Strong type estimates for homogeneous Besov capacities

 Capacitary strong type estimates for homogeneous Besov spaces are established. Moreover, the result is used to study embeddings and dualities of function spaces. Received: 17 October 2001 / Published online: 10 February 2003 Mathematics Subject Classification (2000): 42A16, 46E30, 47B38     

The activation of tertiary amines by osmium cluster complexes: Further studies of the reaction of Os3(CO)10(NCMe)2 with triethylamine

The reactions of Os₃(CO)₁₂ and Os₃(CO)₁₀(NCMe)₂ with NEt₃ have been reinvestigated. Two new products, Os₃(CO)₁₀(μ-CH₂C(H)?NEt₂)(μ-H)) (2) and Os₃(CO)₁₀(syn-μ-η¹-CHCHNEt₂)(μ-H) (3) were obtained in low yields, 4% and 7%, in addition to the previously reported compound Os₃(CO)₁₀(anti-μ-η¹-CHCHNEt₂(μ-H) (1) (20% yield) when the reaction was conducted at 25°C using Os₃(CO)₁₀(NCMe)₂. Compounds 2 and 3 were characterized by IR, ¹H NMR and single-crystal X-ray diffraction analyses. Compound 2 contains a bridging methyl-metallated N-ethylimine ligand formed by the cleavage of one ethyl group from the NEt₃. Compound 3 is an isomer of 1 in which the bridging ligand has a syn conformation with respect to the cluster as compared with the anti conformation in 1. Compound 3 slowly isomerizes to 1. Compound 3 is de-carbonylated by exposure to UV radiation and is transformed to the new compound Os₃(CO)₉(μ₃-CC(H)?NEt₂)(μ-H)₂ (4) (58% yield) by an additional CH activation to form a triply bridging η¹-diethylaminovinylidene ligand. Compound 4 isomerizes to the compound Os₃(CO)₉(μ₃-HCCNEt₂)(μ-H)₂ (5) (70% yield) at 68°C. The latter contains a triply briding ynamine ligand which exhibits structural and reactivity features that are characteristic of a carbene ligand at the amine-substituted carbon atom. Crystal data: for 2, space group = P2₁/c, a = 9.236(2) Å, b = 12.469(2) Å, c = 18.107(3) Å, β = 104.67(1)°, Z = 4, 2518 reflections, R = 0.031; for 3, space group = P2₁/m, a = 7.644(1) Å, b = 12.706(2) Å, c = 11.912(2) Å, β = 108.02(1)°, Z = 2, 1295 reflections, R = 0.030; for 4, space group = P2₁/n, a = 10.233(2) Å, b = 14.834(4) Å, c = 14.538(2) Å, β = 99.88(2)°, Z = 4, 2403 reflections, R = 0.036.     

Ein internationales Ar?ometer

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The excess enthalpy for a mixture of krypton and xenon: experiment and theory

Measurements of the excess enthalpy of krypton and xenon mixtures at 163 K are reported. These results are found to disagree with the only other published result. This discrepancy is discussed. Conformal solution theory is used to provide an unbiased prediction of the excess enthalpy. We review published experimental and calculated excess thermodynamic properties of the K_r/Xe system at zero pressure and 161.38 K and 165 K.     

Latent energy of deformation of bisphenol A polycarbonate

The thermodynamic behavior of poly(bisphenol A carbonate) (PC) during uniaxial cold drawing and the properties of the drawn polymer were examined. Isothermal deformation calorimetric measurements were made during the drawing process. The deformation calorimeter measures heat, work, and internal energy changes for deformation. It was found that PC exhibited nonideal plasticity with approximately 50–80% of the work of deformation dissipated as heat. The remainder of the work of deformation was stored as a latent internal energy change. The value of the internal energy change was dependent on strain rate at 20°C but was not strongly dependent on temperature in the range 20–65°C. Thermomechanical measurements on cold-drawn PC samples demonstrated striking behavior at temperatures far below the glass transition temperature T_g. Stress-temperature experiments showed that the stress increased for uniaxially constrained samples, and this stress increase began at temperatures just above the deformation temperature. Additional experiments indicated that the changes which took place during cold drawing were physical in nature and were thermoreversible. These changes in physical properties are related to those which occur due to physical aging below T_g.     

Weakly elliptic systems of variational inequalities: a 2×2 model problem with obstacles in both components

Summary In this paper we study a model system of2×2 second order, linear variational inequalities in which the solution is subjected to a unilateral constraint, the obstacle. We obtain existence for some systems which are not strongly elliptic, and we give an example of non- uniqueness in a specific case.Research supported in part by FAPESP Grant 93/3732-7.     

Changing Assessment Practices in Science and Mathematics

One recommendation of the national reform movements in mathematics and science is to change the way students are assessed. In this article five formats of alternative assessment forms are described, and suggestions are given on how these methods can be implemented within science and mathematics classrooms. Benefits of each type of assessment are discussed and potential pitfalls are elucidated. Samples of the five formats, journal writing, open-ended problems, portfolios, interviews and performance assessments, are included.     

On Solving Quickest Time Problems in Time-Dependent, Dynamic Networks

In this paper, a pseudopolynomial time algorithm is presented for solving the integral time-dependent quickest flow problem (TDQFP) and its multiple source and sink counterparts: the time-dependent evacuation and quickest transshipment problems. A more widely known, though less general version, is the quickest flow problem (QFP). The QFP has historically been defined on a dynamic network, where time is divided into discrete units, flow moves through the network over time, travel times determine how long each unit of flow spends traversing an arc, and capacities restrict the rate of flow on an arc. The goal of the QFP is to determine the paths along which to send a given supply from a single source to a single sink such that the last unit of flow arrives at the sink in the minimum time. The main contribution of this paper is the time-dependent quickest flow (TDQFP) algorithm which solves the TDQFP, i.e. it solves the integral QFP, as defined above, on a time-dependent dynamic network, where the arc travel times, arc and node capacities, and supply at the source vary with time. Furthermore, this algorithm solves the time-dependent minimum time dynamic flow problem, whose objective is to determine the paths that lead to the minimum total time spent completing all shipments from source to sink. An optimal solution to the latter problem is guaranteed to be optimal for the TDQFP. By adding a small number of nodes and arcs to the existing network, we show how the algorithm can be used to solve both the time-dependent evacuation and the time-dependent quickest transshipment problems. This revised version was published online in August 2006 with corrections to the Cover Date.     

Degeneracy in infinite horizon optimization

We consider sequential decision problems over an infinite horizon. The forecast or solution horizon approach to solving such problems requires that the optimal initial decision be unique. We show that multiple optimal initial decisions can exist in general and refer to their existence as degeneracy. We then present a conceptual cost perturbation algorithm for resolving degeneracy and identifying a forecast horizon. We also present a general near-optimal forecast horizon.This material is based on work supported by the National Science Foundation under Grants ECS-8409682 and ECS-8700836.