Note on loss of regularity for solutions of the 3—D incompressible euler and related equations

One of the central problems in the mathematical theory of turbulence is that of breakdown of smooth (indefinitely differentiable) solutions to the equations of motion. In 1934 J. Leray advanced the idea that turbulence may be related to the spontaneous appearance of singularities in solutions of the 3—D incompressible Navier-Stokes equations. The problem is still open. We show in this report that breakdown of smooth solutions to the 3—D incompressible slightly viscous (i.e. corresponding to high Reynolds numbers, or highly turbulent) Navier-Stokes equations cannot occur without breakdown in the corresponding solution of the incompressible Euler (ideal fluid) equation. We prove then that solutions of distorted Euler equations, which are equations closely related to the Euler equations for short term intervals, do breakdown.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041, and partially supported by the National Science Foundation under Grant No. MCS-82-01599     

Structural characterisation of tyrosine-nitrated peptides by ultraviolet and infrared matrix-assisted laser desorption/ionisation Fourier transform ion cyclotron resonance mass spectrometry

Nitration of tyrosine residues in proteins may occur in cells upon oxidative stress and inflammation processes mediated through generation of reactive nitroxyl from peroxynitrite. Tyrosine nitration from oxidative pathways may generate cytotoxic species that cause protein dysfunction and pathogenesis. A number of protein nitrations in vivo have been reported and some specific Tyrosine nitration sites have been recently identified using mass spectrometric methods. High-resolution Fourier transform ion cyclotron resonance mass spectrometry (MALDI) FT-ICR-MS) is shown here to be a highly efficient method in the determination of protein nitrations. Following the identification of nitration of the catalytic site Tyr-430 residue of bovine prostacyclin synthase, we synthesised several model peptides containing both unmodified tyrosine and 3-nitro-tyrosine residues, using solid-phase peptide synthesis (SPPS). The structures of the nitrotyrosine peptides were characterised both by ESI- and by matrix-assisted laser desorption/ionisation (MALDI)-FT-ICR-MS, using a standard ultraviolet (UV) nitrogen nitrogen laser and a 2.97 microm Nd-YAG infrared laser. Using UV-MALDI-MS, 3-nitrotyrosyl-peptides were found to undergo extensive photochemical fragmentation at the nitrophenyl group, which may hamper or prevent the unequivocal identification of Tyr-nitrations in cellular proteins. In contrast, infrared-MALDI-FT-ICR-MS did not produce fragmentation of molecular ions of Tyr-nitrated peptides.     

Transient Hg,Ba+, Ca+ and Y+ Optical Emission Lines of a Mercury HID Lamp Exposed to X-Ray: Thermal Analysis of the Tungsten Electrode with Emissive Mixture Based on Barium,Calcium and Yttrium

Plasma Chemistry and Plasma Processing - A study is made on optical emission spectrum modification during X-ray exposure, in the case of a high-pressure mercury discharge lamp operated at several...     

Hamilton-Poisson formulation for the rotational motion of a rigid body in the presence of an axisymmetric force field and a gyroscopic torque

We give sufficient conditions for the rigid body in the presence of an axisymmetric force field and a gyroscopic torque to admit a Hamilton-Poisson formulation. Even if by adding a gyroscopic torque we initially lose one of the conserved Casimirs, we recover another conservation law as a Casimir function for a modified Poisson structure. We apply this frame to several well-known results in the literature.     

Fast and efficient separation of cytokinins from auxin and abscisic acid and their purification using mixed-mode solid-phase extraction

A method for separation of cytokinins from auxin and abscisic acid, which allows further separation of cytokinin ribotides from cytokinin bases, ribosides and glucosides and their purification on a single Oasis MCX column was developed. Due to the mixed reversed-phase and cation-exchange mode of the Oasis MCX sorbent the cationic cytokinin bases, ribosides and glucosides as well as the anionic auxin, abscisic acid and cytokinin ribotides are retained and can be sequentially eluted by solvents containing different concentrations of methanol and ammonium hydroxide. Characteristics of the method are high recoveries of analyzed phytohormones and their sufficient purity for quantification by HPLC–ELISA (RIA) or HPLC–MS.     

Influence of Cyclodextrins on the Kinetics of Oxidation of Amino Acids and BSA by Hydrazyl Radicals

The kinetics of oxidation of amino acids (Arg, His, Lys, Phe, Thr and Tyr), a dipeptide (Gly-His), and BSA (bovine serum albumin) by two persistent water soluble free radicals of the hydrazyl type has been studied.The rate decreases in the order Arg>Lys>Tyr>Thr>HisBSAPheGly-His with bothfree radicals. Addition to the reaction mixture of - and -cyclodextrin decreases the oxidation rate, probably due to amino acidencapsulation in the cyclodextrin cavity. -Cyclodextrin protects more efficiently against oxidation than -cyclodextrin.     

<Emphasis Type="Italic">N</Emphasis>-Alkoxy-3,5-dinitro-4-aminobenzoic acid derivatives with controlled physico-chemical properties

Starting from 4-chloro-3,5-dinitrobenzoic acid 1, compounds 2–10 (N-alkoxy-3,5-dinitro-4-aminobenzoic acid esters where alkoxy stands for methoxy, carboxymethoxy, triphenylmethoxy, or corresponding amides) have been obtained, from which compounds 3–5 and 7–10 are new, and for the known compounds 2 and 6 the synthetic procedure has been improved. The new derivatives have been characterized by appropriate means (IR, UV–Vis, ¹H- and ¹³C-NMR, fluorescence) and their properties were studied. Thus, depending on their structure, the compounds have acid properties, fluorescence and complexing properties with alkaline cations.     

New N-aryloxy-phthalimide derivatives. Synthesis,physico-chemical properties,and QSPR studies

Starting from N-hydroxyphthalimide 1 and the reactive fluoro- or chloro-nitroaryl derivatives 2, 3 and 4a-e (2-chloro-3,5-dinitropyridine; 3, NBD-chloride; 4a, 1-fluoro-2,4-dinitrobenzene; 4b, picryl chloride; 4c, 4-chloro-3,5-dinitrobenzotrifluoride; 4d, 2-chloro-3,5- dinitrobenzotrifluoride; 4e, 4-chloro-3,5-dinitrobenzoic acid) the corresponding N-(2-nitroaryloxy)-phthalimide derivatives 5a-e, or 6 and 7 were obtained and characterized by IR, UV-Vis ¹H-NMR and ¹³C-NMR spectroscopy. The TLC behavior and the hydrophobicity of these derivatives have been experimentally evaluated by R_M0 parameters (using RP-TLC). The experimental R_M0 parameters were compared with the calculated partition coefficient, log P. A QSPR study was also performed to establish possible correlations between the structure and physical properties (λ_max and R_M0) of compounds 5a-e, 6, and 7.      

Probing waveforms and adaptive receivers for active sonar

Active sonar systems involve the transmission and reception of one or more probing sequences, which provide a basis for extraction of target information in a region of interest. The probing sequences at the transmitter and signal processing at the receiver play crucial roles in the overall system performance. In this paper, CAN (cyclic algorithm-new) is employed to synthesize probing sequences with good aperiodic autocorrelation properties. The performance of the CAN sequences will be compared with those of pseudo random noise and random phase sequences. Two adaptive receiver designs, namely the iterative adaptive approach (IAA) and the sparse learning via iterative minimization (SLIM) method, will also be considered. IAA and SLIM will be compared with the conventional matched filter method. The performances of the algorithms will be illustrated via numerical examples, which show that CAN, IAA, and SLIM can contribute to the overall performance improvement of the active sonar systems.     

Optical resonator for high-power transverse flow CO2 lasers

A new design of the U-type resonator is described. In this way, a laser beam with symmetrical intensity profile (regarding to a symmetry plane) can be extracted from an active medium that exhibits gain asymmetry along one of the transverse directions. The whole area of the active medium cross-section can be used, and consequently the laser efficiency will be increased. This resonator structure was applied for efficiency power extraction (as a low order TEM modes laser beam) from a DC excited transverse flow CO₂ laser with cylindrical geometry. Although the cross-section area of the discharge was entirely used (including the cathode fall region), a symmetrical intensity profile of the laser beam (regarding to the two orthogonal symmetry planes) was obtained in the near field as well as in the far field; the gain asymmetry along the flow direction was compensated by the gas circulation fluidodynamical circuit with two counterflowing discharge channels. A double-U optical resonator was introduced in order to provide a laser beam with axial symmetry.For the practical construction of these two types of optical resonators we have developed two new types of 90° deflection elements: the first one, which does not reverse the image (and which has the properties of the pentaprism), and the second one, which rotates the image with 90° angle. Both elements exhibit good focusability if they are equipped with two concave mirrors.