Acetylene diethers: Dineopentyloxyethyne

Dineopentyloxyethyne has been synthesized fromtrans-2,3-dichloro-1,4-dioxane according to a general procedure already described. In contrast with alkyl neopentyloxyacetylenes, RC=COCH₂Bu^t, which only polymerize when are strongly heated (150°), dineopentyloxyethyne is a kinetically unstable acetylene diether that polymerizes readily at room temperature. However, the compound has been trapped with Co₂(CO)₈ to give either the corresponding hexacarbonyl complex, m.p. 74–75°, or the cyclic trimer, m.p. 205–206°, depending upon the experimental conditions.     

Remarks on scalar curvature of Yamabe solitons

In this article, we consider the scalar curvature of Yamabe solitons. In particular, we show that, with natural conditions and non-positive Ricci curvature, any complete Yamabe soliton has constant scalar curvature, namely, it is a Yamabe metric. We also show that a complete non-compact Yamabe soliton with the quadratic decay at infinity of its Ricci curvature has non-negative scalar curvature. A new proof of Kazdan?CWarner condition is also presented.     

Ostrowski type methods for solving systems of nonlinear equations

Four generalized algorithms builded up from Ostrowski’s method for solving systems of nonlinear equations are written and analyzed. A development of an inverse first-order divided difference operator for functions of several variables is presented, as well as a direct computation of the local order of convergence for these variants of Ostrowski’s method. Furthermore, a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the methods is well deduced.     

Frozen divided difference scheme for solving systems of nonlinear equations

The development of an inverse first-order divided difference operator for functions of several variables, as well as a direct computation of the local order of convergence of an iterative method is presented. A generalized algorithm of the secant method for solving a system of nonlinear equations is studied and the maximum computational efficiency is computed. Furthermore, a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the methods is well deduced.     

On the computational efficiency index and some iterative methods for solving systems of nonlinear equations

In this paper two new iterative methods are built up and analyzed. A generalization of the efficiency index used in the scalar case to several variables in iterative methods for solving systems of nonlinear equations is revisited. Analytic proofs of the local order of convergence based on developments of multilineal functions and numerical concepts that will be used to illustrate the analytic results are given. An approximation of the computational order of convergence is computed independently of the knowledge of the root and the necessary time to get one correct decimal is studied in our examples.     

Etude dans la série des pyrrolidinones. IV. Formation de quelques dérivés de l'acide L méthylène bis N-(oxo-5 pyrrolidine carboxylique-2)

Starting from the readily available 5-oxo-2-carboxypyrrolidine, methylene-bis-(N-5-oxo-2-carboxypyrrolidine) was prepared and transformed into a diamine, then into two isomeric diols, which cyclised into one ether. The meso configuration has been assigned for this ether. The reduction of both diols and ether was complete and gave rise to methylene-bis-N-pyrrolidine.     

Kähler tubes of constant radial holomorphic sectional curvature

We determine (up to holomorphic isometries) the family of Kähler tubes, around totally geodesic complex submanifolds, of constant radial holomorphic sectional curvature when the centreP of the tube is either simply connected or a complex hypersurface withH ¹ (P, R)=0. In the last case, these tubes have the topology of tubular neighbourhoods of the zero section of the complex lines bundles over symplectic manifolds (when they are Kähler) of the Kostant-Souriau prequantization.     

The Reactivity Of singlet carbenes. An ab initio study

The energy barriers for the addition to ethylene of a series of carbenes have been calculated at an ab initio level. using the STO-3G and 3-21G basis sets. It is shown that the usual extrapolation of experiment results, which predicts that the reactivity of carbenes decreases when increasing its nucleophilic character, is not valid.