partitions of a simplex leading to accurate spectral finite volume reconstruction in this paper we present several systematic techniques based on the voronoi diagram and its variants to partition a one and two dimensional simplex the fekete points are used as input to generate the voronoi diagram as they concentrate near the edges and are almost optimal for polynomial interpolation in a simplex spectral finite volume reconstructions on the resultant partitions have small lebesgue constants when using the dubiner basis the reconstruction matrix is well conditioned moreover the total number of edges of the partitions the total work when being used in spectral volume methods is shown to be at most twice the minimum number of edges of all partitions for reconstructions of the same order accuracy these suggest that the obtained partitions are well suited for spectral volume methods and other numerical methods which rely on reconstructions from cell averages

optimality approximation and complexity in set membership h sub spl infin identification investigates the set membership identification of time invariant discrete time exponentially stable possibly infinite dimensional linear systems from time or frequency domain data corrupted by deterministic noise the aim is to deliver not a single model but a set of models whose size in h sub spl infin norm measures the uncertainty in the identification the main focus of the note is on the optimality properties for finite data and on the tradeoff between optimality and complexity of approximated low order model sets a method is given for evaluating convergent and computationally efficient inner and outer approximations of the value set for a given frequency such approximations allow one to compute within any desired accuracy the identification error of any identified model and to evaluate an optimal model at any given number of frequencies by suitably approximating these values model sets with nominal models in rh sub spl infin are then derived whose order is selected by trading off between model set complexity and identification accuracy degradation this degradation is evaluated by computing the optimality level defined as the ratio between the reduced model identification error and the optimal one a numerical example demonstrates the effectiveness of the presented results

free vibrations of solid and hollow wedge beams with rectangular or circular cross sections and carrying any number of point masses summary since the literature relating to the natural frequencies and mode shapes of the double tapered wedge beams carrying multiple point masses is rare the object of this paper is to present some information in this aspect first of all the closed form solutions in terms of the bessel functions for the natural frequencies and normal mode shapes of the bare wedge beams without carrying any point masses were determined next the partial differential equation of motion for the loading wedge beams carrying any number of point masses were transformed into the matrix equation by using the expansion theorem and the foregoing natural frequencies and normal mode shapes of the bare wedge beam finally the eigenvalue equation associated with the last matrix equation was solved to give the natural frequencies and the mode shapes of the loading wedge beams the formulation of this paper is available for the solid and hollow wedge beams with square rectangular or circular cross sections in other words the taper ratio for the width and that for the depth may be equal or unequal all the numerical results were compared with the existing literature or the conventional finite element method results and good agreement was achieved copyright 2004 john wiley sons ltd

bending vibrations of wedge beams with any number of point masses abstract the natural frequencies and mode shapes of beams with constant width and linearly tapered depth or thickness carrying any number of point masses at arbitrary positions along the length of the beams were investigated using the euler bernoulli equation use of the closed form exact solutions for the natural frequencies and mode shapes of the unconstrained single tapered beam without carrying any point masses and incorporation of the expansion theorem the equation of motion for the associated constrained beam carrying any point masses were derived solution of the last equation will yield the desired natural frequencies and mode shapes of the constrained single tapered beam the bending vibrations of a single tapered beam with six kinds of boundary conditions were investigated comparison with the existing literature or the traditional finite element method results reveals that the adopted approach has excellent accuracy and simple algorithm

a variational formula for the free energy of an interacting many particle system we consider n bosons in a box in r d with volume n rho under the influence of a mutually repellent pair potential the particle density p is an element of 0 infinity is kept fixed our main result is the identification of the limiting free energy f beta p at positive temperature 1 beta in terms of an explicit variational formula for any fixed rho if beta is sufficiently small and for any fixed beta if rho is sufficiently small the thermodynamic equilibrium is described by the symmetrized trace of e beta h n where h n denotes the corresponding hamilton operator the well known feynman kac formula reformulates this trace in terms of n interacting brownian bridges due to the symmetrization the bridges are organized in an ensemble of cycles of various lengths the novelty of our approach is a description in terms of a marked poisson point process whose marks are the cycles this allows for an asymptotic analysis of the system via a large deviations analysis of the stationary empirical field the resulting variational formula ranges over random shift invariant marked point fields and optimizes the sum of the interaction and the relative entropy with respect to the reference process in our proof of the lower bound for the free energy we drop all interaction involving infinitely long cycles and their possible presence is signalled by a loss of mass of the finitely long cycles in the variational formula in the proof of the upper bound we only keep the mass on the finitely long cycles we expect that the precise relationship between these two bounds lies at the heart of bose einstein condensation and intend to analyze it further in future

analogues of non gibbsianness in joint measures of disordered mean field models it is known that the joint measures on the product of spin space and disorder space are very often non gibbsian measures for lattice systems with quenched disorder at low temperature are there reflections of this non gibbsianness in the corresponding mean field models we study the continuity properties of the conditional probabilities in finite volume of the following mean field models a joint measures of random field ising b joint measures of dilute ising c decimation of ferromagnetic ising the conditional probabilities are functions of the empirical mean of the conditionings so we look at the large volume behavior of these functions to discover non trivial limiting objects for a we find 1 discontinuous dependence for almost any realization and 2 dependence of the conditional probabilities on the phase in contrast to that we see continuous behavior for b and c for almost any realization this is in complete analogy to the behavior of the corresponding lattice models in high dimensions it shows that non gibbsian behavior which seems a genuine lattice phenomenon can be partially understood already on the level of mean field models

space time tradeoffs for emptiness queries we develop the first nontrivial lower bounds on the complexity of online hyperplane and halfspace emptiness queries our lower bounds apply to a general class of geometric range query data structures called partition graphs informally a partition graph is a directed acyclic graph that describes a recursive decomposition of space we show that any partition graph that supports hyperplane emptiness queries implicitly defines a halfspace range query data structure in the fredman yao semigroup arithmetic model with the same asymptotic space and time bounds thus results of bronnimann chazelle and pach imply that any partition graph of size s that supports hyperplane emptiness queries in time t satisfies the inequality st d omega n log n d d 1 d 1 using different techniques we improve previous lower bounds for hopcroft s problem given a set of points and hyperplanes does any hyperplane contain a point in dimensions four and higher using this offline result we show that for online hyperplane emptiness queries omega n d mbox polylog n space is required to achieve polylogarithmic query time and omega n d 1 d mbox polylog n query time is required if only o n polylog n space is available these two lower bounds are optimal up to polylogarithmic factors for two dimensional queries we obtain an optimal continuous tradeoff st 2 omega n 2 between these two extremes finally using a lifting argument we show that the same lower bounds hold for both offline and online halfspace emptiness queries in mathbb r d d 3 2

the equivalence of ensembles for classical systems of particles for systems of particles in classical phase space with standard hamiltonian we consider spatially averaged microcanonical gibbs distributions in finite boxes we show that infinite volume limits along suitable subsequences exist and are grand canonical gibbs measures on the way we establish a variational formula for the thermodynamic entropy density as well as a variational characterization of grand canonical gibbs measures

a new approach for free vibration of axially functionally graded beams with non uniform cross section this paper studies free vibration of axially functionally graded beams with non uniform cross section a novel and simple approach is presented to solve natural frequencies of free vibration of beams with variable flexural rigidity and mass density for various end supports including simply supported clamped and free ends we transform the governing equation with varying coefficients to fredholm integral equations natural frequencies can be determined by requiring that the resulting fredholm integral equation has a non trivial solution our method has fast convergence and obtained numerical results have high accuracy the effectiveness of the method is confirmed by comparing numerical results with those available for tapered beams of linearly variable width or depth and graded beams of special polynomial non homogeneity moreover fundamental frequencies of a graded beam combined of aluminum and zirconia as two constituent phases under typical end supports are evaluated for axially varying material properties the effects of the geometrical and gradient parameters are elucidated the present results are of benefit to optimum design of non homogeneous tapered beam structures

quenched asymptotics of the ground state energy of random schrodinger operators with scaled gibbsian potentials this article describes the almost sure infinite volume asymptotics of the ground state energy of random schrodinger operators with scaled gibbsian potentials the random potential is obtained by distributing soft obstacles according to an infinite volume grand canonical tempered gibbs measure with a superstable pair interaction there is no restriction on the strength of the pair interaction it may be taken e g at a critical point the potential is scaled with the box size in a critical way i e the scale is determined by the typical size of large deviations in the gibbsian cloud the almost sure infinite volume asymptotics of the ground state energy is described in terms of two equivalent deterministic variational principles involving only thermodynamic quantities the qualitative behaviour of the ground state energy asymptotics is analysed depending on the dimension and on the holder exponents of the free energy density it is identified which cases lead to a phase transition of the asymptotic behaviour of the ground state energy

relative entropy and variational properties of generalized gibbsian measures we study the relative entropy density for generalized gibbs measures we first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of almost gibbsian measures almost sure continuity of conditional probabilities for quasilocal measures we obtain a full variational principle for the joint measures of the random field ising model we show that the weak gibbs property holds with an almost surely rapidly decaying translation invariant potential for these measures we show that the variational principle fails as soon as the measures lose the almost gibbs property these examples suggest that the class of weakly gibbsian measures is too broad from the perspective of a reasonable thermodynamic formalism

reweighting to achieve elliptically contoured covariates in regression abstract we investigate a method of constructing weights to induce elliptically contoured covariates in regression analyses much recent work in regression has identified various data analytic and model robustness advantages associated with such covariates in particular new estimation methods like sir sirii save and phd have been built around the assumption of elliptically contoured covariates finite samples of regression covariates may deviate from this ideal in practice and the method developed here termed voronoi weighting can be used to induce elliptical symmetry in such samples in a number of examples we show that reweighting cases by the voronoi method can substantially enhance various procedures for covariates that deviate from elliptical symmetry we show that voronoi weighting in conjunction with some trimming via the minimum volume ellipsoid method can be effective

existence of gibbsian point processes with geometry dependent interactions we establish the existence of stationary gibbsian point processes for interactions that act on hyperedges between the points for example such interactions can depend on delaunay edges or triangles cliques of voronoi cells or clusters of k nearest neighbors the classical case of pair interactions is also included the basic tools are an entropy bound and stationarity

r local delaunay inhibition model unlike in the classical framework of gibbs point processes usually acting on the complete graph in the context of nearest neighbour gibbs point processes the nonnegativeness of the interaction functions do not ensure the local stability property this paper introduces domain wise but not pointwise inhibition stationary gibbs models based on some tailor made delaunay subgraphs all of them are subgraphs of the r local delaunay graph defined as the delaunay subgraph specifically not containing the edges of delaunay triangles with circumscribed circles of radii greater than some large positive real value r the usual relative compactness criterion for point processes needed for the existence result is directly derived from the ruelle bound of the correlation functions furthermore assuming only the nonnegativeness of the energy function we have managed to prove the existence of the existence of r local delaunay stationary gibbs states based on nonnegative interaction functions thanks to the use of the compactness of sublevel sets of the relative entropy

hydrodynamical limit for a hamiltonian system with weak noise starting from a general hamiltonian system with superstable pairwise potential we construct a stochastic dynamics by adding a noise term which exchanges the momenta of nearby particles we prolve that in the scaling limit the time conserved quantities energy momenta and density satisfy the euler equation of conservation laws up to a fixed timet provided that the euler equation has a smooth solution with a given initial data up to timet the strength of the noise term is chosen to be very small but nonvanishing so that it disappears in the scaling limit

computing connectedness disconnectedness and discreteness we consider finite point set approximations of a manifold or fractal with the goal of determining topological properties of the underlying set we use the minimal spanning tree of the finite set of points to compute the number and size of its connected components by extrapolating the limiting behavior of these quantities as 0 we can say whether the underlying set appears to be connected totally disconnected or perfect we demonstrate the effectiveness of our techniques for a number of examples including a family of fractals related to the sierpinski triangle cantor subsets of the plane the henon attractor and cantori from four dimensional symplectic sawtooth maps for zero measure cantor sets we conjecture that the growth rate of the number of components as 0 is equivalent to the box counting dimension 2000 elsevier science b v all rights reserved

discrete voronoi diagrams and the skiz operator a dynamic algorithm the voronoi diagram vd is a popular tool for partitioning the support of an image an algorithm is presented for constructing vd when the seed set which determines the voronoi regions can be modified by adding and removing seeds the number of pixels and seeds revisited for updating the diagram and the neighbor relationships among seeds is minimized a result on cocircular seeds is presented the adjacency or dual graph of the vd is readily obtained the use of the algorithm for constructing skeletons by influence zones skiz is demonstrated

polygon based contact resolution for superquadrics the representation of discrete objects in the discrete element modelling is a fundamental issue which has a direct impact on the efficiency of discrete element implementation and the dynamic behaviour of particulate systems disks and spheres are the most commonly used geometric shapes due to their geometric simplicity and computational efficiency but they are unable to provide resistance to rolling motion for this reason some non circular spherical objects such as polygons polyhedrons superquadrics or the clustering of disks spheres to form irregular shapes are introduced when superquadrics are used as discrete elements the bottleneck of contact resolution is associated with the searching for intersections of two non linear functions which is a very expensive operation and may sometimes fail in finding the solution in this work an efficient and robust algorithm is proposed for contact resolution of 2d superquadrics in which any superquadric is approximated with a convex polygon through adaptive sampling then by clipping two polygons an efficient linear algorithm is performed to search for intersections and overlap area of the polygons the contact forces and directions are determined by employing a newly established corner corner contact model it is important to highlight that the proposed methodology can also be extended to general non circular discrete object cases the performance of the algorithm is demonstrated via numerical examples copyright 2005 john wiley sons ltd

weakly gibbsian measures and quasilocality a long range pair interaction counterexample we exhibit an example of a measure on a discrete and finite spin system whose conditional probabilities are given in terms of an almost everywhere absolutely summable potential but are discontinuous almost everywhere

generators extremals and bases of max cones abstract max cones are max algebraic analogs of convex cones in the present paper we develop a theory of generating sets and extremals of max cones in r n this theory is based on the observation that extremals are minimal elements of max cones under suitable scalings of vectors we give new proofs of existing results suitably generalizing restating and refining them of these it is important that any set of generators may be partitioned into the set of extremals and the set of redundant elements we include results on properties of open and closed cones on properties of totally dependent sets and on computational bounds for the problem of finding the essentially unique basis of a finitely generated cone

linearization and completeness results for terminating transitive closure queries on spatial databases we study queries to spatial databases where spatial data are modeled as semi algebraic sets using the relational calculus with polynomial inequalities as a basic query language we work with the extension of the relational calculus with terminating transitive closures the main result is that this language can express the linearization of semialgebraic databases we also show that the sublanguage with linear inequalities only can express all computable queries on semilinear databases as a consequence of these results we obtain a completeness result for topological queries on semialgebraic databases

complete equivalence of the gibbs ensembles for one dimensional markov systems we show the equivalence of the gibbs ensembles at the level of measures for one dimensional markov systems with arbitrary boundary conditions that is the limit of the microcanonical gibbs ensemble is a gibbs measure with an interaction depending on the microcanonical constraint in fact the usual microcanonical condition is replaced by the sharper constraint that all type frequencies of neighboring spins including the boundary spins are fixed when conditioning on a set of different frequencies of neighboring spins compatible with physical quantities like energy density we get the usual microcanonical ensemble we show that the limit is a gibbs measure for a nearest neighbor potential depending on the pair measure which maximizes the entropy on the given set of pair measures for this we show the large deviation property of the pair empirical measure for arbitrary boundary conditions we establish analogous results for finite range potentials

an optimal algorithm for intersecting line segments in the plane the main contribution of this work is an o n log n k time algorithm for computing all k intersections among n line segments in the plane this time complexity is easily shown to be optimal within the same asymptotic cost our algorithm can also construct the subdivision of the plane defined by the segments and compute which segment if any lies right above or below each intersection and each endpoint the algorithm has been implemented and performs very well the storage requirement is on the order of n k in the worst case but it is considerably lower in practice to analyze the complexity of the algorithm an amortization argument based on a new combinatorial theorem on line arrangements is used

non gibbsian states and their gibbs description the driving principle behind this paper is the following thesis every physically reasonable random field has to be a gibbs random field in this paper the so called non gibbsian random fields are considered the usual definition of the gibbs field is generalized in such a way so as to include some of the discovered non gibbsian fields the new definition is then used to show that the projection of the two dimensional ising model onto the one dimensional sublattice 1 falls into the class of the generalized gibbs fields

uniqueness of one dimensional continuum gibbs states we investigate one dimensional continuum grandcanonical gibbs states corresponding to finite range superstable many body potentials absence of phase transitions in the sense of uniqueness of the tempered gibbs state is proved for potentials without hard core by first proving uniqueness of the gibbs measures for related hard core potentials and then taking an appropriate limit of those gibbs measures

an optimal parallel algorithm for the visibility of a simple polygon from a point we present a parallel algorithm for computing the visible portion of a simple polygonal chain with 7i vertices from a point in the plane the algorithm runs in o logn time using 0 nf log n processors in the crew pram computational model and hence is asymptotically optimal

large deviations and the maximum entropy principle for marked point random fields we establish large deviation principles for the stationary and the individual empirical fields of poisson and certain interacting random fields of marked point particles in d the underlying topologies are induced by a class of not necessarily bounded local functions and thus finer than the usual weak topologies our methods yield further that the limiting behaviour of conditional poisson distributions as well as certain distributions of gibbsian type is governed by the maximum entropy principle we also discuss various applications and examples

time discretized variational formulation of non smooth frictional contact the present work extends the non smooth contact class of algorithms introduced by kane et al to the case of friction the formulation specifically addresses contact geometries e g involving multiple collisions between tightly packed non smooth bodies for which neither normals nor gap functions can be properly defined a key aspect of the approach is that the incremental displacements follow from a minimum principle the objective function comprises terms which account for inertia strain energy contact friction and external forcing the euler lagrange equations corresponding to this extended variational principle are shown to be consistent with the equations of motion of solids in frictional contact in addition to its value as a basis for formulating numerical algorithms the variational framework offers theoretical advantages as regards the selection of trajectories in cases of non uniqueness we present numerical and analytical examples which demonstrate the good momentum and energy conservation characteristics of the numerical algorithms as well as the ability of the approach to account for stick and slip conditions

esflib a library to compute the element free galerkin shape functions we present a library for the computation of the shape functions for the element free galerkin efg method while the efg method is in many respects strikingly similar to the nite element method the construction of the shape functions for the efg method is much more complicated than in the fem thus the question arises whether it is possible to encapsulate the complexity of the shape function construction process while providing a simple interface to the shape function data we present a shape function library design which proved unrestrictive it can be used with almost any programming language without any special requirements on application program data structures highly congurable and robust

almost gibbsianness and parsimonious description of the decimated 2d ising model in this paper we complete and provide details for the existing characterizations of the decimation of the ising model on mathbb z 2 in the generalized gibbs context we first recall a few features of the dobrushin program of restoration of gibbsianness and present the construction of global specifications consistent with the extremal decimated measures we use them to prove that these renormalized measures are almost gibbsian at any temperature and to analyse in detail its convex set of dlr measures we also recall the weakly gibbsian description and complete it using a potential that admits a quenched correlation decay i e a well defined configuration dependent length beyond which this potential decays exponentially we use these results to incorporate these decimated measures in the new framework of parsimonious random fields that has been recently developed to investigate probability aspects related to neurosciences

large deviations and the equivalence of ensembles for gibbsian particle systems with superstable interaction for gibbsian systems of particles inr d we investigate large deviations of the translation invariant empirical fields in increasing boxes the particle interaction is given by a superstable regular pair potential the large deviation principle is established for systems with free or periodic boundary conditions and under a stronger stability hypothesis on the potential for systems with tempered boundary conditions and for tempered infinite volume gibbs measures as a by product we obtain the gibbs variational formula for the pressure we also prove the asymptotic equivalence of microcanonical and grand canonical gibbs distributions and establish a variational expression for the thermodynamic entropy density

positivity of the self diffusion matrix of interacting brownian particles with hard core we prove the positivity of the self diffusion matrix of interacting brownian particles with hard core when the dimension of the space is greater than or equal to 2 here the self diffusion matrix is a coefficient matrix of the diffusive limit of a tagged particle we will do this for all activities z 0 of gibbs measures in particular for large z the case of high density particles a typical example of such a particle system is an infinite amount of hard core brownian balls

gibbs delaunay tessellations with geometric hardcore conditions in this paper we prove the existence of infinite gibbs delaunay tessellations on 2 the interaction depends on the local geometry of the tessellation we introduce a geometric hardcore condition on small and large cells consequently we can construct more regular infinite random delaunay tessellations

phase transitions for dilute particle systems with lennard jones potential we consider a classical dilute particle system in a large box with pair interaction given by a lennard jones type potential the inverse temperature is picked proportionally to the logarithm of the particle density we identify the free energy per particle in terms of a variational formula and show that this formula exhibits a cascade of phase transitions as the temperature parameter ranges from zero to infinity loosely speaking the particle system separates into spatially distant components in such a way that within each phase all components are of the same size which is the larger the lower the temperature the main tool in our proof is a new large deviation principle for sparse point configurations

nonlinear flexural response of a slender cantilever beam of constant thickness and linearly varying width to a primary resonance excitation abstract despite the shear amount of research studies on nonlinear flexural dynamics of cantilever beams very few efforts address the practical geometry involving a constant thickness and linearly varying width this stems from the nature of the associated linear eigenvalue problem which cannot be easily solved in closed form in this paper we present a closed form solution to this particular linear eigenvalue problem in the form of a general meijer g differential equation for which a solution is readily available in the shape of the meijer g functions using this approach the exact linear modal frequencies and shapes are obtained and used in the discretization of the nonlinear partial differential equation describing the dynamics of the system the discretized system of ordinary differential equations is then solved using the method of multiple scales to obtain an approximate analytical solution describing the primary resonance behavior of a given vibration mode an analytical expression for the modal effective nonlinearity is obtained and used to analyze the influence of the beam s tapering on the nonlinear primary resonance behavior of the response softening hardening results are then compared to a finite element fe solution of the linear eigenvalue problem in which the modal shapes obtained using the fe method are fit into a set of orthogonal polynomial functions and used to discretize the nonlinear problem it is shown that while the modal frequencies obtained using the fe method approximate those obtained analytically with negligible error less than 1 there is a substantial error in the resulting estimates of the modal effective nonlinearity this indicates that even negligible errors in the approximate solution of the linear problem can propagate to become significant when analyzing the nonlinear problem further reinforcing the importance of the exact solution

the hamiltonian properties of supergrid graphs in this paper we first introduce a novel class of graphs namely supergrid supergrid graphs include grid graphs and triangular grid graphs as their subgraphs the hamiltonian cycle and path problems for grid graphs and triangular grid graphs were known to be np complete however they are unknown for supergrid graphs the hamiltonian cycle path problem on supergrid graphs can be applied to control the stitching traces of computerized sewing machines in this paper we will prove that the hamiltonian cycle problem for supergrid graphs is np complete it is easily derived from the hamiltonian cycle result that the hamiltonian path problem on supergrid graphs is also np complete we then show that two subclasses of supergrid graphs including rectangular parallelism and alphabet always contain hamiltonian cycles

variational principle for some renormalized measures we show that some measures suffering from the so called renormalization group pathologies satisfy a variational principle and that the corresponding limit of the pressure with boundary conditions in a set of measure 1 is equal to the pressure of the ising model module a scale factor

computing farthest neighbors on a convex polytope let n be a set of n points in convex position in r3 the farthest point voronoi diagram of n partitions r3 into n convex cells we consider the intersection g n of the diagram with the boundary of the convex hull of n we give an algorithm that computes an implicit representation of g n in expected o n log2 n time more precisely we compute the combinatorial structure of g n the coordinates of its vertices and the equation of the plane defining each edge of g n the algorithm allows us to solve the all pairs farthest neighbor problem for n in expected time o n log2 n and to perform farthest neighbor queries on n in o log2 n time with high probability

icp registration using invariant features investigates the use of euclidean invariant features in a generalization of iterative closest point icp registration of range images pointwise correspondences are chosen as the closest point with respect to a weighted linear combination of positional and feature distances it is shown that under ideal noise free conditions correspondences formed using this distance function are correct more often than correspondences formed using the positional distance alone in addition monotonic convergence to at least a local minimum is shown to hold for this method when noise is present a method that automatically sets the optimal relative contribution of features and positions is described this method trades off the error in feature values due to noise against the error in positions due to misalignment experimental results suggest that using invariant features decreases the probability of being trapped in a local minimum and may be an effective solution for difficult range image registration problems where the scene is very small compared to the model

global specifications and nonquasilocality of projections of gibbs measures reference gr pf article 1997 001doi 10 1214 aop 1024404514view record in web of science record created on 2008 11 27 modified on 2017 05 12

on the analysis of laterally vibrating slender beams subject to various complicating effects the rayleigh ritz method with orthogonally generated polynomials as admissible functions is used to obtain a simple analysis of the free vibration problem of slender beams subject to various complicating effects these effects are the presence of concentrated masses and or concentrated moments of inertia intermediate supports axial loading and non uniformity of cross section such may exist separately or in any combination numerical results are presented for several example beams illustrating the accuracy and versatility of the approach

existence of delaunay pairwise gibbs point process with superstable component the present stuffy deals with the existence of delaunay pairwise gibbs point process with superstable component by using the well known preston theorem in particular we prove the stability the lower regularity and the quasilocality properties of the delaunay model

variational principle and almost quasilocality for renormalized measures we study the variational principle for some non gibbsian measures we give a necessary and sufficient condition for the validity of the implication zero relative entropy density implies common version of conditional probabilities so called second part of the variational principle applying this to noisy decimations of the low temperature phases of the ising model we obtain almost sure quasilocality for these measures and the second part of the variational principle for the projection of low temperature ising phases on a one dimensional layer we also obtain the second part of the variational principle

the restriction of the ising model to a layer we discuss the status of recent gibbsian descriptions of the restriction projection of the ising phases to a layer we concentrate on the projection of the two dimensional low temperature ising phases for which we prove a variational principle

optimal separable algorithms to compute the reverse euclidean distance transformation and discrete medial axis in arbitrary dimension in binary images the distance transformation dt and the geometrical skeleton extraction are classic tools for shape analysis in this paper we present time optimal algorithms to solve the reverse euclidean distance transformation and the reversible medial axis extraction problems for d dimensional images we also present a d dimensional medial axis filtering process that allows us to control the quality of the reconstructed shape

projections of gibbs measures may be non gibbsian consider the phase of the two dimensional nearest neighbor ferromagnetic ising model at a temperature belowt c let be the restriction of this measure to a coordinate axis we prove that there is no one dimensional translation invariant summable interaction for which is a gibbs measure this is proven by showing that if such an interaction existed would have large deviation properties different from those it actually has percolation methods are used in the proof

structure of a simple scheduling polyhedron in a one machine nonpreemptive scheduling problem the feasible schedules may be defined by the vector of the corresponding job completion times for given positive processing times the associated simple scheduling polyhedronp is the convex hull of these feasible completion time vectors the main result of this paper is a complete description of the minimal linear system definingp we also give a complete combinatorial description of the face lattice ofp and a simple o n logn separation algorithm this algorithm has potential usefulness in cutting plane type algorithms for more difficult scheduling problems

large deviations and maximum entropy principle for interacting random fields on mathbb z d we present a new approach to the principle of large deviations for the empirical field of a gibbsian random field on the integer lattice zd this approach has two main features first we can replace the traditional weak topology by the finer topology of convergence of cylinder probabilities and thus obtain estimates which are finer and more widely applicable second we obtain as an immediate consequence a limit theorem for conditional distributions under conditions on the empirical field the limits being those predicted by the maximum entropy principle this result implies a general version of the equivalence of gibbs ensembles stating that every microcanonical limiting state is a grand canonical equilibrium state we also prove a converse to the last statement and discuss some applications 0 introduction as is well known the study of the asymptotic probabilities of large fluctuations of time averages or space averages away from the mean is based on two fundamental principles the principle of large deviations and the maximum entropy principle the former provides the exact rate of exponential decay of the fluctuation probabilities whereas the latter predicts the limiting conditional distribution under the condition that the fluctuations are large it is obvious that these principles are intimately related in this paper we investigate these principles in the case of interacting random fields on the integer lattice 7zd the setup is the following first we let e 4 be any measurable space we shall assume throughout that e a is standard borel but we shall avoid making any explicit topological assumptions on e so we do not assume that e is polish next we let s zd be the d dimensional integer lattice and q f e gas the associated product space in lattice models of statistical mechanics e is called the state space or single spin space and q f the configuration space we let j s f denote the set of all probability

surface bounded growth modeling applied to human mandibles from a set of longitudinal three dimensional scans of the same anatomical structure the authors have accurately modeled the temporal shape and size changes using a linear shape model on a total of 31 computed tomography scans of the mandible from six patients 14 851 semilandmarks are found automatically using shape features and a new algorithm called geometry constrained diffusion the semilandmarks are mapped into procrustes space principal component analysis extracts a one dimensional subspace which is used to construct a linear growth model the worst case mean modeling error in a cross validation study is 3 7 mm

voronoi diagram and medial axis algorithm for planar domains with curved boundaries i theoretical foundations in this first installment of a two part paper the underlying theory for an algorithm that computes the voronoi diagram and medial axis of a planar domain bounded by free form polynomial or rational curve segments is presented an incremental approach to computing the voronoi diagram is used wherein a single boundary segment is added to an existing boundary segment set at each step the introduction of each new segment entails modifying the voronoi regions of the existing boundary segments and constructing the voronoi region of the new segment we accomplish this by i computing the bisector of the new segment with each of the current boundary segments ii updating the voronoi regions of the current boundary segments by partitioning them with these bisectors and iii constructing the voronoi region of the new segment as a union of regions obtained from the partitioning in ii when all boundary segments are included and their voronoi regions have been constructed the voronoi diagram of the boundary is obtained as the union of the voronoi polygons for each boundary segment to construct the medial axis of a planar domain we first compute the voronoi diagram of its boundary the medial axis is then obtained from the voronoi diagram by i removing certain edges of the voronoi diagram that do not belong to the medial axis and ii adding certain edges that do belong to the medial axis but are absent from the voronoi diagram unambiguous characterizations for edges in both these categories are given details of algorithms based on this theory are deferred to the second installment of this two part paper

convergence of grand canonical gibbs measures we prove existence of gibbs states for a large class of continuum many body potentials through a limit process of hard core approximations to the potential dobrushin uniqueness techniques 1 for the decay of correlations are then extended to a very general class of continuum potentials

phase transition in the nearest neighbor continuum potts model in the present study we establish a phase transition in the nearest neighbor continuum potts model the repulsion between particles of different type acts only on a nearest neighbor graph more precisely a subgraph of the delaunay graph this work is an adaptation of the lebowitz and lieb soft core continuum potts model

computational geometry an introduction from the reviews this book offers a coherent treatment at the graduate textbook level of the field that has come to be known in the last decade or so as computational geometry the book is well organized and lucidly written a timely contribution by two founders of the field it clearly demonstrates that computational geometry in the plane is now a fairly well understood branch of computer science and mathematics it also points the way to the solution of the more challenging problems in dimensions higher than two

geometric classification of triangulations and their enumeration in a convex polygon abstract triangulation of polygons is a classical problem in computational geometry for an arbitrary polygon the triangulation may depend on its shape in this paper we describe a new geometric classification of triangulations of a convex polygon and then derive expressions for counting the number of nonisomorphic triangulations in each class

vibration of an euler bernoulli beam of constant depth and with linearly varying breadth abstract the transverse vibration of a homogeneous euler bernoulli beam of constant depth and linearly varying breadth is investigated in this paper a direct analytical solution is presented for the mode shape equation the constraints imposed by the boundary conditions yield the frequency equation the four ideal boundary conditions considered are clamped pinned sliding and free for a complete beam sharp ended it is a necessary condition that the sharp end remain free and as a result the frequency equations for clamped pinned sliding or free boundary conditions at the large end are the determinant of a 2 2 matrix equated to zero a truncated beam is considered as part of a hypothetical complete beam the frequency equation for truncated beam is the determinant of a 4 4 matrix equated to zero the roots of the frequency equations are determined by an iterative procedure the first four natural frequencies of complete beam and the first three frequencies of truncated beams for 16 combinations of the ideal boundary conditions for various truncation factors are presented the results are benchmarks and are therefore presented in tabular form to preserve the accuracy to six figures

the multipoint morisita index for the analysis of spatial patterns abstract in many fields the spatial clustering of sampled data points has significant consequences therefore several indices have been proposed to assess the degree of clustering affecting datasets e g the morisita index ripley s k function and renyi s information the classical morisita index measures how many times it is more likely to randomly select two sampled points from the same quadrat the dataset is covered by a regular grid of changing size than it would be in the case of a random distribution generated from a poisson process the multipoint version takes into account m points with m 2 the present research deals with a new development of the multipoint morisita index m morisita which is directly related to multifractality this relationship to multifractality is first demonstrated and highlighted on a mathematical multifractal set then the new version of the m morisita index is adapted to the characterization of environmental monitoring network clustering and finally an additional extension the functional m morisita index is presented for the detection of structures in monitored phenomena

reduction of bivariate polynomials from convex dense to dense with application to factorizations in this article we present a new algorithm for reducing the usual sparse bivariate factorization problems to the dense case this reduction simply consists in computing an invertible monomial transformation that produces a polynomial with a dense size of the same order of magnitude as the size of the integral convex hull of the support of the input polynomial this approach turns out to be very efficient in practice as demonstrated with our implementation

consistency of likelihood estimation for gibbs point processes strong consistency of the maximum likelihood estimator mle for parametric gibbs point process models is established the setting is very general it includes pairwise pair potentials finite and infinite multibody interactions and geometrical interactions where the range can be finite or infinite the gibbs interaction may depend linearly or non linearly on the parameters a particular case being hardcore parameters and interaction range parameters as important examples we deduce the consistency of the mle for all parameters of the strauss model the hardcore strauss model the lennard jones model and the area interaction model

optimal expected case planar point location point location is the problem of preprocessing a planar polygonal subdivision s of size n into a data structure in order to determine efficiently the cell of the subdivision that contains a given query point we consider this problem from the perspective of expected query time we are given the probabilities p z that the query point lies within each cell z in s the entropy h of the resulting discrete probability distribution is the dominant term in the lower bound on the expected case query time we show that it is possible to achieve query time h o sqrt h 1 with space o n which is optimal up to lower order terms in the query time we extend this result to subdivisions with convex cells assuming a uniform query distribution within each cell in order to achieve space efficiency we introduce the concept of entropy preserving cuttings

phase transition in continuum potts models we establish phase transitions for a class of continuum multi type particle systems with finite range repulsive pair interaction between particles of different type this proves an old conjecture of lebowitz and lieb a phase transition still occurs when we allow a background pair interaction between all particles which is superstable and has sufficiently short range of repulsion our approach involves a random cluster representation analogous to the fortuin kasteleyn representation of the potts model in the course of our argument we establish the existence of a percolation transition for gibbsian particle systems with random edges between the particles and also give an alternative proof for the existence of gibbs measures with supperstable interaction

high temperature differentiability of lattice gibbs states by dobrushin uniqueness techniques we establish conditions for the differentiability to any order of the gibbs states of classical lattice systems with arbitrary compact single spin space and with interactions in the dobrushin uniqueness region the derivatives are expressed as series expansions and are shown to be continuous on the uniqueness region we also provide a procedure for estimating the size of the derivatives these results verify a conjecture of l gross and extend his results in absence of second order phase transitions in the dobrushin uniqueness region journal of statistical physics25 1 57 72 1981 the techniques of this paper are based on those employed by gross

a fuzzy approach to visibility maps creation over digital terrains the construction of inter visibility models for a terrain is an important tool for environmental and animal studies efficient crisp algorithms are known to address this problem directly on a raster digital elevation map dem of the study area randomness plays an important role several factors like vegetation height of the observer presence of unmapped human artifacts etc cannot be modeled in advance into a traditional dem model we propose the use of fuzzy terrain models to incorporate uncertainty and unpredictable variability of the landscape accordingly we propose a suitable definition of visibility to obtain intervisibility models an algorithm that uses approximation of fuzzy numbers with a discrete family of intervals is proposed the proposed model produces sound results and can be extended to model complex situations like triangulating a radio source using two directional receivers all of these situations are difficult to manage with a precise stochastic model and are a frequent occurrence in animal behavior studies under field conditions the proposed techniques have been implemented inside a user friendly software package that may easily exchange data with the most common giss we report also some experimental results obtained using over artificial terrain under controlled noise and under sampling conditions

a local convergence proof for the minvar algorithm for computing continuous piecewise linear approximations the class of continuous piecewise linear pl functions represents a useful family of approximants because invertibility can be readily imposed and if a pl function is invertible then it can be inverted in closed form many applications arising for example in control systems and robotics involve the simultaneous construction of a forward and inverse system model from data most approximation techniques require that separate forward and inverse models be trained whereas an invertible continuous pl affords simultaneously the forward and inverse system model in a single representation the minvar algorithm computes a continuous pl approximation to data local convergence of minvar is proven for the case when the data generating function is itself a pl function and available directly rather than through data

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

percolation path large deviations and weakly gibbs states we present a unified approach to establishing the gibbsian character of a wide class of non gibbsian states arising in the renormalisation group theory inside the realm of the pirogov sinai theory for lattice spin systems we prove that rg transformations applied to low temperature phases give rise to weakly gibbsian measures in other words we show that the griffiths pearce israel scenario of rg pathologies is carried by atypical configurations the renormalized measures are described by an effective interaction with relative energies well defined on a full measure set of configurations in this way we complete the first part of the dobrushin restoration program to give a gibbsian description to non gibbsian states a disagreement percolation estimate is used in the proof to bound the decay of quenched correlations through which the interaction potential is constructed the percolation is controlled via a novel type of pathwise large deviation theory

a note on the uniqueness result for the inverse henderson problem the inverse henderson problem of statistical mechanics is the theoretical foundation for many bottom up coarse graining techniques for the numerical simulation of complex soft matter physics this inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles roughly stated it asks for the interaction potential given the equilibrium pair correlation function of the system in 1974 henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system here we provide a rigorous proof of a slightly more general version of the latter statement using georgii s variant of the gibbs variational principle the inverse henderson problem of statistical mechanics is the theoretical foundation for many bottom up coarse graining techniques for the numerical simulation of complex soft matter physics this inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles roughly stated it asks for the interaction potential given the equilibrium pair correlation function of the system in 1974 henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system here we provide a rigorous proof of a slightly more general version of the latter statement using georgii s variant of the gibbs variational principle

multidimensional search trees that provide new types of memory reductions an orthogonal query that asks to aggregate the set of records in k dimensional box regions is studied and it is shown that space o n log n log log n k 1 makes possible a combined time complexity o log k n for retrievals insertions and deletions

decay of correlations under dobrushin s uniqueness condition and its applications an estimate on the correlation of functionals of gibbs fields satisfying dobrushin s uniqueness condition is given as a consequence a result of gross saying that the truncated pair correlation function decays in the same weighted summability sense as the potential can be extended to the whole dobrushin uniqueness region applications to the central limit theorem and the second derivative of the pressure are also given

poisson polyhedra in high dimensions abstract the zero cell of a parametric class of random hyperplane tessellations depending on a distance exponent and an intensity parameter is investigated as the space dimension tends to infinity the model includes the zero cell of stationary and isotropic poisson hyperplane tessellations as well as the typical cell of a stationary poisson voronoi tessellation as special cases it is shown that asymptotically in the space dimension with overwhelming probability these cells satisfy the hyperplane conjecture if the distance exponent and the intensity parameter are suitably chosen dimension dependent functions also the high dimensional limits of the mean number of faces are explored and the asymptotic behaviour of an isoperimetric ratio is analysed in the background are new identities linking the f vector of the zero cell to certain dual intrinsic volumes

free energy density for continuous systems with and without superstability assumptions the thermodynamic limit of the free energy density for a large class of continuous charged systems with stable and sufficiently regular many body forces is studied the main effort is placed on demonstrating rigorously that thermodynamic functions do not depend on the typical boundary conditions among the results the most important and new ones are the following 1 for any superstable or superstable in an extended sense and sufficiently regular many body interactions the thermodynamic limit of the conditioned free energy density exists and is equal to that corresponding to the free boundary condition case 2 a new criterion for the nondependence of the limiting free energy density on the typical boundary condition is formulated and proved this criterion does not require any superstability type of assumptions among several applications of the results we list only two a to the case of two dimensional neutral yukawa gas in the monopole phase which is not even stable according to the standard no

free vibration of non uniform euler bernoulli beams with general elastically end constraints using adomian modified decomposition method abstract this paper deals with free vibration problems of non uniform euler bernoulli beam under various supporting conditions the technique we have used is based on applying the adomian modified decomposition method amdm to our vibration problems doing some simple mathematical operations on the method we can obtain ith natural frequencies and mode shapes one at a time the computed results agree well with those analytical and numerical results given in the literatures these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is simple and more straightforward than the other modal analysis