towers of recollement and bases for diagram algebras planar diagrams and a little beyond abstract the recollement approach to the representation theory of sequences of algebras is extended to pass basis information directly through the globalisation functor the method is hence adapted to treat sequences that are not necessarily towers by inclusion such as symplectic blob algebras diagram algebra quotients of the type c hecke algebras by carefully reviewing the diagram algebra construction we find a new set of functors interrelating module categories of ordinary blob algebras diagram algebra quotients of the type b hecke algebras at different values of the algebra parameters we show that these functors generalise to determine the structure of symplectic blob algebras and hence of certain two boundary temperley lieb algebras arising in statistical mechanics we identify the diagram basis with a cellular basis for each symplectic blob algebra and prove that these algebras are quasihereditary over a field for almost all parameter choices and generically semisimple that is we give bases for all cell and standard modules

decomposition numbers for the cyclotomic brauer algebras in characteristic zero we study the representation theory of the cyclotomic brauer algebra via truncation to idempotent subalgebras which are isomorphic to a product of walled and classical brauer algebras in particular we determine the block structure and decomposition numbers in characteristic zero

lyapunov exponents and control sets near singular points abstract we consider control affine systems of the form x f 0 x i 1 m u i t f i x u u u r u loc integrable on r d with compact control range u and a singular point x r d i e f i x 0 i 0 m control sets are maximal subsets of r d with nonvoid interior where the system is approximately controllable we suppose that there is a periodic control functions u h such that linearized the system has positive and negative lyapunov exponents for u h and a periodic control function u s such that the linearized system has only negative lyapunov exponents for u s under an inner pair condition we show the existence of control sets near the singular point by using local stable and unstable manifolds of the system corresponding to u h and its asymptotic phase

parabolic projective functors in type a abstract we classify projective functors on the regular block of rocha caridi s parabolic version of the bgg category o in type a in fact we show that in type a the restriction of an indecomposable projective functor from o to the parabolic category is either indecomposable or zero as a consequence we obtain that projective functors on the parabolic category o in type a are completely determined up to isomorphism by the linear transformations they induce on the level of the grothendieck group which was conjectured by stroppel in 39

high order symplectic integration methods for finite element solutions to time dependent maxwell equations in this paper we motivate the use of high order integration methods for finite element solutions of the time dependent maxwell equations in particular we present a symplectic algorithm for the integration of the coupled first order maxwell equations for computing the time dependent electric and magnetic fields symplectic methods have the benefit a conserving total electromagnetic field energy and are therefore preferred over dissipative methods such as traditional runge kutta in applications that require high accuracy and energy conservation over long periods of time integration we show that in the context or symplectic methods several popular schemes can be elegantly cast in a single algorithm we conclude with some numerical examples which demonstrate the superior performance of high order time integration methods

a pseudospectral method for time domain computation of electromagnetic scattering by bodies of revolution we present a multidomain pseudospectral method for the accurate and efficient time domain computation of scattering by body of revolution bor perfectly electrically conducting objects in the bor formulation of the maxwell equations the azimuthal dependence of the fields is accounted for analytically through a fourier series the numerical scheme in the r z plane is developed in general curvilinear coordinates and the method of characteristics is applied for patching field values in the individual subdomains to obtain the global solution a modified matched layer method is used for terminating the computational domain and special attention is given to proper treatment of the coordinate singularity in the scattered field formulation and correct time domain boundary conditions along edges numerical results for monochromatic plane wave scattering by smooth and nonsmooth axis symmetric objects including spheres cone spheres and finite cylinders is compared with results from the literature illustrating the accuracy and computational efficiency associated with the use of properly constructed spectral methods to emphasize the versatility of the presented framework we compute plane wave scattering by a missile and find satisfactory agreement with method of moment mom computations

two dimensional multidomain pseudospectral time domain algorithm based on alternating direction implicit method in order to deal with the stability problem restricted by the finite difference time domain fdtd and conventional pseudospectral time domain pstd the multidomain pstd algorithm based on alternating direction implicit adi technique is proposed in this paper this algorithm improves the stability and efficiency of conventional pstd while it maintains the accuracy and flexibility of conventional pstd for an accurate treatment of arbitrarily curved objects a compact matrix form is derived to effectively describe two dimensional adi multidomain pseudospectral time domain adi mpstd algorithm numerical results show an excellent agreement with analytical solutions as well as results obtained by the fdtd algorithm and fully demonstrate a remarkable improvement in stability and efficiency

recollements of self injective algebras and classification of self injective diagram algebras diagram algebras in particular brauer algebras birman murakami wenzl algebras and partition algebras are used in representation theory and invariant theory of orthogonal and symplectic groups in knot theory in mathematical physics and elsewhere classifications are known when such algebras are semisimple of finite global dimension or quasi hereditary we obtain a characterisation of the self injective case which is shown to coincide with the previously also unknown symmetric case the main tool is to show that indecomposable self injective algebras in general are derived simple that is their bounded derived module categories admit trivial recollements only as a consequence self injective algebras are seen to satisfy a derived jordan holder theorem

multidomain pseudospectral time domain algorithm using a symplectic integrator the novel multidomain pseudospectral time domain method based on a symplectic integrator scheme is presented in this paper a symplectic integrator scheme is a decomposition of the exponential operator or a general propagation technique the scheme is nondissipative and does not require additional memory for temporary storage of data for the internal stages the good performance of the scheme is demonstrated by numerical examples

toward the construction of a fourth order difference scheme for transient em wave simulation staggered grid approach a compact central difference approximation in conjunction with the yee 1966 grid is used to compute the spatial derivatives in maxwell s equations to advance the semi discrete equations the four stage runge kutta rk integrator is invoked this combination of spatial and temporal differencing leads to a scheme that is fourth order accurate conditionally stable and highly efficient moreover the use of compact differencing allows one to apply the compact operator in the vicinity of a perfect conductor an attribute not found in other higher order methods results are provided that quantify the spectral properties of the method simulations are conducted on problem spaces that span one and three dimensions and whose domains are of the open and closed type results from these simulations are compared with exact closed form solutions the agreement between these results is consistent with numerical analysis

cohomological stratification of diagram algebras the class of cellularly stratified algebras is defined and shown to include large classes of diagram algebras while the definition is in combinatorial terms by adding extra structure to graham and lehrer s definition of cellular algebras various structural properties are established in terms of exact functors and stratifications of derived categories the stratifications relate large algebras such as brauer algebras to smaller ones such as group algebras of symmetric groups among the applications are relative equivalences of categories extending those found by hemmer and nakano and by hartmann and paget as well as identities between decomposition numbers and cohomology groups of large and small algebras

the classification of blocks in bgg category mathcal o o we classify all equivalences between the indecomposable abelian categories which appear as blocks in bgg category mathcal o for reductive lie algebras our classification implies that a block in category mathcal o only depends on the bruhat order of the relevant parabolic quotient of the weyl group as part of the proof we observe that any finite dimensional algebra with simple preserving duality admits at most one quasi hereditary structure

on the semisimplicity of the cyclotomic brauer algebras ii abstract in this paper we give a necessary and sufficient condition for the semisimplicity of cyclotomic brauer algebras b m n of types g m 1 n with m 2 this generalizes h rui a criterion on the semisimple brauer algebras j combin theory ser a 111 2005 78 88 1 2 1 3 and h rui m si a criterion on the semisimple brauer algebras ii j combin theory ser a 113 2006 1199 1203 2 5 on brauer algebras

fourth order symplectic integration abstract in this paper we present an explicit fourth order method for the integration of hamilton s equations this method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state that is the integration step is an explicit symplectic map although the result is first derived for a specific type of hamiltonian it is shown to be quite general in particular the results can be applied to any lie group

schur weyl duality for infinitesimal q schur algebras sq 2 r 1 abstract using the result of s r doty d k nakano k m peters polynomial representations of frobenius kernels of gl 2 in contemp math vol 194 1996 pp 57 67 s konig c xi when is a cellular algebra quasi hereditary math ann 315 1999 281 293 we prove that a non semisimple infinitesimal schur algebra s 2 r 1 is not cellular furthermore we determine the structure of the endomorphism ring of tensor space as a module for the infinitesimal schur algebra s 2 r 1 up to morita equivalence both results generalize to the quantum case

affine cellular algebras abstract graham and lehrer have defined cellular algebras and developed a theory that allows in particular to classify simple representations of finite dimensional cellular algebras many classes of finite dimensional algebras including various hecke algebras and diagram algebras have been shown to be cellular and the theory due to graham and lehrer successfully has been applied to these algebras we will extend the framework of cellular algebras to algebras that need not be finite dimensional over a field affine hecke algebras of type a and infinite dimensional diagram algebras like the affine temperley lieb algebras are shown to be examples of our definition the isomorphism classes of simple representations of affine cellular algebras are shown to be parameterised by the complement of finitely many subvarieties in a finite disjoint union of affine varieties in this way representation theory of non commutative algebras is linked with commutative algebra moreover conditions on the cell chain are identified that force the algebra to have finite global cohomological dimension and its derived category to admit a stratification these conditions are shown to be satisfied for the affine hecke algebra of type a if the quantum parameter is not a root of the poincare polynomial

borelic pairs for stratified algebras abstract we determine all values of the parameters for which the cell modules form a standard system for a class of cellular diagram algebras including partition brauer walled brauer temperley lieb and jones algebras for this we develop and apply a general theory of finite dimensional algebras with borelic pairs the theory is also applied to give new uniform proofs of the cellular and quasi hereditary properties of the diagram algebras and to construct quasi hereditary 1 covers in the sense of rouquier with exact borel subalgebras in the sense of konig another application of the theory leads to a proof that auslander dlab ringel algebras admit exact borel subalgebras

a split step approach for the 3 d maxwell s equations split step procedures have previously been used successfully in a number of situations e g for hamiltonian systems such as certain nonlinear wave equations in this study we note that one particular way to write the 3 d maxwell s equations separates these into two parts requiring only the solution of six uncoupled 1 d wave equations the approach allows arbitrary orders of accuracy in both time and space and features in many cases unconditional stability

regular article spectral collocation time domain modeling of diffractive optical elements a spectral collocation multi domain scheme is developed for the accurate and efficient time domain solution of maxwell s equations within multi layered diffractive optical elements special attention is being paid to the modeling of out of plane waveguide couplers emphasis is given to the proper construction of high order schemes with the ability to handle very general problems of considerable geometric and material complexity central questions regarding efficient absorbing boundary conditions and time stepping issues are also addressed the efficacy of the overall scheme for the time domain modeling of electrically large and computationally challenging problems is illustrated by solving a number of plane as well as non plane waveguide problems

a characteristic free approach to brauer algebras brauer algebras arise in representation theory of orthogonal or symplectic groups these algebras are shown to be iterated inflations of group algebras of symmetric groups in particular they are cellular as had been shown before by graham and lehrer this gives some information about block decomposition of brauer algebras

homological epimorphisms recollements and hochschild cohomology with a conjecture by snashall solberg in view abstract we show that recollements of module categories give rise to homomorphisms between the associated hochschild cohomology algebras which preserve the strict gerstenhaber structure i e the cup product the graded lie bracket and the squaring map we review various long exact sequences in hochschild cohomology and apply our results in order to realise that the occurring maps preserve the strict gerstenhaber structure as well as a byproduct we generalise a known long exact cohomology sequence of koenig nagase to arbitrary surjective homological epimorphisms we use our observations to motivate and formulate a variation of the finite generation conjecture by snashall solberg