on the existence of local observables in theories with a factorizing s matrix the scaling limit of the two dimensional ising model above the critical temperature is considered as an example for relativistic quantum theories on two dimensional minkowski space exhibiting a factorizing s matrix in this model a recently proposed criterion for the existence of local quantum field theories with a prescribed factorizing scattering matrix is verified thereby establishing a new constructive approach to two dimensional quantum field theory in a particular example the existence proof is accomplished by analysing the nuclearity properties of certain specific subsets of fermionic fock spaces and yields as a byproduct also a verification of the energy nuclearity condition of buchholz and wichmann in models of free fermions in four spacetime dimensions

on the continuity of the map ϑ ϑ from the predual of a w algebra abstract let be elements in the predual of a w algebra for their absolute value parts the estimate 2 1 2 is obtained

the boundary of the irreducible components for invariant subspace varieties given partitions alpha beta gamma the short exact sequences begin aligned 0 longrightarrow n alpha longrightarrow n beta longrightarrow n gamma longrightarrow 0 end aligned of nilpotent linear operators of jordan types alpha beta gamma respectively define a constructible subset mathbb v alpha gamma beta of an affine variety geometrically the varieties mathbb v alpha gamma beta are of particular interest as they occur naturally and since they typically consist of several irreducible components in fact each littlewood richardson tableau vargamma of shape alpha beta gamma contributes one irreducible component overline mathbb v vargamma we consider the partial order vargamma le mathsf boundary widetilde vargamma on lr tableaux which is the transitive closure of the relation given by mathbb v widetilde vargamma cap overline mathbb v vargamma ne emptyset in this paper we compare the boundary relation with partial orders given by algebraic combinatorial and geometric conditions it is known that in the case where the parts of alpha are at most two all those partial orders are equivalent we prove that those partial orders are also equivalent in the case where beta setminus gamma is a horizontal and vertical strip moreover we discuss how the orders differ in general

a geometrical characterization of banach spaces in which martingale difference sequences are unconditional we study banach space valued martingale transforms and in particular characterize those banach spaces for which the classical theorems of the real valued case carry over for example if b is a banach space and 1 0 and zeta x y leq x y text if x leq 1 leq y

invariant subspaces of nilpotent linear operators i let k be a field we consider triples v u t where v is a finite dimensional k space u a subspace of v and t v v a linear operator with t n 0 for some n and such that t u u thus t is a nilpotent operator on v and u is an invariant subspace with respect to t we will discuss the question whether it is possible to classify these triples these triples v u t are the objects of a category with the krullremak schmidt property thus it will be sufficient to deal with indecomposable triples obviously the classification problem depends on n and it will turn out that the decisive case is n 6 for n 6 we deal with what is called wild representation type so no complete classification can be expected for n 6 we will exhibit a complete description of all the indecomposable triples let k be a field and v a finite dimensional k vector space we consider a linear operator t v v which is nilpotent say satisfying t n 0 for some fixed natural number n and we are interested in the subspaces u of v which are t invariant this means that t u u to be more precise we are going to consider the corresponding triples v u t and ask for a classification of all the isomorphism classes in order to do so we consider these triples v u t as the objects of a category s n or sk n in case a reference to the base field

translation group and spectrum condition let a d be ac dynamical system where d is thed dimensional vector group letv be a convex cone in d and hat v its dual cone we will characterize those representations ofa with the properties i a a d is weakly inner ii the corresponding unitary representationu a is continuous and iii the spectrum ofu a is contained in hat v

c algebras and automorphism groups let a g be ac dynamical system withg a topological group let be a representation ofa we will show that there exists a quasiequivalent representation hat pi to which is a covariant representation if and only if the folium of is invariant under the action ofg and this action is strongly continuous

norm inequalities for the absolute value of hilbert space operators we use norm inequalities for operators such as cauchy schwarz inequality and minkowski inequality to establish sharp norm inequalities for the absolute value of operators among other inequalities it is shown that if a b and x are operators on a hilbert space such that x is self adjoint and r 1 then this inequality generalizes some earlier related results other related inequalities are also discussed

representations of groups with ordered duals and generalized analyticity let g be a locally compact abelian group whose dual group g has a haar measurable order we show that for each strongly continuous uniformly bounded representation r of g in a umd space x there is a corresponding direct sum decomposition of x which reflects the order in g the projections in x corresponding to this direct sum decomposition have norms controlled solely by the bound of r and a constant depending only on x we illustrate how this vector valued harmonic conjugation result generalizes the various abstract successors of the m riesz theorem and we introduce an application to the superdiagonalization of kernels for abstract integral operators

isometries of non commutative lorentz spaces on determine la forme generale d une isometrie positive d un espace symetrique non commutatif sur un espace totalement symetrique non commutatif on decrit toutes les isometries d un espace de lorentz non commutatif

an analytic approach to solve multiple solutions of a strongly nonlinear problem based on a new kind of analytic method namely the homotopy analysis method an analytic approach to solve multiple solutions of strongly nonlinear problems is described by using gelfand equation as an example its validity is verified by comparing the approximation series with the known exact solution and different from perturbation techniques this approach is independent upon any small large perturbation quantities so the basic ideas of this approach can be employed to search for multiple solutions of strongly nonlinear problems in science and engineering

semi analytic solutions to nonlinear vibrations of microbeams under suddenly applied voltages in this study nonlinear oscillations of microbeams actuated by suddenly applied electrostatic force are investigated effects of electrostatic actuation residual stress midplane stretching and fringing fields are considered in modeling galerkin s decomposition method is utilized to convert the governing nonlinear partial differential equation to a nonlinear ordinary differential equation homotopy analysis method is used to find semi analytic solutions to the vibrations of microbeams convergence regions of the solution series are determined influences of increasing the voltage and midplane stretching on the frequency of vibrations are also studied results are in good agreement with numerical and experimental findings

fractional powers on noncommutative lp for p 1 abstract we prove that the homogeneous functional calculus associated to x x or x sgn x x for 0 1 is holder on selfadjoint elements of noncommutative l p spaces for 0 p with values in l p this extends an inequality of birman koplienko and solomjak also obtained by ando

on subspaces of non commutative lp spaces abstract we study some structural aspects of the subspaces of the non commutative haagerup l p spaces associated with a general non necessarily semi finite von neumann algebra if a subspace x of l p contains uniformly the spaces l p n n 1 it contains an almost isometric almost 1 complemented copy of l p if x contains uniformly the finite dimensional schatten classes s p n it contains their l p direct sum too we obtain a version of the classical kadec pelczynski dichotomy theorem for l p spaces p 2 we also give operator space versions of these results the proofs are based on previous structural results on the ultrapowers of l p together with a careful analysis of the elements of an ultrapower l p u which are disjoint from the subspace l p these techniques permit to recover a recent result of n randrianantoanina concerning a subsequence splitting lemma for the general non commutative l p spaces various notions of p equiintegrability are studied one of which is equivalent to randrianantoanina s one and some results obtained by haagerup rosenthal and sukochev for l p spaces based on finite von neumann algebras concerning subspaces of l p containing l p are extended to the general case

box moves on littlewood richardson tableaux and an application to invariant subspace varieties abstract in his 1951 book infinite abelian groups kaplansky gives a combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group in this paper we first use partial maps on littlewood richardson tableaux to generalize this result to finite direct sums of such embeddings our main interest is an application to invariant subspaces of nilpotent linear operators we develop a criterion to decide if two irreducible components in the representation space are in the boundary partial order

construction of quantum field theories with factorizing s matrices the subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two dimensional minkowski space employing the algebraic framework of quantum field theory it is shown under which conditions an algebra of observables localized in a wedge shaped region of spacetime can be used to construct model theories a crucial input in this context is the modular nuclearity condition for wedge algebras which implies the existence of local observables as an application of the new method a rigorous construction of a large family of models with factorizing s matrices is obtained in an inverse scattering approach a given factorizing scattering operator is used to define certain semi localized wightman fields associated to it with the help of these fields a wedge algebra can be defined which determines the local observable content of a well defined quantum field theory in this approach the modular nuclearity condition translates to certain analyticity and boundedness conditions on the formfactors of wedge local observables these conditions are shown to hold for a large class of underlying s matrices including the scattering operators of the sinh gordon model and the scaling ising model as special examples the so constructed models are investigated with respect to their scattering properties they are shown to solve the inverse scattering problem for the underlying s matrices and a proof of asymptotic completeness for these models is given

causal independence and the energy level density of states in local quantum field theory within the general framework of local quantum field theory a physically motivated condition on the energy level density of well localized states is proposed and discussed it is shown that any model satisfying this condition obeys a strong form of the principle of causal statistical independence which manifests itself in a specific algebraic structure of the local algebras split property it is also shown that the proposed condition holds in a free field theory

algebraic tensor products and internal homs of noncommutative lp spaces abstract we prove that the multiplication map is an isometric isomorphism of quasi banach m m bimodules here is the noncommutative l p space of an arbitrary von neumann algebra m and m denotes the algebraic tensor product over m equipped with the quasi projective tensor norm but without any kind of completion similarly the left multiplication map is an isometric isomorphism of quasi banach m m bimodules where hom m denotes the algebraic internal hom in particular we establish an automatic continuity result for such maps applications of these results include establishing explicit algebraic equivalences between the categories of modules of junge and sherman for all p 0 as well as identifying subspaces of the space of bilinear forms on spaces this paper is also available at arxiv 1309 7856v2

crossed products of c algebras for singular actions abstract we consider group actions g aut a of topological groups g on c algebras a of the type which occurs in many physics models these are singular actions in the sense that they need not be strongly continuous or the group need not be locally compact we develop a crossed product host in analogy to the usual crossed product for strongly continuous actions of locally compact groups in the sense that its representation theory is in a natural bijection with the covariant representation theory of the action g aut a we prove a uniqueness theorem for crossed product hosts and analyze existence conditions we also present a number of examples where a crossed product host exists but the usual crossed product does not for actions where a crossed product host does not exist we obtain a maximal invariant subalgebra for which a crossed product host exists we further study the case of a discontinuous action g aut a of a locally compact group in detail

majorizations and inequalities in matrix theory abstract in matrix theory majorization plays a significant role for instance majorization relations among eigenvalues and singular values of matrices produce a lot of norm inequalities and even matrix inequalities this survey article is intended as a review of recent results in matrix theory related to majorization

parametric resonance voltage response of electrostatically actuated micro electro mechanical systems cantilever resonators abstract this paper investigates the parametric resonance voltage response of nonlinear parametrically actuated micro electro mechanical systems mems cantilever resonators a soft ac voltage of frequency near natural frequency is applied between the resonator and a parallel ground plate this produces an electrostatic force that leads the structure into parametric resonance the model consists of an euler bernoulli thin cantilever under the actuation of electrostatic force to include fringe effect and damping force two methods of investigation are used namely the method of multiple scales mms and reduced order model rom method rom convergence of the voltage response and the limitation of mms to small to moderate amplitudes with respect to the gap gap amplitudes are reported mms predicts accurately both hopf supercritical and supercritical bifurcation voltages however mms overestimates the large gap amplitudes of the resonator and misses completely or overestimates the saddle node bifurcation occurring at large gap amplitudes rom produces valid results for small and or large gap amplitudes for a sufficient number of terms vibration modes as the voltage is swept up at constant frequency the resonator maintains zero amplitude until reaches the subcritical hopf bifurcation voltage where it loses stability and jumps up to large gap amplitudes next the gap amplitude decreases until it reaches the supercritical hopf bifurcation point and after that the gap amplitude remains zero for the voltage range considered in this work as the voltage is swept down at constant frequency the zero gap amplitude of the resonator starts increasing continuously after reaching the supercritical hopf bifurcation voltage until it reaches the saddle node bifurcation voltage when a sudden jump to zero gap amplitude occurs effects of frequency damping and fringe parameters on the voltage response show that 1 the supercritical hopf bifurcation is shifted to lower voltage values with the increase of any of the mentioned parameters 2 the subcritical hopf bifurcation is shifted to larger voltage values with the increase of damping shifted to lower voltage values with the increase of the fringe parameter and not significantly altered by the change in frequency 3 the saddle node bifurcation voltage decreases with the increase of frequency and damping and decrease of fringe parameter and 4 the saddle node bifurcation gap amplitude decreases with the increase of frequency and damping and it is not significantly altered by the change of the fringe parameter

matrix factorizations and their perturbations there are several ways in which a matrix can be factorized as a product of two special matrices these factorizations are often used in numerical analysis and many perturbation bounds useful in such analysis have been proved by various authors in this paper a simple method which leads to these results and several new ones is discussed in the last section related results on the lipschitz continuity of the matrix absolute value are surveyed

lipschitz continuity of the absolute value and riesz projections in symmetric operator spaces a principal result of the paper is that ifeis a symmetric banach function space on the positive half line with the fatou property then for all semifinite von neumann algebras m the absolute value mapping is lipschitz continuous on the associated symmetric operator spacee m with lipschitz constant depending only oneif and only ifehas non trivial boyd indices it follows that if m is any von neumann algebra then the absolute value map is lipschitz continuous on the corresponding haageruplp space provided 1 p

electrostatic coupling of mems structures transient simulations and dynamic pull in abstract in micro electromechanical systems mems coupling of structures through electrostatic forces is a primordial phenomenon simulating the dynamics of mems and taking into account such strong coupling effects allows one to predict dynamical performance and stability and is therefore an essential issue in the design of highly effective and reliable devices analysis techniques for such systems require special attention in order to provide to the designer accurate and fast tools we propose a finite element approach fem that properly handles the strong electromechanical coupling in mems in the simulation example of a micro bridge we show that such simulation techniques can reveal complex dynamical behaviors of mems such as dynamic pull in

non commutative orlicz spaces associated to a modular on τ measurable operators abstract in this paper we consider non commutative orlicz spaces as modular spaces and show that they are complete with respect to their modular we prove some convergence theorems for measurable operators and deal with uniform convexity of non commutative orlicz spaces

triangular mindlin microplate element in this article based on the most general form of strain gradient theory mgsgt a novel extended triangular mindlin plate element is proposed to accomplish this aim first the quadratic form of energy functional is obtained by vectorizing the higher order tensors of energy pairs from which the stiffness and mass matrices of the element are readily derived in comparison with the standard mindlin plate element the new element needs three additional nodal degrees of freedom dof including derivatives of lateral deflection and rotations which means a total of nine dofs per node also as compared to the standard mindlin plate element which requires only c0 shape functions the present one requires c1 continuous smooth shape functions due to second derivatives of deflection and rotations hence cubic polynomials are used to interpolate the displacement components the new element can be reduced to that based on the modified strain gradient theory msgt and the modified couple stress theory mcst moreover the standard mindlin plate element is recovered when the gradient based material parameters tend to zero the mindlin microplates with different boundary conditions are considered as the problem under study whose free vibration and bending are analyzed the results are compared with the exact solutions and excellent agreement is achieved

non commutative banach function spaces in this paper we survey some aspects of the theory of non commutative banach function spaces that is spaces of measurable operators associated with a semi finite von neumann algebra these spaces are also known as non commutative symmetric spaces the theory of such spaces emerged as a common generalization of the theory of classical commutative rearrangement invariant banach function spaces in the sense of w a j luxemburg and a c zaanen and of the theory of symmetrically normed ideals of bounded linear operators in hilbert space in the sense of i c gohberg and m g krein these two cases may be considered as the two extremes of the theory in the first case the underlying von neumann algebra is the commutative algebra l on some measure space with integration as trace in the second case the underlying von neumann algebra is b the algebra of all bounded linear operators on a hilbert space with standard trace important special cases of these non commutative spaces are the non commutative l p spaces which correspond in the commutative case with the usual l p spaces on a measure space and in the setting of symmetrically normed operator ideals they correspond to the schatten p classes mathfrak s p