Multiterminal flows in outerplanar networks

An outerplanar network is an undirected network whose underlying graph is a triangulation of a polygon. We give a linear algorithm for finding maximum flow values between all pairs of nodes in the outerplanar network. Our algorithm constructs the cut-tree of the outerplanar network without using any maximum flow computation.     

Exact solution of a simple finite infinite source interaction model

Networks of queues with finite and infinite source customers have been used to study the interaction between the batch jobs and interactive jobs in computer systems. Earlier Kaufman ([1], PP-345-348) developed accurate approximations for a simple nonproduct form network of this type. In this paper we offer exact solutions for the same model with one finite source customer. We study both FIFO and LIFO disciplines at the contention node. The results are derived for the case where the finite source think time and service time distributions are generalized hyperexponential.     

Scalar curvature,non-abelian group actions,and the degree of symmetry of exotic spheres

It is proved that if a compact manifold admits a smooth action by a compact, connected, non-abelian Lie group, then it admits a metric of positive scalar curvature. This result is used to prove that if ∑ ⁿ is an exoticn-sphere which does not bound a spin manifold, then the only possible compact connected transformation groups of ∑ ⁿ are tori of dimension ≤[(n+1)/2]. Research partially supported by the Sloan Foundation and NSF Grant GP-34785X.     

Alternating copolymerization of carbon monoxide and vinyl arenes using [N,N] bidentate palladium catalysts

The alternating copolymers of carbon monoxide (CO) and vinyl arene monomers, namely aromatic polyketones, are a family of attractive engineering plastic. In the catalytic synthesis of this kind of polymeric materials, [N,N] bidentate palladium catalysts represent the most successful catalytic systems. In this review, we introduce the present status of polyketone synthesis, with a focus on the aromatic polyketones made from vinyl arene and CO. We also address the palladium-catalyzed CO/vinyl arene alternating copolymerization mechanism. A variety of [N,N] bidentate palladium catalysts bearing 2,2′-bipyridine, 1,10-phenanthroline, α-diimine, and pyridine-imine ligands are surveyed for CO/vinyl arene copolymerization. The effects of vinyl arene monomer, counteranion, and solvent on copolymerization are also discussed. The copolymerization stereochemistry including chain end-control and enantiomorphic site control mechanisms is introduced. This review aims to promote the design of [N,N] bidentate palladium catalysts for CO/vinyl arene copolymerization for the development of high-performance aromatic polyketones.     

Copoly(p‐phenylene) containing azacrown ether: Synthesis,optical properties,and application for chemical sensor

Copoly(p‐phenylene) ( P1 ) containing pendent azacrown ether and ethylene glycol ether was prepared by the Suzuki coupling reaction and applied for chemical sensor. Poly(p‐phenylene) derivative P0 without the azacrown ether groups were also synthesized for comparative study. The photophysical and sensing properties were investigated by absorption and photoluminescence (PL) spectroscopy to elucidate the influence of the azacrown ether groups. The P1 exhibited specific selectivity and high sensitivity toward Zn²⁺, with the Stern‐Volmer coefficient (K_sv) being 3.66 × 10⁶ M^?1 at low concentration in mixture solvent of tetrahydrofuran and water (THF/H₂O = 9/1, v/v). The P1 maintained high selectivity toward Zn²⁺ in the presence of fifteen interfering metal cations. This results indicate that copoly(p‐phenylene) ( P1 ) is a promising functional material for chemical sensors. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 3975–3984     

Force-driven migration of particles in ordered porous media

Brownian dynamics simulation has been employed to study the behavior of force-driven particle migration in different ordered porous media comprised of periodically interconnected spherical cavities, representing inverted colloidal crystals. The effects of the imposed field strength and direction on the particle mobility and direction are investigated. The simulation results find that in a weak or intermediate field, the mobility normalized by the value in free solvent behaves in a similar way as the normalized diffusivity when the porosity is varied. Under a strong field, the normalized mobility can increase or decrease with the field strength, depending on the field direction relative to the cavity arrangement. If the imposed field is not aligned with any unobstructed pathway, the mobility tensor may become anisotropic and prolonged particle entrapment may also take place.     

Scanning optical reconstruction of coded aperture images

A scanning optical technique is described and used to reconstruct coded aperture images obtained with four different kinds of arrays. The feasibility and advantages of the technique are demonstrated experimentally. The results are used to compare the imaging properties of these arrays, i.e.: lateral resolution, background noise and axial (tomographic) resolution.