Reducing systems of linear differential equations to a passive form

In this paper, an application of the Riquer-Thomas-Janet theory is described for the problem of transforming a system of partial differential equations into a passive form, i.e., to a special form which contains explicitly both the equations of the initial system and all their nontrivial differential consequences. This special representation of a system markedly facilitates the subsequent integration of the corresponding differential equations. In this paper, the modern approach to the indicated problem is presented. This is the approach adopted in the Knuth-Bendix procedure [13] for critical-pair/completion and then Buchberger's algorithm for completion of polynomial ideal bases [13] (or, alternatively, for the construction of Groebner bases for ideals in a differential operator ring [14]). The algorithm of reduction to the passive form for linear system of partial differential equations and its implementation in the algorithmic language REFAL, as well as the capabilities of the corresponding program, are outlined. Examples illustrating the power and efficiency of the system are presented.     

Angle theorems for the Lagrangian mean curvature flow

We prove that symplectic maps between Riemann surfaces L, M of constant, nonpositive and equal curvature converge to minimal symplectic maps, if the Lagrangian angle for the corresponding Lagrangian submanifold in the cross product space satisfies . If one considers a 4-dimensional K?hler-Einstein manifold of nonpositive scalar curvature that admits two complex structures J, K which commute and assumes that is a compact oriented Lagrangian submanifold w.r.t. J such that the K?hler form w.r.t.K restricted to L is positive and , then L converges under the mean curvature flow to a minimal Lagrangian submanifold which is calibrated w.r.t. . Received: 11 April 2001 / Published online: 29 April 2002     

Symmetries and conservation laws of partial differential equations: Basic notions and results

The main notions and results which are necessary for finding higher symmetries and conservation laws for general systems of partial differential equations are given. These constitute the starting point for the subsequent papers of this volume. Some problems are also discussed.     

On the density of the space of continuous and uniformly continuous functions

For X a metrizable space and (Y,ρ) a metric space, with Y pathwise connected, we compute the density of (C(X,(Y,ρ)),σ)—the space of all continuous functions from X to (Y,ρ), endowed with the supremum metric σ. Also, for (X,d) a metric space and (Y,‖⋅‖) a normed space, we compute the density of (UC((X,d),(Y,ρ)),σ) (the space of all uniformly continuous functions from (X,d) to (Y,ρ), where ρ is the metric induced on Y by ‖⋅‖). We also prove that the latter result extends only partially to the case where (Y,ρ) is an arbitrary pathwise connected metric space.To carry such an investigation out, the notions of generalized compact and generalized totally bounded metric space, introduced by the author and A. Barbati in a former paper, turn out to play a crucial rôle. Moreover, we show that the first-mentioned concept provides a precise characterization of those metrizable spaces which attain their extent.     

Compatible relations on filters and stability of local topological properties under supremum and product

An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Fréchetness, strong Fréchetness, countable tightness and countable fan-tightness, some of which recover or refine classical results, some of which are new. The reader may find other applications as well.     

A study of structural, compositional and optical properties of spray-deposited non-stoichiometric (Zn,Fe)S thin films

Non-stoichiometric ternary chalcogenides (Zn,Fe)S were prepared in the film form by pyrolytic spray deposition technique, using air/nitrogen as the carrier gas. The precursor solution comprised of ZnCl₂, FeCl₂ and thiourea. The depositions were carried out under optimum conditions of experimental parameters viz. carrier gas (air/nitrogen) flow rate, concentration of precursor constituents, nozzle substrate distance and temperature of quartz substrate. The deposited thin films were later sintered in argon at 1073 K for 120 min.The structural, compositional and optical properties of the sintered thin films were studied. X-ray diffraction studies of the thin films indicated the presence of (Zn,Fe)S solid solution with prominent cubic sphalerite phase while surface morphology as determined by scanning electron microscopy (SEM) revealed a granular structure.The chemical composition of the resulting thin films as analyzed by energy dispersive X-ray analysis (EDAX) reflected the composition of the precursor solutions from which the depositions were carried out with Fe at% values ranging from 0.4 up to 33.SEM micrographs of thin films reveal that the grain sizes of the thin films prepared using air as carrier gas and N₂ as carrier gas are in the vicinity of 300 and 150 nm, respectively.The diffuse transmittance measurements for thin films, as a function of wavelength reveal the dependence of direct optical band gap on Fe content and type of phase.     

Syntactic characterization of closure under connected limits

Summary We give a syntactic characterization of (finitary) theories whose categories of models are closed under the formation of connected limits (respectively the formation of pullbacks and substructures) in the category of all structures. They are also those theories whose consistent extensions by new atomic facts admit in each component an initial structure (respectively an initial term structure), and also thoseT for whichM(T) is locally finitely multi-presentable in a canonical way. We also show that these two properties of theories are nonuniform.     

Magnetic properties of oxygenated carbon nitride films from RF-discharge in an acetylene, nitrogen, and oxygen mixture environments

Properties of oxygenated carbon nitride films have attracted the attention of physics researchers due to their magnetic and physical properties, as well as for their usefulness in the industry. The free radicals were investigated using electron paramagnetic resonance applied in the study of spin concentration due to the different mechanism of preparation of carbon nitride films by RF-discharge with different kinds of plasma. Unpaired spin concentrations, in the order of 10²⁰ per cm³, were measured and their time recombination dependency was important in those films. The films were grown by plasma enhanced chemical vapor deposition using mixtures of hydrocarbons, N₂ and O₂ in different proportions.     

Three New Polyoxygenated Steroids from Two Species of the South China Sea Gorgonian Muricella flexuosa and Menella verrucosa Brundin

Three new polyoxygenated steroids, muricesteroid ( 1 ), and menellsteroids A ( 2 ) and B ( 3 ), were isolated from two species of the South China Sea gorgonian Muricella flexuosa and Menella verrucosa Brundin , respectively. The structures of these new compounds were elucidated on the basis of extensive spectroscopic analysis, chemical methods and comparison with known related compounds.