thin coverings of modules abstract thin coverings are a method of constructing graded simple modules from simple ungraded modules after a general discussion we classify the thin coverings of quasifinite simple modules over associative algebras graded by finite abelian groups the classification uses the representation theory of cyclotomic quantum tori we close with an application to representations of multiloop lie algebras

algebraic reflexivity of the isometry group of some spaces of lipschitz functions abstract we show that the isometry groups of lip x d and lip x d with 0 1 for a compact metric space x d are algebraically reflexive we also prove that the sets of isometric reflections and generalized bi circular projections on such spaces are algebraically reflexive in order to achieve this we characterize generalized bi circular projections on these spaces

extreme points and isometries on vector valued lipschitz spaces abstract for a banach space e and a compact metric space x d a function f x e is a lipschitz function if there exists k 0 such that f x f y k d x y for all x y x the smallest such k is called the lipschitz constant l f for f the space lip x e of all lipschitz functions from x to e is a banach space under the norm defined by f max l f f where f sup f x x x recent results characterizing isometries on these vector valued lipschitz spaces require the banach space e to be strictly convex we investigate the nature of the extreme points of the dual ball for lip x e and use the information to describe the surjective isometries on lip x e under certain conditions on e where e is not assumed to be strictly convex we make use of an embedding of lip x e into a space of continuous vector valued functions on a certain compact set

lie algebras graded by finite root systems and intersection matrix algebras this paper classifies the lie algebras graded by doubly laced finite root systems and applies this classification to identify the intersection matrix algebras arising from multiply affinized cartan matrices of types b c f and g this completes the determination of the lie algebras graded by finite root systems initiated by berman and moody who studied the simply laced finite root systems of rank 2

weighted composition operators ofc0 x s abstract in this paper we prove that into isometries and disjointness preserving linear maps from c 0 x into c 0 y are essentially weighted composition operators tf h f for some continuous map and some continuous scalar valued function h

differential conformal superalgebras and their forms abstract we introduce the formalism of differential conformal superalgebras which we show leads to the correct automorphism group functor and accompanying descent theory in the conformal setting as an application we classify forms of n 2 and n 4 conformal superalgebras by means of galois cohomology

parallel lagrange newton krylov schur methods for pde constrained optimization part i the krylov schur solver large scale optimization of systems governed by partial differential equations pdes is a frontier problem in scientific computation reduced quasi newton sequential quadratic programming sqp methods are state of the art approaches for such problems these methods take full advantage of existing pde solver technology and parallelize well however their algorithmic scalability is questionable for certain problem classes they can be very slow to converge in this two part article we propose a new method for steady state pde constrained optimization based on the idea of using a full space newton solver combined with an approximate reduced space quasi newton sqp preconditioner the basic components of the method are newton solution of the first order optimality conditions that characterize stationarity of the lagrangian function krylov solution of the karush kuhn tucker kkt linear systems arising at each newton iteration using a symmetric quasi minimum residual method preconditioning of the kkt system using an approximate state decision variable decomposition that replaces the forward pde jacobians by their own preconditioners and the decision space schur complement the reduced hessian by a bfgs approximation initialized by a two step stationary method accordingly we term the new method it lagrange newton krylov schur lnks it is fully parallelizable exploits the structure of available parallel algorithms for the pde forward problem and is locally quadratically convergent in part i of this two part article we investigate the effectiveness of the kkt linear system solver we test our method on two optimal control problems in which the state constraints are described by the steady state stokes equations the objective is to minimize dissipation or the deviation from a given velocity field the control variables are the boundary velocities numerical experiments on up to 256 cray t3e processors and on an sgi origin 2000 include scalability and performance assessment of the lnks algorithm and comparisons with reduced sqp for up to 1 000 000 state and 50 000 decision variables in part ii of the article we address globalization and inexactness issues and apply lnks to the optimal control of the steady incompressible navier stokes equations

investigations on boundary temperature control analysis considering a moving body based on the adjoint variable and the fictitious domain finite element methods summary this paper presents an examination of moving boundary temperature control problems with a moving boundary problem a finite element mesh is generated at each time step to express the position of the boundary on the other hand if an overlapped domain that is comprising foreground and background meshes is prepared the moving boundary problem can be solved without mesh generation at each time step by using the fictitious domain method in this study boundary temperature control problems with a moving boundary are formulated using the finite element the adjoint variable and the fictitious domain methods and several numerical experiments are carried out copyright 2015 john wiley sons ltd

noncompactness and noncompleteness in isometries of lipschitz spaces abstract we solve the following three questions concerning surjective linear isometries between spaces of lipschitz functions lip x e and lip y f for strictly convex normed spaces e and f and metric spaces x and y i characterize those base spaces x and y for which all isometries are weighted composition maps ii give a condition independent of base spaces under which all isometries are weighted composition maps iii provide the general form of an isometry both when it is a weighted composition map and when it is not in particular we prove that requirements of completeness on x and y are not necessary when e and f are not complete which is in sharp contrast with results known in the scalar context

covering algebras ii isomorphism of loop algebras this paper studies the loop algebras that arise from pairs consisting of a symmetrizable kac moody lie algebra g and a finite order automorphism of g we obtain necessary and sufficient conditions for two such loop algebras to be isomorphic

isometries on spaces of absolutely continuous functions in a noncompact framework abstract in this paper we deal with surjective linear isometries between spaces of scalar valued absolutely continuous functions on arbitrary not necessarily closed or bounded subsets of the real line with at least two points as a corollary it is shown that when the underlying spaces are connected each surjective linear isometry of these function spaces is a weighted composition operator a result which generalizes all the previous known results concerning such isometries

examinations for terminal condition of lagrange multiplier for heat transfer control problems this paper presents a method to express the terminal condition of lagrange multiplier by the solution of the steady adjoint equation in the control problem based on the adjoint equation method the terminal condition of lagrange multiplier has been set zero to satisfy the stationary condition of the extended performance function therefore there is a possibility that the control value near the terminal time cannot be appropriately expressed to solve this problem a method to express the terminal condition of lagrange multiplier by the solution of the steady adjoint equation is proposed and examined finally to confirm the propriety of the proposed method this method is applied to the sequential control problem and some remarks are made copyright 2007 john wiley sons ltd

galois cohomology and forms of algebras over laurent polynomial rings 3 loop torsors 8 3 1 the witt tits index of a loop torsor 9 3 2 reducibility 12 3 3 almost commutative subgroups 14 3 4 almost commuting families of elements of finite order 16 3 5 almost commuting pairs and their invariants 17 3 6 failure in the anisotropic case 24

when do the c0 1 k x spaces determine the locally compact subspaces k of the real line r abstract let x be a finite dimensional space and k a locally compact subspace of the real line r without isolated points the space c 0 1 k x will stand for the banach space of all x valued continuously differentiable functions f such that f and f vanish at infinity endowed with the norm f max f f it is shown that if there is an isomorphism t c 0 1 k x c 0 1 s x satisfying t t 1 x and t t 1 then k and s are homeomorphic where x is a parameter introduced by jarosz in 1989 and t is the norm of t when c 0 1 k x and c 0 1 s x are considered as subspaces of c 0 k x and c 0 s x respectively

algebraic reflexivity of isometry groups of algebras of lipschitz maps abstract we study groups of surjective linear isometries on banach algebras of lipschitz maps with values in some unital c algebras in this paper these spaces are endowed with the sum norm for the case where the c algebras are commutative whose groups of all surjective isometries are algebraically reflexive we prove that the group of all surjective isometries on the corresponding banach algebra of lipschitz maps are algebraically reflexive we also prove that the group of unital surjective isometries between matrix valued lipschitz algebras are reflexive

quantum tori and the structure of elliptic quasi simple lie algebras abstract we study and classify those tame irreducible elliptic quasi simple lie algebras which are simply laced and of rankl 3 the first step is to identify the core of such an algebra up to central isogeny by identifying the coordinates when the type isdorethe coordinates are laurent polynomials in variables while for typeathe coordinates can be any quantum torus in variables the next step is to study the universal central extension as well as the derivation algebra of the core these are related to the first connes cyclic homology group of the coordinates the final step is to use this information to give constructions of lie algebras which we then prove yield representatives of all isomorphism classes of the above types of algebras

optimal extensions of the banach stone theorem abstract let c 0 k x denote the banach space of all x valued continuous functions defined on the locally compact hausdorff space k which vanish at infinity provided with the supremum norm we prove that if x is a real banach space and t is an isomorphism from c 0 k 1 x onto c 0 k 2 x satisfying j x t t 1 2 where j x is the james constant of x then k 1 is homeomorphic to k 2 in the complex case we provide a similar result for reflexive spaces x in other words we obtain a vector valued extension of the classical amir cambern theorem x r or x c which at the same time unifies and strengthens several generalizations of the classical banach stone theorem due to cambern 1976 and 1985 behrends cambern 1988 and jarosz 1989 in the case where x l p 2 p our results are optimal

isometries on spaces of absolutely continuous vector valued functions abstract this paper investigates the surjective not necessarily linear isometries between spaces of absolutely continuous vector valued functions with respect to the norm max v where and v denote the supremum norm and the total variation of a function respectively and gives an absolutely continuous version of a celebrated theorem by jerison as a consequence in the scalar valued case we obtain generalizations of all known results concerning such isometries by a different approach

isometries between function spaces surjective isometries between some classical function spaces are investigated we give a simple technical scheme which verifies whether any such isometry is given by a homeomorphism between corresponding hausdorff compact spaces in particular the answer is positive for the c x ac 0 1 lip0 x and lip0 x spaces provided with various natural norms

infinite flag varieties and conjugacy theorems abstract we study the orbit of a highest weight vector in an integrable highest weight module of the group g associated to a kac moody algebra unk a we obtain applications to the geometric structure of the associated flag varieties and to the algebraic structure of unk a in particular we prove conjugacy theorems for cartan and borel subalgebras of unk a so that the cartan matrix a is an invariant of unk a

derivations of certain algebras defined by etale descent we give an explicit description of the lie algebra of derivations for a class of infinite dimensional algebras which are given by etale descent the algebras under consideration are twisted forms of central algebras over rings and include the multiloop algebras that appear in the construction of extended affine lie algebras

lie algebras graded by finite root systems and the intersection matrix algebras of slodowy this paper is about toroidal lie algebras certain intersection matrix lie algebras defined by slodowy and their relationship to one another and to certain lie algebra analogues of steinberg groups the main result of the paper is the identification of the intersection matrix algebras arising from multiply affinized cartan matrices of types a d and e with certain steinberg lie algebras and toroidal lie algebras propositions 5 9 and 5 10 a major part of the paper studies and classifies lie algebras graded by finite root systems these become the princi pal tool in our analysis of intersection matrix algebras each lie algebra graded by a simply laced finite root system of rank 2 has attached to it an algebra which according to the type and rank is either commutative and associative only associative or alternative all these possibilities occur in our description of inter section matrix algebras let r be any associative algebra with identity not necessarily finite dimen sional over a field k of characteristic 0 for each positive integer n the associative algebra m r of n n matrices with coefficients in r forms a lie algebra over k under the commutator product we denote this lie algebra by ol r let eis be the i j matrix unit of m r and assume that n 2 the subalgebra e r of oi r generated by the elements reis r r i 4 j is an ideal of 91 r and is perfect i e it is its own derived algebra now any perfect lie algebra o has a universal central extension also perfect called a universal covering algebra u c a of o ga so in particular e r has a u c a that we will denote by t r we define 112 r by the exact sequence 0 1 0 f2 r t r e r 0 dedicated to our teacher maria j wonenburger both authors gratefully acknowledge the support of the natural sciences and engineering research council of canada