non commutative martingale transforms abstract we prove that non commutative martingale transforms are of weak type 1 1 more precisely there is an absolute constant c such that if m is a semi finite von neumann algebra and m n n 1 is an increasing filtration of von neumann subalgebras of m then for any non commutative martingale x x n n 1 in l 1 m adapted to m n n 1 and any sequence of signs e n n 1 e 1 x 1 n 2 n e n x n x n 1 1 c x n 1 for every n 2 this generalizes a result of burkholder from classical martingale theory to non commutative setting and answers positively a question of pisier and xu as applications we get the optimal order of the unconditional martingale differences umd constants of the schatten class s p when p similarly we prove that the umd constant of the finite dimensional schatten class s n 1 is of order log n 1 we also discuss the pisier xu non commutative burkholder gundy inequalities

representation of certain homogeneous hilbertian operator spaces and applications following grothendieck s characterization of hilbert spaces we consider operator spaces f such that both f and f completely embed into the dual of a c algebra due to haagerup musat s improved version of pisier shlyakhtenko s grothendieck inequality for operator spaces these spaces are quotients of subspaces of the direct sum c r of the column and row spaces the corresponding class being denoted by qs c r we first prove a representation theorem for homogeneous f qs c r starting from the fundamental sequences phi c n bigg sum k 1 ne k1 otimes e k bigg c otimes min f 2 quad mbox and quad phi r n bigg sum k 1 ne 1k otimes e k bigg r otimes min f 2 given by an orthonormal basis ek of f under a mild regularity assumption on these sequences we show that they completely determine the operator space structure of f and find a canonical representation of this important class of homogeneous hilbertian operator spaces in terms of weighted row and column spaces this canonical representation allows us to get an explicit formula for the exactness constant of an n dimensional subspace fn of f mathit ex f n sim biggl frac n phi c n phi r bigg frac phi c n phi r n bigg frac n phi r n phi c bigg frac phi r n phi c n bigg biggr 1 2 in the same way the projection injectivity constant of fn is explicitly expressed in terms of c and r too orlicz space techniques play a crucial role in our arguments they also permit us to determine the completely 1 summing maps in effros and ruan s sense between two homogeneous spaces e and f in qs c r the resulting space 1o e f isomorphically coincides with a schatten orlicz class s moreover the underlying orlicz function is uniquely determined by the fundamental sequences of e and f in particular applying these results to the column subspace cp of the schatten p class we find the projection and exactness constants of cpn and determine the completely 1 summing maps from cp to cq for any 1 p q

an efficient high order nystrom scheme for acoustic scattering by inhomogeneous penetrable media with discontinuous material interface this text proposes a fast rapidly convergent nystrom method for the solution of the lippmann schwinger integral equation that mathematically models the scattering of time harmonic acoustic waves by inhomogeneous obstacles while allowing the material properties to jump across the interface the method works with overlapping coordinate charts as a description of the given scatterer in particular it employs partitions of unity to simplify the implementation of high order quadratures along with suitable changes of parametric variables to analytically resolve the singularities present in the integral operator to achieve desired accuracies in approximations to deal with the discontinuous material interface in a high order manner a specialized quadrature is used in the boundary region the approach further utilizes an fft based strategy that uses equivalent source approximations to accelerate the evaluation of large number of interactions that arise in the approximation of the volumetric integral operator and thus achieves a reduced computational complexity of o n log n for an n point discretization a detailed discussion on the solution methodology along with a variety of numerical experiments to exemplify its performance are presented in this paper

embedding of the operator space oh and the logarithmic little grothendieck inequality we use voiculescu s concept of free probability to construct a completely isomorphic embedding of the operator space oh in the predual of a von neumann algebra we analyze the properties of this embedding and determine the operator space projection constant of oh n frac 1 108 sqrt frac n 1 ln n le inf p mathcal b ell 2 to oh n p 2 p left p right cb le 288 pi sqrt frac 2n 1 ln n the lower estimate is a recent result of pisier and shlyakhtenko that improves an estimate of order 1 1 lnn of the author the additional factor 1 sqrt 1 ln n indicates that the operator space oh n behaves differently than its classical counterpart ell 2 n we give an application of this formula to positive sesquilinear forms on mathcal b ell 2 this leads to logarithmic characterization of c algebras with the weak expectation property introduced by lance

hp adaptive finite elements in electromagnetics a model problem for the steady state form of maxwell s equations is considered the problem is formulated in a weak form using a lagrange multiplier laying down a foundation for a general class of novel hp adaptive fe approximations a convergence proof for curvilinear elements is presented the proposed method is illustrated and verified by a series of 2d experiments which include elements with curved boundaries and nonhomogeneous media

gundy s decomposition for non commutative martingales and applications we provide an analogue of gundy s decomposition for l 1 bounded non commutative martingales an important difference from the classical case is that for any l 1 bounded non commutative martingale the decomposition consists of four martingales this is strongly related with the row column nature of non commutative hardy spaces of martingales as applications we obtain simpler proofs of the weak type 1 1 boundedness for non commutative martingale transforms and the non commutative analogue of burkholder s weak type inequality for square functions a sequence x n n ge 1 in a normed space mathrm x is called 2 co lacunary if there exists a bounded linear map from the closed linear span of x n n ge 1 to l 2 taking each x n to the n th vector basis of l 2 we prove using our decomposition that any relatively weakly compact martingale difference sequence in l 1 mathcal m tau whose sequence of norms is bounded away from zero is 2 co lacunary generalizing a result of aldous and fremlin to non commutative l 1 spaces

noncommutative maximal ergodic theorems for positive contractions let m be a von neumann algebra equipped with a normal semifinite faithful trace let t be a positive linear contraction on m such that t and such that the numerical range of t as an operator on l2 m is contained in a stoltz region with vertex 1 we show that junge and xu s noncommutative stein maximal ergodic inequality holds for the powers of t on lp m 1 p we apply this result to obtain the noncommutative analogue of a recent result of cohen concerning the iterates of the product of a finite number of conditional expectations

a high order mixed vector finite element method for solving the time dependent maxwell equations on unstructured grids we present a mixed vector finite element method for solving the time dependent coupled ampere and faraday laws of maxwell s equations on unstructured hexahedral grids that employs high order discretization in both space and time the method is of arbitrary order accuracy in space and up to 4th order accurate in time making it well suited for electrically large problems where grid anisotropy and numerical dispersion have plagued other methods in addition the method correctly models both the jump discontinuities and the divergence free properties of the electric and magnetic fields is charge and energy conserving conditionally stable and free of spurious modes several computational experiments are performed to demonstrate the accuracy efficiency and benefits of the method

atomic decomposition and interpolation for hardy spaces of noncommutative martingales we prove that atomic decomposition for the hardy spaces h1 and h1 is valid for noncommutative martingales we also establish that the conditioned hardy spaces of noncommutative martingales hp and bmo form interpolation scales with respect to both complex and real interpolations

pml enhanced with a self adaptive goal oriented hp finite element method simulation of through casing borehole resistivity measurements we describe the application of a perfectly matched layer pml combined with a self adaptive goal oriented hp finite element fe method to the simulation of borehole resistivity measurements the adaptive refinements and fast convergence of the self adaptive hp fe method enhance the performance of the pml thereby enabling the accurate and efficient truncation of the computational domain in open domain problems we apply this method to the simulation of axisymmetric through casing resistivity measurements acquired in a borehole environment that are typically used for the assessment of rock formation properties our numerical results confirm the accuracy and efficiency of our method and provide evidence of highly accurate and reliable simulations of borehole logging measurements in the presence of a conductive steel casing and material contrast of fourteen orders of magnitude in electrical conductivity moreover the combination of adaptivity and pml enables us to significantly reduce the size of the computational domain with substantial savings in computer time and memory

modeling of electromagnetic absorption scattering problems using hp adaptive finite elements a model problem for the steady state form of maxwell s equations is considered the problem is formulated in a weak form using a lagrange multiplier laying down a foundation for a general class of novel hp adaptive fe approximations a convergence proof for affine elements is presented the proposed method is illustrated and verified with a series of 2d experiments including elements with curved boundaries and nonhomogeneous media

learning mutation and long run equilibria in games an evolutionary model with a finite number of players and with stochastic mutations is analyzed the expansion and contraction of strategies is linked to their current relative success but mutuation perturbing the system from its deterministic evolution are present as well the focus is on the long run implications of ongoing mutations which drastically reduce the set of equilibria for 2 by 2 symmetric games with two symmetric strict nash equilibria the risk dominant equilibrium is selected in particular if both strategies have equal security levels the pareto dominant nash equilibrium is selected in particular if both strategies have equal security levels the pareto dominant nash equilibrium is selected even though there is another strict nash equilibrium copyright 1993 by the econometric society

towards optimal control of evolutionary games on networks we investigate the control of evolutionary games on networks in which each edge represents a two player repeating game between neighboring agents after each round of games agents can imitate the strategies of better performing neighbors while a subset of agents can be assigned strategies and thus serve as control inputs we seek here the smallest set of control agents needed to drive the network to a desired uniform strategy state after presenting exact solutions for complete and star networks and describing a general solution approach that is computationally practical only for small networks we design a fast algorithm for approximating the solution on arbitrary networks using a weighted minimum spanning tree and strategy propagation algorithm the resulting approximation is exact for certain classes of games on complete and star networks and simulations suggest that the algorithm performs well in more general cases

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

maxwell eigenvalues and discrete compactness in two dimensions abstract we present an elementary proof of the discrete compactness result for a general class of hp finite elements introduced in 1 2 we discuss h convergence of 2d elements only and in this context the results are not new as the analysis of h curl conforming elements for maxwell s equations can be reduced to the long known results for raviart thomas elements 3 the work is based on the result of kikuchi 4 5 for nedelec s edge triangular elements of the lowest order and presents an alternative to techniques presented in 3 6 in particular the present version does not use an inverse inequality argument and therefore is valid for h adaptive meshes we conclude the presentation with a number of 2d computational experiments including nonconvex domains

hp vector finite element method for eigenmode analysis of waveguides a new stable variational formulation for full wave analysis of waveguides is presented numerical experiments show that the method remains stable at very low frequencies theoretical results apply to a wide class of vector finite elements including two families of nedelec numer math 35 1980 315 numer math 50 1986 57 and their generalization hp edge elements comput methods appl mech engrg 152 1998 103 comput methods appl mech engrg 169 1999 331

an efficient high order algorithm for acoustic scattering from penetrable thin structures in three dimensions this paper presents a high order accelerated algorithm for the solution of the integral equation formulation of volumetric scattering problems the scheme is particularly well suited to the analysis of thin structures as they arise in certain applications e g material coatings in addition it is also designed to be used in conjunction with existing low order fft based codes to upgrade their order of accuracy through a suitable treatment of material interfaces the high order convergence of the new procedure is attained through a combination of changes of parametric variables to resolve the singularities of the green function and partitions of unity to allow for a simple implementation of spectrally accurate quadratures away from singular points accelerated evaluations of the interaction between degrees of freedom on the other hand are accomplished by incorporating two face equivalent source approximations on cartesian grids a detailed account of the main algorithmic components of the scheme are presented together with a brief review of the corresponding error and performance analyses which are exemplified with a variety of numerical results

maximal theorems of menchoff rademacher type in non commutative lq spaces abstract estimates for maximal functions provide the fundamental tool for solving problems on pointwise convergence this applies in particular for the menchoff rademacher theorem on orthogonal series in l 2 0 1 and for results due independently to bennett and maurey nahoum on unconditionally convergent series in l 1 0 1 we prove corresponding maximal inequalities in non commutative l q spaces over a semifinite von neumann algebra the appropriate formulation for non commutative maximal functions originates in pisier s recent work on non commutative vector valued l q spaces

a two dimensional self adaptive hp finite element method for the characterization of waveguide discontinuities part i energy norm based automatic hp adaptivity abstract the accurate analysis and characterization of waveguide discontinuities is an important issue in microwave engineering in some cases the discontinuities are an unavoidable result of mechanical or electric transitions which effects have to be minimized in other cases the discontinuities are deliberately introduced into the waveguide to perform a certain electric function this is the first of two papers analyzing different types of rectangular waveguide discontinuities by using a fully automatic hp adaptive finite element method in this paper a fully automatic energy norm based hp adaptive finite element fe strategy applied to a number of relevant waveguide structures is presented the methodology produces exponential convergence rates in terms of the energy norm error of the solution against the problem size number of degrees of freedom extensive numerical results demonstrate the suitability of the hp method for solving different rectangular waveguide discontinuities these results illustrate the flexibility reliability and high accuracy of the method the self adaptive hp fem provides similar sometimes more accurate results than those obtained with semi analytical techniques such as the mode matching method for problems where semi analytical methods can be applied at the same time the hp fem provides the flexibility of modeling more complex waveguide structures and including the effects of dielectrics metallic screws round corners etc which cannot be easily considered when using semi analytical techniques in the second part the work is extended by presenting a fully automatic goal oriented hp adaptive fe in terms of the scattering or s parameters which are widely used in microwave engineering for the characterization of microwave devices

grothendieck s theorem for operator spaces we prove several versions of grothendieck s theorem for completely bounded linear maps t e f when e and f are operator spaces we prove that if e f are c algebras of which at least one is exact then every completely bounded t e f can be factorized through the direct sum of the row and column hilbert operator spaces equivalently t can be decomposed as t t r t c where t r resp t c factors completely boundedly through a row resp column hilbert operator space this settles positively at least partially some earlier conjectures of effros ruan and blecher on the factorization of completely bounded bilinear forms on c algebras moreover our result holds more generally for any pair e f of exact operator spaces this yields a characterization of the completely bounded maps from a c algebra or from an exact operator space to the operator hilbert space oh as a corollary we prove that up to a complete isomorphism the row and column hilbert operator spaces and their direct sums are the only operator spaces e such that both e and its dual e are exact we also characterize the schur multipliers which are completely bounded from the space of compact operators to the trace class

mathematical analysis and finite element simulation of a magnetized ferrite model microwave scattering by obstacles made of ferrite materials has been studied for a long time because of its important applications in radar satellite optical imaging system signal processing atmospheric science and even cloaking device design in this paper we present for the first time the rigorous mathematical analysis of a magnetized ferrite model widely used by engineers the well posedness of the model is established first then we develop a finite element time domain method for solving this model numerical stability similar to the continuous stability is proved for our scheme and the optimal error estimate in the l 2 norm is obtained numerical results are consistent with our theoretical analysis and show how wave propagates in the ferrite material

noncommutative maximal ergodic theorems this paper is devoted to the study of various maximal ergodic theorems in noncommutative spaces in particular we prove the noncommutative analogue of the classical dunford schwartz maximal ergodic inequality for positive contractions on and the analogue of stein s maximal inequality for symmetric positive contractions we also obtain the corresponding individual ergodic theorems we apply these results to a family of natural examples which frequently appear in von neumann algebra theory and in quantum probability

an infinite element for maxwell s equations a new infinite element ie approximation for steady state maxwell s equations is proposed the ie is compatible with a new class of hp finite element fe discretizations presented in 13 32 following 12 a convergence analysis for the proposed coupled fe ie approximations is presented

an hp adaptive finite element method for electromagnetics part 1 data structure and constrained approximation abstract this is the first of papers describing an implementation of the hp adaptive mixed finite element fe method for the solution of steady state maxwell s equations proposed in l demkowicz and l vardapetyan modeling of electromagnetic absoption scattering problems using hp adaptive finite elements computer methods in applied mechanics and engineering 152 1998 103 124 the discretization is defined on a hybrid grid consisting of both triangles and quads and allows for both h and p refinements of the mesh the paper focuses on the data structure and constrained approximation issues and provides a number of illustrative examples

an hp adaptive finite element method for electromagnetics part 3 a three dimensional infinite element for maxwell s equations this paper is a continuation of reference 26 cecot demkowicz and rachowicz computer methods in applied mechanics and engineering 2000 188 625 643 and describes an implementation of the infinite element for three dimensional time harmonic maxwell s equations proposed in reference 15 demkowicz and pal computer methods in applied mechanics and engineering 1998 164 77 94 the element is compatible with the hp finite element discretizations for maxwell s equations in bounded domains reported in references 16 18 computer methods in applied mechanics and engineering 1998 152 103 124 1999 169 331 344 2000 187 307 337 copyright 2003 john wiley sons ltd

a two dimensional infinite element for maxwell s equations abstract the paper describes an implementation of the infinite element for two dimensional steady state maxwell s equations proposed by l demkowicz and m pal comput meth appl mech engrg in press the element is compatible with the hp fe element discretizations for maxwell s equations in bounded domains reported in l demkowicz and l vardapetyan comput meth appl mech engrg 152 1 2 1996 103 124 and w rachowicz and l demkowicz comput meth appl mech engrg in press

noncommutative burkholder rosenthal inequalities we investigate martingale inequalities in noncommutative lp spaces associated with a von neumann algebra equipped with a faithful normal state we prove the noncommutative analogue of the classical burkholder inequality on the conditioned or little square function and extend the noncommutative burkholder gundy inequalities from comm math phys 189 1997 667 698 to this nontracial setting we include several related results

a self adaptive goal oriented hp finite element method with electromagnetic applications part ii electrodynamics abstract we present the formulation implementation and applications of a self adaptive goal oriented hp finite element fe method for electromagnetic em problems the algorithm delivers without any user interaction a sequence of optimal hp grids this sequence of grids minimizes the error in a prescribed quantity of interest with respect to the problem size and it converges exponentially in terms of the relative error in a user prescribed quantity of interest against the cpu time including problems involving high material contrasts boundary layers and or several singularities the goal oriented refinement strategy is an extension of a fully automatic energy norm based hp adaptive algorithm we illustrate the efficiency of the method with 2d numerical simulations of maxwell s equations using both h 1 conforming continuous elements and h curl conforming nedelec edge elements applications include alternate current ac resistivity logging instruments in a borehole environment with steel casing for the assessment of rock formation properties behind casing logging instruments steel casing and rock formation properties are assumed to exhibit axial symmetry around the axis of a vertical borehole for the presented challenging class of problems the self adaptive goal oriented hp fem delivers results with 5 7 digits of accuracy in the quantity of interest

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

networks of conforming or nonconforming individuals tend to reach satisfactory decisions binary decisions of agents coupled in networks can often be classified into two types coordination where an agent takes an action if enough neighbors are using that action as in the spread of social norms innovations and viral epidemics and anticoordination where too many neighbors taking a particular action causes an agent to take the opposite action as in traffic congestion crowd dispersion and division of labor both of these cases can be modeled using linear threshold based dynamics and a fundamental question is whether the individuals in such networks are likely to reach decisions with which they are satisfied we show that in the coordination case and perhaps more surprisingly also in the anticoordination case the agents will indeed always tend to reach satisfactory decisions that is the network will almost surely reach an equilibrium state this holds for every network topology and every distribution of thresholds for both asynchronous and partially synchronous decision making updates these results reveal that irregular network topology population heterogeneity and partial synchrony are not sufficient to cause cycles or nonconvergence in linear threshold dynamics rather other factors such as imitation or the coexistence of coordinating and anticoordinating agents must play a role

conditioned square functions for noncommutative martingales we prove a weak type 1 1 inequality involving conditioned versions of square functions for martingales in noncommutative l p spaces associated with finite von neumann algebras as application we determine the optimal orders for the best constants in the noncommutative burkholder rosenthal inequalities from ann probab 31 2003 948 995 we also discuss bmo norms of sums of noncommuting order independent operators

adaptive finite element techniques for the maxwell equations using implicit a posteriori error estimates we consider an implicit a posteriori error estimation technique for the adaptive solution of the maxwell equations with nedelec edge finite element methods on three dimensional domains on each element of the tessellation an equation for the error is formulated and solved with a properly chosen local finite element basis the discrete bilinear form of the local problems is shown to satisfy an inf sup condition which ensures the well posedness of the error equations an adaptive solution algorithm is developed based on the obtained error estimates the performance of the method is tested on various problems including non convex domains with non smooth boundaries the numerical results show that the estimated error computed by the implicit a posteriori error estimation technique correlates well with the actual error on the meshes generated adaptively with the help of the error estimator the achieved accuracy is higher than on globally refined meshes with comparable number degrees of freedom moreover the rate of the error convergence on the locally adapted meshes is faster than that on the globally refined meshes

interpolation and φ moment inequalities of noncommutative martingales this paper is devoted to the study of moment inequalities for noncommutative martingales in particular we prove the noncommutative moment analogues of martingale transformations stein s inequalities khintchine s inequalities for rademacher s random variables and burkholder gundy s inequalities the key ingredient is a noncommutative version of marcinkiewicz type interpolation theorem for orlicz spaces which we establish in this paper

the multi level hp method for three dimensional problems dynamically changing high order mesh refinement with arbitrary hanging nodes abstract one main challenge of the h p version of the finite element method is the high implementational complexity of the method resulting from the added need of handling hanging nodes appropriately the multi level h p formulation recently introduced for two dimensional applications aims at alleviating these difficulties without compromising the approximation quality this is achieved by changing from the conventional refine by replacement approach to a refine by superposition idea the current work shows that the multi level h p approach can be extended naturally to three dimensional refinement without increasing the complexity of the rule set ensuring linear independence and compatibility of the shape functions in this way a three dimensional h p refinement scheme is formulated in which hanging nodes are avoided by definition this ease of complexity allows for a highly flexible discretization kernel featuring arbitrary irregular meshes and a continuous refinement and coarsening throughout the simulation runtime different numerical examples demonstrate that even in the presence of singularities this novel refinement scheme yields exponential convergence with respect to both the number of unknowns and the computational time it is further shown that the refinement scheme is able to capture complex solution features that demand for three dimensional refinement patterns the dynamic discretization properties of the approach are demonstrated by continuously refining and coarsening the mesh during the simulation runtime to keep the refinement zone local to a moving singularity finally it is shown that the high approximation power of the multi level h p scheme also carries over to curved geometries common in engineering practice without a significant detrimental effect on the conditioning of the stiffness matrix

inhomogeneous lossy waveguide mode analysis abstract this paper discusses electromagnetic numerical mode analysis in waveguides with materially inhomogeneous cross sections and material dissipation a full wave formulation of maxwell s homogeneous equations including gauss electric law stable at vanishing propagation constant is implemented and verified in terms of the hp adaptive version of the finite element method it provides the possibility to use high order polynomial enrichments combined with strongly graded meshes it is considered most efficient in resolving the loss of solution regularity at material interfaces with large contrast numerical examples including materially lossless homogeneous and inhomogeneous cross sections with and without losses are analysed to corroborate the implementation the efficiency of using higher order polynomial enrichments is shown the approach is anticipated to have a broad application from modern on chip interconnect and antenna technologies to the design of low observable aerial vehicles

a fast higher order solver for scattering by penetrable bodies in three dimensions in this paper we introduce a new fast higher order solver for scattering by inhomogeneous media in three dimensions as in previously existing methods the low complexity of our integral equation method o nlogn operations for an n point discretization is obtained through extensive use of the fast fourier transform fft for the evaluation of convolutions however the present approach obtains significantly higher order accuracy than these previous approaches yielding at worst third order far field accuracy or substantially better for smooth scatterers even for discontinuous and complex refractive index distributions possibly containing severe geometric singularities such as corners and cusps the increased order of convergence of our method results from i a partition of unity decomposition of the green s function into a smooth part with unbounded support and a singular part with compact support and ii replacement of the possibly discontinuous scatterer by an appropriate fourier smoothed scatterer the resulting convolutions can then be computed with higher order accuracy by means of o nlogn ffts we present a parallel implementation of our approach and demonstrate the method s efficiency and accuracy through a variety of computational examples for a very large scatterer considered earlier in the literature with a volume of 3648 l 3 where l is the wavelength using the same number of points per wavelength and in computing times comparable to those required by the previous approach the present algorithm produces far field values whose errors are two orders of magnitude smaller than those reported previously

fourier series expansion in a non orthogonal system of coordinates for the simulation of 3d dc borehole resistivity measurements abstract we describe a new method to simulate 3d borehole resistivity measurements at zero frequency dc the method combines the use of a fourier series expansion in a non orthogonal system of coordinates with an existing 2d goal oriented higher order self adaptive hp finite element algorithm the new method is suitable for simulating measurements acquired with borehole logging instruments in deviated wells it delivers high accuracy simulations and it enables a considerable reduction of the computational complexity with respect to available 3d simulators since the number of fourier modes basis functions needed to solve practical applications is limited typically below 10 furthermore numerical results indicate that the optimal 2d grid based on the 0th fourier mode also called central fourier mode can be employed to efficiently solve the final 3d problem thereby avoiding the expensive construction of optimal 3d grids specifically for a challenging through casing resistivity application we reduce the computational time from several days using a 3d simulator to just 2 h with the new method while gaining accuracy the new simulation method can be easily extended to different physical phenomena with similar geometries as those arising in the simulation of 3d borehole electrodynamics and sonic acoustics coupled with elasticity measurements in addition the method is especially suited for inversion since we demonstrate that the number of fourier modes needed for the exact representation of the materials is limited to only one the central mode for the case of borehole measurements acquired in deviated wells

stochastic stability analysis of evolutionary two player games on regular graphs abstract we study evolutionary two player games and identify stochastically stable equilibria of the network games restricted to infinite populations on regular graphs the players update their strategies according to four different rules birth death death birth imitation and pairwise comparison for prisoner s dilemma and snowdrift games respectively for two player games on regular graphs we show that there is a unique stochastically stable equilibrium for infinite populations for the prisoner s dilemma game if the benefit to cost ratio is larger than k 2 k is the degree of a regular graph the networked game has a higher fraction of cooperators than that for a well mixed population for the snowdrift game the fraction of cooperators in a regular graph would be higher than that of the well mixed population if the benefit to cost ratio is larger than 1 5 under certain conditions the lower graph connectivity can lead to the emergence of more cooperators finally some numerical simulation examples are given to demonstrate the theoretical results

higher order fourier approximation in scattering by two dimensional inhomogeneous media this paper provides a theoretical analysis of a higher order fft based integral equation method introduced recently ieee trans antennas and propagation 48 2000 pp 1862 1864 for the evaluation of transverse electric polarized electromagnetic scattering from a bounded penetrable inhomogeneity in two dimensional space roughly speaking this method is based on fourier smoothing of the integral operator and the refractive index n x here we prove that the solution of the resulting integral equation approximates the solution of the exact integral equation with higher order accuracy even when n x is a discontinuous function as suggested by the numerical experiments contained in the paper mentioned above in detail we relate the convergence rates of the computed interior and exterior fields to the regularity of the scatterer and we demonstrate with a few numerical examples that the predicted convergence rates are achieved in practice

non commutative martingale inequalities we prove the analogue of the classical burkholder gundy inequalites for non commutative martingales as applications we give a characterization for an ito clifford integral to be an lp martingale via its integrand and then extend the ito clifford integral theory in l2 developed by barnett streater and wilde to lp for all 1 p we include an appendix on the non commutative analogue of the classical fefferman duality between h1 and bmo

computation of resonant modes for axisymmetric maxwell cavities using hp version edge finite elements the computation of the resonant frequencies for closed cavities is not a trivial task multi materials and sharp corners all give rise to highly singular eigenfunctions however an approach using hp finite elements is well suited to such problems and with the correct combination of h and p refinements it yields the theoretically predicated exponential rates of convergence in this paper we present a novel approach to the solution of axisymmetric cavity problems which uses a hierarchic h1 and h curl conforming finite element basis a selection of numerical examples is included and these demonstrate that the exponential rates of convergence are achieved in practice copyright 2005 john wiley sons ltd