Norm convolution inequalities in Lebesgue spaces

We obtain upper and lower estimates of the (p; q) norm of the con-volution operator. The upper estimate sharpens the Young-type inequalities due to O'Neil and Stepanov.

A Schoenflies extension theorem for a class of locally bi-Lipschitz homeomorphisms

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Weighted norm inequalities for Fourier transforms of radial functions

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Wiener type theorems for Jacobi series with nonnegative coefficients

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A sharp Remez inequality for trigonometric polynomials

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Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates

We prove two-sided inequalities between the integral moduli of smoothness of a function on R d[superscript] / T d[superscript] and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is given by the equivalence results for functions satisfying certain regular conditions. Applications include a quantitative form of the Riemann-Lebesgue lemma as well as several other questions in approximation theory and the theory of function spaces.

Integral inequalities for algebraic and trigonometric polynomials

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Sobolev orthogonal polynomials on a simplex

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Filamin depletion blocks endoplasmic spreading and destabilizes force-bearing adhesions

Cell motility is an essential process that depends on a coherent, cross-linked actin cytoskeleton that physically coordinates the actions of numerous structural and signaling molecules. The actin cross-linking protein, filamin (Fln), has been implicated in the support of three-dimensional cortical actin networks capable of both maintaining cellular integrity and withstanding large forces. Although numerous studies have examined cells lacking one of the multiple Fln isoforms, compensatory mechanisms can mask novel phenotypes only observable by further Fln depletion. Indeed, shRNA-mediated knockdown of FlnA in FlnB¿/¿ mouse embryonic fibroblasts (MEFs) causes a novel endoplasmic spreading deficiency as detected by endoplasmic reticulum markers. Microtubule (MT) extension rates are also decreased but not by peripheral actin flow, because this is also decreased in the Fln-depleted system. Additionally, Fln-depleted MEFs exhibit decreased adhesion stability that appears in increased ruffling of the cell edge, reduced adhesion size, transient traction forces, and decreased stress fibers. FlnA¿/¿ MEFs, but not FlnB¿/¿ MEFs, also show a moderate defect in endoplasm spreading, characterized by initial extension followed by abrupt retractions and stress fiber fracture. FlnA localizes to actin linkages surrounding the endoplasm, adhesions, and stress fibers. Thus we suggest that Flns have a major role in the maintenance of actin-based mechanical linkages that enable endoplasmic spreading and MT extension as well as sustained traction forces and mature focal adhesions.

Zenith angle distributions at Super-Kamiokande and SNO and the solution of the solar neutrino problem

We have performed a detailed study of the zenith angle dependence of the regeneration factor and distributions of events at SNO and SK for different solutions of the solar neutrino problem. In particular, we discuss the oscillatory behavior and the synchronization effect in the distribution for the LMA solution, the parametric peak for the LOW solution, etc. A physical interpretation of the effects is given. We suggest a new binning of events which emphasizes the distinctive features of the zenith angle distributions for the different solutions. We also find the correlations between the integrated day-night asymmetry and the rates of events in different zenith angle bins. The study of these correlations strengthens the identification power of the analysis.

Design of surface forces apparatus for tribology studies combined with nonlinear optical spectroscopy

We describe the design, calibration, and performance of surface forces apparatus with the capability of illumination of the contact interface for spectroscopic investigation using optical techniques. The apparatus can be placed in the path of a Nd-YAG laser for studies of the linear response or the second harmonic and sum-frequency generation from a material confined between the two surfaces. In addition to the standard fringes of equal chromatic order technique, which we have digitized for accurate and fast analysis, the distance of separation can be measured with a fiber-optic interferometer during spectroscopic measurements (2 Å resolution and 10 ms response time). The sample approach is accomplished through application of a motor drive, piezoelectric actuator, or electromagnetic lever deflection for variable degrees of range, sensitivity, and response time. To demonstrate the operation of the instrument, the stepwise expulsion of discrete layers of octamethylcyclotetrasiloxane from the contact is shown. Lateral forces may also be studied by using piezoelectric bimorphs to induce and direct the motion of one surface.

Magnetic properties and giant magnetoresistance in melt-spun CoCu alloys

Magnetic, structural, and transport properties of as quenched and annealed Co10Cu90 samples have been investigated using x¿ray diffraction and a SQUID magnetometer. The largest value of MR change was observed for the as¿quenched sample annealed at 450°C for 30 min. The magnetic and transport properties closely correlate with the microstructure, mainly with Co magnetic particle size and its distribution. For thermal annealing the as quenched samples below 600°C, the Co particle diameters increase from 4.0 to 6.0 nm with a magnetoresistance (MR) drop from 33.0% to 5.0% at 10 K. Comparison with the theory indicates that the interfacial electron spin¿dependent scattering mechanism correlates with GMR for Co particle diameters up to about 6.0 nm.

Asymmetric giant magnetoresistance in Co10Cu90 magnetic granular alloys

We have observed a type of giant magnetoresistance (GMR) in magnetic granular Co10Cu90 alloys. The asymmetric GMR depends strongly on the size of magnetic Co particles, which exhibit superparamagnetic behavior at given measured temperature. The asymmetric GMR points to a metastable state that develops when the sample is field-cooled, which is lost after recycling. We propose that high-field cooling produces more effective parallel alignment of small unblocked Co particle moments and interfacial magnetizations, which contributes to the further decrease of the resistance in comparison with the samples zero-field-cooled, and then applied to the same field.