a continuous dc programming approach to the strategic supply chain design problem from qualified partner set we present a new continuous approach based on the dc difference of convex functions programming and dc algorithms dca to the problem of supply chain design at the strategic level when production of a new market opportunity has to be launched among a set of qualified partners a well known formulation of this problem is the mixed integer linear program in this paper we reformulate this problem as a dc program by using an exact penalty technique the proposed algorithm is a combination of dca and branch and bound scheme it works in a continuous domain but provides mixed integer solutions numerical simulations on many empirical data sets show the efficiency of our approach with respect to the standard branch and bound algorithm

a class of exceptional polynomials we present a class of indecomposable polynomials of non primepower degree over the finite field of two elements which are permutation polynomials on infinitely many finite extensions of the field the associated geometric monodromy groups are the simple groups where k 3 and odd the first member of this class was previously found by p muller 17 this realises one of only two possibilities for such a class which remain following deep work of fried guralnick and saxl 7 the other is associated with psl 3 k 3 and odd in fields of characteristic 3

on hilbertian ideals abhyankar defined the index of a monomial in a matrix of indeterminates x to be the maximal size of any minor of x whose principal diagonal divides the given monomial using this concept he characterized a free basis for general type of determinantal ideals formed by the minors coming from a saturated subset of x in this paper to a monomial in x of index p we associate a combinatorial object called a superskeleton of latitude p which can loosely be described as a p tuple of almost nonintersecting paths in a rectangular lattice of points using this map we prove that the ideal generated by the p by p minors of a saturated set in x is hilbertian i e the hilbert polynomial of this ideal coincides with its hilbert function for all nonnegative integers

on the subgroup structure of classical groups in this paper we establish a result on the subgroup structure of classical groups over algebraically closed elds and use this to give a new proof of a fundamental theorem of m aschbacher on subgroups of nite classical groups let v be a nite dimensional vector space over an algebraically closed eld k and let g be one of the classical algebraic groups sl v sp v or so v our result is a reduction theorem concerning the subgroups of g we de ne a certain collection c of natural proper subgroups of g and prove that any closed nite or in nite subgroup of g either lies in a member of c or is roughly speaking a simple group acting irreducibly on v aschbacher s result is an analogous reduction theorem for subgroups of nite classical groups we obtain this as a relatively easy consequence of our main result by taking xed points under the action of a frobenius morphism using a standard process involving lang s theorem the proof of the main result uses elementary linear algebra together with a few basic facts from the theory of algebraic groups various complications which arise in the nite group setting in as become much more straightforward in the algebraic group setting in particular questions involving extension elds do not occur and issues of conjugacy are easily settled when we descend to nite invent math 134 427 453 1998

on finitely terminating branch and bound algorithms for some global optimization problems global optimization algorithms are typically terminated with an epsilon approximate solution after a finite number of iterations this paper shows how existing infinitely convergent branch and bound algorithms can be augmented to guarantee finite termination with an exact global solution for problems having extreme point solutions

galois embeddings for linear groups a criterion is given for the solvability of a central galois embedding problem to go from a projective linear group covering to a vectorial linear group covering

resolution of singularities and modular galois theory i shall sketch a brief history of the desingularization problem from riemann thru zariski to hironaka including the part i played in it and the work on galois theory which this led me to and how that caused me to search out many group theory gurus i shall also formulate several conjectures and suggest numerous thesis problems

the critical contact process seen from the right edge durrett 1984 proved the existence of an invariant measure for the critical and supercritical contact process seen from the right edge galves and presutti 1987 proved in the supercritical case that the invariant measure was unique and convergence to it held starting in any semi infinite initial state we prove the same for the critical contact process we also prove that the process starting with one particle conditioned to survive until timet converges to the unique invariant measure ast

an efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints in this paper we investigate two approaches to minimizing a quadratic form subject to the intersection of finitely many ellipsoids the first approach is the d c difference of convex functions optimization algorithm abbr dca whose main tools are the proximal point algorithm and or the projection subgradient method in convex minimization the second is a branch and bound scheme using lagrangian duality for bounding and ellipsoidal bisection in branching the dca was first introduced by pham dinh in 1986 for a general d c program and later developed by our various work is a local method but from a good starting point it provides often a global solution this motivates us to combine the dca and our branch and bound algorithm in order to obtain a good initial point for the dca and to prove the globality of the dca in both approaches we attempt to use the ellipsoidal constrained quadratic programs as the main subproblems the idea is based upon the fact that these programs can be efficiently solved by some available polynomial and nonpolynomial time algorithms among them the dca with restarting procedure recently proposed by pham dinh and le thi has been shown to be the most robust and fast for large scale problems several numerical experiments with dimension up to 200 are given which show the effectiveness and the robustness of the dca and the combined dca branch and bound algorithm

a branch and reduce approach for solving a class of low rank d c programs various classes of d c programs have been studied in the recent literature due to their importance in applicative problems in this paper we consider a branch and reduce approach for solving a class of d c problems seven partitioning rules are analyzed and some techniques aimed at improving the overall performance of the algorithm are proposed the results of a computational experience are provided in order to point out the performance effectiveness of the proposed techniques

further nice equations for nice groups nice sextinomial equations are given for unramified coverings of the affine line in nonzero characteristic p with p 2m q and 2m q as galois groups where m 3 is any integer and q 1 is any power of p 2

a branch and bound algorithm for solving a class of d c programming the d c difference of convex functions programming occurs very often in economic and financial field in this paper a class of d c programming problems be studied witch objection function is the sum of a convex quadratic function and a separable concave function the constrains is the intersection of a polytop and a rectangular a branch and bound algorithm is given for solving it we compare the largest distance bisection with subdivision in branch and bound algorithm numerical tests on different dimensions showed that the proposed branch and bound algorithm is efficient for solving medium scale problems and the efficiency of the largest distance bisection and subdivision is nearly

bivariate factorizations connecting dickson polynomials and galois theory in his ph d thesis of 1897 dickson introduced certain permutation polynomials whose galois groups are essentially the dihedral groups these are now called dickson polynomials of the first kind to distinguish them from their variations introduced by schur in 1923 which are now called dickson polynomials of the second kind in the last few decades there have been extensive investigations of both of these types which are related to the classical chebyshev polynomials we give new bivariate factorizations involving both types of dickson polynomials these factorizations demonstrate certain isomorphisms between dihedral groups and orthogonal groups and lead to the construction of explicit equations with orthogonal groups as galois groups