Spline collocation methods for nonlinear Volterra integral equations with unknown delay

In this paper we introduce and study polynomial spline collocation methods for systems of Volterra integral equations with unknown lower integral limit arising in mathematical economics. Their discretization leads to implicit Runge-Kutta-type methods. The global convergence and local superconvergence properties of these methods are proved, and the theory is illustrated by a numerical example arising in the application of such equations in certain mathematical models of liquidation.     

Spectral methods for pantograph-type differential and integral equations with multiple delays

We analyze the convergence properties of the spectral method when used to approximate smooth solutions of delay differential or integral equations with two or more vanishing delays. It is shown that for the pantograph-type functional equations the spectral methods yield the familiar exponential order of convergence. Various numerical examples are used to illustrate these results.      

Blow-up behavior of Hammerstein-type delay Volterra integral equations

We consider the blow-up behavior of Hammerstein-type delay Volterra integral equations (DVIEs). Two types of delays, i.e., vanishing delay (pantograph delay) and non-vanishing delay (constant delay), are considered. With the same assumptions of Volterra integral equations (VIEs), in a similar technology to VIEs, the blow-up conditions of the two types of DVIEs are given. The blow-up behaviors of DVIEs with non-vanishing delay vary with different initial functions and the length of the lag, while DVIEs with pantograph delay own the same blow-up behavior of VIEs. Some examples and applications to delay differential equations illustrate this influence.     

Splines (with optimal knots) are better

Let S^M _k be the Polynominal splines of degree n-1, and with K segments. If f∈ C ⁿ [a,b],then the distance in the L^p-norm form(0< p ≦ ∞)of from S ^M _k is boundedby M/K ⁿ , with a much smaller M than in similar estimates for other processes of approximation.     

The Molecular and Crystal Structure of the Glycopeptide A-40926 Aglycone

The crystal structure of a glycopeptide antibiotic A–40926 aglycone was investigated by X-ray analysis at ?120°. A-40926 crystallises in the orthorhombic space group P2₁2₁2₁ with two monomers in the asymmetric unit, a = 21.774(4), b = 28.603(7), c = 29.757(4) Å. ‘Conventional’ direct methods approach failed to solve the structure, but a novel iterative real/reciprocal space procedure was successful. Refinement against 11248 F² data led to R1 = 13.3% for 6770 F > 4σ (F). The two monomers of A-40926 have similar conformations and are bound by antiparallel H-bonds to form a ‘chain’ structure of connecting dimers. The antibiotic molecule possesses a ‘binding pocket’ for the C-terminal carboxy group of the cell-wall protein, which is consisten with suggestions based on NMR data and the recently reported crystal structure of ureido-balhimycin. In A-40926 the monomers are polymerically linked by H-bonds, quite unlike the tight dimer formation observed in ureido-balhimycin.     

Non-Watson-Crick base pairs in RNA-protein recognition

The cellular functions of most RNA molecules involve protein binding, and non-Watson-Crick base pairs are hallmark sites for interactions with proteins. The determination of three-dimensional structures of RNA-peptide and RNA-protein complexes reveals the molecular basis of non-Watson-Crick base-pair recognition.     

Recent advances in capillary electrophoretic migration techniques for pharmaceutical analysis (2013–2015)

This review updates and follows‐up a previous review by highlighting recent advancements regarding capillary electromigration methodologies and applications in pharmaceutical analysis. General approaches such as quality by design as well as sample injection methods and detection sensitivity are discussed. The separation and analysis of drug‐related substances, chiral CE, and chiral CE‐MS in addition to the determination of physicochemical constants are addressed. The advantages of applying affinity capillary electrophoresis in studying receptor–ligand interactions are highlighted. Finally, current aspects related to the analysis of biopharmaceuticals are reviewed. The present review covers the literature between January 2013 and December 2015.     

Crystal‐Structure‐Guided Design of Self‐Assembling RNA Nanotriangles

RNA nanotechnology uses RNA structural motifs to build nanosized architectures that assemble through selective base‐pair interactions. Herein, we report the crystal‐structure‐guided design of highly stable RNA nanotriangles that self‐assemble cooperatively from short oligonucleotides. The crystal structure of an 81 nucleotide nanotriangle determined at 2.6 Å resolution reveals the so‐far smallest circularly closed nanoobject made entirely of double‐stranded RNA. The assembly of the nanotriangle architecture involved RNA corner motifs that were derived from ligand‐responsive RNA switches, which offer the opportunity to control self‐assembly and dissociation.