Approximation by translates of refinable functions

Summary. The functions are refinable if they are combinations of the rescaled and translated functions . This is very common in scientific computing on a regular mesh. The space of approximating functions with meshwidth is a subspace of with meshwidth . These refinable spaces have refinable basis functions. The accuracy of the computations depends on , the order of approximation, which is determined by the degree of polynomials that lie in . Most refinable functions (such as scaling functions in the theory of wavelets) have no simple formulas. The functions are known only through the coefficients in the refinement equation – scalars in the traditional case, matrices for multiwavelets. The scalar "sum rules" that determine are well known. We find the conditions on the matrices that yield approximation of order from . These are equivalent to the Strang–Fix conditions on the Fourier transforms , but for refinable functions they can be explicitly verified from the . Received August 31, 1994 / Revised version received May 2, 1995     

Classification of Nonexpansive Symmetric Extension Transforms for Multirate Filter Banks

This paper describes and classifies a family of invertible discrete-time signal transforms, referred to assymmetric extension transforms(SET's), for finite-length signals. SET's are algorithms for applying perfect reconstruction multirate filter banks to symmetric extensions of finite-length signals, thereby avoiding the boundary artifacts introduced by simple periodic extension. A key point is when such symmetric decompositions can be formed with no increase in data storage requirements (“nonexpansive decompositions”). Transforms based on three types of symmetric extension and four classes of linear phase filters are analyzed in terms of their memory requirements for generalM-channel perfect reconstruction filter banks. The classification is shown to be complete in the sense that it contains all possible nonexpansive SET's. Completeness is then used to deduce design constraints on the construction of nonexpansiveM-channel SET's, including new obstructions to the existence of certain classes of filter banks. This paper also forms the principal technical reference on the SET algorithms incorporated in the Federal Bureau of Investigation's digital fingerprint image coding standard.     

Butylated hydroxytoluene enediyne: access to diradical and electrophilic quinone methide intermediates

A theoretical study was carried out on the unimolecular reaction of an enediyne with a fused butylated hydroxytoluene to internally scavenge the p‐benzyne diradical sites formed after the Bergman cyclization. The calculations revealed that the conversion of the p‐benzyne diradical (2‐tert‐butyl‐4‐methyl‐5,8‐didehydro‐1‐naphthalenol) to p‐quinone methide is favored over the conversion to a phenoxy/benzene diradical 4 in an approximate 95:5 ratio. Based on this model, the Bergman cyclization leads in a bifunctional manner to intermediates for competing reactivity with intermolecular H‐atom abstraction. Copyright © 2015 John Wiley & Sons, Ltd.     

Development of Surface Nano-Crystallization in Alloys by Surface Mechanical Attrition Treatment (SMAT)

Nanometer-sized grain structures that exhibit a large number of grain boundaries on the surface of a bulk material demonstrate excellent properties relative to their coarse-grained (CG) equivalents. Surface modification using surface mechanical attrition treatment (SMAT) is an option that cab be used to tailor the corrosion, tribological, mechanical, and chemical reaction properties of a surface. SMAT is an effective route to create the nanostructured surface layer. The SMAT process has unique advantages compared with the other coating and deposition techniques for surface nanocrystallization. For example, SMAT does not alter the chemical composition of the nanocrystalline surface layer in the matrix. In addition, SMAT has been demonstrated to activate the material surface layer by surface modification and enhance the atomic diffusivity. This article presents a review of the advantages offered by the SMAT technique for the creation of high performance surface layers. The influence of the created nanocrystalline layer on mechanical, physical, and chemical properties is assessed. Developments and the current status of the surface nanolayer that are formed are evaluated from a physical approach. Finally, prospects for the future development of grain refinement on the surface of a material matrix and potential applications are presented.     

Approximations of open quotient and speed quotient from glottal airflow and egg waveforms : Effects of measurement criteria and sound pressure level

Noninvasive measures of vocal fold activity are useful for describingnormal and disordered voice production. Measures of open and speed quotient from glottal airflow and electroglottographic (EGG) waveforms have been used to describe timing events associated with vocal fold vibration. To date, there has been little consistency in the measurement criteria used to calculate quotient values. In this study, criteria of 20% and 50% were applied to the AC amplitude of glottal airflow and inverted EGG waveforms for measurement of open quotient. Criteria of 20%, 50%, and 80%, and a midslope criterion that segmented the waveform between 20% and 80% of the waveform amplitude, were used for the calculation of speed quotient. Subjects produced waveforms at sound pressure levels (SPL) of 70, 75, 80 and 85 dB. Results indicated that approximations of open quotient obtained from the glottal airflow waveform significantly decreased using both the 20% and 50% criteria as SPL increased from 80 to 85 dB. No significant changes were found in open quotient from the EGG waveform as a function of SPL. Results of speed quotient measures from the glottal airflow and EGG waveforms showed a generally increasing trend as SPL increased, although the differences were not statistically significant. The data suggest that the signal type, measurement criterion and SPL must be considered in interpreting quotient measures.     

Optical Thin-Film Sensors for the Determination of Aqueous Halide Ions

Fourteen thin-film optical sensors in which halide-sensitive fluorophores are immobilized in a thin copolymer film (50 m, dry) have been developed and characterized. The sensor films use rhodamine, 6-methoxyquinoline, and harmane dyes which have been functionalized and bound to a hydrophilic copolymer. The sensor films are reversibly capable of determining aqueous bromide and iodide with 4 and 2% accuracy, respectively, at concentrations of around 10^–3 mol dm^–3, and are more sensitive than previous plastic sensor fabrications. The 90% response time to molar iodide is 30–60 s. A combination of sensor films allows the simultaneous determination of both I^– and Br^– in a mixed-halide solution. The interference of several ions, including pseudo-halides, on the sensor films has been studied.     

<Emphasis Type="Italic">L</Emphasis><Subscript>∞</Subscript>-Algebras from Multisymplectic Geometry

A manifold is multisymplectic, or more specifically n-plectic, if it is equipped with a closed nondegenerate differential form of degree n + 1. In previous work with Baez and Hoffnung, we described how the ‘higher analogs’ of the algebraic and geometric structures found in symplectic geometry should naturally arise in 2-plectic geometry. In particular, just as a symplectic manifold gives a Poisson algebra of functions, any 2-plectic manifold gives a Lie 2-algebra of 1-forms and functions. Lie n-algebras are examples of L _∞-algebras: graded vector spaces equipped with a collection of skew-symmetric multi-brackets that satisfy a generalized Jacobi identity. Here, we generalize our previous result. Given an n-plectic manifold, we explicitly construct a corresponding Lie n-algebra on a complex consisting of differential forms whose multi-brackets are specified by the n-plectic structure. We also show that any n-plectic manifold gives rise to another kind of algebraic structure known as a differential graded Leibniz algebra. We conclude by describing the similarities between these two structures within the context of an open problem in the theory of strongly homotopy algebras. We also mention a possible connection with the work of Barnich, Fulp, Lada, and Stasheff on the Gelfand–Dickey–Dorfman formalism.     

Depth-profiling the composition of bimetallic nanoparticles using medium energy ion scattering

The near monolayer depth resolution of medium energy ion scattering is utilized to develop a probe of the depth dependent composition of bimetallic nanoparticles supported on planar oxide supports. The approach fits spectra of scattered ion intensity versus ion energy at well-defined scattering angles taking into account the asymmetric line shape in such spectra and also the depth dependent loss processes encountered by incident ions as they pass through the bimetallic particles.