tightness and distinguished frechet spaces in this chapter we apply the concept of tightness to study distinguished frechet spaces we show that a frechet space is distinguished if and only if its strong dual has countable tightness this approach to studying distinguished frechet spaces leads to a rich supply of df spaces whose weak duals are quasi suslin but not k analytic the small cardinals mathfrak b and mathfrak d will be used to improve the analysis of kothe s echelon nondistinguished frechet space 1 a

resolutions of topological linear spaces and continuity of linear maps abstract the main result of the paper is the following if an f space x is covered by a family e n n of sets such that e e whenever and f is a linear map from x to a topological linear space y which is continuous on each of the sets e then f is continuous this provides a very strong negative answer to a problem posed recently by j kakol and m lopez pellicer a number of consequences of this result are given some of which are quite curious also inspired by a related question asked by j kakol it is shown that if a linear map is continuous on each member of a sequence of compact sets then it is also continuous on every compact convex set contained in the linear span of the sequence the construction applied to prove this is then used to interpret a natural linear topology associated with the sequence as the inductive limit topology in the sense of ph turpin and thus derive its basic properties

modeling the amplitude statistics of ultrasonic images in this paper a new statistical model for representing the amplitude statistics of ultrasonic images is presented the model is called the rician inverse gaussian riig distribution due to the fact that it is constructed as a mixture of the rice distribution and the inverse gaussian distribution the probability density function pdf of the riig model is given in closed form as a function of three parameters some theoretical background on this new model is discussed and an iterative algorithm for estimating its parameters from data is given then the appropriateness of the riig distribution as a model for the amplitude statistics of medical ultrasound images is experimentally studied it is shown that the new distribution can fit to the various shapes of local histograms of linearly scaled ultrasound data better than existing models a log likelihood cross validation comparison of the predictive performance of the riig the k and the generalized nakagami models turns out in favor of the new model furthermore a maximum a posteriori map filter is developed based on the riig distribution experimental studies show that the riig map filter has excellent filtering performance in the sense that it smooths homogeneous regions and at the same time preserves details

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

birkhoff integral for multi valued functions abstract the aim of this paper is to study birkhoff integrability for multi valued maps f cwk x where is a complete finite measure space x is a banach space and cwk x is the family of all non empty convex weakly compact subsets of x it is shown that the birkhoff integral of f can be computed as the limit for the hausdorff distance in cwk x of a net of riemann sums n an f tn we link birkhoff integrability with debreu integrability a notion introduced to replace sums associated to correspondences when studying certain models in mathematical economics we show that each debreu integrable multi valued function is birkhoff integrable and that each birkhoff integrable multi valued function is pettis integrable the three previous notions coincide for finite dimensional banach spaces and they are different even for bounded multi valued functions when x is infinite dimensional and x is assumed to be separable we show that when f takes values in the family of all non empty convex norm compact sets of a separable banach space x then f is pettis integrable if and only if f is birkhoff integrable in particular these pettis integrable f s can be seen as single valued pettis integrable functions with values in some other adequate banach space incidentally to handle some of the constructions needed we prove that if x is an asplund banach space then cwk x is separable for the hausdorff distance if and only if x is finite dimensional

network characterization of gul ko compact spaces and their relatives abstract in this paper we characterize the classes of gul ko and talagrand compact spaces through a network condition leading us to answer two questions posed by g gruenhage proc amer math soc 100 1987 371 376 on covering properties

a quantitative approach to weak compactness in frechet spaces and spaces c x let ee be a frechet space i e a metrizable and complete locally convex space lcs e e its strong second dual with a defining sequence of seminorms n n induced by a decreasing basis of absolutely convex neighbourhoods of zero unun and let h eh e be a bounded set let ck h sup d cluste e hn ck h sup d cluste e hn be the worst distance of the set of weak cluster points in e e of sequences in hh to ee and k h sup d h e h h the worst distance of h the weak closure in the bidual of hh to ee where dd means the natural metric of e e let n h sup limplimmup hm limmlimpup hm up un0 hm h provided the involved limits exist we extend a recent result of angosto cascales to frechet spaces by showing that if x h there is a sequence xp p xp p in hh such that dn x y n h dn x y n h for each e e e e cluster point y y of xp p xp p and n nn n moreover k h 0k h 0 iff ck h 0ck h 0 this provides a quantitative version of the weak angelicity in a frechet space also we show that ck h d h c x z 17ck h where h zxh zx is relatively compact and c x z c x z is the space of zz valued continuous functions for a web compact space xx and a separable metric space zz being now ck h ck h the worst distance of the set of cluster points in zxzx of sequences in hh to c x z c x z respect to the standard supremum metric dd and d h c x z sup f c x z f h this yields a quantitative version of orihuela s angelic theorem if xx is strongly web compact then ck h d h c x z 5ck h this happens if x e e e x e e e for e ge g for instance if ee is a df space or an lf space in the particular case that ee is a separable metrizable locally convex space then d h c x z ck h for each bounded h rxh rx

an adaptive finite element procedure for compressible high speed flows abstract a two step explicit finite element procedure for obtaining time accurate solutions to the compressible euler equations is described the method is coupled with an adaptive mesh refinement process which enables steady state solutions of improved quality to be obtained

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

existence of solutions for a class of multivalued functional integral equations of volterra type via the measure of nonequicontinuity on the frechet space c ω e abstract the existence of continuous not necessarily bounded solutions of nonlinear functional volterra integral inclusions in infinite dimensional setting is shown with the aid of the measure of nonequicontinuity new abstract topological fixed point results for admissible condensing operators are introduced weak compactness criterion in the space of locally integrable functions in the sense of bochner is set forth some examples illustrating the usefulness of the presented approach are also included

weight of precompact subsets and tightness pfister 1976 and cascales and orihuela 1986 proved that precompact sets in df and lm spaces have countable weight i e are metrizable improvements by valdivia 1982 cascales and orihuela 1987 and kakol and saxon preprint have varying methods of proof for these and other improvements a refined method of upper semi continuous compact valued maps applied to uniform spaces will suffice at the same time this method allows us to dramatically improve kaplansky s theorem that the weak topology of metrizable spaces has countable tightness extending it to include all lm spaces and all quasi barrelled df spaces both in the weak and original topologies one key is showing that for a large class g including all df and lm spaces countable tightness of the weak topology of e in g is equivalent to realcompactness of the weak topology of the dual of e

an implicit explicit scheme for compressible viscous high speed flows abstract an implicit explicit finite element based algorithm for the solution of 2d steady compressible viscous high speed flows is presented a structured grid is employed in the vicinity of solid walls and the implicit form of the algorithm is implemented in this region the explicit form of the algorithm is used in the remainder of the flow domain which is discretised with an unstructured assembly of triangles the quality of the computed solution is improved by the application of solution adaptive remeshing the computed results for two examples are compared with experimental observations to illustrate the performance of the proposed scheme

an approach to refining three dimensional tetrahedral meshes based on delaunay transformations a technique for refining three dimensional tetrahedral meshes is proposed in this paper the proposed technique is capable of treating arbitrary unstructured tetrahedral meshes convex or non convex with multiple regions resulting in high quality constrained delaunay triangulations the tetrahedra generated are of high quality nearly equilateral sliver tetrahedra which present a real problem to many algorithms are not produced with the new method the key to the generation of high quality tetrahedra is the iterative application of a set of topological transformations based on the voronoi delaunay theory and a reposition of nodes technique the computational requirements of the proposed technique are in linear relationship with the number of nodes and tetrahedra making it ideal for direct employment in a fully automatic finite element analysis system for 3 d adaptive mesh refinement application to some test problems is presented to show the effectiveness and applicability of the new method

a new parametric method of estimating the joint probability density abstract we present simple parametric methods that overcome major limitations of the literature on joint marginal density estimation in doing so we do not assume any form of marginal or joint distribution furthermore using our method a multivariate density can be easily estimated if we know only one of the marginal densities we apply our methods to financial data

on some properties of digamma and polygamma functions in this note we present some new and structural inequalities for digamma polygamma and inverse polygamma functions we also extend generalize and refine some known inequalities for these important functions

compact covers and function spaces abstract for a tychonoff space x we denote by c p x and c c x the space of continuous real valued functions on x equipped with the topology of pointwise convergence and the compact open topology respectively providing a characterization of the lindelof property of x in terms of c p x we extend okunev s results by showing that if there exists a surjection from c p x onto c p y resp from l p x onto l p y that takes bounded sequences to bounded sequences then y is a lindelof space respectively k analytic if x has this property in the second part applying christensen s theorem we extend pelant s result by proving that if x is a separable completely metrizable space and y is first countable and there is a quotient linear map from c c x onto c c y then y is a separable completely metrizable space we study also a non separable case and consider a different approach to the result of j baars j de groot j pelant and v valov which is based on the combination of two facts complete metrizability is preserved by l p equivalence in the class of metric spaces j baars j de groot j pelant if x is completely metrizable and l p equivalent to a first countable y then y is metrizable v valov some additional results are presented

blockwise adaptivity for time dependent problems based on coarse scale adjoint solutions we describe and test an adaptive algorithm for evolution problems that employs a sequence of blocks consisting of fixed though nonuniform space meshes this approach offers the advantages of adaptive mesh refinement but with reduced overhead costs associated with load balancing remeshing matrix reassembly and the solution of adjoint problems used to estimate discretization error and the effects of mesh changes a major issue with a block adaptive approach is determining block discretizations from coarse scale solution information that achieve the desired accuracy we describe several strategies for achieving this goal using adjoint based a posteriori error estimates and we demonstrate the behavior of the proposed algorithms as well as several technical issues in a set of examples

unstructured grid generation using iterative point insertion and local reconnection a procedure is presented for efficient generation of high quality two or three dimensional unstructured grids of triangular or tetrahedral elements the present procedure uses an iterative point creation and insertion scheme wherein points are created using advancing front type point placement initially the connectivity for these generated points is obtained by directly subdividing the elements which contain them without regard to quality this connectivity is then improved by iteratively using local reconnection subject to a quality criterion for two dimensions a min max criterion is used and for three dimensions a delaunay in sphere criterion followed by a min max type criterion is used the overall procedure is applied repetitively until a complete field grid is generated with a desired point distribution grid quality and performance statistics are presented for a variety of two and three dimensional configurations the combined quality and efficiency attributes of this procedure appear to be a substantial improvement over existing methods

convex decomposition of polyhedra and robustness this paper presents a simple algorithm to compute a convex decomposition of a nonconvex polyhedron of arbitrary genus handles and shells internal voids for such a polyhedron s with n edges and rnotches features causing nonconvexity in polyhedra the algorithm produces a worst case optimal o r 2 number of convex polyhedra s i with u i 1 k s i s in o nr 2 r 7 2 time and o nr r 5 2 space recently chazelle and palios have given a fast o n r 2 log r time and o n r 2 space algorithm to tetrahedralize a nonconvex polyhedron their algorithm however works for a simple polyhedron of genus zero and with no shells internal voids the algorithm presented here is based on the simple cut and split paradigm of chazelle with the help of zone theorems on arrangements it is shown that this cut and split method is quite efficient the algorithm is extended to work for a certain class of nonmanifold polyhedra also presented is an algorithm for the same problem

on countable bounded tightness for spaces cp x abstract it is well known that the space cp 0 1 has countable tightness but it is not frechet urysohn let x be a cech complete topological space we prove that the space cp x of continuous real valued functions on x endowed with the pointwise topology is frechet urysohn if and only if cp x has countable bounded tightness i e for every subset a of cp x and every x in the closure of a in cp x there exists a countable and bounding subset of a whose closure contains x we study also the problem when the weak topology of a locally convex space has countable bounded tightness additional results in this direction are provided

weak barrelledness for c x spaces abstract buchwalter and schmets reconciled cc x and cp x spaces with most of the weak barrelledness conditions of 1973 but could not determine if 0 barrelled l barrelled for cc x the areas grew apart full reconciliation with the fourteen conditions adopted by saxon and sanchez ruiz needs their 1997 characterization of ruess property l which allows us to reduce the cc x problem to its 1973 status and solve it by carefully translating the topology of kunen 1980 and van mill 1982 to find the example that eluded buchwalter and schmets the more tractable cp x readily partitions the conditions into just two equivalence classes the same as for metrizable locally convex spaces instead of the five required for cc x spaces our paper elicits others soon to appear that analytically characterize when the tychonov space x is pseudocompact or warner bounded or when cc x is a df space jarchow s 1981 question

tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions the input to the method consists of the boundary faces of the polyhedral region and possibly internal and hole interfaces plus the desired number of tetrahedra and other scalar parameters the region is decomposed into convex polyhedra in two stages so that tetrahedra of one length scale can be generated in each subregion a mesh distribution function which is either automatically constructed from the first stage convex polyhedron decomposition or supplied by the user is used to determine the tetrahedron sizes in the subregions then a boundary constrained triangulation is constructed in each convex polyhedron with local transformations being used to improve the quality of the tetahedra

a finite element formulation of compressible flows using various sets of independent variables abstract this paper presents a finite element method for the simulation of compressible flows the navier stokes and euler equations are solved in the conservation form using various sets of independent variables a variational formulation is developed based upon a variant of the petrov galerkin method and uses a shock capturing operator an adaptive algorithm based on a particular residual norm is proposed several numerical examples are presented to demonstrate the performances of each set of variables in solving compressible high speed flows

the advancing front mesh generation method revisited this paper presents a mesh generation method of the advancing front type which is designed in such a way that the well known difficulties of the classical advancing front method are not present the retained solution consists of using the first steps of a voronoi delaunay method to construct a background mesh which is then used to govern the algorithm the two dimensional case is considered in detail and possible extensions to adaption problems and three dimensions are indicated

surface mesh sizing control a method is presented for controlling element sizes on the interior of areas during surface meshing a delaunay background mesh is defined over which natural neighbour interpolation a neighbourhood based interpolation scheme is used to generate a sizing function the sizing function may be used to interpolate element sizes anisotropic stretching parameters or other surface characteristics required during meshing a brief description of natural neighbour interpolation is included and the sizing results obtained from this interpolation method are compared to those obtained using linear interpolation three specific applications are presented that utilize the sizing function namely boundary layer meshing surface curvature refinement and anisotropic mesh generation for these applications criteria used for augmenting the sizing function based on insertion of additional interior vertices into the background mesh are discussed copyright 2000 john wiley sons ltd

globally convergent algorithms for estimating generalized gamma distributions in fast signal and image processing many applications in real time signal image and video processing require automatic algorithms for rapid characterizations of signals and images through fast estimation of their underlying statistical distributions we present fast and globally convergent algorithms for estimating the three parameter generalized gamma distribution g gamma d the proposed method is based on novel scale independent shape estimation sise equations we show that the sise equations have a unique global root in their semi infinite domains and the probability that the sample sise equations have a unique global root tends to one the consistency of the global root its scale and index shape estimators is obtained furthermore we establish that with probability tending to one newton raphson nr algorithms for solving the sample sise equations converge globally to the unique root from any initial value in its given domain in contrast to existing methods another remarkable novelty is that the sample sise equations are completely independent of gamma and polygamma functions and involve only elementary mathematical operations making the algorithms well suited for real time both hardware and software implementations the sise estimators also allow the maximum likelihood ml ratio procedure to be carried out for testing the generalized gaussian distribution ggd versus the g gamma d finally the fast global convergence and accuracy of our algorithms for finite samples are demonstrated by both simulation studies and real image analysis

borel selectors for upper semi continuous multi valued functions on presente un theoreme de selection plus fin qui s applique dans plusieurs espaces de banach non separables

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

weakly k analytic spaces and the three space property for analyticity abstract let e e be a dual pair of vector spaces the paper studies general conditions which allow to lift analyticity or k analyticity from the weak topology e e to stronger ones in the frame of e e first we show that the mackey dual of a space c p x is analytic iff the space x is countable this yields that for uncountable analytic spaces x the mackey dual of c p x is weakly analytic but not analytic we show that the mackey dual e of an lf space of a sequence of reflexive separable frechet spaces with the heinrich density condition is analytic i e e is a continuous image of the polish space n n this extends a result of valdivia we show also that weakly quasi suslin locally convex baire spaces are metrizable and complete this extends a result of de wilde and sunyach we provide however a large class of weakly analytic but not analytic metrizable separable baire topological vector spaces not locally convex this will be used to prove that analyticity is not a three space property but we show that a metrizable topological vector space e is analytic if e contains a complete locally convex analytic subspace f such that the quotient e f is analytic several questions remarks and examples are included

adaptive remeshing for three dimensional compressible flow computations an adaptive mesh procedure for computing steady state solutions of the compressible euler equations in three dimensions is presented the method is an extension of previous work in two dimensions the approach requires the coupling of a surface triangulator an automatic tetrahedral mesh generator a finite element flow solver and an error estimation procedure an example involving flow at high mach number is included to demonstrate the numerical performance of the proposed approach the example shows that the use of this form of adaptivity in three dimensions offers the potential of even greater computational savings than those attained in the corresponding two dimensional implementation

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

on the method of logarithmic cumulants for parametric probability density function estimation parameter estimation of probability density functions is one of the major steps in the area of statistical image and signal processing in this paper we explore several properties and limitations of the recently proposed method of logarithmic cumulants molc parameter estimation approach which is an alternative to the classical maximum likelihood ml and method of moments mom approaches we derive the general sufficient condition for a strong consistency of the molc estimates which represents an important asymptotic property of any statistical estimator this result enables the demonstration of the strong consistency of molc estimates for a selection of widely used distribution families originating from but not restricted to synthetic aperture radar image processing we then derive the analytical conditions of applicability of molc to samples for the distribution families in our selection finally we conduct various synthetic and real data experiments to assess the comparative properties applicability and small sample performance of molc notably for the generalized gamma and k families of distributions supervised image classification experiments are considered for medical ultrasound and remote sensing sar imagery the obtained results suggest that molc is a feasible and computationally fast yet not universally applicable alternative to mom molc becomes especially useful when the direct ml approach turns out to be unfeasible

centroidal voronoi tessellation based finite element superconvergence in this article a finding on finite element superconvergence is reported the laplacian operator with dirichlet boundary condition is considered the linear finite element solutions have an o h2 0 5 superconvergence in l2 norm at nodes on an almost equilateral triangular mesh generated based on centroidal voronoi tessellation for an arbitrary 2d bounded domain extensive numerical examples are presented to demonstrate the superconvergence property copyright 2008 john wiley sons ltd

mackey ℵ0 barrelled spaces abstract in the context of reinventing weak barrelledness the best possible versions of the robertson saxon robertson splitting theorem and the saxon tweddle fit and flat components theorem are obtained by weakening the hypothesis from barrelled to mackey and 0 barreled an example showing that the latter does not imply the former validates novelty answers an old question and completes a robust linear picture of mackey weak barrelledness begun several decades ago

a normal offsetting technique for automatic mesh generation in three dimensions a technique based on a normal offsetting procedure for the fully automatic generation of meshes suitable for finite element analysis in three dimensions is presented the method is completely automatic requiring no user intervention in the process and no special modelling procedures the method is applied to three dimensional solid geometries the procedure positions nodes in the interior domain of an object by offsetting an initial set of nodes on the object boundary along vectors normal to the boundary to define a layer of new interior point locations the offset points are processed to ensure good nodal spacing appropriate for generating well shaped elements following processing the offset points become a new boundary surrounding the remaining unmeshed region in the interior of the geometric domain the offsetting procedure is applied again to this new boundary layer to form another offset layer farther into the domain interior the offset process offset cycle is repeated until the entire region is filled with nodes tetrahedral elements are then formed by triangulation of the nodes the boundary based technique ensures good quality element shapes for analysis in critical boundary regions and facilitates applications involving integration of mesh generation with design geometry databases calculation of nodal locations are based on local parameters avoiding the higher order time complexities associated with global calculations

metrizability of precompact subsets in lf spaces in this paper we prove that every precompact subset in any lf space has a metrizable completion as a consequence every lf space is angelic and in this way the answer to a question posed by k floret 3 is given some contributions to the general problem of regularity in inductive limits posed by k floret 3 are also given particularly extensions of well known results of h neuss and m valdivia are provided in the general setting of lf spaces it should also be noted that our results hold for inductive limits of an increasing sequence of metrizable spaces

sar amplitude probability density function estimation based on a generalized gaussian model in the context of remotely sensed data analysis an important problem is the development of accurate models for the statistics of the pixel intensities focusing on synthetic aperture radar sar data this modeling process turns out to be a crucial task for instance for classification or for denoising purposes in this paper an innovative parametric estimation methodology for sar amplitude data is proposed that adopts a generalized gaussian gg model for the complex sar backscattered signal a closed form expression for the corresponding amplitude probability density function pdf is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model specifically the recently proposed method of log cumulants molc is applied which stems from the adoption of the mellin transform instead of the usual fourier transform in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant for the developed gg based amplitude model the resulting molc estimates turn out to be numerically feasible and are also analytically proved to be consistent the proposed parametric approach was validated by using several real ers 1 xsar e sar and nasa jpl airborne sar images and the experimental results prove that the method models the amplitude pdf better than several previously proposed parametric models for backscattering phenomena

if cp x is strongly dominated by a second countable space then x is countable abstract we establish that a tychonoff space x is countable if and only if c p x is strongly dominated by a second countable space the same is true for a compact space k such that c p k 0 1 is strongly dominated by a second countable space we also prove that strong domination by a second countable space of the complement of the diagonal of a tychonoff space x implies that x is an 0 space our results solve several published open questions

maximum likelihood estimation of k distribution parameters via the expectation maximization algorithm maximum likelihood ml estimates of k distribution parameters are derived using the expectation maximization em approach this approach demonstrates the computational advantages compared with 2 d numerical maximization of the likelihood function using a nelder mead approach for large datasets the em approach yields more accurate estimates than those of a non ml estimation technique

non baire hyperplanes in non separable baire spaces abstract given an infinite dimensional banach space e one may ask does e have 1 a properly separable quotient 2 a dense non baire hyperplane every closed hyperplane in a baire space is baire the famous separable quotient problem 1 remains unsolved and question 2 is question 13 1 1 of p perez carreras and j bonet north holland math stud vol 131 north holland amsterdam 1987 in 1966 wilansky klee conjectured the answer to 2 is always no j arias de reyna denied the conjecture math ann 249 1980 111 114 proving the answer to 2 is yes whenever the answer to 1 is yes under assumption of c additivity c a a condition weaker than martin s axiom m valdivia extended the result to e a baire 2nd category in itself topological vector space collect math 34 1983 287 296 in general 2 is non trivial only in case e is baire with e e an extension of valdivia s extension yields the complete answer for 2 in the general locally convex setting affirming question 13 1 1 of perez carreras and bonet referenced above in particular a not necessarily hausdorff locally convex space e has a dense non baire hyperplane if and only if dim e and e e even for e non locally convex dim e and e e suffices but is not necessary whereas e e is obviously always necessary in order that e have a dense non baire hyperplane whether e e suffices in the hausdorff non locally convex case and whether the assumption of c a can be omitted we do not know contrastingly any infinite dimensional e is the union of a sequence of hyperplanes and if e is baire one of the hyperplanes must be dense and baire and every hyperplane of e must be unordered baire like if e is

tetrahedral meshes from planar cross sections in biomedicine many three dimensional 3d objects are sampled in terms of slices such as computed tomography ct magnetic resonance imaging mri and ultrasound imaging it is often necessary to construct surface meshes from the cross sections for visualization and thereafter construct tetrahedra for the solid bounded by the surface meshes for the purpose of finite element analysis in ref 1 c bajaj e coyle and k lin graphical models and image processing 58 6 1996 524 543 we provided a solution to the construction of a surface triangular mesh from planar section contours here we provide an approach to tetrahedralize the solid region bounded by planar contours and the surface mesh it is a difficult task because the solid can be of high genus several through holes as well as have complicated branching regions we develop an algorithm to effectively reduce the solid into prismatoids and provide an approach to tetrahedralize the prismatoids our tetrahedralization approach is similar to the advancing front technique aft for its flexible control of mesh quality the main criticism of aft is that the remaining interior may be badly shaped or even untetrahedralizable the emphasis of our prismatoid tetrahedralization approach is on the characterization and prevention of untetrahedralizable parts ruppert and seidel j ruppert r seidel on the difficulty of tetrahedralizing three dimensional non convex polyhedra in proceedings 5th annual acm symposium comput geom 1989 p 380 392 have shown that the problem of deciding whether a polyhedron is tetrahedralizable without adding steiner points is np complete we characterize this problem under certain constraints and design one rule to reduce the chance of generating untetrahedralizable shapes the characterization also leads to the classification of two common untetrahedralizable categories which can be better processed if they do occur

note on reflexivity of some spaces of continuous integer valued functions abstract given a topological group g we denote by g the group of characters on g and reflexivity of g means that the natural map from g to g is a topological isomorphism we show that for any zero dimensional realcompact k space x and a discrete finitely generated abelian group a the group a x of continuous maps from x to a with pointwise addition and compact open topology is reflexive and we construct a countable non reflexive closed subgroup of z x where x is a countable subspace of the plane this group embeds as a closed subgroup in many copies of the product z c of continuum of the discrete specker group we show also that for metrizable separable x analyticity of z x is equivalent to complete metrizability of x

quasi suslin weak duals abstract cascales kakol and saxon cks ushered kaplansky and valdivia into the grand setting of cascales orihuela spaces e by proving k if e is countably tight then so is the weak space e e e and v e e e is countably tight iff weak dual e e e is k analytic the ensuing flow of quasi suslin weak duals that are not k analytic a la valdivia s example continues here where we argue that locally convex spaces e with quasi suslin weak duals are k v s best setting largest by far optimal vis a vis valdivia the vaunted cks setting proves not larger in fact than kaplansky s we refine and exploit the quasi lb strong dual interplay

locally convex properties of free locally convex spaces abstract let l x be the free locally convex space over a tychonoff space x we show that the following assertions are equivalent i l x is l barrelled ii l x is l quasibarrelled iii l x is c 0 barrelled iv l x is 0 quasibarrelled and v x is a p space if x is a non discrete metrizable space then l x is c 0 quasibarrelled but it is neither c 0 barrelled nor l quasibarrelled we prove that l x is a d f space iff x is a countable discrete space we show that there is a countable tychonoff space x such that l x is a quasi d f space but is not a c 0 quasibarrelled space for each non metrizable compact space k the space l k is a d f space but is not a quasi d f space if x is a space then l x has the grothendieck property iff every compact subset of x is finite we show that l x has the dunford pettis property for every tychonoff space x if x is a sequential space and a space for example metrizable then l x has the sequential dunford pettis property iff x is discrete

compressible flowfield solutions with unstructured grids generated by delaunay triangulation a method is described that constructs three dimensional unstructured tetrahedral meshes using the delaunay triangulation criterion the approach includes an automatic point creation technique and ensures that given an initial surface triangulation which bounds a domain a valid boundary conforming assembly of tetrahedra is produced the efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities the grids generated are used with two finite element algorithms to simulate inviscid transonic compressible flows flow solutions for aerospace configurations are presented and computed results compared with experimental data

a method for estimating the parameters of the k distribution a method that combines the maximum likelihood and the method of moments for estimating the parameters of the k distribution is proposed the method results in the lowest variance of parameter estimates when compared with existing non ml techniques

a convexity result for the range of vector measures with applications to large economies on a boolean algebra we consider the topology u induced by a finitely additive measure mu with values in a locally convex space and formulate a condition on u that is sufficient to guarantee the convexity and weak compactness of the range of mu this result a la lyapunov extends those obtained in khan sagara 2013 to the finitely additive setting through a more direct and less involved proof we will then give an economical interpretation of the topology u in the framework of coalitional large economies to tackle the problem of measuring the bargaining power of coalitions when the commodity space is infinite dimensional and locally convex we will show that our condition on u plays the role of the many more agents than commodities condition introduced by rustichini and yannelis in 1991 as a consequence of the convexity theorem we will obtain two straight generalizations of schmeidler s and vind s theorems on the veto power of coalitions of arbitrary economic weight

efficient three dimensional delaunay triangulation with automatic point creation and imposed boundary constraints a method is described which constructs three dimensional unstructured tetrahedral meshes using the delaunay triangulation criterion several automatic point creation techniques will be highlighted and an algorithm will be presented which can ensure that given an initial surface triangulation which bounds a domain a valid boundary conforming assembly of tetrahedra will be produced statistics of measures of grid quality are presented for several grids the efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities

compact coverings for baire locally convex spaces very recently tkachuk has proved that for a completely regular hausdorff space x the space cp x of continuous real valued functions on x with the pointwise topology is metrizable complete and separable iff cp x is baire i e of the second baire category and is covered by a family k n n of compact sets such that k k if our general result which extends some results of de wilde sunyach and valdivia states that a locally convex space e is separable metrizable and complete iff e is baire and is covered by an ordered family k n n of relatively countably compact sets consequently every baire locally convex space which is quasi suslin is separable metrizable and complete

finite element euler computations in three dimensions an explicit finite element solution procedure for the three dimensional euler equations is presented the solution domain is automatically meshed using a tetrahedral mesh generator which is an extension of our previous two dimensional work several examples are included to illustrate the performance of the generator and solver an adaptive mesh regeneration procedure is used for the first time in three dimensions

generation of oriented three dimensional delaunay grids suitable for the control volume integration method a fully automatic algorithm for three dimensional mesh generation is presented the algorithm preserves the robustness and time efficiency of the finite octree technique replacing octrees by more general 2 4 8 trees it is capable of generating oriented meshes in a post processing step meshes are transformed in order to satisfy the delaunay criterion and so that non overlapping closed control volumes can be defined for each mesh point through edge bisectors the method is shown to be appropriate for modelling semiconductor devices where the control volume scheme is the method of choice due to the peculiarities of the partial differential equations involved and where locally refined and oriented meshes are essential to describe the relevant internal physical quantities adequately while keeping the number of mesh points practical

an automatic adaptive meshing technique for delaunay triangulations abstract a new algorithm is described for adaptivity of delaunay triangulations it distinguishes between regions of mesh according to whether they are to be refined unaltered or coarsened the method automatically identifies nodes of the mesh which are candidates for deletion for a region to be coarsened a node deletion process is proposed and it is proved that the resulting triangulation is delaunay after coarsening the mesh retains a high quality for two reasons the first is because a set of nodes have been used to obtain the coarse mesh which are equi distant apart in some sense defined by the original mesh the second is because the triangulation is delaunay the mesh refinement procedure sub divides elements into a number of similar elements in the regions to be refined two dimensional examples demonstrate the quality of the mesh after coarsening refinement

compactoid filters and usco maps the aim of this paper is to report in a short and self contained way on the properties of compactoid and countably compactoid filters we apply them to some questions in both topology and analysis such as the generation and extension of usco maps the study of some properties of k analytic spaces and the study of bounds for the weight of compact sets in spaces obtained through inductive operations

on structure of upper semicontinuity abstract the refinement of a choquet theorem on strong upper semi continuity and its relation to the vainstein lemma are dealt with here relevance of subcontinuity is discussed consequently an improvement of a characterization theorem of dolecki and rolewicz is achieved

a new parametric method of estimating the joint probability density revisited abstract we significantly extend alghalith 2017 in doing so we show that the joint probability density can be estimated without knowing any of the marginal densities or the conditional density moreover we provide a simpler superior alternative to copulas

compact nets filters and relations abstract the notion of compact filter is introduced and compared to related notions of compact nets and compact relations a characterization of compact nets is given in regular spaces several applications in optimization theory and nonlinear analysis are presented

incompressibility without tears how to avoid restrictions of mixed formulation the severe restrictions of the babuska brezzi stability criteria permit only a limited number of interpolations for velocities displacements and pressure to be used for incompressible behaviour these restrictions preclude the use of many useful elements we show in this paper how such difficulties can be side stepped by seeking the steady state solution through the use of various time marching schemes this permits a simple iterative approach to incompressible or nearly incompressible problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow etc

on a theorem of choquet and dolecki abstract the results of this paper clarify and extend slightly the previous work of dolecki and lechicki c r acad sci paris 293 1981 219 221 j math anal appl 88 1982 547 584 and hansell jayne rogers and the author math z 189 1985 297 318 let x y be hausdorff spaces and f x y an upper semicontinuous set valued map a subset k of f x is said to be a peak of f at x if for every open set v containing k there exists a neighbourhood u of x such that f u f x t v criteria choquet dolecki theorems are given in order that f has the smallest possible peak it turns out that in unexpectedly general situations an upper semicontinuous map f has for every x in x a peak which is the smallest possible at x and moreover compact

bounded tightness for locally convex spaces and spaces c x abstract we show that metrizability and bounded tightness are actually equivalent for a large class g of locally convex spaces including lf spaces df spaces the space of distributions d etc a consequence of this fact is that for x g the bounded tightness for the weak topology of x is equivalent to the following one x is linearly homeomorphic to a subspace of r n this nicely supplements very recent results of cascales and raja moreover we show that a metric space x is separable if the space cp x has bounded tightness

on weakly countably determined banach spaces for a topological space x let ci x denote the banach space of all bounded functions x r such that for every e 0 the set x x f x e is closed and discrete in x endowed with the supremum norm the main theorem is the following let l be a weakly countably determined subset of a banach space then there exist a subset e of the baire space e a compact space k and a bounded linear one to one operator t c l ci e x k that is pointwise to pointwise continuous in the case where l is weakly analytic e can be replaced by e this theorem is connected with the basic result of amir lindenstrauss on wcg banach spaces and has corresponding consequences such as the representation of gulko resp ta lagrand compact spaces as pointwise compact subsets of ci e x k resp ci e x k a compact space f is called gulko or talagrand compact if c o is wcd or a weakly k analytic banach space the characterization of wcd resp weakly k analytic banach spaces e using one to one operators from e into ci e x k resp ci e x k and the existence of equivalent good norms on e and e simultaneously

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner