Identities of arithmetic type between values of the theta function associated to a lattice in ℝ d and its derivatives

In this paper, we introduce a notion of similarly self dual lattice in a d-dimensional Euclidean space and a classical Jacobi theta function is associated to such a lattice. We establish identities of arithmetic type between values of this theta function and its successive derivatives. This work can be related to the spectral theory of the Landau operators.      

A second-order boundary value problem with impulsive effects on an unbounded domain

We study a second-order nonlinear differential equation on an unbounded domain with solutions subject to impulsive conditions and the Sturm–Liouville type boundary conditions. The existence results are obtained via applications of Krasnosel’ski?’s fixed point theorem for the sum of a completely continuous operator and a contraction.     

Synthesis,reactions, and antioxidant activity of 3-(pyrrol-1-yl)-4,6-dimethyl selenolo[2,3-b]pyridine derivatives

Ethyl 4,6-dimethyl-3-(pyrrol-1-yl) selenolo[2,3-b]pyridine-2-carboxylate (2) was synthesized by the reaction of previously prepared ethyl 3-amino-4,6-dimethyl selenolo[2,3-b]pyridine-2-carboxylate (1) with 2,5-dimethoxytetrahydrofuran in acetic acid. The pyrrolyl ester (2) was converted into the corresponding carbohydrazide 3 which reacted with acetyl acetone, aromatic aldehydes, carbon disulfide in pyridine, and sodium nitrite to afford the corresponding dimethyl pyrazolyl 4, arylidene carbohydrazides 5a–d, oxadiazolyl thiole 6, and caboazide compound 8, respectively. The carboazide 8 reacted with different alcohols and amines to give the corresponding carbamates 9a–c and the aryl urea derivatives 10a–d. Heating of carboazide 8 in dry xylene afforded the pyridoselenolo-pyrrolopyrazinone 11. The latter compound was used as a versatile starting precursor for synthesis of other pyridoselenolo-pyrrolopyrazine compounds. The newly synthesized compounds and their derivatives were characterized by elemental analysis and spectroscopy (IR, ¹H-NMR, and mass spectra). Some of the newly synthesized pyrrolyl selenolopyridine compounds showed remarkable antioxidant activity compared to ascorbic acid.     

Purification and Biochemical Characterization of an Acid-Stable Lipase from the Pyloric Caeca of Sardine (Sardinella aurita)

A lipolytic activity was located in the sardine digestive glands (pyloric caeca), from which a sardine digestive lipase (SaDL) was purified. Pure SaDL has a molecular mass of 43 kDa as determined by sodium dodecyl sulfate polyacrylamide gel electrophoresis analysis. The enzyme was found to be more active on short-chain triacylglycerols than on long-chain ones. SaDL does not present the interfacial activation phenomenon. Control experiments were performed under the same experimental conditions, with dromedary and turkey pancreatic lipases and showed a positive interfacial activation phenomenon. Sodium deoxycholate (NaDC) has an inhibitory effect on the lipase activity. The pure enzyme lost 40% of its activity in presence of 8 mM NaDC. SaDL was found to be mostly stable at low pH values. Interestingly, no colipase was detected in the sardine pyloric caeca. Analogous results were reported for the scorpion and the crab digestive systems. This is in line with the idea that colipase might has evolved in mammal animals simultaneously with the appearance of an exocrine pancreas. No similarity was found between the NH₂-terminal amino acid residues of SaDL and those of lipases from the digestive tract of other species. Altogether, these results suggest that SaDL is a member of a new group of lipases belonging to aquatic species.     

d-Symmetric d-orthogonal polynomials of Brenke type

In this paper, we characterize the d-symmetric d-orthogonal polynomials of Brenke type. We obtain two new families of polynomials and the moments of the corresponding d-dimensional vectors of linear functionals. Weights, providing integral representations for these moments, were also given.     

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 \(\mathbb{C}\) .     

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.