Protter-Morawetz multidimensional problems

About 50 years ago M.H. Protter introduced boundary value problems that are multidimensional analogues of the classical plane Morawetz problems for equations of mixed hyperbolic-elliptic type that model transonic fluid flows. Up to now there are no general existence results for the Protter-Morawetz multidimensional problems, and an understanding of the situation is not at hand. At the same time, Protter also formulated boundary value problems in the hyperbolic part of the domain??the nonhomogeneous wave equation is studied in a (3+1)-D domain bounded by two characteristic cones and a non-characteristic ball. These problems could be considered as multidimensional variants of the Darboux problem in ?². In the frame of classical solvability the hyperbolic Protter problem is not Fredholm, because it has an infinite-dimensional cokernel. On the other hand, it is known that the unique generalized solution of a Protter problem may have a strong power-type singularity even for some very smooth right-hand side functions. This singularity is isolated at the vertex O of the boundary light cone and does not propagate along the characteristic cone. In the general case of smooth right-hand side function, some necessary and sufficient conditions for the existence of a bounded solution are given and a priori estimates for the solution are found. The semi-Fredholm solvability of the problem is proved.     

Relaxation methods for solving linear inequality systems: converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In González-Gutiérrez and Todorov (Optim. Lett. doi:10.1007/s11590-010-0244-4, 2011), an algorithm, called extended relaxation method, for solving the feasibility problem has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we consider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.     

Some Data on the Dynamics of Corrosion Processes in Water Circulation Cooling Systems

 Both origin and changes in phase composition of corrosion products deposited on Standard Carbon Steel during 313 days of exposure were monitored by X-ray diffraction analysis. The corrosion was caused by water from industrial cooling systems in the presence as well as in the absence an inhibitor. The predominant components of the corrosion products were initially found to be carbonates such as CaCO₃ as well as hydroxycarbonates like Fe₂(OH)₂CO₃; they were followed by the appearance of other products such as γ-FeOOH, Fe₃O₄, and α-FeOOH. The corresponding chemical reactions were found to comply with first-order kinetics. The rate constants were calculated from changes in the relative intensities of the corresponding X-ray patterns of Standard Carbon Steel samples. In absence of the inhibitor the rate of the corrosion processes were found to be 2.3 to 3 times higher than in its presence.     

Indicator space configuration for early warning of violent political conflicts by genetic algorithms

Recognition of preconflict situations has a powerful potential for early warning of violent political conflicts. This paper focuses on the design and application of artificial neural networks as classifiers of preconflict situations. Achieving a desired level of performance of the neural network relies on the appropriate construction of recognition space (selection of indicators) and the choice of network architecture. A fast and effective method for the design of reliable neural recognition systems is described. It is based on genetic algorithm techniques and optimizes both the configuration of input space and the network parameters. The implementation of the methodology provides for increased performance of the classifier in terms of accuracy, generalization capacity, computational and data requirements. This revised version was published online in June 2006 with corrections to the Cover Date.     

On Linear Inequality Systems with Smooth Coefficients

A linear inequality system with infinitely many constraints is polynomial [analytical] if its index set is a compact interval of the real line and all its coefficients are polynomial [analytical] functions of the index on this interval. This paper provides sufficient conditions for a given closed convex set to be the solution set of a certain polynomial or at least analytical system.The authors are indebted to Dr. J. M. Almira for valuable comments and suggestions.     

Photoinduced dichroism and birefringence in films of Mordant Pure Yellow/poly(vinyl alcohol): simultaneous real-time investigations at two wavelengths

Photoinduced anisotropy in films of azo-dye Mordant Pure Yellow (MPY) dissolved in a polyvinyl alcohol matrix, is investigated. The photodichroism and photoinduced birefringence are measured in real time for two wavelengths, 488 nm (in the absorption band) and 633 nm (outside it), on excitation with an Ar⁺ laser beam. It is shown that strong dichroism is induced without changing the average optical density of the film, and the kinetic curves of the birefringence and the dichroism are substantially different. The conclusion is made that the photoprocesses of the dye molecules cause a reconstruction of the matrix.     

Production of high-energy muons in gamma showers

We have calculated the number of high-energy muons in gamma showers generated by photoproduction and by muon pair creation. The prompt muons have flatter energy spectrum than the muons, which come from photoproduction and contribute significant fraction of the total muon rates for E_μ ? 1 TeV. The total rate of high-energy muons in gamma showers is, however, very low.     

On Subspace Lattices I. Closedness Type Properties and Tensor Products

We study properties of subspace lattices related to the continuity of the map Lat and the notion of reflexivity. We characterize various “closedness” properties in different ways and give the hierarchy between them. We investigate several properties related to tensor products of subspace lattices and show that the tensor product of the projection lattices of two von Neumann algebras, one of which is injective, is reflexive.