Mixed symbolic–numerical computations with general DAEs II: An applications case study

A variety of theorems and properties of nonlinear DAEs were discussed in part I. This paper illustrates many of these ideas within the context of analyzing a specific nonlinear system that exhibits a variety of interesting features. This revised version was published online in June 2006 with corrections to the Cover Date.     

Existence of solutions to BVP for linear differential-functional equations of elliptic type

We consider a homogeneous boundary value problem for a linear partial differential-functional equation of elliptic type. We prove the existence of a unique solution to such problem in a Sobolev space.     

Quantified functional analysis and seminormed spaces: A dual adjunction

In this work we investigate the natural algebraic structure that arises on dual spaces in the context of quantified functional analysis. We show that the category of absolutely convex modules is obtained as the category of Eilenberg-Moore algebras induced by the dualization functor [−,R] on locally convex approach spaces. We also establish a dual adjunction between the latter category and the category of seminormed spaces.     

Mean oscillation of functions and the Paley-Wiener space

The oscillatory behavior of functions with compactly supported Fourier transform is characterized in a quantified way using various function spaces. In particular, the results in this article show that the oscillations of a function at large scale are comparable to the oscillations of its samples on an appropriate discrete set of points. Several open questions about spaces of sequences are answered and applications in the study of commutator operators on the Paley-Wiener space are shown. Acknowledgements and Notes. Supported in part by NSF grants DMS 9303363 and DMS 9623251.     

On holomorphic Banach vector bundles over Banach spaces

Let X be a Banach space with a countable unconditional basis (e.g., X = ℓ ₂ Hilbert space), Ω ⊂ X pseudoconvex open, E → Ω a locally trivial holomorphic vector bundle with a Banach space Z for fiber type, the sheaf of germs of holomorphic sections of E → Ω, and Z ₁ the Banach space . Then and Ω × Z ₁ are holomorphically isomorphic, is acyclic and E is so to speak stably trivial over Ω in a generalized sense. We also show that if E is continuously trivial over Ω, then E is holomorphically trivial over Ω. In particular, if Z = ℓ ₂ or Ω is contractible, then E is holomorphically trivial over Ω. Some applications are also given. To my dear little daughter, Sári Mangala, on her third birthday. Supported in part by a Research Initiation Grant from Georgia State University.     

Asymptotics of the 1/2-dimension,Discrete Airy Equation and its Approximating Differential Equation

A discrete finite difference model is constructed for the Airy equation using a nonstandard scheme formulated by Mickens and Ramadhani. The method of dominant balance is then applied to obtain a first-order difference equation for the solution that increases sufficiently fast as k→∞. We then calculate the corresponding approximating differential equation and obtain its exact solution as well as its “exact” discrete finite difference representation. The application of various symmetry operations allows the determination of the related rapidly decreasing solution and the oscillatory solutions for negative values of x k>=hk, where h=?x.     

Identification and Biological Activity of Volatile Organic Compounds Emitted by Plants and Insects. IV. Composition of Vapor Isolated from Certain Species of Artemisia Plants

The components of fragrance from four wormwood species of theArtemisiaL. genus were analyzed by GC-MS. The major and minor components of volatile essential oils typical of the studied plant species were determined.     

A new lactam alkaloid from Portulaca oleracea L. and its cytotoxity

A new lactam alkaloid named oleraciamide D (1), indentified as (5R)-4-(3-methoxy-4-hydroxyphenyl)-5-(4-hydroxyphenyl)-5,6-dihydropyridin-2(1H)-one, together with five known compounds, indole-3-aldehyde (2), portulacatone (3), N-trans-feruloyloctopamine (4), N-trans-feruloyl-3′-O-methyldopamine (5) and N-trans-feruloyltyramine (6) were isolated from Potulaca oleracea L. Among them, indole-3-aldehyde (2) was isolated from the medicine for the first time. The structure of the new alkaloid was elucidated via UHPLC-ESI-Q-TOF/MS, 1D NMR and 2D NMR. The five known compounds were established by comparing the ¹H-NMR and ¹³C NMR with the reported literature. Oleraciamide D (1) showed cytotoxicity against SH-SY5Y cells when concentration at 50 uM by CCK-8 method.     

Novel spectrofluorimetric method for the determination of sulfite with rhodamine B hydrazide in a micellar medium

A novel spectrofluorimetric method for the determination of sulfite using rhodamine B hydrazide as fluorogenic reagent in the presence of polyoxyethylene sorbitan monooleate (Tween 80) surfactant micelles is described. The method is based on the mixture of sulfite with rhodamine B hydrazide, a colorless, non-fluorescent substance in Tween 80 surfactant micelles which gives rhodamine B-like fluorescence emission. The fluorescence intensity increase is linearly related to the concentration of sulfite in the range 5-800 ng ml⁻¹ with a detection limit of 1.4 ng ml⁻¹ (3σ). The optimal conditions for the detection of sulfite are evaluated and the possible detection mechanism is also discussed. The method has been successfully applied to the determination of total sulfite in wines and compares well with the standard iodimetric method.     

Hydrolyzed Tannins from Geranium pusillum

The polyphenolic compound 1-O-galloyl-3,6-hexahydroxybiphenyl-D-galactopyranoside (pusilagin) was isolated from the aerial part. The tannin structure was established using acid hydrolysis and IR, PMR, and ¹³C NMR spectral methods.