Pairs of Dual Wavelet Frames from Any Two Refinable Functions

Starting from any two compactly supported refinable functions in L₂(R) with dilation factor d,we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L₂(R). Moreover, the number of vanishing moments of each of these wavelet frames is equal to the approximation order of the dual MRA; this is the highest possible. In particular, when we consider symmetric refinable functions, the constructed dual wavelets are also symmetric or antisymmetric. As a consequence, for any compactly supported refinable function in L₂(R), it is possible to construct, explicitly and easily, wavelets that are finite linear combinations of translates (d · – k), and that generate a wavelet frame with an arbitrarily preassigned number of vanishing moments.We illustrate the general theory by examples of such pairs of dual wavelet frames derived from B-spline functions.     

A nonmusical paradigm for identifying absolute pitch possessors

The ability to identify and reproduce sounds of specific frequencies is remarkable and uncommon. The etiology and defining characteristics of this skill, absolute pitch (AP), have been very controversial. One theory suggests that AP requires a specific type of early musical training and that the ability to encode and remember tones depends on these learned musical associations. An alternate theory argues that AP may be strongly dependent on hereditary factors and relatively independent of musical experience. To date, it has been difficult to test these hypotheses because all previous paradigms for identifying AP have required subjects to employ knowledge of musical nomenclature. As such, these tests are insensitive to the possibility of discovering AP in either nonmusicians or musicians of non-Western training. Based on previous literature in pitch memory, a paradigm is presented that is intended to distinguish between AP possessors and nonpossessors independent of the subjects' musical experience. The efficacy of this method is then tested with 20 classically defined AP possessors and 22 nonpossessors. Data from these groups strongly support the validity of the paradigm. The use of a nonmusical paradigm to identify AP may facilitate research into many aspects of this phenomenon.     

Off‐diagonal and asymptotic results on the Ramsey number r(K2,m,K2,n)

An upper bound on the Ramsey number r(K_2,n‐s,K_2,n) where s ≥ 2 is presented. Considering certain r(K_2,n‐s,K_2,n)‐colorings obtained from strongly regular graphs, we additionally prove that this bound matches the exact value of r(K_2,n‐s,K_2,n) in infinitely many cases if holds. Moreover, the asymptotic behavior of r(K_2,m,K_2,n) is studied for n being sufficiently large depending on m. We conclude with a table of all known Ramsey numbers r(K_2,m,K_2,n) where m,n ≤ 10. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 252–268, 2003     

Novel polyesteramide-based di- and triblock copolymers: From thermo-mechanical properties to hydrolytic degradation

Two types of biodegradable poly(ε-caprolactone (CLo))-co-poly(ε-caprolactam (CLa)) copolymers were prepared by catalyzed hydrolytic ring-opening polymerization. For the first type of materials, the respective cyclic comonomers were added simultaneously in the reaction medium leading to the formation of copolymers having a random distribution of co-units within the polyesteramide sequence, as evidenced by ¹H and ¹³C NMR. For the second type of copolymers, the cyclic comonomers were added sequentially in the reaction medium yielding diblock polyesteramides, again evidenced by NMR. The thermal and thermo-mechanical properties of the copolymers were investigated by DSC and DMA and correlated with the copolymer topology and composition. The copolymers were characterized by a storage modulus and α transition temperature intermediate to the modulus and T_g of the corresponding homopolymers. The chemical composition and molecular weight of the copolymers proved to have only a limited effect on the thermo-mechanical properties of the materials. The hydrolytic degradation of random copolymers was studied in a phosphate buffer at 60 °C and discussed in terms of chemical composition and molecular weight of the copolymers.     

Highly Sensitive Differential Pulse Voltammetric Determination of Cd,Zn and Pb Ions in Water Samples Using Stable Carbon‐Based Mercury Thin‐Film Electrode

A new carbon‐based mercury thin‐film electrode consisting of screen‐printed carbon on a low temperature co‐fired ceramic substrate was made. Ex‐situ mercury deposition in a potassium thiocyanate solution was used. This approach an electrode with high long‐term stability (>500 measurement cycles) and reproducibility (≤2 %) for sensitive determination of ultra trace heavy metals, using differential pulse anodic stripping voltammetry. The detection limits were 0.25, 0.08 and 5.5 ng mL^?1 for Cd(II), Pb(II), and Zn(II), respectively. The method was applied to the determination of the analytes in water, wastewater, lake water, and certified reference material samples with satisfactory results.