A highly efficient and cost-effective method for the preparation of α,β,β-trifluorostyrene (TFS) and its derivatives is described. The method required only 0.2 mol % of Pd(dba)(2) and 0.4 mol % of P(t)Bu(3) and occurred to full conversion within 2.0 h. With this method, a wide range of arylboronic acids were efficiently incorporated to generate α,β,β-trifluorostyrene derivatives.

We present a simple numerical method for constructing the optimal (generalized) averaged Gaussian quadrature formulas which are the optimal stratified extensions of Gauss quadrature formulas. These extensions exist in many cases in which real positive Kronrod formulas do not exist. For the Jacobi weight functions w(x) ≡ w(α,β)(x) = (1− x)α(1 + x)β (α, β > −1) we give a necessary and sufficient ...

Let S denote the unit sphere in Euclidean 3-space. A spherical triangle T is a region enclosed by three great circles on S; a great circle is a circle whose center is at the origin. The sides of T are arcs of great circles and have length a, b, c. Each of these is ≤ π. The angle α opposite side a is the dihedral angle between the two planes passing through the origin and determined by arcs b, c...

BACKGROUND Accurate assessment of glenoid inclination is of interest for a variety of conditions and procedures. The purpose of this study was to develop an accurate and reproducible measurement for glenoid inclination on standardized anterior-posterior (AP) radiographs and on computed tomography (CT) images. MATERIALS AND METHODS Three consistently identifiable angles were defined: Angle α b...

objective: eucalyptus (fam. myrtaceae) is a medicinal plant and various eucalyptus species possess potent pharmacological actions against diabetes, hepatotoxicity, and inflammation. this study aims to investigate essential oil compositionfrom leaves and flowers of e. microthecaand e. viminalisleavesgrowing in the southeast of iran. materials and methods: the aerial parts of these plants were co...