Reactions of pyrrolidine enamines of cyclic and acyclic 3,4-dioxobutanoic acid Derivatives with dimethyl acetylenedicarboxylate. A new case of atropoisomerism.

Reaction conditions and structure of the starting enamines (cyclic or open-chain) determine greatly the final products of the title reactions. Whereas in benzene and acetonitrile, DMAD and 1 give a mixture of the diastereoisomeric dienamines 5, in methanol they afford pirrolizine 3. Enaminofuranones 2 and 10 furnish the corresponding “Michael adducts” 7a,b,c and 11a,b,c but fail to yield pirrolizines. It has been demonstrated that above b and c adducts differ exclusively on the arrangement of groups around a chiral axis.     

A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires

In this paper, we introduce a new proximal algorithm for equilibrium problems on a genuine Hadamard manifold, using a new regularization term. We first extend recent existence results by considering pseudomonotone bifunctions and a weaker sufficient condition than the coercivity assumption. Then, we consider the convergence of this proximal-like algorithm which can be applied to genuinely Hadamard manifolds and not only to specific ones, as in the recent literature. A striking point is that our new regularization term have a clear interpretation in a recent “variational rationality” approach of human behavior. It represents the resistance to change aspects of such human dynamics driven by motivation to change aspects. This allows us to give an application to the theories of desires, showing how an agent must escape to a succession of temporary traps to be able to reach, at the end, his desires.

     

Optimization model to support sustainable crop planning for reducing unfairness among farmers

Central European Journal of Operations Research - Agri-food production must increase while food waste needs to be reduced for improving the position of farmers. To do so it is necessary to...     

Directional operators and radial functions on the plane

LetEçS ¹ be a set with Minkowski dimensiond(E)1. We consider the Hardy-Littlewood maximal function, the Hilbert transform and the maximal Hilbert transform along the directions ofE. The main result of this paper shows that these operators are bounded onL _rad ^p (R²) forp>1+d(E) and unbounded whenp<1+d(E). We also give some end-point results.     

Lines of curvature near umbilical points on surfaces immersed in R4

LetM be a compact orientable surface,I:M R⁴ an immersion of classC ^r and a normal unitary smooth vector field. We prove that in the space of pairs (I, ) the family of pairs all whose umbilical points are Darbouxian is generic.     

A one-parameter family of hamiltonian structures for the KP hierarchy and a continuous deformation of the nonlinear WKP algebra

The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting W-algebra is a one-parameter deformation of W_KP admitting a central extension for generic values of the parameter, reducing naturally to W _n for special values of the parameter, and contracting to the centrally extended W₁₊, W and further truncations. In the classical limit, all algebras in the one-parameter family are equivalent and isomorphic tow _KP. The reduction induced by setting the spin-one field to zero yields a one-parameter deformation of which contracts to a new nonlinear algebra of the W-type.Address after October 1993: Queen Mary and Westfield College, UK