Exponential generating function of hyperharmonic numbers indexed by arithmetic progressions

There is a circle of problems concerning the exponential generating function of harmonic numbers. The main results come from Cvijovic, Dattoli, Gosper and Srivastava. In this paper, we extend some of them. Namely, we give the exponential generating function of hyperharmonic numbers indexed by arithmetic progressions; in the sum several combinatorial numbers (like Stirling and Bell numbers) and the hypergeometric function appear.     

Inhibitory Effect of Multivalent Rhamnobiosides on Recombinant Horseshoe Crab Plasma Lectin Interactions with Pseudomonas aeruginosa PAO1

To evaluate the molecular interaction of recombinant horseshoe crab plasma lectin (rHPL) with Pseudomonas aeruginosa PAO1, multivalent rhamnobioside derivatives were designed. Eight rhamnoclusters with three or four α(1–3)‐rhamnobiosides attached to different central cores, such as methyl gallate, pentaerythritol, and N‐Boc Tris, through either an ethylene glycol or a tetraethylene glycol linker, were assembled in two consecutive azide–alkyne cycloaddition click reactions. The synthetic method embraced the preparation of two α(1–3)‐rhamnobiosides with different linker arms and their conjugation, in stoichiometric or substoichiometric amounts, to propargyl ether‐functionalized tri‐ or tetravalent scaffolds. A divalent derivative and two self‐assembling rhamnobiosides were also prepared. The different architectures and valences of the rhamnoclusters provided an opportunity to evaluate the impact of topology and valency on the binding properties toward rHPL. Inhibitory ELISA data showed that all covalently linked rhamnoclusters could inhibit P. aeruginosa PAO1 recognition activity of rHPL with high efficacy. Trivalent rhamnobiosides showed a stronger inhibitory effect on P. aeruginosa PAO1 binding, and the more flexible clusters on a pentaerythritol or a Tris core were superior to the less flexible methyl gallate‐based clusters. Interestingly, the length of the linker arms had a very low impact on the binding ability of the rhamnoclusters. Herein, the two trivalent derivatives on an N‐Boc protected Tris central core were the best inhibitors. The self‐assembling amphiphilic rhamnobioside derivatives were found to display no multivalent effect.     

Matrix/analyte ratio influencing polymer molecular weight distribution in matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry

Matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry (MALDI‐TOF‐MS) has been used to characterize poly(L‐lysine) polymers and unique oligomer peptides, like 10‐, 15‐ and 25‐mer [Lys]_n oligolysine peptides. Several matrices have been tried in order to find optimal conditions, but only α‐cyano‐4‐hydroxycinnamic acid gave analytically useful spectra. The synthetic oligomers and their mixtures gave good quality spectra, showing protonated and cationized molecules, including doubly charged species. The polymers, analogously, gave a wide distribution of single‐ and double‐cationized peak series. The polymer distributions observed indicate the presence of significant suppression effects. The concentration (matrix/analyte ratio) was found to influence the results significantly; distributions shifting to higher masses when higher polymer concentrations were used. This effect was studied in detail using the synthetic (‘monodisperse’) oligolysine peptides. It was found that the relative intensities change by over an order of magnitude in the 0.1–10 pmol/µL concentration range (typical for most proteomic analyses). The results indicate that concentration effects need to be considered when MALDI‐MS is used for quantitative purposes. Copyright © 2009 John Wiley & Sons, Ltd.     

Some identities of the r-Whitney numbers

In this paper we establish some algebraic properties involving r-Whitney numbers and other special numbers, which generalize various known identities. These formulas are deduced from Riordan arrays. Additionally, we introduce a generalization of the Eulerian numbers, called r-Whitney–Eulerian numbers and we show how to reduce some infinite summation to a finite one.     

Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence

In this paper we use the Euler-Seidel method for deriving new identities for hyperharmonic and r-Stirling numbers. The exponential generating function is determined for hyperharmonic numbers, which result is a generalization of Gosper’s identity. A classification of second order recurrence sequences is also given with the help of this method.      

Scaling tests of the cross section for deeply virtual Compton scattering

We present the first measurements of the e[over -->]p-->epgamma cross section in the deeply virtual Compton scattering (DVCS) regime and the valence quark region. The Q(2) dependence (from 1.5 to 2.3 GeV(2)) of the helicity-dependent cross section indicates the twist-2 dominance of DVCS, proving that generalized parton distributions (GPDs) are accessible to experiment at moderate Q(2). The helicity-independent cross section is also measured at Q(2)=2.3 GeV(2). We present the first model-independent measurement of linear combinations of GPDs and GPD integrals up to the twist-3 approximation.