Synthesis of rhodium(II) pyrazolate complexes: Crystal structure of tetra-μ-3,5-dimethylpyrazolato dirhodium(II) bis-acetonitrile, (Rh-Rh)

The reaction of Rh₂(O₂CMe)₄ with the sodium salt of 3,5-dimethylpyrazole (3,5-Me₂pzH) in acetonitrile gives Rh₂(3,5-Me₂pz)₄ · 2MeCN. This yellow diamagnetic compound on heating gives Rh(3,5-Me₂pz)₄ which in turn forms adducts with different unidentate ligands, L, to give Rh₂(3,5-Me₂pz)₄ · 2L. The binuclear tetra bridged structure has been established for the acetonitrile complex by X-ray diffraction. The Rh-Rh distance is 2.353(3) Å and the Rh-N (acetonitrile) distance is 2.202(5) Å. Some unsubstituted pyrazolates have been made.     

Semicontinuous solutions for Hamilton-Jacobi equations and theL ∞control problem

We prove uniqueness for extended real-valued lower semicontinuous viscosity solutions of the Bellman equation forL -control problems. This result is then used to prove uniqueness for lsc solutions of Hamilton-Jacobi equations of the form –u _t +H(t, x, u, –Du)=0, whereH(t, x, r, p) is convex inp. The remaining assumptions onH in the variablesr andp extend the currently known results.Supported in part by Grant DMS-9300805 from the National Science Foundation.     

Total risk aversion,stochastic optimal control,and differential games

We present a connection between the theory of risk in the context of a stochastic optimal control problem and its relation to the theory of differential games. In particular, we define the notion of total risk aversion from the viewpoint of the upper value of a differential game. We prove that as the index of absolute risk aversion of a utility function in a stochastic control problem converges to infinity the (certainty equivalent) optimal payoff converges to the upper value of an associated deterministic differential game. The two main points of this paper are (1) a precise characterization oftotal risk aversion and (2) the construction of a stochastic optimal control problem intimately connected to a deterministic differential game.Partially supported by the Air Force Office of Scientific Research Grant No. AFOSR-86-0202.Partially supported by a grant from the National Science Foundation.     

Determination of absolute configurations from vibrational raman optical activity: (trans)-2,3-dimethylthiirane

Experimental and theoretical vibrational Raman optical activity (VROA) spectra of (2R,3R)-2,3-dimethylthiirane in the 200-1500 cm(-1) region are presented. The level of agreement obtained for the observed and predicted VROA signs suggests that the absolute configurations of chiral molecules can be determined confidently using VROA.     

Transition-metal complexes of a bifunctional tetradentate gallium alkoxide ligand

The mixed gallium transition-metal complexes [FeCl[Ga(2)((t)Bu)(4)(neol)(2)]] (1) and [M[Ga(2)((t)Bu)(4)(neol)(2)]], M = Co (2), Ni (3), Cu (4), have been prepared by the reaction of [Ga(2)((t)Bu)(4)(neol-H)(2)] (neol-H(2) = 2,2-dimethyl-propane-1,3-diol) with the appropriate metal halide and Proton Sponge. Compounds 1-4 have been characterized by NMR (3), UV/vis, and IR spectroscopy and magnetic susceptibility (solution and solid state), and their molecular structures have been confirmed by X-ray crystallography. The molecular structure of compounds 1-4 consists of a tetracyclic core formed from two four-membered and two six-membered rings. The central metal atom adopts a square pyramidal (1) or square planar (2-4) geometry. The magnetic susceptibilities for 1, 2, and 4 are as expected for strong ligand field environments. On the basis of spectroscopic and structural data, the [Ga(2)((t)Bu)(4)(neol)(2)](2-) ligand appears to be more flexible than other chelating ligands; this is proposed to be due to the flexibility in the O-Ga-O bond angle.     

Technical challenges in applying capillary electrophoresis-single strand conformation polymorphism for routine genetic analysis

Recent and future advances in population genetics will have a significant impact on health care practices and the economics of health care provision only if a spectrum of patient-tailored, effective methods of DNA screening for sequence alterations has been developed. Genetic screening by capillary electrophoresis-single strand conformation polymorphism (CE-SSCP), which is based upon the differences in electrophoretic mobilities of wild-type and mutant DNA species, offers an important complement to other presently available techniques such as Sanger sequencing and DNA hybridization arrays due to its simplicity, versatility, and low cost of analysis. A two-part review of CE-SSCP that discusses its advantages and limitations is presented. Emphasis is placed on technological aspects of CE-SSCP (including such rarely addressed issues as sample preparation protocols and the nature of the polymeric DNA separation matrix) as well as on the potential of CE-SSCP for routine genetic analysis. An attempt is made to organize and present the information in sufficient detail to allow the use of SSCP for routine genetic screening even by those inexperienced in CE. Some discussion of CE-based heteroduplex analysis (HA) is also presented.