Periodic wavelets on the <Emphasis Type="Italic">p</Emphasis>-adic Vilenkin group

Using the Walsh-Dirichlet type kernel, we construct periodic wavelets on the p-adic Vilenkin group. These wavelets are similar to the trigonometric wavelets which were introduced by C. K. Chui and H. N. Mhaskar [1]. Results on the corresponding fast algorithms for decomposition and reconstruction are also discussed.     

q-Moduli of Continuity in H( ), p>0, and an Inequality of Hardy and Littlewood

Some aspects of the interplay between approximation properties of analytic functions and the smoothness of its boundary values are discussed. One main result describes the equivalence of a special q-modulus of continuity and an intrinsic K-functional. Further, a generalization of a theorem due to G. H. Hardy and J. E. Littlewood (1932, Math. Z.34, 403–439) on the growth of fractional derivatives is deduced with the help of this K-functional.     

One-sided invertibility of binomial functional operators with a shift on rearrangement-invariant spaces

Let be an oriented Jordan smooth curve and a diffeomorphism of onto itself which has an arbitrary nonempty set of periodic points. We prove criteria for one-sided invertibility of the binomial functional operator

The Newton Bracketing Method for Convex Minimization

An iterative method for the minimization of convex functions f :ⁿ , called a Newton Bracketing (NB) method, is presented. The NB method proceeds by using Newton iterations to improve upper and lower bounds on the minimum value. The NB method is valid for n = 1, and in some cases for n > 1 (sufficient conditions given here). The NB method is applied to large scale Fermat–Weber location problems.     

Sonochemical preparation of GaSb nanoparticles

A room temperature sonochemical method for the preparation of GaSb nanoparticles using less hazardous Ga and antimony chloride (SbCl(3)) as the precursors has been described. The formation of GaSb has been confirmed by means of XRD, EDAX, and XPS characterization. TEM and SAED results show that the as-prepared solid consists of nanosized GaSb crystals with sizes in the range 20-30 nm. The photoacoustic spectrum result reveals that the GaSb nanoparticles have a direct band gap of about 1.21 eV. On the basis of the control experiments and the extreme conditions produced by ultrasound, an ultrasound-assisted in-situ reduction/combination mechanism has been proposed to explain the reaction.     

Release of nitrosating species in the course of reduction of benzo-1,2,3,4-tetrazine 1,3-dioxides

[reaction: see text] The reduction of benzo-1,2,3,4-tetrazine 1,3-dioxides (BTDOs) 1 with Na(2)S(2)O(4) or SnCl(2) is suggested to proceed via intermediate N-nitrosobenzotriazoles 3 to afford benzotriazoles 2. The (15)N-labeling experiments exhibit that the N-3 atom of the tetrazine ring is incorporated into the nitroso group of 3 that is ultimately released into solution. It is possible that the biological activity of BTDOs is due to their ability to release nitrosating species, i.e., N-nitrosotriazol 3 or HNO(2), in the course of reduction.     

Universal scaling in transient creep

We present experimental evidence that pressure solution creep does not establish a steady-state interface microstructure as previously thought. Conversely, pressure solution controlled strain and the characteristic length scale of interface microstructures grow as the cubic root of time. Transient creep with the same scaling is known in metallurgy (Andrade creep). The apparent universal scaling of pressure solution transient creep is explained using an analogy with spinodal dewetting.