Dynamics of electron hopping in redox polymer electrodes using kinetic Ising model

The analysis of diffusion-migration equations pertaining to electron hopping and physical displacement in redox polymer electrodes is carried out using kinetic Ising model formalism. It is shown that, by the appropriate choice of transition probabilities obeying detailed balancing conditions, a hierarchy of transport equations can be derived. Earlier transport equations due to Nernst-Planck and Savéant are derived as special cases. The dependence of apparent diffusion coefficient on number density of redox centres, polymer morphology etc. are pointed out. Several new insights concerning the microscopic basis underlying the hitherto known phenomenological equations are demonstrated. Received: 27 May 1997 / Accepted: 24 July 1997     

Existence of a unique solution to a quasilinear elliptic equation

The purpose of this paper is to prove the existence of a unique classical solution u(x) to the quasilinear elliptic equation −∇⋅(a(u)∇u)+v⋅∇u=f, where u(x₀)=u₀ at x₀∈Ω and where n⋅∇u=g on the boundary ∂Ω. We prove that if the functions a, f, v, g satisfy certain conditions, then a unique classical solution u(x) exists. Applications include stationary heat/diffusion problems with convection and with a source/sink, where the value of the solution is known at a spatial location x₀∈Ω, and where n⋅∇u is known on the boundary.     

A unique solution to a nonlinear elliptic equation

The purpose of this paper is to prove the existence of a unique, classical solution to the nonlinear elliptic partial differential equation −∇⋅(a(u(x))∇u(x))=f(x) under periodic boundary conditions, where u(x₀)=u₀ at x₀∈Ω, with Ω=TN, the N-dimensional torus, and N=2,3. The function a is assumed to be smooth, and a(u(x))>0 for , where G⊂R is a bounded interval. We prove that if the functions f and a satisfy certain conditions, then a unique classical solution u exists. The range of the solution u is a subset of a specified interval . Applications of this work include stationary heat/diffusion problems with a source/sink, where the value of the solution is known at a spatial location x₀.     

Nylon–MOF Composites through Postsynthetic Polymerization

Hybridization of metal–organic frameworks (MOFs) and polymers into composites yields materials that display the exceptional properties of MOFs with the robustness of polymers. However, the realization of MOF–polymer composites requires efficient dispersion and interactions of MOF particles with polymer matrices, which remains a significant challenge. Herein, we report a simple, scalable, bench‐top approach to covalently tethered nylon–MOF polymer composite materials through an interfacial polymerization technique. The copolymerization of a modified UiO‐66‐NH₂ MOF with a growing polyamide fiber (PA‐66) during an interfacial polymerization gave hybrid materials with up to around 29 weight percent MOF. The covalent hybrid material demonstrated nearly an order of magnitude higher catalytic activity for the breakdown of a chemical warfare simulant (dimethyl‐4‐nitrophenyl phosphate, DMNP) compared to MOFs that are non‐covalently, physically entrapped in nylon, thus highlighting the importance of MOF–polymer hybridization.     

Integrated receiver architectures for board-to-board free-space optical interconnects

In many computer and server communications copper cables and wires are currently being used for data transmission and interconnects. However, due to significant shortcomings, such as long transmission time, high noise level, unstable electrical properties, and high power consumption for cooling, researchers are increasingly turning their research interests toward alternatives, such as fiber optic interconnects and free-space optical communication technologies. In this paper, we present design considerations for an integrated receiver for high-speed free-space line-of-sight optical interconnects for distortion-free data transmission in an environment with mechanical vibrations and air turbulences. The receiver consists of an array of high-speed photodiodes for data communication and an array of quadrant photodiodes for real-time beam tracking in order to compensate for the beam misalignment caused by vibrations in servers. Different configurations for spatially positioning the quadrant and data photodiodes are discussed for 4×4 and 9×9 multielement optical detector arrays. We also introduce a new beam tracking device, termed the strip quadrant photodiodes, in order to accurately track highly focused optical beams with very small beam diameter.     

Factoring operators through Hilbert space

We give an example of a pair of Banach spacesE andF so that neitherE′ norF has cotype 2, but every bounded linear operator fromE intoF factors through Hilbert space.     

Benzothiazoline derivatives. I. Reaction of 2-benzothiazolinethione with ethylene oxide

Treatment of 2-benzothiazolinethione with excess ethylene oxide in acetic acid resulted in N-hydroxyethylation and thiono-oxo replacement to give 3-(2-hydroxyethyl)-2-benzothiazolinone. This product was also obtained when S-alkylthiobenzothiazoles were treated in this way. Similar treatment of the N-substituted compounds 3-methyl-2-benzothiazolinethione and 3-(2-hydroxyethyl)-2-benzothiazolinethione gave simple thiono-oxo replacement.     

The normed and Banach envelopes of WeakL 1

The space WeakL ¹ consists of all Lebesgue measurable functions on [0,1] such thatq(f)=supcλ{t:|f(t)|>c} c>0 is finite, where λ denotes Lebesgue measure. Let ρ be the gauge functional of the convex hull of the unit ball {f:q(f)≤1} of the quasi-normq, and letN be the null space of ρ. The normed envelope of WeakL ¹, which we denote byW, is the space (WeakL ¹/N, ρ). The Banach envelope of WeakL ¹, , is the completion ofW. We show that is isometrically lattice isomorphic to a sublattice ofW. It is also shown that all rearrangement invariant Banach function spaces are isometrically lattice isomorphic to a sublattice ofW.     

Symmetric Sequence Subspaces of C({alpha})

Two main results are shown: (1) a characterisation of the symmetricsequence spaces which embed into C(), and (2) a characterisation,in terms of the Orlicz function M, of the Orlicz sequence spacesh_M which embed into C(K) for some countable compact Hausdorffspace K. The proofs make use of the Schreier families of sets,which have found wide applications in Banach space theory.