intersection forms of non spin four manifolds 1 introductionit remains a central question in four manifold topology which quadratic formoccurs as the intersection form of an orientable four manifold in the topologicalcategory there is a beautiful answer the celebrated result of freedman assertsthat all the quadratic forms can be realized however in the smooth category wehave a rather different picture by the surprising result of donaldson d fs a among the de nite quadratic forms only the diagonalizable ones can berealized thereisalsoalongstanding11

the mixed vertex packing problem we study a generalization of the vertex packing problem having both binary and bounded continuous variables called the mixed vertex packing problem mvpp the well known vertex packing model arises as a subproblem or relaxation of many 0 1 integer problems whereas the mixed vertex packing model arises as a natural counterpart of vertex packing in the context of mixed 0 1 integer programming we describe strong valid inequalities for the convex hull of solutions to the mvpp and separation algorithms for these inequalities we give a summary of computational results with a branch and cut algorithm for solving the mvpp and using it to solve general mixed integer problems

on the stable set polytope of a series parallel graph we give a short proof of chvatal s conjecture that the nontrivial facets of the stable set polytope of a series parallel graph all come from edges and odd holes

text pin 2 monopole equations and intersection forms with local coefficients of four manifolds we introduce a variant of the seiberg witten equations text pin 2 monopole equations and give its applications to intersection forms with local coefficients of four manifolds the first application is an analogue of froyshov s results on four manifolds with definite intersection forms with local coefficients the second is a local coefficient version of furuta s 10 8 inequality as a corollary we construct nonsmoothable spin four manifolds satisfying rohlin s theorem and the 10 8 inequality

set packing relaxations of some integer programs this paper is about set packing relaxations of combinatorial optimization problems associated with acyclic digraphs and linear orderings cuts and multicuts and set packings themselves families of inequalities that are valid for such a relaxation as well as the associated separation routines carry over to the problems under investigation

dipper donkin algebra as global symmetry of quantum chains we analyse the role of gl2 a quantum group constructed by dipper and donkin 1991 proc london math soc 63 165 211 as a global symmetry for quantum chains and show how to construct all possible hamiltonians for four state quantum chains with gl2 global symmetry in doing this we search for and present all inner actions of gl2 on the clifford algebra c 1 3 we also introduce the corresponding operator algebras invariants and hamiltonians explicitly

magnetic monopoles on three manifolds on etudie des monopoles magnetiques sur une 3 variete de riemann complete orientee m on associe a m une collection d espaces de modules de solutions des equations des monopoles pourvu que m soit non compacte et que la metrique de riemann sur m soit bonne pres de l infini

new topological field theories in two dimensions it is shown that two 1 1 dimensional 2d free abelian and self interacting non abelian gauge theories without any interaction with matter fields belong to a new class of topological field theories tfts these new theories capture together some of the key features of witten and schwarz types of tft because they are endowed with symmetries that are reminiscent of the schwarz type theories but their lagrangian density has the appearance of the witten type theories the topological invariants for these theories are computed on a 2d compact manifold and their recursion relations are obtained these new theories are shown to provide a class of tractable field theoretical models for the hodge theory in two dimensions of flat minkowski spacetime where there are no propagating degrees of freedom associated with the 2d gauge boson

shape reconstruction of three dimensional conducting curved plates using physical optics nurbs modeling and genetic algorithm a microwave inverse scattering problem including a method for shape reconstruction of three dimensional electrically large conducting patches with simple geometries using genetic algorithm is presented unknown shape reconstruction algorithm starts from the knowledge of the simulated radar cross section rcs data through back scattering far field computation using physical optics approximation the forward problem involves the computation of the multiple frequency and multiple direction rcs of three dimensional large conducting patches modeled by nonuniform rational b spline nurbs surfaces the control points of nurbs are the geometrical parameters which are optimized for the shape reconstruction procedure the extended stationary phase method and critical cases which occur in physical optics computations in the forward problem are also discussed noise effect and the influence of increment in the number of control points of a nurbs over the inversion algorithm are investigated as well numerical results are presented to verify the operation of the proposed algorithm

uniform asymptotic evaluation of surface integrals with polygonal integration domains in terms of utd transition functions the field scattered by a scattering body or by an aperture in the free space or in an unbounded homogenous medium can be described in terms of a double integral in this paper we show how a canonical integral on a polygonal domain with a constant amplitude function and a quadratic phase variation can be exactly expressed in terms of special functions namely fresnel integrals and generalized fresnel integrals this exact reduction represents a paradigm for deriving a new asymptotic evaluation for a more general integral this new asymptotic uniform integral evaluation is expressed in the format of the uniform geometrical theory of diffraction which is convenient for numerical computations

wheel inequalities for stable set polytopes we introduce new classes of valid inequalities called wheel inequalities for the stable set polytopepg of a graphg each wheel configuration gives rise to two such inequalities the simplest wheel configuration is an odd subdivisionw of a wheel and for these we give necessary and sufficient conditions for the wheel inequality to be facet inducing forpw generalizations arise by allowing subdivision paths to intersect and by replacing the hub of the wheel by a clique the separation problem for these inequalities can be solved in polynomial time

antiweb wheel inequalities and their separation problems over the stable set polytopes a stable set in a graph g is a set of pairwise nonadjacent vertices the problem of finding a maximum weight stable set is one of the most basic hard problems an important approach to this problem is to formulate it as the problem of optimizing a linear function over the convex hull stab g of incidence vectors of stable sets since it is impossible unless co to obtain a concise characterization of stab g as the solution set of a system of linear inequalities it is a more realistic goal to find large classes of valid inequalities with the property that the corresponding separation problem given a point x find if possible an inequality in the class that x violates is efficiently solvable some known large classes of separable inequalities are the trivial edge cycle and wheel inequalities in this paper we give a polynomial time separation algorithm for the t antiweb inequalities of trotter we then introduce an even larger class in fact a sequence of classes of valid inequalities called t antiweb s wheel inequalities this class is a common generalization of the t antiweb inequalities and the wheel inequalities we also give efficient separation algorithms for them

a stable cohomotopy refinement of seiberg witten invariants ii the monopole map defines an element in an equivariant stable cohomotopy group refining the seiberg witten invariant part i discusses the definition of this stable homotopy invariant and its relation to the integer valued seiberg witten invariants

the orientation of yang mills moduli spaces and 4 manifold topology si x est une 4 variete lisse orientee fermee dont la forme intersection q h 2 x z torsion z est definie negative alors la forme est equivalente sur les entiers a la forme standard 1 1 1 soit x une 4 variete lisse orientee fermee avec les trois proprietes suivantes 1 h 1 x z n a pas de 2 torsion 2 la forme intersection q sur h 2 x torsion a une partie positive de rang 1 ou 2 3 la forme intersection est paire alors q est equivalente sur les entiers a une des formes 01 10 01 10 01 10

strong lift and project cutting planes for the stable set problem a great deal of research has been focusing since the early seventies on finding strong relaxations for the stable set problem polyhedral combinatorics techniques have been at first developed to strengthen the natural linear formulation afterward strong semidefinite programming relaxations have been deeply investigated nevertheless the resulting integer programming ip algorithms cannot be regarded as being quite successful in practice as most of the relaxations give rise to one out of two extreme situations either provide weak bounds at low computational cost or give good bounds sometimes excellent but too demanding to compute in this paper we present a method to bridge such a gap in particular a new lift and project relaxation is obtained by a problem specific variant of the lifting operator m k k by lovasz and schrijver combined with benders decomposition this yields strong cutting planes generated by solving a cut generating linear program an extensive computational experience shows that embedding these cuts in a branch and cut framework significantly reduces the size of the enumeration trees as well as the cpu times with respect to state of the art ip algorithms

representations of quantum matrix algebra mq 2 and its q boson realization in this paper it is proved that the nontrivial finite dimensional irreducible representations of the quantum matrix algebra mq 2 or the coordinate ring of the quantum group glq 2 exist only when q is a root of unity and thereby construct such representations for mq 2 some finite dimensional indecomposable representations of mq 2 are also explicitly presented finally the q boson realization of mq 2 is discussed and it is shown that it works in this case as well as in the quantum algebra case

quantum chains with glq 2 symmetry usually quantum chains with quantum group symmetry are associated with representations of quantized universal algebras uq g here we propose a method for constructing quantum chains with cq g global symmetry where cq g is the algebra of functions on the quantum group in particular we will construct a quantum chain with glq 2 symmetry which interpolates between two classical ising chains it is shown that the hamiltonian of this chain satisfies the generalized braid group algebra

an application of gauge theory to four dimensional topology soit x une u variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee q est definie positive alors cette forme est equivalente sur les entiers a la forme diagonale standard soit dans une base q u 1 u 2 u 2 u 2 1 u 2 2 u 2 2