Long cycles passing through a specified edge in a 3-connected graph

We prove the following theorem: For a connected noncomplete graph G, let τ(G): = min{d_G(u) + d_G(v)|d_G(u, v) = 2}. Suppose G is a 3-connected noncomplete graph. Then through each edge of G there passes a cycle of length ≥ min{|V(G)|, τ (G) − 1}. © 1997 John Wiley & Sons, Inc.     

A predual of a predual of B_σ and its applications to commutators

A predual of B_σ-spaces is investigated. A predual of a predual of B_σ-spaces is also investigated,which can be used to investigate the boundedness property of the commutators. The relation between Herz spaces and local Morrey spaces is discussed. As an application of the duality results, one obtains the boundedness of the singular integral operators, the Hardy-Littlewood maximal operators and the fractional integral operators, as well as the commutators generated by the bounded mean oscillation(BMO) and the singular integral operators.What is new in this paper is that we do not have to depend on the specific structure of the operators. The results on the boundedness of operators are formulated in terms of B_σ-spaces and B_σ-spaces together with the detailed comparison of the ones in Herz spaces and local Morrey spaces. Another application is the nonsmooth atomic decomposition adapted to B_σ-spaces.     

Effects of encounters on phase separation dynamics from diffusion-controlled growth to coarsening

We investigate the dynamics of phase separations in quenched binary mixtures, such as binary alloys and polymer blends with low mobilities, at higher volume fractions. Computer simulations are performed using simple model equations in the presence of encounters of droplets. Four characteristics stages with three crossovers, including dynamical scaling behavior and temporal power laws, are found beyond a volume fraction of approximately 0.14, where each crossover is attributed to a transition from one growth mechanism to the other. The encounter effect is thus shown to strongly influence a transition from the diffusion-controlled (t^1/2) stage to the coarsening (t^1/3) stage. A simple analytical argument for the simulation results is also presented.     

UVB DNA Dosimeters Analyzed by Polymerase Chain Reactions

Abstract— Purified bacteriophage Λ DNA was dried on a UV-tran-sparent polymer film and served as a UVB dosimeter for personal and ecological applications. Bacteriophage Λ. DNA was chosen because it is commercially available and inexpensive, and its entire sequence is known. Each dosimeter contained two sets of DNA sandwiched between UV-transparent polymer films, one exposed to solar radiation (experimental) and another protected from UV radiation by black paper (control). The DNA dosimeter was then analyzed by a polymerase chain reaction (PCR) that amplifies a 500 base pair specific region of Λ DNA. Photoinduced damage in DNA blocks polymerase from synthesizing a new strand; therefore, the amount of amplified product in UV-exposed DNA was reduced from that found in control DNA. The average lesion frequency per 500 base pair per strand at 16 PCR cycles was –1.22, 1.00, 0.70 and 0.50 for 30 ng, 50 ng, 100 ng and 150 ng of dried DNA, respectively, after a total dose of 60 kj m 2 delivered with a solar UVB simulator. Although the average lesion frequency increases linearly with increasing doses for four different amounts of template DNA, the lesion frequency seems to be averaged by the amplified products from the protected Λ DNA molecules below the top few layers. The average daily dose, equivalent to the UV dose applied with the solar UVB simulator, was 10.2±0.4 kj m2 with the 50 ng containing DNA dosimeter in September 1995 in Melbourne, FL. Both 50 ng and 150 ng containing DNA dosimeters produced the same average daily dose within experimental error in January 1996, which was 5.2±0.3 kj m 2 at the same location. The dried Λ DNA dosimeter is compact, robust, safe and transportable, stable over long storage times and provides the total UVB dose integrated over the exposure time.     

Absolute configuration and conformation of 1,1′-spirob[benz[g]indan]

Two diastereomers of 3,3′-di-t-butyl-1,1′-spirobi[benz[g]indan] have been prepared; c.d. spectral evidence is presented for the difference between their conformations.     

Packing of simulated friction modifier additives under confinement

Molecular dynamics simulations have been conducted to obtain detailed information regarding molecular structure and packing of surfactant-like "friction modifier" (FM) chains adsorbed to two confining surfaces under sliding conditions. The simulations are interpreted via the density profile, position-dependent fluctuations in the density profile, and parallel, interlayer position correlation functions. Heterogeneous FM structures were obtained. The adsorbed FM chains were found to form semi-ordered monolayers perpendicular to the atomically well-defined surface, with distinct segment positions in the density profile. More fluid layers with broader density profiles and larger fluctuations were formed by some unoriented FM chains oriented preferentially parallel to the surface, between the opposing monolayers. Segment position correlations parallel to the surface in the adsorbed layers were found at separations up to 30 A. These packings persisted for longer than 4 ns under sliding conditions that ranged from 0 to 7.5 m s(-1) (0 to 0.075 A ps(-1)). Monolayer structures were observed to remain unchanged under a wide range of normal pressures, with the corresponding changes in volume occurring in the gap between monolayers or between a monolayer and trapped fluid.