Synthesis of pyrimidine derivatives using N-bis(methylthio)methylenecyanamide

N-Bis(methylthio)methylenecyanamide ( 1 ) was allowed to react with active methylene compounds (methyl cyanoacetate, dimethyl malonate, ethyl acetoacetate, ethyl phenylacetate) in the presence of potassium carbonate or potassium hydroxide in dimethyl sulfoxide followed by the treatment using appropriate a base or an acid to give the corresponding 6-methylthiouracil derivatives in 15–80% yields. These uracil derivatives are found to be useful intermediates for the synthesis of 6-aminouracils and fused pyrimidine derivatives.     

Non-linear structures in the non-critical NSR string

We investigate the Ward identities of theW symmetry in the super-Liouville theory coupled to the super-conformal matter of central charge . The theory is classified into two chiralities. For the positive chirality, all gravitationally dressed scaling operators are generated from theq–1 gravitational primaries by one of the ring generators in the R-sector acting on them repeatedly. After fixing the normalizations of the dressed scaling operators, we find that the Ward identities are expressed in the form of theusual W _q algebra constraints as in the bosonic case:W _n ^(k+1) ,=0, (k=1,...,q–1;nZ1–k), where the equations for even and oddn come from the currents in the NS- and the R-sector respectively. The non-linear terms come from the anomalous contributions at the boundaries of moduli space. The negative chirality is defined by interchanging the roles ofp andq. Then we get theW _p algebra constraints.     

A generalized Dantzig—Wolfe decomposition principle for a class of nonconvex programming problems

Since Dantzig—Wolfe's pioneering contribution, the decomposition approach using a pricing mechanism has been developed for a wide class of mathematical programs. For convex programs a linear space of Lagrangean multipliers is enough to define price functions. For general mathematical programs the price functions could be defined by using a subclass of nondecreasing functions. However the space of nondecreasing functions is no longer finite dimensional. In this paper we consider a specific nonconvex optimization problem min {f(x):h _j (x)g(x),j=1, ,m, xX}, wheref(·),h _j (·) andg(·) are finite convex functions andX is a closed convex set. We generalize optimal price functions for this problem in such a way that the parameters of generalized price functions are defined in a finite dimensional space. Combining convex duality and a nonconvex duality we can develop a decomposition method to find a globally optimal solution.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.