The Clock Paradox in a Static Homogeneous Gravitational Field1

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars. ¹ Both authors contributed equally to this paper.     

Jacobi elliptic functions and change of variable in a convolution

We solve the functional equation

Wiener-Hopf factorisation of Brownian motion

Summary We study how Brownian motion behaves under time change by a fluctuating additive functionalA _t , in particular letting be the first passage time ofA _t to zero we computeP _–x[B dy] explicitly in certain cases. The calculation is not an easy one, our method uses the Désiré André relation for the overshoot of a Lévy process and depends on some elliptic function identities. This paper only considers the one boundary case whereA _t is increasing (resp. decreasing) on the positive (resp. negative) half line.     

Rational materials design of sorbent coatings for explosives: applications with chemical sensors

A series of chemoselective polymers had been designed and synthesized to enhance the sorption properties of polymer coated chemical sensors for polynitroaromatic analytes. To evaluate the effectiveness of the chemoselective coatings, a polynitroaromatic vapor test bed was utilized to challenge polymer coated surface acoustic wave (SAW) devices with different explosive vapors. Dinitrotoluene detection limits were determined to be in the <100 parts per trillion ranges. ATR-FTIR studies were used to determine the nature of the polymer-polynitroaromatic analyte interactions, and confirm the presence of hydrogen-bonding between polymer pendant groups and the nitro functional groups of polynitroaromatic explosive materials.     

New high temperature polymers. I. Wholly aromatic ordered copolyamides

Wholly aromatic ordered copolyamides of unusually high thermal stability were prepared by the condensation of aromatic diacid chlorides with symmetrical diamines containing preformed aromatic amide units in an ordered arrangement. The preservation of order in the condensation step was assured by using interfacial or solution polymerization techniques at temperatures below 50°C. Each polymer contains units derived from aminobenzoic acids, arylene diamines, and arylene diacids. By use of para- and meta- phenylene units, eight different polymers are possible; all were prepared. Differential thermal analyses and thermogravimetric analyses showed these polymers to have melting points or decomposition temperatures in a range from 410°C. for the all-meta polymer to 555°C. for the all-para one. Substitution of the internal N-hydrogens of the diamines with methyl groups or phenyl groups leads to additional ordered copolymers. Several were prepared, but their melting points were much lower than those of the parent polymers limiting their usefulness in high temperature applications. Tough pliable films were prepared from all eight unsubstituted polymers, and crystalline fibers with tenacities of ca. 6 g./den. were prepared from three of the polymers. The properties of the fibers were retained to a high degree even when determined at temperatures up to 400°C. Fibers aged at 300°C. for extended periods of time showed remarkable retention of fiber properties.     

Substituent effects on monoboronic acid sensors for saccharides based on N-phenyl-1,8-naphthalenedicarboximides

In the course of our investigations on new monoboronic acid saccharide sensors with C(0) spacers, a series of probes 1-6 based on 1,8-naphthalenedicarboximide were synthesized. Sensor 1 displays features typical of PET monoboronic acid sensors and shows high selectivity to fructose. Sensor 2 exhibits a novel dual emission and remarkable sensitivity for glucose relative to fructose and galactose through subtle changes in pH. Sensor 3 displays significantly enhanced fluorescence in the presence of galactose at low pH. Although probes 4-6 exhibit unique properties such as high quantum yield (Phi(F) = 0.407) and excellent solubility in water, they did not show significant change in fluorescence intensity in the presence of monosaccharides. The effects of substituent on all six probes lend support to the proposed photoelectrochemical model.     

Where organometallics and dendrimers merge: the incorporation of organometallic species into dendritic molecules

This review will describe the ongoing efforts being made to incorporate organometallic fragments into the framework of dendrimers. While purely dendritic organic molecules are well known and well studied, species incorporating organometallic moieties potentially offer many benefits that are not available to only organic containing dendrimers. For example, catalytic or redox active organometallic functions can be included in the dendritic framework and impart these characteristics onto the dendrimer. This report will give an overview of the latest developments in this field by highlighting selected examples that detail novel synthetic strategies or dendrimer construction methodologies, interesting practical applications or address specific problems associated with organometallic dendrimers.