Preparation of Nitriles by the Modification of Mitsunobu-Wilk Procedure III Carbon Elongation of Hydroxy Esters

An efficient one-step procedure for the conversion of hydroxy esters into the corresponding nitrile esters using triphenylphosphine (PPh₃)-diethyl azodicarboxylate (DEAD) in the presence of acetone cyanohydrin is described.     

A reformulation of the nonsmooth approaches of M. Frémond and J.J. Moreau for rigid body dynamics

This paper deals with the nonsmooth dynamics of a rigid bodies system. The proposed theory is inspired by the formalism of J.J. Moreau and that of M. Frémond and relies on the notion of percussion which is the integral of the contact force during the duration of the collision. Contrary to classical discrete element models, it is here assumed that percussions can be expressed as a function of only the velocity before the impact. This assumption is checked for the usual mechanical constitutive laws for collisions derived from a pseudopotential of dissipation or the Coulomb friction law. Motion equations are then reformulated taking into account simultaneous collisions of solids. A mathematical study of the new model is presented: the existence and uniqueness of the solution are discussed according to the regularity of both the forces (Lebesgue‐density occurring during the regular evolution of the system) and the percussions (Dirac‐density describing the collision). In the light of the principles of thermodynamics, a condition on the internal percussion assuring that the collision is thermodynamically admissible, is established. Finally, an application of this new model to the motion of a system of rigid disks, including simultaneous collisions is presented.     

GRPIA: a new algorithm for computing interpolation polynomials

Numerical Algorithms - Let x0,x1, ? , xn, be a set of n + 1 distinct real numbers (i.e., xm ≠ xj, for m ≠ j) and let ym,k, for m = 0, 1, ? , n, and k = 0, 1, ? , rm,...     

Support vector regression with digital band pass filtering for the quantitative analysis of near‐infrared spectra

This paper proposes a novel calibration technique based on combining support vector regression with a digital band pass (DBP) filter for the quantitative analysis of near‐infrared spectra. The efficacy of the proposed method is investigated and validated in the determination of glucose from near‐infrared spectra of a mixture composed of urea, triacetin and glucose. In this paper, the DBP filtering was implemented as a pre‐processing technique in the frequency domain as a Gaussian band pass filter and in the time domain as a Chebyshev filter. The grid‐search optimization method was used to optimize the filter parameters. The results demonstrate that utilization of the optimized DBP filters as a pre‐processing technique improved the performance of the predictive models. Copyright © 2013 John Wiley & Sons, Ltd.     

On an elliptic equation of Kirchhoff-type with a potential asymptotically linear at infinity

This paper examines the existence of positive solutions for a boundary value problem of Kirchhoff-type involving a positive potential function which is asymptotically linear at infinity.     

On the Fukaya categories of higher genus surfaces

We construct the Fukaya category of a closed surface equipped with an area form using only elementary (essentially combinatorial) methods. We also compute the Grothendieck group of its derived category.     

An algorithm for achieving proportional delay differentiation

We consider the implementation of the proportional delay differentiation model with adaptive waiting time priority scheduler and we address the problem of finding the appropriate scheduler differentiation parameters that achieve this model. In this paper, we propose an algorithm that can compute an analytical solution of this problem.     

Crystal structure and in vitro antitumour activity of dibutylbis(5-chloro-2-hydroxybenzoato)tin(IV)

The crystal structure of the title compound, [nBu₂Sn(5-Cl-2-OH-C₆H₃CO₂)₂], shows that in the monomeric species the six-coordinate Sn atom exists in a skew trapezoidal bipyramidal geometry in which the four O donor atoms, derived from two asymmetrically chelating carboxylate ligands, define the basal plane and the n-butyl substituents lie over the weaker Sn? O interactions defining a C? Sn? C angle of 147.6(2)°. An unusual feature of the structure is the presence of both intra- and inter-molecular hydrogen bonding contacts which serve to stabilize the structure. The in vitro antitumour activity of this compound against mammary and colon carcinoma cell lines is also reported.     

Long division for Laurent series matrices and the optimal assignment problem

We present a necessary and sufficient condition to represent a Laurent series matrix A(x) as a product where is a Laurent series matrix whose leading scalar matrix is nonsingular and U(x) and V(x) are diagonal matrices whose nonzero entries are powers of x. If A(x) can be written in this form, then the matrix equation A(x)Y(x) = B(x) can be solved by long division. Our result relies on a classical theorem on optimal assignments.