Statistical convergence of sequences and series of complex numbers with applications in Fourier Analysis and Summability

This is a survey paper on recent results indicated in the title. In contrast to the famous examples of Kolmogorov and Fejér on the pointwise divergence of Fourier series, the statistical convergence of the Fourier series of any integrable function takes place at almost every point; and the statistical convergencr of the Fourier series of any continuous function is uniform. Furthermore, Tauberian conditions are also presented, under which ordinary convergence of any sequence of real or complex numbers follows from its statistical summability.     

Racemization-Free Recovery of α-Hydroxyphosphonates from Their Carboxylic Esters

Ammonolysis (25% aqueous NH₃ - alcohols or THF) of carboxylic esters obtained from diastereoisomerically pure α-hydroxyphosphonates leads to recovery of the phosphonates without racemization in good to excellent yields.     

The Lp dual Minkowski problem for p > 1 and q > 0

General $L_p$ dual curvature measures have recently been introduced by Lutwak, Yang and Zhang [24]. These new measures unify several other geometric measures of the Brunn–Minkowski theory and the dual Brunn–Minkowski theory. $L_p$ dual curvature measures arise from qth dual intrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang [24] formulated the $L_p$ dual Minkowski problem, which concerns the characterization of $L_p$ dual curvature measures. In this paper, we solve the existence part of the $L_p$ dual Minkowski problem for $p>1$ and $q>0$, and we also discuss the regularity of the solution.     

Pore size distribution of micelle-templated silicas studied by thermoporosimetry using water and n-heptane

Thermoporosimetry, i.e., DSC measurements of melting point depression of water and heptane confined in mesopores, has been used for determination the pore size distribution of several mesoporous silicas synthesized with the use of micelle templates. Porosity of these materials was additionally characterized by low-temperature nitrogen adsorption and quasi-equilibrated thermodesorption of nonane. The pore size distributions obtained using the water thermoporosimetry were similar to those determined using the other methods, but the pore size values found for the narrow pore materials were underestimated by ca 1?nm. Too large pore sizes obtained for the wide pore silica from heptane thermoporosimetry were attributed to nonlinear dependence of the melting point depression on the reciprocal of the pore size.     

Vitamin B12 Phosphate Conjugation and Its Effect on Binding to the Human B12‐Binding Proteins Intrinsic Factor and Haptocorrin

The binding of vitamin B₁₂ derivatives to human B₁₂ transporter proteins is strongly influenced by the type and site of modification of the cobalamin original structure. We have prepared the first cobalamin derivative modified at the phosphate moiety. The reaction conditions were fully optimized and its limitations examined. The resulting derivatives, particularly those bearing terminal alkyne and azide groups, were isolated and used in copper‐catalyzed alkyne–azide cycloaddition reactions (CuAAC). Their sensitivity towards light revealed their potential as photocleavable molecules. The binding abilities of selected derivatives were examined and compared with cyanocobalamin. The interaction of the alkylated derivatives with haptocorrin was less affected than the interaction with intrinsic factor. Furthermore, the configuration of the phosphate moiety was irrelevant to the binding process.