Synthesis and distribution of glycosaminoglycans in human leukemic B- and T-cells and monocytes studied using specific enzymic treatments and high-performance liquid chromatography

Identification of glycosaminoglycans (GAGs) synthesized by three human leukaemic cell lines-Jurkat (T-cell leukaemia), Daudi (Burkitt's lymphoma, B-cell leukaemia) and THP-1 (acute monocytic leukemia)-and normal peripheral blood mononuclear cells (PBMC) and their distribution among cell membrane and culture medium were studied. GAGs were isolated using ion-exchange chromatography on DEAE-Sephacel and their composition and fine chemical structure were studied using high-performance liquid chromatography with radiochemical detection. All cell lines synthesize chondroitin sulphate (CS) and heparan sulphate (HS) in both cell membrane and culture medium. No hyaluronan was detected using treatment with specific lyases and highly sensitive HPLC methodology. CS is the major secreted GAG in all cell lines tested and the major cell retained GAG in Jurkat and Daudi. HS is the major GAG in the cell membrane of THP-1. The amounts of distinct GAGs synthesized by all cancer cell lines differ from those produced by normal PBML indicating a major role of GAGs in malignant transformation of human lymphocytes and monocytes.     

Multivariate probabilistic approximation in wavelet structure

Letotherwiseand F(x,y).be a continuous distribution function on R~2.Then there exist linear wavelet operators L_n(F,x,y)which are also distribution functionand where the defining them mother wavelet is(x,y).These approximate F(x,y)in thesupnorm.The degree of this approximation is estimated by establishing a Jackson typeinequality.Furthermore we give generalizations for the case of a mother wavelet ≠,whichis just any distribution function on R~2,also we extend these results in R~r,r>2.     

Monotone and probabilistic wavelet approximation

Continuous functions are approximated by wavelet operators. These preserve mone tonicity and transform continuous probability distribution functions into probability distribution functions. The degree of this approximation is estimated by establishing some Jackson type inequalities     

Poincaré like inequalities for semigroups, cosine and sine operator functions

Here we present Poincaré type general L _p inequalities regarding semigroups, cosine and sine operator functions.     

Higher order Ostrowski type inequalities over Euclidean domains

The classical Ostrowski inequality for functions on intervals estimates the value of the function minus its average in terms of the maximum of its first derivative. This result is extended to functions on general domains using the L^∞ norm of its nth partial derivatives. For radial functions on balls the inequality is sharp.     

Global smoothness and uniform convergence of smooth Gauss–Weierstrass singular operators

In this article we continue with the study of smooth Gauss–Weierstrass singular integral operators over the real line regarding their simultaneous global smoothness preservation property with respect to the L_p norm, 1≤p≤∞, by involving higher order moduli of smoothness. Also we study their simultaneous approximation to the unit operator with rates involving the modulus of continuity with respect to the uniform norm. The produced Jackson type inequalities are almost sharp containing elegant constants, and they reflect the high order of differentiability of the engaged function.     

The Levy radius of a set of probability measures satisfying basic moment conditions involving {t,t 2}

TheLevy radius for a set of probability measures satisfying certain standard moment conditions is introduced, through the Levy distance of these measures from the unit measure at a fixed point of the real line. Using a moment optimal result of Selberg, an algebraic algorithm is given for the exact calculation of this radius.     

Distributional Taylor formula

We derive a distributional Taylor formula with precise integral remainder. We give applications of it and estimates for the remainder.     

Univariate hyperbolic tangent neural network approximation

Here we study the univariate quantitative approximation of real and complex valued continuous functions on a compact interval or all the real line by quasi-interpolation hyperbolic tangent neural network operators. This approximation is derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its high order derivative. Our operators are defined by using a density function induced by the hyperbolic tangent function. The approximations are pointwise and with respect to the uniform norm. The related feed-forward neural network is with one hidden layer.