Synthetic approach to malibatol A

[reaction: see text] A synthetic approach to malibatol A featuring a novel benzofuran synthesis is described.     

Synthesis of biologically active dicarba analogues of the peptide hormone oxytocin using ring-closing metathesis

Facile synthesis of cis and trans olefinic analogues of oxytocin 1 that have carbon in place of sulfur is achieved via ring-closing metathesis (RCM) on a resin-bound linear precursor peptide. Hydrogenation of the cis olefin, 3, proceeds selectively to generate the previously reported saturated derivative 5. Biological testing on rat uterus strips shows that cis compound 3 has an EC50 value of 38 ng/mL (EC50 for oxytocin is 2.7 ng/mL) whereas 5 and trans olefin 4 are less active. [reaction--see text]     

Preparation of hydroxyapatite via microemulsion route

Hydroxyapatite (HAp) was prepared using a microemulsion route in combination with the pH-shock wave method. The samples as received consisted of amorphous aggregated particles, which had remarkable mesoporosity with a narrow pore size distribution. After being heated at 650 degrees C, the A-type carbonate hydroxyapatite was crystallized at 635 degrees C in particles of similar size (40--120 nm) with no internal porosity. At a higher temperature (900 degrees C) a sintering process took place, resulting in network of a larger particles, consisting of HAp and beta-tricalcium phosphate (beta-TCP). The crystallization of HAp occurs at 635 degrees C with an activation energy of 62.7--72.2 kcalmol(-1).     

Synthesis,Spectral Properties,and Crystal Structure of {Methoxo[4-phenylbutane-2,4-dione(p-nitrobenzoyl) hydrazonato(2-)]oxovanadium(V)}

The hydrazino complex {methoxo[4-phenylbutane-2,4-dione(p-nitrobenzoyl)hydrazonato(2-)]oxovanadium(V)}, VO(p-NO₂bhbzac)OCH₃, (1), has been prepared by the direct reaction of bis(benzoylacetonato) oxovanadium(IV), VO(bza)₂, with p-NO₂-C₆H₄C(O)NHNH₂, p-NO₂bh, in CH₃OH. The resulting compound contains benzoylacetone-(p-NO₂)benzoyl hydrazone as tridentate Schiff base-type ligand and OCH₃ group as Lewis base, both ligated to vanadium. The crystals are orthorhombic, with Z = 8, space group Pbca, a = 11.699(5) Å, b = 14.035(5) Å, c = 22.564(5) Å, R1 = 0.0756 and wR2 = 0.1302. The crystal structure demonstrated the square-pyramidal geometry of the VO_oxo(ONO)O coordination sphere with the oxo ligand at the apical position. The electronic absorption spectra revealed a ligand-to-metal charge-transfer (LMCT) band in the near UV region at _max = 23,700 cm^–1 (B = 5640 dm³ mol^–1 cm^–1) in CH₃CN, _max = 23,420 cm^–1 (B = 5550 dm³ mol^–1 cm^–1) in DMSO, and _max near 26,950 (sh) cm^–1 (B = 10,550 dm³ mol^–1 cm^–1) in CH₂Cl₂. The FT-IR spectra of (1) show the characteristic strong (V = O) stretching vibration at 993 cm^–1 and support the view that the oxovanadium complex is pentacoordinated and monomeric.     

On idempotents in reduced enveloping algebras

Explicit constructions are given for idempotents that generate all projective indecomposable modules for certain finite-dimensional quotients of the universal enveloping algebra of the Lie algebra in odd prime characteristic. The program is put in a general context, although constructions are only carried through in the case of .

     

On periodic solutions of nonlinear integral equations modelling infectious disease on measure chain

The modelling of the spread of infectious disease is carried out for time t on a measure chain T. Our approach unifies the continuous case and the discrete case . The model is described by the integral equation

where x(t) represents the proportion of the population infected at time t, f(t,x(t)) denotes the proportion of the population newly infected per unit time, and τ is the length of time an individual remains infectious. Using the measure chain calculus, we shall develop criteria for the existence of a nontrivial and nonnegative periodic solution for the modelling equation. The criteria can be implemented numerically, for this we shall give an algorithm as well as illustrative examples.     

Electronic imaging using a logarithmic asphere

Transmission functions are derived that are valid in the nonparaxial case for a class of lenses that will image a continuum of points along an optical axis to a single image point. This lens, which we call a logarithmic asphere, is then used in a digital camera. The resolution of the camera is limited by the pixel size of the CCD; i.e., it is not diffraction limited. Digital processing is used to recover the image, and image-plane processing is used for speed. We find a tenfold increase in the depth of field over that for the diffraction-limited case.     

Decision Theoretic Estimation of the Ratio of Variances in a Bivariate Normal Distribution

In this paper the problem of estimating the ratio of variances, , in a bivariate normal distribution with unknown mean is considered from a decision-theoretic point of view. First, the UMVU estimator of is derived, and then it is shown to be inadmissible under two specific loss functions, namely, the squared error loss and the entropy loss. The derivation of the results is done by conditioning on an auxiliary negative binomial random variable.