine hydrate yielded the (E)‐configurated isomer hydrazide (E)‐ 2 (low yield).The hydrazide derivative (Z)‐ 3 has been utilized as synthon for the synthesis of 1,2,4‐triazinone, imidazolone, and oxadiazole derivatives through appropriate routes. The thiosemicarbazide and semicarbazide derivatives are synthesized by different routes. The structures of the new compounds were established on the basis of IR, ¹H‐NMR, mass spectral data, and elemental analysis.     

Action of Hydrazines on 2‐(2‐Oxindolin‐3‐ylidene)malononitrile, (E,Z)‐Ethyl 2‐cyano‐2‐(2‐oxindolin‐3‐ylidene)acetate and Isatin‐β‐thiosemicarbazone as a Source of Spiro Indoline‐pyrazole Systems

2‐(2‐Oxindolin‐3‐ylidene)malononitrile ( 1a ) or (E,Z)‐ethyl 2‐cyano‐2‐(2‐oxindolin‐3‐ylidene)acetate ( 1b ) or isatin‐β‐thiosemicarbazone ( 1c ) undergoes reactions with prototype hydrazine hydrate itself and some of its simple congeners to give hydrazone derivatives bearing indoline‐2‐one moiety ( 2 ). The hydrazone derivatives ( 2 ) when heated with acetyl acetone or ethyl acetoacetate in dry pyridine afforded the spiro indoline derivatives ( 3a , 3b ). Also, cinnoline derivative ( 9 ) is obtained by action of hydrazine hydrate on the N‐acetyl derivative of ( 6a ). The structures of the newly synthesized compounds were evaluated by IR, ¹H‐NMR spectroscopy, mass spectra and elemental analyses.     

A Validated TLC-Densitometric Method for the Simultaneous Determination of Formoterol Fumarate and Budesonide in Pressurized Metered-Dose Inhaler

JPC – Journal of Planar Chromatography – Modern TLC - A simple and robust thin-layer chromatography (TLC) method has been developed and validated for the simultaneous quantitative...     

On von Neumann regular elements in <Emphasis Type="Italic">f</Emphasis>-rings

Let B be an Archimedean reduced f-ring. A positive element \({\omega}\) in B is said to satisfy the property \({(\ast)}\) if for every f-ring A with identity e and every \({\ell}\)-group homomorphism \({\gamma : A \rightarrow B}\) with \({\gamma(e) = \omega}\), there exists a unique \({\ell}\)-ring homomorphism \({\rho: B \rightarrow B}\) such that \({\gamma = \omega \rho}\) and \({\rho(e)^{\perp \perp} = \omega^{\perp \perp}}\). Boulabiar and Hager proved that any (positive) von Neumann regular element in B satisfies the property \({(\ast)}\) and proved that the converse holds in the C(X)-case. In this regard, they asked about this converse in the general case. Our main purpose in this note is to prove, via a counter-example, that the converse in question fails in general. In addition, we shall take the opportunity to extend the direct result obtained by Boulabiar and Hager, and to get the C(X)-case we were talking about in an easier way.     

Synthesis,Characterization, and Antimicrobial Evaluation of Some Novel 4-Hydroxyquinolin-2(1H)-ones

Vilsmeier–Haack formylation of 3-acetyl-1-methyl-4-hydroxyquinolin-2(1H)-one (2) produced the novel 6-methyl-4,5-dioxo-5,6-dihydro-4H-pyrano[3,2-c]quinoline-3-carboxaldehyde (3). Reactions of carboxaldehyde 3 with a diversity of nucleophilic reagents were studied and a variety of products were obtained via ring-opening, ring-closing (RORC) sequence. Also, some novel heteroannulated pyrano[3,2-c]quinolines were prepared. Structures of the new synthesized products were deduced on the basis of their analytical and spectral data.     

Polyethylenimine-impregnated mesoporous silica: effect of amine loading and surface alkyl chains on CO2 adsorption

Poly(ethyleneimine) (PEI) supported on pore-expanded MCM-41 whose surface is covered with a layer of long-alkyl chains was found to be a more efficient CO(2) adsorbent than PEI supported on the corresponding calcined silica and all PEI-impregnated materials reported in the literature. The layer of surface alkyl chains plays an important role in enhancing the dispersion of PEI, thus decreasing the diffusion resistance. It was also found that at low temperature, adsorbents with relatively low PEI contents are more efficient than their highly loaded counterparts because of the increased adsorption rate. Extensive CO(2) adsorption-desorption cycling showed that the use of humidified feed and purge gases affords materials with enhanced stability, despite limited loss due to amine evaporation.