Spectroscopic analysis and kinetics of intermolecular hydrogen bond formation in poly‐pyridobisimidazole (M5) fiber

Poly‐pyridobisimiazole (M5) single filaments subjected to varying degrees of heat treatment have been analyzed using Fourier Transform Infrared (FTIR) microspectroscopy in transmission mode to detect changes in the state of intermolecular hydrogen bonding as a function of fiber annealing conditions. The FTIR absorbance bands associated with hydrogen bonding in M5 fiber have been identified, and the integrated molar absorption coefficients for the bands of interest have been determined experimentally, which allows to quantify the concentration of N? H vibration groups hydrogen‐bonded (H‐bonded) to water molecules, and the concentration of N? H vibration groups H‐bonded to adjacent polymer chains in the fiber. A dual mechanism kinetic rate expression is used to describe intermolecular H‐bond formation in M5 fiber as a function of annealing conditions, from which an activation energy for H‐bond formation of 14.8 kJ/mol is obtained. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1809–1824, 2009     

Geodesic ideal triangulations exist virtually

It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability of peripheral subgroups.

     

Millimeter-scale contact printing of aqueous solutions using a stamp made out of paper and tape

This communication describes a simple method for printing aqueous solutions with millimeter-scale patterns on a variety of substrates using an easily fabricated, paper-based microfluidic device (a paper-based "stamp") as a contact printing device. The device is made from inexpensive materials, and it is easily assembled by hand; this method is thus accessible to a wide range of laboratories and budgets. A single device was used to print over 2500 spots in less than three minutes at a density of 16 spots per square centimetre. This method provides a new tool to pattern biochemicals-reagents, antigens, proteins, and DNA-on planar substrates. The accuracy of the volume of fluid delivered in simple paper-to-paper printing is low, and although the pattern transfer is rapid, it is better suited for qualitative than accurate, quantitative work. By patterning the paper to which the transfer occurs using wax printing or an equivalent technique, accuracy increases substantially.     

Mirror and synchronous couplings of geometric Brownian motions

The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and show that, unlike in the case of Brownian motion, the optimality fails in general even if the geometric Brownian motions are martingales. On the other hand, we prove that in the cases of the ergodic average and the infinite time horizon criteria, the mirror coupling and the synchronous coupling are always optimal for general (possibly non-martingale) geometric Brownian motions. We show that the two couplings are efficient if and only if they are optimal over a finite time horizon and give a conjectural answer for the efficient couplings when they are suboptimal.     

Nontrivial application of Nielsen theory to differential systems

In reply to a problem of Jean Leray concerning application of the Nielsen theory to differential systems for obtaining multiplicity results, we present a nontrivial example of such an application. The emphasis is on the parameter space in order to ensure that no subdomain becomes subinvariant under the related Hammerstein solution operator. To achieve this goal, we develop a general method applicable also for ordinary differential equations with or without uniqueness as well as for upper-Carathéodory differential inclusions. We are not aware that any alternative approach can be employed, even in the single-valued case.     

A package for symbolic solution of real functional equations of real variables

Summary This paper discusses the problems associated with the symbolic treatment of functional equations and presents a Mathematica package for the solution of real functional equations of real variables. The package includes a minimal basic database which contains a reduced set of functional equations with its four components: equation, domain, class and the corresponding solution. The word minimal is used in the sense that any equation that is solvable by the system using non-searching methods is excluded from the database. The package incorporates a searching algorithm which can solve functional equations independently of their notation and their algebraic representation. Not only general solutions but particular and candidate solutions are dealt with. This implies a careful analysis of domains and classes. The package includes some methods for solving functional equations, which are used when the input functional equations are not found in the database. Some methods have been implemented internally and some are in an external package. Finally, some examples illustrate the use of the package.