A Schur test for weighted mixed-norm spaces

Summary We prove a Schur test for mixed-norm spaces L^p,q, 1 < p,q < ∞. Also we prove another version of the Schur test for discrete weighted mixed-norm spaces l^p,q _w, 1 < p,q < ∞, and wis a weight. We show that if w ₁, and w ₂are two weight functions on the index sets Jx Iand K x Lrespectively, and A =(a _{ji, kl} ) _{j∈J, i∈I, k∈K, l∈L} is an infinite matrix, then under certain conditions, Ais a bounded operator from l^p,q _w1, 1 < p,q < ∞ to l^p,q _w2. This will be a key result in proving boundedness of important operators in our work in time-frequency analysis.</o:p>     

求解线性方程组的顺序算法和并行算法的理论时耗估价

本文讨论了求解密集型线性方程组的两种并行算法。这两种算法都在下上单元(LU)分解。法的基础上使用了前向和后向置换进行的。这些算法在数值上是稳定的,并在顺序平衡机上用各种处理程序进行试验,都得到良好效果。     

A note on a theorem of Fejér

There is well known classical Theorem of Fejér [2] on determination of jump of a function of the classV ₁. This Theorem has been generalized for different method of summability by various mathematicians in the classV _t only. In this paper we extend the Theorem of Fejér and of Siddiqi [3] to the strictly larger classV _p (1<p<∞).     

Conformational preference of substituted naphthalenes. 2—proton–proton coupling constants of hydroxy derivatives of naphthalene

Long-range proton–proton coupling constants between the hydroxy proton and ring protons were employed to deduce the conformational preferences of 1- and 2-hydroxynaphthalene. 2,6-Dibromo-1,5-dihydroxy-naphthalene, 2-acetyl-1-hydroxynaphthalene, 1,6-dibromo-2-hydroxynaphthalene and 2-hydroxy-1-naphthaldehyde were used as model compounds. Molecular orbital calculations at the CNDO/2 and INDO level were used to calculate the energy and the long-range proton–proton coupling of different conformers of 1- and 2-hydroxynaphthalene.     

Pentacoordinated Tin(IV) chloride complexes

Preparation and I.R. spectra of tin(IV) chloride complexes with acridine and piperazine have been described and their structures have been suggested.     

Proton magnetic resonance spectra of 2,6-disubstituted naphthalenes

The spectra of several 2-methyl-6-R-disubstituted naphthalenes (R=H, Me, I, NO₂, Cl, SO₂Cl, OH, OMe, COMe, Br, F and NHCOMe), have been analysed. Chemical shift and coupling constant values of these compounds are presented. The proton chemical shifts have been found to correlate with the ortho parameter, Q.     

Transfer of radioactivity from soil to vegetation in Rechna Doab, Pakistan

In Rechna Doab, samples of the most common vegetation, perennial grass Desmostachya bipinnata (dab), were collected along with soil samples from 29 sites. Natural radioactivity of 22?Ra, 232Th/22?Ac and ??K was measured by using high purity germanium-based gamma ray spectrometer. Activity concentration levels of 22?Ra, 232Th/22?Ac and ??K in soil were found to be 46.8 ± 6.2 (36.0-57.6), 61.4 ± 5.9 (48.2-73.2) and 644.8 ± 73.9 (537.7-868.4) Bq kg?1 (dry mass), respectively, and those in vegetation were 2.74 ± 1.70 (1.00-6.39), 2.24 ± 0.59 (1.56-2.61) and 172.72±113.37 (53.14-469.24) Bq kg?1 (dry mass), respectively. The measured values of the activity concentration in vegetation are comparable with some other international data. Calculated soil to vegetation transfer factors of 22?Ra, 22?Ac and ??K were 0.06 ± 0.03 (0.02-0.14), 0.04 ± 0.01 (0.03-0.04) and 0.26 ± 0.16 (0.09-0.69). The mean outdoor absorbed dose rate in air for the area under study was determined as 8.22 nGy h?1 and the mean indoor absorbed dose rate in air was 11.52 nGy h?1. The total annual effective dose to the general public from the vegetation was found to be (0.02-0.16) mSv, which is below the recommended limit value of 1 mSv y?1 for the general public. The dab vegetation under study was found to be radiologically safe for the population and environment.     

Dual beam method for laser welding of galvanized steel: Experimentation and prospects

Laser welding of zinc-coated steel sheets in lap configuration poses a challenging problem, because of the zinc vapours spoiling the quality of the weld. In continuation to the earlier work, the novel solution of dual laser beam method for lap welding of galvanized steel sheets is discussed here in view of the recently obtained observations and ensuing concerns. In this method the precursor beam cuts a slot, thus making an exit path for the zinc vapours, while the second beam performs the needed welding. The metallurgical analysis of the welds is encouraging showing absence of zinc in the welded area. In the current work on this technique, new experimental results have been obtained verifying the earlier observations. Along with this, the possibility of using a transversely split-up beam for the welding purposes with this approach is discussed and analyzed in this paper. This new technique is expected to be very useful in prospective industrial applications requiring higher welding throughput along with the needed quality.     

Generalized Contour Dynamics: A Review

Contour dynamics is a computational technique to solve for the motion of vortices in incompressible inviscid flow. It is a Lagrangian technique in which the motion of contours is followed, and the velocity field moving the contours can be computed as integrals along the contours. Its best-known examples are in two dimensions, for which the vorticity between contours is taken to be constant and the vortices are vortex patches, and in axisymmetric flow for which the vorticity varies linearly with distance from the axis of symmetry. This review discusses generalizations that incorporate additional physics, in particular, buoyancy effects and magnetic fields, that take specific forms inside the vortices and preserve the contour dynamics structure. The extra physics can lead to time-dependent vortex sheets on the boundaries, whose evolution must be computed as part of the problem. The non-Boussinesq case, in which density differences can be important, leads to a coupled system for the evolution of both mean interfacial velocity and vortex sheet strength. Helical geometry is also discussed, in which two quantities are materially conserved and whose evolution governs the flow.