cluster values of holomorphic functions of bounded type we study the cluster value theorem for hb x the frechet algebra of holomorphic functions bounded on bounded sets of x we also describe the size of fibers of the spectrum of hb x our results are rather complete whenever x has an unconditional shrinking basis and for x 1 as a byproduct we obtain results on the spectrum of the algebra of all uniformly continuous holomorphic functions on the ball of 1

envelopes of holomorphy and extension of functions of bounded type abstract we study the extension of holomorphic functions of bounded type defined on an open subset of a banach space to larger domains for this we first characterize the envelope of holomorphy of a riemann domain over a banach space with respect to the algebra of bounded type holomorphic functions in terms of the spectrum of the algebra we then give a simple description of the envelopes of balanced open sets and relate the concepts of domain of holomorphy and polynomial convexity we show that for bounded balanced sets extensions to the envelope are always of bounded type and that this does not necessarily hold for unbounded sets answering a question posed by hirschowitz in 1972 we also consider extensions to open subsets of the bidual present some banach stone type results and show some properties of the spectrum when the domain is the unit ball of l p

spectra of weighted lb algebras of entire functions on banach spaces abstract given a decreasing family of continuous weights on a banach space x we consider the weighted inductive limits of spaces of entire functions v h x and v h 0 x motivated by recent research by d carando and p sevilla peris on weighted frechet algebras of entire functions on banach spaces we determine conditions on the family of weights to ensure that the corresponding weighted space is an algebra or has polynomial schauder decompositions we study hormander algebras of entire functions defined on a banach space and we give a description of them in terms of sequence spaces we also focus on algebra homomorphisms between these spaces and obtain a banach stone type theorem for a particular decreasing family of weights finally we study the spectra of these weighted algebras endowing them with an analytic structure

continuum approach for second order shape design sensitivity of three dimensional elastic solids a second order shape design sensitivity analysis method for three dimensional linear elastic solids is derived using a continuum approach with the material derivative to compute the second order shape design sensitivity a shape design acceleration field is defined which is similar to the shape design velocity field for the first order shape design sensitivity both direct differentiation and hybrid methods are presented in this paper the shape changes are assumed on the traction free boundary only a numerical method which can be implemented using established finite element analysis codes is developed to demonstrate feasibility and accuracy of the proposed second order shape design sensitivity analysis method

second order design sensitivity analysis of structural systems esign sensitivity analysis methods for calculation of first derivatives of structural performance with respect to design parameters have become quite well developed and applied 1 2 it is the purpose of this note to extend the adjoint method of design sensitivity analysis to calculation of second derivatives of performance with respect to design parameters the value of second deriva tive information in design optimization is well known using only first order gradient information optimization algorithms must resort to onedimensional search or heuristic step size selection methods if second derivative information is available at a reasonable computing cost much more powerful iterative optimization algorithms are possible 3 finite dimensional matrix structural models are considered here even though the methods presented can be extended to distributed parameter boundary value problem structural models structural design is presumed to be described by a vector of design parameters b b1 b2 bk t structural response is described by a vector of nodal displacement coordinates z zi z2 zn 7

second order sensitivity derivatives in structural analysis haug s 1981 expressions for the calculation of static constraint function second derivatives have resulted in an order of magnitude saving over conventional methods for the calculation of such derivatives a similar but simplified procedure is presented which results in a reduction of computational cost by an additional factor of two the results are presented in a notation that is different from that of haug but more common in other work on structural synthesis and analysis

total pressure losses minimization in turbomachinery cascades using the exact hessian abstract a method for the design of turbomachinery cascades with minimum total pressure losses subject to constraints on the minimum blade thickness and flow turning is presented it is based on the newton lagrange method which requires the computation of first and second order sensitivities of the objective function and the constraints with respect to the design variables the computation of the exact hessian of the function which expresses the difference in total pressure between the inlet to and the outlet from the cascade is new in the literature to compute the hessian the direct differentiation of the viscous flow equations is used for the first order sensitivities of the functional and the flow related constraints followed by the discrete adjoint method since the objective function is defined along boundaries other than those controlled by the design variables it is challenging to investigate the significance of all terms comprising the exact second order sensitivity expressions all these terms were temporarily computed using automatic differentiation and those which proved to be significant are hand differentiated to minimize cpu cost and memory requirements insignificant terms are eliminated giving rise to the so called exact hessian matrix an exactly initialized quasi newton method was also programmed and tested in the latter at the first cycle the exact gradients and hessians are computed and used during the subsequent optimization cycles the discrete adjoint method provides the exact gradient whereas the hessian is updated as in quasi newton methods the comparison of the efficiency of the aforementioned methods depends on the number of design variables used the exactly initialized quasi newton method constantly outperforms its conventional variant in terms of cpu cost particularly in non convex and or constrained optimization problems

the polynomial cluster value problem abstract the polynomial cluster value problem replaces the role of the continuous linear functionals in the original cluster value problem for the continuous polynomials to describe the corresponding cluster sets and fibers we prove several polynomial cluster value theorems for uniform algebras h b between a u b and h b where b is the open unit ball of a complex banach space x we also obtain new results about the original cluster value problem especially for a b examples of spaces x considered here are spaces of continuous functions l 1 and locally uniformly convex spaces

spectra of weighted algebras of holomorphic functions we consider weighted algebras of holomorphic functions on a banach space we determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial schauder decompositions we study the spectra of weighted algebras and endow them with an analytic structure we also deal with composition operators and algebra homomorphisms in particular to investigate how their induced mappings act on the analytic structure of the spectrum moreover a banach stone type question is addressed

polynomial approximation in banach spaces abstract we define new classes of topological algebras of holomorphic functions on open subsets of banach spaces and on open subsets of dual banach spaces we investigate properties and derive results concerning polynomial approximation on such algebras we give an explicit description of their spectra derive results on finitely generated ideals and theorems of banach stone type we show that under certain conditions on the open subset u this new algebra coincides with h w u u deriving new results on h w u u

on the castelnuovo mumford regularity of rings of polynomial invariants we show that when a group acts on a polynomial ring over a eld the ring of invariants has castelnuovo mumford regularity at most zero as a consequence we prove a well known conjecture that the invariants are always generated in degrees at most n jgj 1 where n 1 is the number of polynomial generators andjgj 1 is the order of the group we also prove some other related conjectures in invariant theory

corrigendum to cluster values for algebras of analytic functions adv math 329 2018 157 173 abstract while the article was in publication process we found a mistake in a key tool for the proof one of the main results as a consequence our result on the ball a u b x algebra remains open for the algebra h b x we obtain a weaker statement which still extends previous work in the subject in this note we enumerate those results which should be omitted or modified

second order design sensitivity analysis of mechanical system dynamics dependence of dynamic response of nonlinear mechanical systems on design variables is analysed an adjoint variable method is used to derive first and second order derivatives of measures of dynamic response with respect to design variables a computational algorithm is presented for numerical calculation of first and second design derivatives a simple oscillator example is solved analytically and by the adjoint variable method with identical results a burst fire automatic weapon mechanism with linear and nonlinear damping is treated numerically it is shown that quadratic appriximations of dynamic response using results of second order design sensitivity analysis can be substantially better than conventional linear approximations

cluster values for algebras of analytic functions abstract the cluster value theorem is known for being a weak version of the classical corona theorem given a banach space x we study the cluster value problem for the ball algebra a u b x the banach algebra of all uniformly continuous holomorphic functions on the unit ball b x and also for the frechet algebra h b x of holomorphic functions of bounded type on x more generally for h b u the algebra of holomorphic functions of bounded type on a given balanced open subset u x we show that cluster value theorems hold for all of these algebras whenever the dual of x has the bounded approximation property these results are an important advance in this problem since the validity of these theorems was known only for trivial cases where the spectrum is formed only by evaluation functionals and for the infinite dimensional hilbert space as a consequence we obtain weak analytic nullstellensatz theorems and several structural results for the spectrum of these algebras

first and second order sensitivity analysis of linear and nonlinear structures this paper employs the principle of virtual work to derive sensitivity derivatives of structural response with respect to stiffness parameters using both direct and adjoint approaches the computations required are based on additional load conditions characterized by imposed initial strains body forces or surface tractions as such they are equally applicable to numerical or analytical solution techniques the relative efficiency of various approaches for calculating first and second derivatives is assessed it is shown that for the evaluation of second derivatives the most efficient approach is one that makes use of both the first order sensitivities and adjoint vectors two example problems are used for demonstrating the various approaches

extensions of multilinear operators and banach space properties a new characterization of the dunford pettis property in terms of the extensions of multilinear operators to the biduals is obtained for the first time multilinear characterizations of the reciprocal dunford pettis property and pelczynski s property v are also found polynomial and holomorphic versions of these properties are given as well

symmetric powers of the p 1 dimensional indecomposable module of a cyclic p group and the λ structure of its green ring let k be a field of order p and let g be a cyclic group of order pk k 2 we explicitly decompose the symmetric powers of the indecomposable kg module of dimension p 1 into indecomposable kg modules using this result for every odd prime p we give a negative answer to the conjecture posed by kouwenhoven f m kouwenhoven the structure of the green rings of cyclic p groups proc sympos pure math 47 1987 451 466

second order adjoint sensitivity analysis methodology 2nd asam for computing exactly and efficiently first and second order sensitivities in large scale linear systems i computational methodology abstract this work presents the second order forward and adjoint sensitivity analysis methodologies 2nd fsam and 2nd asam for computing exactly and efficiently the second order functional derivatives of physical engineering biological etc system responses i e system performance parameters to the system s model parameters the definition of system parameters used in this work includes all computational input data correlations initial and or boundary conditions etc for a physical system comprising n parameters and n r responses we note that the 2nd fsam requires a total of n 2 2 3 n 2 large scale computations for obtaining all of the first and second order sensitivities for all n r system responses on the other hand for one functional type system response the 2nd asam requires one large scale computation using the first level adjoint sensitivity system for obtaining all of the first order sensitivities followed by at most n large scale computations using the second level adjoint sensitivity systems for obtaining exactly all of the second order sensitivities therefore the 2nd fsam should be used when n r n while the 2nd asam should be used when n n r the original 2nd asam presented in this work should enable the hitherto very difficult if not intractable exact computation of all of the second order response sensitivities i e functional gateaux derivatives for large systems involving many parameters as usually encountered in practice very importantly the implementation of the 2nd asam requires very little additional effort beyond the construction of the adjoint sensitivity system needed for computing the first order sensitivities

extending bounded type holomorphic mappings on a banach space we show that a riemann domain over a symmetrically regular banach space e admits holomor phic extension to pseudo convex domains over e with respect to two natural spaces of holomorphic there are many classical results in several complex variables theory on the construc tion of the envelope of holomorphy of a domain c n with respect to an subalgebra a h the set of all holomorphic functions on similar results have been obtained in the banach space setting but mainly for h in examining the spectrum of hb the space of holomorphic functions of bounded type on the open subset u of the banach space e aron galindo garcia and maestre show that sb u the spectrum of hb could be endowed with the structure of a riemann domain over e when e is symmetri cally regular 2 we continue this line of investigation but found it convenient to begin with a riemann domain we show that sb is a domain of holomorphy with respect to the space of all holomorphic functions when the underlying space e is symmetrically regular the question of whether or not it is also a domain of holomorphy with respect to hb

frechet algebras formal power series and analytic structure abstract the notion of locally riemann algebras is introduced by studying the ideal structure of frechet algebras we provide sufficient conditions for the existence of local analytic structure in the spectrum of a frechet algebra and as a welcome bonus we characterize locally riemann algebras

sensitivity theory for nonlinear systems ii extensions to additional classes of responses this work extends a recent functional analytic formulation of sensitivity theory to include treatment of additional types of responses there are physical systems where a critical point of a function that depends on the system s state vector and parameters defines the location in phase space where the response functional is evaluated the g teaux differentials giving the sensitivities of both the functional and the critical point to changes in the system s parameters are obtained by alternative formalisms the foward sensitivity formalism is the simpler and more general but may be prohibitively expensive for problems with large data bases the adjoint sensitivity formalism although less generally applicable and requiring several adjoint calculations is likely to be the only practical approach sensitivity theory is also extended to include treatment of general operators acting on the system s state vector and parameters as response in this case the forward sensitivity formalism is the same as for functional responses but the adjoint sensitivity formalism is considerably different the adjoint sensitivity formalism requires expanding the indirect effect term an element of a hilbert space in terms of elements of an orthonormal basis since as many calculations of adjoint functions are required as there are nonzero terms in this expansion careful consideration of truncating the expansion is needed to assess the advantages of the adjoint sensitivity formalism over the forward sensitivity formalism

centralisers of spaces of symmetric tensor products and applications we show that the centraliser of the space of n fold symmetric injective tensors n 2 on a real banach space is trivial with a geometric condition on the set of extreme points of its dual the space of integral polynomials we obtain the same result for complex banach spaces we give some applications of this results to centralisers of spaces of homogeneous polynomials and complex banach spaces in addition we derive a banach stone theorem for spaces of vector valued approximable polynomials

binomial determinants paths and hook length formulae abstract we give a combinatorial interpretation for any minor or binomial determinant of the matrix of binomial coefficients this interpretation involves configurations of nonintersecting paths and is related to young tableaux and hook length formulae

cluster values of analytic functions on a banach space we investigate uniform algebras of bounded analytic functions on the unit ball of a complex banach space we prove several cluster value theorems relating cluster sets of a function to its range on the fibers of the spectrum of the algebra these lead to weak versions of the corona theorem for l2 and for c0 in the case of the open unit ball of c0 we solve the corona problem whenever all but one of the functions comprising the corona data are uniformly approximable by polynomials in functions in c 0

isometries between spaces of homogeneous polynomials abstract we derive banach stone theorems for spaces of homogeneous polynomials we show that every isometric isomorphism between the spaces of homogeneous approximable polynomials on real banach spaces e and f is induced by an isometric isomorphism of e onto f with an additional geometric condition we obtain the analogous result in the complex case isometries between spaces of homogeneous integral polynomials and between the spaces of all n homogeneous polynomials are also investigated

fredholm composition operators on algebras of analytic functions on banach spaces we prove that fredholm composition operators acting on the uniform algebra h be of bounded analytic functions on the open unit ball of a complex banach space e with the approximation property are invertible and arise from analytic automorphisms of the ball

homomorphisms and composition operators on algebras of analytic functions of bounded type abstract let u and v be convex and balanced open subsets of the banach spaces x and y respectively in this paper we study the following question given two frechet algebras of holomorphic functions of bounded type on u and v respectively that are algebra isomorphic can we deduce that x and y or x and y are isomorphic we prove that if x or y has the approximation property and h wu u and h wu v are topologically algebra isomorphic then x and y are isomorphic the converse being true when u and v are the whole space we get analogous results for h b u and h b v giving conditions under which an algebra isomorphism between h b x and h b y is equivalent to an isomorphism between x and y we also obtain characterizations of different algebra homomorphisms as composition operators study the structure of the spectrum of the algebras under consideration and show the existence of homomorphisms on h b x with pathological behaviors

structural optimization by multilevel decomposition a method for decomposing an optimization problem into a set of subproblems and a coordination problem that preserves coupling between the subproblems is described the decomposition is achieved by separating the structural element optimization subproblems from the assembled structural optimization problem each element optimization and optimum sensitivity analysis yields the cross sectional dimensions that minimize a cumulative measure of the element constraint violation as a function of the elemental forces and stiffness the assembled structural optimization produces the overall mass and stiffness distributions optimized for minimum total mass subject to constraints that include the cumulative measures of the element constraint violations extrapolated linearly with respect to the element forces and stiffnesses the method is introduced as a special case of a multilevel multidisciplinary system optimization and its algorithm is fully described for two level optimization for structures assembled of finite elements of arbitrary type numerical results are given as an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition it is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers using different computers to work concurrently on the same large problem

analytic structure in fibers of h bc0 abstract let h b c 0 be the algebra of all bounded holomorphic functions on the open unit ball of c 0 and m h b c 0 the spectrum of h b c 0 we prove that for any point z in the closed unit ball of l there exists an analytic injection of the open ball b l into the fiber of z in m h b c 0 which is an isometry from the gleason metric of b l to the gleason metric of m h b c 0 we also show that for some banach spaces x b l can be analytically injected into the fiber m z h b x for every point z b x

reduced order design oriented stress analysis using combined direct and adjoint solutions a new method for extracting accurate stress information from reduced order structural and aeroelastic models is presented the method has second order accuracy when approximate reduced order direct and adjoint solutions based on different reduced order bases are used simultaneously to obtain approximate stresses the method is applicable to both static and dynamic linear analysis a review of four common methods for structural model order reduction two variants of the mode displacement method standard mode displacement and the fictitious mass method the mode acceleration method and the ritz vector method identifies sources of difficulty and causes of errors in stress behavior sensitivity calculations considerations used for selection of the reduced order direct and adjoint bases are discussed a series of static and dynamic test cases is used to assess accuracy of the new method in an analysis mode accuracy studies of sensitivity calculations follow we hope to contribute to the field of design oriented structural dynamics in terms of both insight and practice

dynamics of weighted composition operators on weighted banach spaces of entire functions abstract we study the dynamics of the weighted composition operator c w on weighted banach spaces of entire functions h v c and h v 0 c we characterize the continuity and compactness of the operator and in the case of affine symbols z a z b a b c and exponential weights we analyze when the operator is power bounded uniformly mean ergodic and hypercyclic continuous weighted composition operators when a 1 are just multiples of composition operators c c when a 1 we consider as a multiplier w the product of a polynomial by an exponential function for multiples of composition operators we get a complete characterization of power boundedness and mean ergodicity and we study the hypercyclicity in terms of an example of a power bounded but not mean ergodic operator on h v 0 c is provided for the case of composition operators we obtain the spectrum and a complete characterization of the dynamics

aron berner extensions of triple maps with application to the bidual of jordan banach triple systems abstract by extending the notion of arens regularity of bilinear mappings we say that a bounded trilinear map on the cartesian product of banach spaces is aron berner regular when all its six aron berner extensions to the cartesian product of the bidual spaces coincide we give some results on the aron berner regularity of certain trilinear maps we then focus on the bidual e of a jordan banach triple system e and investigate those conditions under which e is itself a jordan banach triple system under each of the aron berner extensions of the triple product we also compare these six triple products with those arising from certain ultrafilters based on the ultrapower formulation of the principle of local reflexivity in particular we examine the aron berner triple products on the bidual of a jb triple in relation with the so called dineen s theorem some illuminating examples are included and some questions are also left undecided

representing measures and infinite dimensional holomorphy we consider some applications of the bishop de leeuw theorem about representing measures for some algebras of analytic functions on unit balls of banach spaces in particular we investigate hardy spaces h2 associated with corresponding algebras some examples are considered

on algebras of holomorphic functions of a given type we show that several spaces of holomorphic functions on a riemann domain over a banach space including the nuclear and hilbert schmidt bounded type are locally m convex frechet algebras we prove that the spectrum of these algebras has a natural analytic structure which we use to characterize the envelope of holomorphy we also show a cartan thullen type theorem

the symmetric radon nikodým property for tensor norms abstract we introduce the symmetric radon nikod m property srn property for finitely generated s tensor norms of order n and prove a lewis type theorem for s tensor norms with this property as a consequence if is a projective s tensor norm with the srn property then for every asplund space e the canonical mapping n s e n s e is a metric surjection this can be rephrased as the isometric isomorphism q min e q e for some polynomial ideal q we also relate the srn property of an s tensor norm with the asplund or radon nikod m properties of different tensor products as an application results concerning the ideal of n homogeneous extendible polynomials are obtained as well as a new proof of the well known isometric isomorphism between nuclear and integral polynomials on asplund spaces an analogous study is carried out for full tensor products

multilinear forms subsymmetric polynomials and spreading models on banach spaces abstract some applications of ramsey theory to the study of multilinear forms and polynomials on banach spaces are given related to the existence of lower l q estimates of sequences we give an explicit representation of subsymmetric polynomials in banach spaces with subsymmetric basis finally we apply our results to get approximation of polynomials by subsymmetric polynomials and to the problem of stabilization of a certain chain of algebras generated by polynomials

weakly continuous mappings on banach spaces abstract it is shown that every n homogeneous continuous polynomial on a banach space e which is weakly continuous on the unit ball of e is weakly uniformly continuous on the unit ball of e applications of the result to spaces of polynomials and holomorphic mappings on e are given

structural design sensitivity analysis with generalized global stiffness and mass matrices first and second order derivatives of measures of structural response with respect to design variables are calculated using the generalized global stiffness and mass matrix formulation of structural equations the adjoint variable method is extended for first order design sensitivity calculation and a mixed direct differentiationadjoint variable method is employed to calculate second derivatives of static structural response measures the variational or virtual work form of the structural equations is shown to be well suited for design sensitivity analysis with generalized global stiffness and mass matrices avoiding the requirement for explicit reduction of the matrices the method is illustrated using a simple structure with a multipoint constraint

sensitivity theory for nonlinear systems i nonlinear functional analysis approach concepts of nonlinear functional analysis are employed to investigate the mathematical foundations underlying sensitivity theory this makes it possible not only to ascertain the limitations inherent in existing analytical approaches to sensitivity analysis but also to rigorously formulate a considerably more general sensitivity theory for physical problems characterized by systems of nonlinear equations and by nonlinear functionals as responses two alternative formalisms labeled the forward sensitivity formalism and the adjoint sensitivity formalism are developed in order to evaluate the sensitivity of the response to variations in the system parameters the forward sensitivity formalism is formulated in normed linear spaces and the existence of the g teaux differentials of the operators appearing in the problem is shown to be both necessary and sufficient for its validity this formalism is conceptually straightforward and can be advantageously used to assess the effects of relatively few parameter alterations on many responses on the other hand for problems involving many parameter alterations or a large data base and comparatively few functional type responses the alternative adjoint sensitivity formalism is computationally more economical however it is shown that this formalism can be developed only under conditions that are more restrictive than those underlying the validity of the forward sensitivity formalism in particular the requirement that operators acting on the state vector and on the system parameters must admit densely defined g teaux derivatives is shown to be of fundamental importance for the validity of this formalism the present analysis significantly extends the scope of sensitivity theory and provides a basis for still further generalizations

numerical methods for second order shape sensitivity analysis with applications to heat conduction problems in this paper two finite element based schemes for second order shape sensitivity analysis are presented in the first formulation the av dd method the first order shape sensitivity equation is derived and expressed in terms of state and adjoint variables the resultant equation is then directly differentiated to obtain the second order shape sensitivity equation in the second formulation the dd av method the functional of concern is differentiated twice to yield the second order sensitivity equation in which the second order shape derivatives can be eliminated by introducing a proper adjoint equation a thermal fin problem and a thermal insulation layer problem have been studied to validate the proposed schemes it is shown that both methods yield identical results though the dd av method is computationally more efficient

the noether bound in invariant theory of finite groups abstract let r be a commutative ring v a finitely generated free r module and g glr v a finite group acting naturally on the graded symmetric algebra a sym v let ag denote the minimal number m such that the ring ag of invariants can be generated by finitely many elements of degree at most m furthermore let h g be a normal subgroup such that the index g h is invertible in r in this paper we prove the inequality a g a h g h for h 1 and g invertible in r we obtain noether s bound ag g which so far had been shown for arbitrary groups only under the assumption that the factorial of the group order g is invertible in r

nonlinear transient response and second order sensitivity using time finite element method a procedure based on time finite element method to obtain the second order sensitivity of the transient response with respect to various system parameters is developed and applied to single and two degree of freedom structural dynamic systems the proposed method directly differentiates the algebraic equations resulting from the time finite element formulation with respect to system parameters computational algorithms are given and detailed derivations are presented the second order sensitivity analysis has been used for approximation schemes for efficient solution of design optimization problems also the results can be applied to gradient based parameter identification schemes the results are found to be in excellent agreement with those obtained using the finite difference method the main advantages of the time finite element approach are the ease of use and the numerical efficiency with which the sensitivity of the transient response can be obtained

second order adjoint sensitivity analysis methodology 2nd asam for computing exactly and efficiently first and second order sensitivities in large scale linear systems this work presents an illustrative application of the second order adjoint sensitivity analysis methodology 2nd asam to a paradigm neutron diffusion problem which is sufficiently simple to admit an exact solution thereby making transparent the underlying mathematical derivations the general theory underlying 2nd asam indicates that for a physical system comprising n parameters the computation of all of the first and second order response sensitivities requires per response at most 2 n 1 large scale computations using the first level and respectively second level adjoint sensitivity systems 1st lass and 2nd lass very importantly however the illustrative application presented in this work shows that the actual number of adjoint computations needed for computing all of the first and second order response sensitivities may be significantly less than 2 n 1 per response for this illustrative problem four large scale adjoint computations sufficed for the complete and exact computations of all 4 first and 10 distinct second order derivatives furthermore the construction and solution of the 2nd lass requires very little additional effort beyond the construction of the adjoint sensitivity system needed for computing the first order sensitivities very significantly only the sources on the right sides of the diffusion differential operator needed to be modified the left side of the differential equations and hence the solver in large scale practical applications remained unchanged all of the first order relative response sensitivities to the model parameters have significantly large values of order unity also importantly most of the second order relative sensitivities are just as large and some even up to twice as large as the first order sensitivities in the illustrative example presented in this work the second order sensitivities contribute little to the response variances and covariances however they have the following major impacts on the computed moments of the response distribution a they cause the expected value of the response to differ from the computed nominal value of the response and b they contribute decisively to causing asymmetries in the response distribution indeed neglecting the second order sensitivities would nullify the third order response correlations and hence would nullify the skewness of the response consequently any events occurring in a response s long and or short tails which are characteristic of rare but decisive events e g major accidents catastrophes would likely be missed the 2nd asam is expected to affect significantly other fields that need efficiently computed second order response sensitivities e g optimization data assimilation adjustment model calibration and predictive modeling we apply the second order adjoint sensitivity analysis methodology 2nd asam to a paradigm diffusion problem four 2nd asam adjoint computations exactly determine all fourteen 1st and 2nd order sensitivities non zero second order response sensitivities decisively skew response distributions

a homogenization method for shape and topology optimization abstract shape and topology optimization of a linearly elastic structure is discussed using a modification of the homogenization method introduced by bendsoe and kikuchi together with various examples which may justify validity and strength of the present approach for plane structures

hardy type spaces associated with compact unitary groups abstract we investigate hilbertian hardy type spaces of complex analytic functions of infinite many variables associated with compact unitary groups and the corresponding invariant haar s measures for such analytic functions we establish a cauchy type integral formula and describe natural domains also we show some relations between constructed spaces of analytic functions and the symmetric fock space

the approximation property for spaces of holomorphic functions on infinite dimensional spaces ii let h u denote the vector space of all complex valued holomorphic functions on an open subset u of a banach space e let and respectively denote the compact ported topology and the bornological topology on h u we show that if e is a banach space with a shrinking schauder basis and with the property that every continuous polynomial on e is weakly continuous on bounded sets then h u and h u have the approximation property for every open subset u of e the classical space c0 the original tsirelson space t and the tsirelson james space tj are examples of banach spaces which satisfy the hypotheses of our main result our results are actually valid for riemann domains

λ ring structure of the green ring of a cyclic p group abstract let f p be a field of order p g a cyclic group of order p k and rs p k the green ring of g over f p this paper concerns the conjecture on the ring structure of a certain quotient ring rs p k i p k of rs p k when k 2 which was originally due to kouwenhoven to be more precise he conjectured that the ideal i p k is closed under the exterior powers and rs p k i p k is equipped with the ring structure for the induced exterior powers we show that kouwenhoven s conjecture turns out to be true when p 2 but false when p 3 for other primes except p 2 3 it will be demonstrated that rs p k i p k cannot have the ring structure for the induced exterior powers

combinatorial verification of the elementary divisors of tensor products abstract using combinatorial arguments we determine the determinantal divisors for the tensor product of two matrices thereby obtaining its elementary divisors and jordan canonical form

exterior and symmetric powers of modules for cyclic 2 groups abstract we prove a recursive formula for the exterior and symmetric powers of modules for a cyclic 2 group this makes computation straightforward previously a complete description was only known for cyclic groups of prime order

high order sensitivity analysis of complex coupled systems the sobieszczanski sobieski 1988 algorithm is extended to include second and higher order derivatives while retaining the obviation of finite differencing of the system analysis this is accomplished by means of a recursive application of the same implicit function theorem as in the original algorithm in optimization the computational cost of the higher order derivatives is relative to the aggregate cost of analysis together with a repetition of the first order sensitivity analysis as often as is required to produce the equivalent information by successive linearizations within move limits

efficient approximation concepts using second order information the primary goal of this paper is to show how second derivative information can be used in an effective way in structural optimization problems the basic idea is to generate such an information at the expense of only one more virtual load case in the sensitivity analysis part of the finite element code to achieve this goal a primal dual approach is employed that can also be interpreted as a sequential quadratic programming method another objective is to relate the proposed method to the well known family of approximation concepts techniques where the primary optimization problem is transformed into a sequence of non linear explicit subproblems when restricted to diagonal second derivatives the new approach can be viewed as a recursive convex programming method similar to the convex linearization method conlin and to its recent generalization the method of moving asymptotes mma this new method has been successfully tested on simple problems that can be solved in closed form as well as on sizing optimization of trusses in all cases the method converges faster than conlin mma or other approximation techniques based on reciprocal variables

polynomial algebras and smooth functions in banach spaces abstract let a n x be the algebra of polynomials on a real banach space x which is generated by all continuous polynomials of degree not exceeding n let m be the minimal integer such that there is a non compact m homogeneous polynomial p p x m l 1 then n m implies that the uniform closure of a n x does not contain all polynomials of degree n 1 and hence the chain of closures a n x n m is strictly increasing in the rest of the note we give solutions to three problems concerning the behaviour of smooth functions on banach spaces posed in the literature in particular we construct an example of a uniformly differentiable real valued function f on the unit ball of a certain banach space x such that there exists no uniformly differentiable function g on b x for any 1 which coincides with f in some neighbourhood of the origin

second order approximations in structural genesis and shape finding the introduction of second order sensitivities to behaviour approximation in structural optimization is applied and investigated numerical computation of second derivatives is considered and evaluated two approaches in shape optimization are involved namely shape finding by moving boundaries and shape genesis by distributing mass in a specified design domain a series of examples is engaged to work out the benefits of second order information in both the above fields

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

orthogonally additive polynomials on spaces of continuous functions we show that for every orthogonally additive homogeneous polynomial p on a space of continuous functions c k with values in a banach space y there exists a linear operator s c k y such that p f s f n this is the c k version of a related result of sundaresam for polynomials on l p spaces

the spectrum of analytic mappings of bounded type abstract a banach space e is said to be symmetrically regular if every continuous symmetric linear mapping from e to e is weakly compact for a complex banach space e and a complex banach algebra f let h b e f denote the algebra of holomorphic mappings from e to f which are bounded on bounded sets we endow h b e f with the usual frechet topology m h b e f f denotes the set of all non null continuous homomorphisms from h b e f to f a subset of g ef on which the extension of zalduendo is multiplicative is presented and it is shown that in general the sets g ef and m h b e f f do not coincide we prove that if e is symmetrically regular and every continuous linear mapping from e to f is weakly compact then there exists an analytic structure on m h b e f f

the noether numbers for cyclic groups of prime order abstract the noether number of a representation is the largest degree of an element in a minimal homogeneous generating set for the corresponding ring of invariants we compute the noether number for an arbitrary representation of a cyclic group of prime order and as a consequence prove the 2 p 3 conjecture

spectra of algebras of holomorphic functions on infinite dimensional riemann domains let x be a connected riemann domain over a fr6chet space e and let a x be the algebra of all holomorphic functions on x with the compact open topology let so x and sb x respectively denote the continuous spectrum and the bounded spectrum of x if e is finite dimensional then it is well known that sb x coincides with so x and this set endowed with the structure of a riemann domain can be identified with the envelope of holomorphy x of x the question as to whether this result holds for infinite dimensional riemann domains has been investigated by alexander 11 coeur 3 hirschowitz 8 and schottenloher 19 20 23 by adapting a construction of rossi 18 alexander 1 endowed so x with the structure of a not necessarily connected riemann domain and proved that if c denotes the connected component of sc x containing all point evaluations s with x x then the evaluation mapping e x xr is a normal holomorphic extension of x which is maximal among all normal holomorphic extensions of x but in general is not the envelope of holomorphy of x that is the holomorphic extension e x c is not maximal among all holomorphic extensions of x indeed josefson 10 gave an example of a domain x in a nonseparable banach space for which not every point of x defines a continuous complex homomorphism of g x however coeur6 3 and hirschowitz 8 showed that the complex homomorphisms defined by the points of x are at least bounded and using this result schottenloher 19 20 proved that t x can always beidentified as a riemann domain with a suitably structured subset xb of sb x thl x us slways equals xb but all questions concerning the nontrivial relations between c x s x j c and b remained unanswered in a recent paper schottenloher 23 proved that if e is a separable fr6chet space with the bounded approximation property then the sets sc x 2 and x all coincide but the problem as to whether these sets coincide or not with s x remained open in this note this problem is solved in the affirmative under

sensitivity analysis of discrete structural systems methods for calculating sensitivity derivatives for discrete structural systems are surveyed primarily covering literature published during the past two decades methods are described for calculating derivatives of static displacements and stresses eigenvalues and eigenvectors transient structural response and derivatives of optimum structural designs with respect to problem parameters the survey is focused on publications developed in nonstructural fields such as electronics controls and physical chemistry which are directly applicable to structural problems most notable among the nonstructural based methods are the adjoint variable technique from control theory and the green s function and fast methods from physical chemistry

adams operations on the green ring of a cyclic group of prime power order we consider the green ring r kc for a cyclic p group c over a field k of prime characteristic p and determine the adams operations psi n in the case where n is not divisible by p this gives information on the decomposition into indecomposables of exterior powers and symmetric powers of kc modules

differences of composition operators between weighted type spaces of holomorphic functions on the unit ball of cn we consider differences of composition operators between weighted type or little weighted type spaces of analytic functions on the unit ball with weighted sup norms and give estimates for the distance of these differences to the space of compact operators we also study the boundedness and compactness of these operators

duality in spaces of nuclear and integral polynomials abstract we study the spaces of nuclear and integral vector valued polynomials and their duals we prove that if e is asplund p n ne f p i ne f isometrically for any banach space f we describe p n ne f as a subspace of p ne f in terms of weak star continuous polynomials we show that p w ne f p c ne f when e has the approximation property

geometric theory of spaces of integral polynomials and symmetric tensor products abstract we investigate the nature of extreme weak exposed and weak strongly exposed points of the unit ball of spaces of n homogeneous integral polynomials on and n fold symmetric products of a banach space e for the space of integral polynomials we show the set of extreme points is contained in the set n e 1 we give smul yan type theorems for spaces of n homogeneous polynomials and n fold symmetric tensors that characterise weak exposed resp weak strongly exposed points in terms of g teaux resp frechet differentiability of the norm on various spaces of tensor products and polynomials our study of the geometry of these spaces has many applications when e has the radon nikod m property we show that the spaces of n homogeneous integral and nuclear polynomials are isomerically isomorphic for each integer n when the dimensions of e and n are both at least 2 then the space of n homogeneous polynomials on e is neither smooth nor rotund for a certain class of reflexive banach space the space of n homogeneous approximable polynomials on e is either reflexive or is not isometric to a dual banach space we conclude with a choquet theorem for a space of homogeneous polynomials

envelopes of open sets and extending holomorphic functions on dual banach spaces abstract we investigate certain envelopes of open sets in dual banach spaces which are related to extending holomorphic functions we give a variety of examples of absolutely convex sets showing that the extension is in many cases not possible we also establish connections to the study of iterated weak sequential closures of convex sets in the dual of separable spaces

elementary divisors of tensor products and p ranks of binomial matrices abstract let f be a field of characteristic p and let a and b be two jordan blocks with nonzero eigenvalues the reduction formulas of c w norman enable us to compute the elementary divisors of a b we investigate connections between the elementary divisors of a b and binomial matrices in particular we show that norman s reduction formulas can be used to compute the p rank of certain binomial matrices

symmetric powers and modular invariants of elementary abelian p groups abstract let e be an elementary abelian p group of order q p n let w be a faithful indecomposable representation of e with dimension 2 over a field k of characteristic p and let v s m w with m q we prove that the rings of invariants k v e are generated by elements of degree q and relative transfers this extends recent work of wehlau 18 on modular invariants of cyclic groups of order p if m p we prove that k v e is generated by invariants of degree 2 q 3 extending a result of fleischmann sezer shank and woodcock 6 for cyclic groups of order p our methods are primarily representation theoretic and along the way we prove that for any d q with d m q s d v is projective relative to the set of subgroups of e with order m and that the sequence s d v d 0 is periodic with period q modulo summands which are projective relative to the same set of subgroups these results extend results of almkvist and fossum 1 on cyclic groups of prime order

decomposing modular tensor products and periodicity of jordan partitions let jr denote an r r matrix with minimal and characteristic polynomials t 1 r suppose r 6 s it is not hard to show that the jordan canonical form of jr js is similar to j 1 jr where 1 r 0 and p r 1 i rs the partition r s p 1 r of rs which depends only on r s and the characteristic p char f has many applications including to the study of algebraic groups we prove new periodicity and duality results for r s p that depend on the smallest p power exceeding r this generalizes results of j a green b srinivasan and others which depend on the smallest p power exceeding the potentially large integer s we show that for fixed r we can construct a finite table allowing the computation of r s p for all s r and all primes p this generalizes work of k i iima and r iwamatsu

bases in spaces of multilinear forms over banach spaces fil dimant veronica universidad de san andres departamento de matematica y ciencias argentina