completely bounded multipliers over locally compact quantum groups in this paper we consider several interesting multiplier algebras associated with a locally compact quantum groupg firstly we study the completely bounded right multiplier algebra m r cb l1 g we show that m r cb l1 g is a dual banach algebra with a natural operator predual q r l1 g and the completely isometric representation of m r cb l1 g on b l2 g studied recently by junge neufang and ruan is actually weak weak continuous secondly we study the left uniformly continuous space luc g and its banach algebra dual luc g we prove that luc g is a unital c subalgebra of l1 g if the quantum groupg is semi regular we show the connection between luc g and the quan tum measure algebra m g as well as their representations on l1 g and b l2 g finally we study the right uniformly complete qotient space ucq r l1 g and its banach algebra dual ucq r l1 g for co amenable quanum groupsg we obtain the weak homeomorphic completely isometric algebra iso morphism m r cb l1 g m g and the completely isometric isomorphism ucq r l1 g luc g

on topological centre problems and sin quantum groups let a be a banach algebra with a faithful multiplication anda a be the quotient banach algebra of a with the left arens product we introduce a natural banach algebra which is a closed subspace of a a but equipped with a distinct multiplication with the help of this banach algebra new characteriza tions of the topological centre zt a a ofa a are obtained and a characterization of zt a a by lau and ulger for a having a bounded approximate identity is extended to all banach algebras the study of this banach algebra motivates us to introduce the notion of sin locally compact quantum groups and the concept of quotient strong arens irregularity we give characterizations of co amenable sin quan tum groups which are even new for locally compact groups our study shows that the sin property is intrinsically related to topological centre problems we also give characterizations of quotient strong arens irregularity for all quantum group algebras within the class of banach algebras introduced recently by the authors we characterize the unital ones generalizing the corresponding result of lau and ulger we study the interrelationships between strong arens irregularity and quotient strong arens irregularity revealing the complex nature of topological centre problems some open questions by lau and ulger on zt a a are also answered

metric projection onto a closed set necessary and sufficient conditions for the global minimum necessary and sufficient conditions for a local minimum form a well developed chapter of optimization theory determination of such conditions for the global minimum is a challenging problem useful conditions are currently known only for a few classes of nonconvex optimization problems it is important to find different classes of problems for which the required conditions can be obtained in this paper we examine one of these classes the minimization of the distance to an arbitrary closed set in a class of ordered normed spaces we use the structure of the objective function in order to present necessary and sufficient conditions that give a clear understanding of the structure of a global minimizer and can be easily verified for some problems under consideration

proof of the ghahramani lau conjecture abstract the ghahramani lau conjecture is established in other words the measure algebra of every locally compact group is strongly arens irregular to this end we introduce and study certain new classes of measures called approximately invariant respectively strongly singular which are of interest in their own right moreover we show that the same result holds for the measure algebra of any not necessarily locally compact polish group

discontinuous robust mappings are approximatable the concepts of robustness of sets and and functions were introduced to form the foundation of the theory of integral global optimization a set a of a topological space x is said to be robust iff cl a cl int a a mapping f x y is said tobe robust iffforeach open set uy of y f i uy is robust we prove that if x is a baire space and y satisfies the second axiom of countability then a mapping f x y is robust iff it is approximatable in the sense that the set of points of continuity of f is dense in x and that for any other point x e x x f x is the limit of x f x where for all a x is a continuous point of f this result justifies the notion of robustness

multipliers and modulus on banach algebras related to locally compact groups abstract let g be a locally compact group in this paper we study moduli of products of elements and of multipliers of banach algebras which are related to locally compact groups and which admit lattice structure as a consequence we obtain a characterization of operators on l g which commute with convolutions when g is amenable as discrete

global optimum shape design abstract an optimum shape design problem can be formulated as a minimization problem of a functional subject to certain constraints usually it is nonlinear and nonconvex conventional optimization techniques are gradient based they highly depend on the initial design and are difficult to be applied to find a global solution integral global optimization algorithm is proposed to solve optimum shape design problems three design examples are given to illustrate the effectiveness of the algorithm

completely isometric representations of _ and let g be a locally compact group it is shown that there exists a natural completely isometric representation of the completely bounded fourier multiplier algebra m cb a g which is dual to the representation of the measure algebra m g on b l 2 g the image algebras of m g and m cb a g in cb b l 2 g are intrinsically characterized and some commutant theorems are proved it is also shown that for any amenable group g there is a natural completely isometric representation of ucb g on b l 2 g which can be regarded as a duality result of neufang s completely isometric representation theorem for luc g

multipliers and ideals in second conjugate algebras related to locally compact groups abstract let g be a locally compact group in this paper we study compact or weakly compact multipliers on the second conjugate algebras l 1 g and m g we prove among other things that g is amenable if and only if there is a non zero compact or weakly compact right multiplier on l 1 g or m g we show that if g is compact non compact then l 1 g cannot have any non zero weakly compact left multipliers t with t n 1 0 for some n l 1 g we also study maximal regular ideals of l 1 g w when g is a locally compact abelian group and w is a weight function on g and a p g 1 p g

topological centers of certain dual algebras let a be a banach algebra with a bounded approximate identity let z1 and z2 be respectively the topological centers of the algebras a and a a in this paper for weakly sequentially complete banach algebras in particular for the group and fourier algebras l1 g and a g we study the sets z1 z2 the relations between them and with several other subspaces of a or a

module maps on duals of banach algebras and topological centre problems we study various spaces of module maps on the dual of a banach algebra a and relate them to topological centres we introduce an auxiliary topological centre zt a a for the left quotient banach algebra a a of a our results indicate that zt a a is indispensable for investigating properties of module maps over a and for understanding some asymmetry phenomena in topological centre problems as well as the interrelationships between different arens irregularity properties for the class of banach algebras of type m introduced recently by the authors we show that strong arens irregularity can be expressed both in terms of automatic normality of a module maps on a and through certain commutation relations this in particular generalizes the earlier work on group algebras by ghahramani and mcclure 1992 13 and by ghahramani and lau 1997 12 we link a module map property over a to the space wap a of weakly almost periodic functionals on a generalizing a result by lau and ulger 1996 34 for banach algebras with a bounded approximate identity we also show that for a locally compact quantum group g the quotient strong arens irregularity of l1 g can be obtained from that of m g and can be characterized via the canonical c0 g module structure on luc g

exact penalty functions in constrained optimization in this paper formal definitions of exactness for penalty functions are introduced and sufficient conditions for a penalty function to be exact according to these definitions are stated thus providing a unified framework for the study of both nondifferentiable and continuously differentiable penalty functions in this framework the best known classes of exact penalty functions are analyzed and new results are established concerning the correspondence between the solutions of the constrained problem and the unconstrained minimizers of the penalty functions

on a conjecture by ghahramani lau and related problems concerning topological centres abstract let a be a banach algebra and consider a equipped with the first arens product we establish a general criterion which ensures that a is left strongly arens irregular i e the first topological centre of a is reduced to a itself using this criterion we prove that for a very large class of locally compact groups ghahramani lau s conjecture cf lau 94 and gha lau 95 stating the left strong arens irregularity of the measure algebra m g holds true our methods obviously yield as well the right strong arens irregularity in the situation considered furthermore the same condition used above implies that every linear left a module homomorphism on a is automatically bounded and w continuous we finally show that our criterion also yields a partial answer to a question raised by lau ulger trans amer math soc 348 3 1996 1191 on the topological centre of the algebra a a for a having a right approximate identity bounded by 1

module homomorphisms and topological centres associated with weakly sequentially complete banach algebras abstract this paper is a contribution to the theory of weakly sequentially complete banach algebras a we require them to have bounded approximate identities and for the most part to be ideals in their second duals so that examples are the group algebras l 1 g for compact groups g or the fourier algebras a g for discrete amenable groups g in section 2 we present our main result that the topological centre or set of weak bicontinuous elements of a is identifiable with a as a corollary we deduce in section 3 that each left a module homomorphism from a to a a can be realized as right translation by an element of a these conclusions generalise recent advances in the subject in section 4 we take a special algebra l 1 s for a commutative discrete semigroup s and show that if its second dual has an identity then that identity must lie in l 1 s

a low dimensional semidefinite relaxation for the quadratic assignment problem the quadratic assignment problem qap is arguably one of the hardest np hard discrete optimization problems problems of dimension greater than 25 are still considered to be large scale current successful solution techniques use branch and bound methods which rely on obtaining strong and inexpensive bounds in this paper we introduce a new semidefinite programming sdp relaxation for generating bounds for the qap in the trace formulation we apply majorization to obtain a relaxation of the orthogonal similarity set of the quadratic part of the objective function this exploits the matrix structure of qap and results in a relaxation with much smaller dimension than other current sdp relaxations we compare the resulting bounds with several other computationally inexpensive bounds such as the convex quadratic programming relaxation qpb we find that our method provides stronger bounds on average and is adaptable for branch and bound methods

reflection and transmission of transverse waves at a plane interface between two different porous elastic solid half spaces abstract a problem of reflection and transmission of obliquely incident plane transverse wave at a plane interface between two porous elastic half spaces in welded contact is investigated the theory developed by cowin and nunziato s c cowin j w nunziato linear elastic materials with voids journal of elasticity 13 1983 125 147 has been used to write down the equations of motion and constitutive relations for the elastic medium with voids potential method is used to obtain the reflection and transmission coefficients it is found that these coefficients are functions of angle of incident elastic constants void parameters and that of the frequency of the incident wave numerical computations have been performed for a particular model and the results obtained are depicted graphically the results of ciarletta and sumbatyan m ciarletta m a sumbatyan reflection of plane waves by the free boundary of a porous elastic half space journal of sound and vibration 259 2 2003 253 264 have been reduced as a special case of the present formulation the expression for the partition of energy at the interface during transmission and reflection of waves have also been presented

reflection of plane waves by the free boundary of a porous elastic half space in the present paper we study reflection of inclined incident plane waves from a free boundary of the half space in which the material is described by constitutive equations valid for elastic solids with voids both the cases of the transverse and longitudinal incident waves are considered and it is shown that only the transverse one can propagate in the solid without attenuation after having been reflected from the free boundary surface the reflection coefficient and the amplitude of the surface oscillations are expressed in explicit form the general results are demonstrated for several hypothetical porous materials and it is shown that the reflection coefficient and the vibration amplitude are typically less than in classical media without voids however for relatively large transverse wave speed and high porosity free boundary oscillation can exceed the classical one

the c algebra generated by operators with compact support on a locally compact group abstract let g be a locally compact group and vn g be the von neumann algebra generated by the left regular representation of g let ucb denote the c subalgebra generated by operators in vn g with compact support when g is abelian ucb corresponds to the space of bounded uniformly continuous functions on the dual group of g in this paper we prove among other things that for a large class of locally compact groups which include the heisenberg group the ax b group and the motion group the centre of the banach algebra ucb is the fourier stieltjes algebra b g

global optimality conditions for quadratic optimization problems with binary constraints we consider nonconvex quadratic optimization problems with binary constraints our main result identifies a class of quadratic problems for which a given feasible point is global optimal we also establish a necessary global optimality condition these conditions are expressed in a simple way in terms of the problem s data we also study the relations between optimal solutions of the nonconvex binary quadratic problem versus the associated relaxed and convex problem defined over the l infty norm our approach uses elementary arguments based on convex duality

optimality conditions in global optimization and their applications in this paper we derive necessary and sufficient conditions for some problems of global minimization our approach is based on methods of abstract convexity we use a representation of an upper semicontinuous function as the lower envelope of a family of convex functions we discuss applications of conditions obtained to the examination of some tractable sufficient conditions for the global minimum and to the theory of inequalities

geometry of c algebras and the bidual of their projective tensor product abstract given c algebras a and b consider the banach algebra a b where denotes the projective banach space tensor product if a and b are commutative this is the varopoulos algebra v a b we write v a for v a a it has been an open problem for almost 40 years to determine precisely when a b is arens regular see e g 33 48 49 we solve this classical question for arbitrary c algebras indeed we show that a b is arens regular if and only if a or b has the phillips property note that a has the latter property if and only if it is scattered and has the dunford pettis property a further equivalent condition is that a has the schur property or again equivalently the enveloping von neumann algebra a is finite atomic i e a direct sum of matrix algebras hence arens regularity of a b is entirely encoded in the geometry of the c algebras in case a and b are von neumann algebra we conclude that a b is arens regular if and only if a or b is finite dimensional we also show that this characterization does not generalize to the class of non selfadjoint dual even commutative operator algebras specializing to commutative c algebras a and b we obtain that v a b is arens regular if and only if a or b is scattered we further describe the centre z v a showing that it is banach algebra isomorphic to a e h a where e h denotes the extended haagerup tensor product we deduce that v a is strongly arens irregular if and only if a is finite dimensional hence v a is neither arens regular nor strongly arens irregular if and only if a is non scattered this is the case e g for a l

some theorems about spectrum and finite element approach for eigenvalue problems for elastic bodies with voids the paper concerns eigenvalue problems for elastic bodies with voids in contact with massive rigid plane punches the linear theory of elastic materials with voids according to the cowin nunziato model is used a variational principle is constructed which has the properties of minimality similar to the well known variational principle for problems with pure elastic media the discreteness of the spectrum and completeness of the eigenfunctions are proved as a consequence of variational principles the properties of an increase or a decrease in the natural frequencies when the mechanical and porous boundary conditions and the modulus of elastic solid with voids change are established a finite element method is proposed for numerical solution of eigenvalue problems for elastic media with voids some effective block algorithms for finite element eigenvalue problems with partial coupling are described numerical experiments are presented for determining the first eigenfrequencies of an axisymmetric elastic body with voids

weak factorizations of operators in the group von neumann algebras of certain amenable groups and applications let g be a compact group whose local weight b g has uncountable cofinality let h be an amenable locally compact group and a g h be the fourier algebra of g h we prove that the group von neumann algebra vn g h a g h has the weak uniform a g h factorization property of level b g as a corollary we show that a g h is strongly arens irregular and the topological centre of uc2 g h is equal to the fourier stieltjes algebra b g h