Deterministic phase unwrapping in the presence of noise

We present a new Fourier-based exact solution for deterministic phase unwrapping from experimental maps of wrapped phase in the presence of noise and phase vortices. This single-step approach has superior performance for images with high phase gradients or insufficient digital sampling approaching 2pi/pixel and therefore performs as a fast and practical solution for the phase-unwrapping problem for experimental applications in applied optics, physics, and medicine.     

Generalized Variation of Mappings with Applications to Composition Operators and Multifunctions

We study (set-valued) mappings of bounded -variation defined on the compact interval I and taking values in metric or normed linear spaces X. We prove a new structural theorem for these mappings and extend Medvedev's criterion from real valued functions onto mappings with values in a reflexive Banach space, which permits us to establish an explicit integral formula for the -variation of a metric space valued mapping. We show that the linear span GV (I;X) of the set of all mappings of bounded -variation is automatically a Banach algebra provided X is a Banach algebra. If h:I× X Y is a given mapping and the composition operator is defined by (f)(t)=h(t,f(t)), where tI and f:I X, we show that :GV (I;X) GV (I;Y) is Lipschitzian if and only if h(t,x)=h₀(t)+h₁(t)x, tI, xX. This result is further extended to multivalued composition operators with values compact convex sets. We prove that any (not necessarily convex valued) multifunction of bounded -variation with respect to the Hausdorff metric, whose graph is compact, admits regular selections of bounded -variation.     

Embedding obstructions and -complexes

The vanishing of Van Kampen's obstruction is known to be necessary and sufficient for embeddability of a simplicial -complex into for , and it was recently shown to be incomplete for . We use algebraic-topological invariants of four-manifolds with boundary to introduce a sequence of higher embedding obstructions for a class of -complexes in .

     

Tridiagonal canonical matrices of bilinear or sesquilinear forms and of pairs of symmetric,skew-symmetric,or Hermitian forms

Tridiagonal canonical forms of square matrices under congruence or *congruence, pairs of symmetric or skew-symmetric matrices under congruence, and pairs of Hermitian matrices under *congruence are given over an algebraically closed field of characteristic different from 2.     

On the application of a ZrO2‐based solid electrolyte in isotope ratio mass spectrometry

The application of a high‐temperature electrochemical reactor based on stabilized zirconium dioxide (0.9 ZrO₂0.1 Y₂O₃) for organic gas sampling in continuous‐flow isotope‐ratio mass spectrometry (CF‐IRMS) has been found to be efficient. This solid electrolyte reactor (SER) can also be used as a chromatographic detector for the quantitative measurements of organic gases. A three‐electrode SER system was studied. Complete stoichiometric oxidation of organic gases has been achieved at 900–950°C due to the large catalytic surface area of the porous platinum coating. At this temperature, the oxygen ions formed from the oxygen of ambient air on the outer surface of the reactor migrate through the solid electrolyte under the action of the applied electric field and allow combustion of gases being analyzed to be effected. It should be noted that oxygen gas was not introduced into the gas‐carrier flow. Similar results for the measurements of carbon isotope ratios were obtained at the oxidation of hydrocarbon gases in both the standard and the solid electrolyte reactors. Copyright © 2009 John Wiley & Sons, Ltd.     

Effect of Electron–Ion Collisions on the Generation of Terahertz Radiation at the Interaction of Femtosecond Pulse with Plasma in Magnetic Field

Journal of Russian Laser Research - We establish the conditions under which collisions of electrons with ions affect the generation of terahertz radiation at normal incidence of a laser pulse on a...     

Reactivity of 3-formyl- and 3-cyanothiochromones toward some N- and C-nucleophiles. Novel synthesis of 3-substituted 2-aminothiochromones

The reactions of 3-formylthiochromone with o-phenylenediamines, o-aminobenzenethiol, and indoles proceeded at the aldehyde group to give 3-(benzimidazol-2-yl)thiochromone, 3-(benzothiazol-2-yl)thiochromone, and 3-di(indol-3-yl)methylthiochromones, respectively. 3-Formyl- and 3-cyanothiochromones react with primary aromatic amines and phenylhydrazine to give the corresponding anils and phenylhydrazones of 3-formyl- and 2-amino-3-formylthiochromones. The reaction of 3-cyanochromones with o-phenylenediamines gave 2-amino-3-[(2-aminophenyl)iminomethyl]-4H-chromen-4-ones.