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.     

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.     

On Angles Whose Squared Trigonometric Functions Are Rational

We consider the rational linear relations between real numbers whose squared trigonometric functions have rational values, angles we call ``geodetic.' We construct a convenient basis for the vector space over Q generated by these angles. Geodetic angles and rational linear combinations of geodetic angles appear naturally in Euclidean geometry; for illustration we apply our results to equidecomposability of polyhedra. Received April 7, 1998, and in revised form September 2, 1998.     

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.     

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.     

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.