Linear combinations of prime powers in X-coordinates of Pell equations

The Ramanujan Journal - We give q-analogues of three Ramanujan-type series for $$1/\pi $$ from q-analogues of ordinary WZ pairs. The first one is a new q-analogue of the following Ramanujan’s...     

Synergy Between Cell‐Penetrating Peptides and Singlet Oxygen Generators Leads to Efficient Photolysis of Membranes

Cell‐penetrating peptides such as TAT or R9 labeled with small organic fluorophores can lyse endosomes upon light irradiation. The photoendosomolytic activity of these compounds can in turn be used to deliver proteins and nucleic acids to the cytosol of live cells with spatial and temporal control. In this report, we examine the mechanisms by which such fluorescent peptides exert a photolytic activity using red blood cells as a membrane model. We show that the peptides TAT and R9 labeled with tetramethylrhodamine photolyze red blood cells by promoting the formation of singlet oxygen in the vicinity of the cells' membranes. In addition, unlabeled TAT and R9 accelerate the photolytic activity of the membrane‐bound photosensitizer Rose bengal in trans, suggesting that the cell‐penetrating peptides participate in the destabilization of photo‐oxidized membranes. Peptides and singlet oxygen generators therefore act in synergy to destroy membranes upon irradiation.     

The effect of carbon sources on the single cell proteins and extracellular enzymes production byChrysonilia sitophila (TFB 27441 strain)

The single cell protein and extracellular enzyme production from a lignocellulolytic fungus,Chrysonilia sitophila, using different carbon sources were evaluated. The mycelial dry mass composition showed a high protein (39.2%) and low nucleic acid content (3.3%), as well as carbohydrate, fatty acid, fiber, and ash levels comparable with single cell proteins currently studied. Mycelial protein showed amino acid content similar to or higher than FAO standard requirements. The amino acid, fatty acid, and carotenoid composition, as well as mycelial mass yield and enzyme production, were dependent on the carbon source used. Glucose, saccharose, cellobiose, cellulose, microcrystal-line cellulose, lactose, and rice hull as carbon sources were studied.     

An exponential Diophantine equation related to the sum of powers of two consecutive terms of a Lucas sequence and x-coordinates of Pell equations

Periodica Mathematica Hungarica - For the Fibonacci sequence the identity $$F_n^2+F_{n+1}^2 = F_{2n+1}$$ holds for all $$n \ge 0$$ . Let $${\mathcal {X}}:= (X_\ell )_{\ell \ge 1}$$ be the sequence...     

Two new dammarane triterpenoids from Kageneckia angustifolia D. Don

Two new dammarane triterpenoids, 20R,21-epoxydammar-24-ene-3,23-dione and 20R,21-epoxy-3beta-hydroxydammar-24-ene-23-one have been isolated from the aerial parts of Kageneckia angustifolia D. Don, Rosaceae, along with the previously reported triterpenoids oleanolic acid and 3beta-(beta-D-glucosyloxy)-16alpha,23alpha-epoxycucurbita-5,24-dien-11-one and the phenolic prunasin. The structures of these compounds were established by MS, 1D- and 2D-NMR experiments, and the structure of the new compounds were confirmed by X-ray diffraction analysis.     

Stability analysis of the extended state observers by Popov criterion

The analysis and design of the extended state observer (ESO) involves a continuous non-smooth structure, thus the study of the ESO dynamic requires mathematical tools of the nonlinear systems analysis. This paper establishes the sufficient conditions for absolute stability of the ESO. Based on this study, a methodology to estimate several nonlinear functions in dynamics systems is proposed.     

Structural and electronic properties of La‐doped CaTiO3 crystal

There is experimental and computational evidence that some important properties such as electrical conductivity and ferroelectricity in the CaTiO₃ crystal change according to the dopant states. Using an INDO quantum‐chemical computational method modified for crystal calculations we explore the stability of the La‐doped CaTiO₃ crystal in both phases, cubic and orthorhombic. The calculations are carried out by means of the supercell model based on the LUC (large unit cell) approach as it is implemented into the CLUSTERD computer code. The equilibrium geometry for impurity is found together with the crystalline lattice distortions. Atomic displacements and relaxation energies are analyzed in a comparative manner for the two crystallographic phases. A new effect of electron transfer from the local one‐electron energy level within the band‐gap to the conduction band is observed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002