Distributed-order fractional wave equation on a finite domain: creep and forced oscillations of a rod

We study waves in a rod of finite length with a viscoelastic constitutive equation of distributed fractional order type for the special choice of weight functions. Prescribing boundary conditions on displacement and stress, we obtain, as special solutions, cases corresponding to creep and forced oscillations. In solving system of differential and integro-differential equations, we use the Laplace transformation in the time domain.     

Intramolecular Hydrogen Bonding Restricts Gd–Aqua-Ligand Dynamics

Aqua ligands can undergo rapid internal rotation about the M−O bond. For magnetic resonance contrast agents, this rotation results in diminished relaxivity. Herein, we show that an intramolecular hydrogen bond to the aqua ligand can reduce this internal rotation and increase relaxivity. Molecular modeling was used to design a series of four Gd complexes capable of forming an intramolecular H-bond to the coordinated water ligand, and these complexes had anomalously high relaxivities compared to similar complexes lacking a H-bond acceptor. Molecular dynamics simulations supported the formation of a stable intramolecular H-bond, while alternative hypotheses that could explain the higher relaxivity were systematically ruled out. Intramolecular H-bonding represents a useful strategy to limit internal water rotational motion and increase relaxivity of Gd complexes.     

Suppleness of the sheaf of algebras of generalized functions on manifolds

We show that the sheaves of algebras of generalized functions Ω→G(Ω) and Ω→G^∞(Ω), Ω are open sets in a manifold X, are supple, contrary to the non-suppleness of the sheaf of distributions.     

Harmonic generalized functions in generalized function algebras

We investigate basic properties of harmonic generalized functions within the framework of J. F. Colombeau??s theory of generalized functions. In particular, we present various theorems concerning the Maximum principle, Liouville??s theorem, singularities and Poisson formula.     

Small molecule library synthesis using segmented flow

Flow chemistry has gained considerable recognition as a simple, efficient, and safe technology for the synthesis of many types of organic and inorganic molecules ranging in scope from large complex natural products to silicon nanoparticles. In this paper we describe a method that adapts flow chemistry to the synthesis of libraries of compounds using a fluorous immiscible solvent as a spacer between reactions. The methodology was validated in the synthesis of two small heterocycle containing libraries. The reactions were performed on a 0.2 mmol scale, enabling tens of milligrams of material to be generated in a single 200 mL reaction plug. The methodology allowed library synthesis in half the time of conventional microwave synthesis while maintaining similar yields. The ability to perform multiple, potentially unrelated reactions in a single run is ideal for making small quantities of many different compounds quickly and efficiently.     

Gabor pairs, and a discrete approach to wave-front sets

We introduce admissible lattices and Gabor pairs to define discrete versions of wave-front sets with respect to Fourier–Lebesgue and modulation spaces. We prove that these wave-front sets agree with each other and with corresponding wave-front sets of “continuous type”. This implies that the coefficients of a Gabor frame expansion of f are parameter dependent, and describe the wave-front set of f.     

Experimental transition probabilities in the Ar III and Ar IV UV spectra

We present transition probabilities (Einstein's A values) for 38 Ar III (doubly ionized argon) and 14 Ar IV (triply ionized argon) spectral lines from the wavelength interval 240–308 nm. Considered spectral lines are recorded in laboratory pulsed discharge. The relative line intensity ratio procedure has been applied in evaluation of transition probabilities. As a reference for transition probability evaluation we have chosen A value of 241.884 nm spectral line in Ar III spectrum and A value of 280.947 nm in Ar IV spectrum, both obtained theoretically. Careful analysis of experimental and existing theoretical data is conducted in order to deduce uncertainties. Presented Ar III and Ar IV A values are for the first time obtained relying on experimental data.