Banach algebras of singular integral operators with piecewise continuous coefficients. General contour and weight

The Banach algebra generated by one-dimensional linear singular integral operators with matrix valued piecewise continuous coefficients in the spaceL _p (,) with an arbitrary weight is studied. The contour consists of a finite number of closed curves and open arcs with satisfy the Carleson condition. The contour may have a finite number of points of selfintersection. The symbol calculus in this algebra is the main result of the paper.     

Counterexamples in optimal quadrature

It is widely believed that order of exactness is a good measure of the quality of an algorithm for numerical quadrature. We show that this is not the case, by exhibiting a situation in which the optimal algorithm does not even integrate constants exactly. We also show that there are situations in which the penalty for using equidistant nodes is unbounded. Finally, we show that the complexity of obtaining an -approximation can be an arbitrary function of , i.e., there is no hardest quadrature problem.     

About the ratio of the size of a maximum antichain to the size of a maximum level in finite partially ordered sets

LetP be a finite partially ordered set. The lengthl(x) of an elementx ofP is defined by the maximal number of elements, which lie in a chain withx at the top, reduced by one. Letw(P) (d(P)) be the maximal number of elements ofP which have the same length (which form an antichain). Further let . The numbers and as well as all partially ordered sets for which these maxima are attained are determined.     

Surface chemical analysis of raw cotton fibres and associated materials

The surface chemical composition of raw unscoured cotton was successfully investigated by the surface analytical techniques X-ray Photoelectron Spectroscopy (XPS) and Time of Flight Secondary Ion Mass Spectrometry (ToF-SIMS). The presence of non-cellulosic material at the fibre surface was established and determined to be a complex mixture of fatty acids, alcohols, alkanes, esters and glycerides. The effect of scouring and bleaching was to reduce the surface concentration of these materials but even after aqueous processing some non-cellulosic material residue was still detected at the fibre surface.     

Theoretical Study on the Structures and Electronic Spectra of the Derivatives of C_(60)-P-2,4,6-Triphenyl Borazinc

1 INTRODUCTION The electron-transfer reaction of C60 derivatives, especially light-induced electron-transfer reaction, has been an active research field for a long time. Many researches are focused on the long-live charge- separated state caused by electron-transfer[1]. And several electron-transfers between electron donor and C60 or intramolecular electron-transfer have been confirmed. As an example, TTF-C60 is proved to be a short-live charge-separated compound[2].Due to the excelle…     

Bifunctional pyridyl alcohols with the bicyclo[3.3.0]octane scaffold in the asymmetric addition of diethylzinc to aldehydes

Some new pyridyl alcohols with the cis-bicyclo[3.3.0]octane scaffold were synthesized and used as chiral ligands for the enantioselective addition of diethylzinc to aldehydes. Ligands 4 were found to be far superior to the C₂-symmetric ligands 2 in terms of enantioselectivities. Quantitative yields and enantiomeric excesses of up to 92% were obtained when the ligand 4 was used. The carbonyl function in 4 proved to be beneficial for the high enantioselectivities in the addition of diethylzinc to aldehydes. Conversion of the carbonyl group into oxime or oxime ether group led to a sort of more active ligands, which catalyzed the same reaction with rate acceleration.     

On a pair of functional equations of combinatorial interest

The equations of the title appear in the author's paper Chromatic Sums for Rooted Planar Triangulations, V: Special Equations. (Canadian Journal of Mathematics, 26 (1974), 893–907). They appear in that paper as Equations (24) and (25). They are simultaneous equations for two unknown functionsl andy ₂ of two variablesy ₁ andz. A parameter is involved. The main result is that for = 2 cos (2/n), wheren is a positive integer >1, the two equations can be reduced to a single equation (numbered (49)). Solutions of this are known forn <7. From such solutions we can expect to get information about the averaged chromatic polynomials of planar triangulations with a given number of triangles.The present work is basically an expository paper on the theory given in Chromatic Sums, V, but it includes some new results and many simplifications.     

Characterization of the normal distribution by constant regression of quadratic statistics on linear statistics

This paper contains applications of theorems of [1] for quadratic statistics which have constant regression on linear statistics. Two theorems are proved. The first is a sufficient condition which assumes that the characteristic function of a sample is an entire function. The second gives a new characterization of the normal distribution.     

Secondary and Tertiary Structure of Polysaccharides in Solutions and Gels

Many polysaccharide chains can adopt ordered helical and ribbon-like secondary structures. It seems however that these chains are often so stiff and extended that the cooperative interactions necessary for stability in the solvent environment can only be achieved when inter-chain as well as intra-chain interactions are favorable. Hence we commonly find two-or more-stranded associations of helices, of ribbons, or of helices with ribbons. These can be regarded as tertiary and higher levels of structure. The ordered secondary structure characteristically requires a regular repeating sequence of sugar residues, and the termination of this sequence by insertion of a residue of different type may also terminate the secondary structure and hence the association in which it is involved. This is the mechanism by which native polysaccharides may link up to form three dimensional networks, or gels, in which state they perform their natural roles in maintaining the hydration and integrity of biological tissues. For several polysaccharides there is evidence that the mechanism of biological control over the fine topology and properties of the gel network is mediated by enzymes which modify sugar residues at the polymer level to change the pattern of “interrupting” sugar residues.     

Linear combination of concomitants of order statistics with application to testing and estimation

Summary Let (X ₁,Y ₁), (X ₂,Y ₂),…, (X _n,Y _n) be i.i.d. as (X, Y). TheY-variate paired with therth orderedX-variateX _rn is denoted byY _rn and terms the concomitant of therth order statistic. Statistics of the form are considered. The asymptotic normality ofT _n is established. The asymptotic results are used to test univariate and bivariate normality, to test independence and linearity ofX andY, and to estimate regression coefficient based on complete and censored samples.