A type 2 Ferrier rearrangement-based synthesis of d-myo-inositol 1,4,5-trisphosphate

The synthesis of d-myo-inositol 1,4,5-trisphosphate (InsP₃) from methyl α-d-glucopyranose, via a type 2 Ferrier rearrangement is reported. A key intermediate in this synthesis possesses orthogonal protecting groups at the 1-, 4- and 5-position, making it a versatile starting point for the synthesis of unnatural InsP₃ derivatives. Biological evaluation of the synthetic InsP₃ demonstrates that this compound evokes selective Ca²⁺ release via activation of InsP₃ receptors.     

The S.M.A.R.T. (small mass,affordable, rapid,transfer-less) digestion method for heavy metal determinations

The S.M.A.R.T. (small mass, affordable, rapid, transfer-less) digestion method was developed to determine heavy metal concentrations in small sample masses. The S.M.A.R.T. digestion method is a hot water bath digestion where sample digestion and dilution are performed in the original sample tube. This method is faster than the typical methods used and reduces potential sources of error. Masses as small as 0.01 g have been digested and analysed using this method. The preparation and digestion time is reduced from 10 h to less than 4 h. Acid volumes are reduced from millilitres to microlitres and the only disposable supplies needed are sample tubes and pipette tips. Method accuracy was determined by digesting seven replicates of two standard reference materials using the S.M.A.R.T. method and analysing samples by inductively coupled plasma mass spectrometry. The S.M.A.R.T. digestion method was found to provide excellent recoveries for Al (76 ± 2.7%), Mn (99 ± 11%), Co (92 ± 17%), Ni (93 ± 28%), Cu (109 ± 33%), Zn (97 ± 7.1%), As (108 ± 20%), Sr (90 ± 12%), Mo (84 ± 23%), Ag (91 ± 1.8%), Cd (95 ± 6.2%), Sn (139 ± 52%) and Pb (95 ± 22%). This study has successfully developed an efficient and reproducible digestion method for heavy metal determination in limited biomass samples.     

Thou Shalt Not Clone One Bit!

We prove a no-triplets theorem for spin 1 particles, which implies a strengthened form of the no-cloning theorem.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Structural properties of a family of hydrogen-bonded co-crystals formed between gemfibrozil and hydroxy derivatives of t-butylamine, determined directly from powder X-ray diffraction data

We report the formation and structural properties of co-crystals containing gemfibrozil and hydroxy derivatives of t-butylamine H₂NC(CH₃)_3−n(CH₂OH)_n, with n=0, 1, 2 and 3. In each case, a 1:1 co-crystal is formed, with transfer of a proton from the carboxylic acid group of gemfibrozil to the amino group of the t-butylamine derivative. All of the co-crystal materials prepared are polycrystalline powders, and do not contain single crystals of suitable size and/or quality for single crystal X-ray diffraction studies. Structure determination of these materials has been carried out directly from powder X-ray diffraction data, using the direct-space Genetic Algorithm technique for structure solution followed by Rietveld refinement. The structural chemistry of this series of co-crystal materials reveals well-defined structural trends within the first three members of the family (n=0, 1, 2), but significantly contrasting structural properties for the member with n=3.     

Indefinite integrals of incomplete elliptic integrals from Jacobi elliptic functions

Integration formulas are derived for the three canonical Legendre elliptic integrals. These formulas are obtained from the differential equations satified by these elliptic integrals when the independent variable u is the argument of Jacobian elliptic function theory. This allows a limitless number of indefinite integrals with respect to the amplitude to be derived for these three elliptic integrals. Sample results are given, including the integrals derived from powers of the 12 Glaisher elliptic functions. New recurrence relations and integrals are also given for the 12 Glaisher elliptic functions.     

Indefinite integrals involving complete elliptic integrals of the third kind

A method developed recently for obtaining indefinite integrals of functions obeying inhomogeneous second-order linear differential equations has been applied to obtain integrals with respect to the modulus of the complete elliptic integral of the third kind. A formula is derived which gives an integral involving the complete integral of the third kind for every known integral for the complete elliptic integral of the second kind. The formula requires only differentiation and can therefore be applied for any such integral, and it is applied here to almost all such integrals given in the literature. Some additional integrals are derived using the recurrence relations for the complete elliptic integrals. This gives a total of 27 integrals for the complete integral of the third kind, including the single integral given in the literature. Some typographical errors in a previous related paper are corrected.     

Bond stresses for a composite material reinforced with various arrays of fibers

The problem treated here is that of an isotropic body having a doubly periodic rectangular or triangular array of perfectly bonded circular elastic inclusions. The body is in tension or compression. This simulates a composite material wherein a relatively weak matrix is reinforced by stronger (and more rigid) fibers. Bond stresses for both rectangular and triangular arrays have been calculated using either boundary point matching or boundary point least squares techniques. Numerical results based on a plane strain analysis are given in graphical form.