kadison singer algebras ii general case a new class of operator algebras kadison singer ks algebras is introduced these highly noncommutative non self adjoint algebras generalize triangular matrix algebras they are determined by certain minimally generating lattices of projections in the von neumann algebras corresponding to the commutant of the diagonals of the ks algebras it is shown that these lattices and their reduced forms are often homeomorphic to classical manifolds such as the sphere

an efficient strategy for generating all descendant subtree patterns from phylogenetic trees with its implementation abstract phylogenetic trees are an important tool to help in the understanding of relationships between objects that evolve through time in particular molecular sequences in this paper we efficiently solve two subtree comparison problems on a set of phylogenetic trees which have practical applications to analyze the evolution and co evolution genes clustering of genomic sequences let t 1 t 2 t k be a set of k phylogenetic trees such that the leaves of each tree are drawn from 1 2 n and the leaves for two arbitrary trees are not necessary the same where n is the maximum number of the leaves among the k trees we present a linear time algorithm to find all the leaf agreement descendant subtrees by further extending this result we present a linear time algorithm to find all the leaf agreement isomorphic descendant subtrees based on our algorithms a web based system using input tree files from treebase is also implemented

finite element analysis of viscoelastic solids responding to periodic disturbances a finite element analysis for viscoelastic solids responding to periodic disturbances travelling at constant speed is developed the disturbance is decomposed into harmonic components using the discrete fourier series and the viscoelastic material response is determined using the correspondence principle the procedure is used to solve two and three dimensional contact problems to demonstrate its effectiveness

the fourier finite element method for poisson s equation in axisymmetric domains with edges the fourier finite element method which combines the approximating fourier and finite element method is applied to the dirichlet problem of the poisson equation delta 3 hat u hat f in axisymmetric domains hat omega subset r 3 with reentrant edges the edge singularity function is given by a suitable nontensor product representation and treated numerically by mesh grading in the two dimensional meridian of hat omega with linear finite elements for hat f in l 2 hat omega the rate of convergence of the combined approximation in the sobolev spaces h l hat omega l 0 1 is proved to be of the order o n 2 l h 2 l owing to some mixed projection and estimation techniques the degree n of trigonometric polynomials and the mesh size h of the triangular mesh occurring in the error estimates are not coupled and are of the same order as is known for regular solutions hat u in h 2 hat omega the results are illustrated by numerical experiments

optimal shape design of axisymmetric structures subject to asymmetric loading abstract this article describes an efficient method for the shape optimization of axisymmetric structures under asymmetric loads our method employs the semi analytical method for both the primal and adjoint sensitivity analyses to convert the three dimensional problem into a more manageable two dimensional problem by using the kronecker product and the matrix and vector representations of fourth and second order tensors respectively we obtain finite element formulas for the primal and sensitivity analyses that are succinct can be readily programmed and accommodate different element orders and topologies with minimal changes to the code instead of imposing local stress constraints on the surface of the component as it is often done in shape optimization methods that update the design by deforming the mesh we employ the stress p norm over the body to approximate the maximum stress a technique we borrow from recent developments in topology optimization by doing this we need not track stresses at specific locations of the body surface nor impose many local stress constraints to assess the procedure the shape of axisymmetric cantilevers subject to a variety of loadings is optimized to minimize their mass subject to von mises stress constraints these designs are compared to analytical solutions obtained from beam theory we also present a shaft shoulder design example that addresses concentrations

finding maximal leaf agreement isomorphic descendent subtrees from phylogenetic trees with different species phylogenetic trees are an important tool to help in the understanding of relationships between objects that evolve through time in particular molecular sequences in this paper we consider two descendent subtree comparison problems on phylogenetic trees given a set of k phylogenetic trees whose leaves are drawn from 1 2 n and the leaves for two arbitrary trees are not necessary the same we first present a linear time algorithm to final all the maximal leaf agreement descendent subtrees based on this result we also present a linear time algorithm to find all the maximal leaf agreement isomorphic descendent subtrees

isomorphisms of certain csl algebras abstract we show that an isomorphism between two reflexive operator algebras on hilbert space with commutative subspace lattices csl is automatically continuous and induces an isomorphism between the lattices for such algebras with completely distributive subspace lattices cdc algebras the quasi spatially implemented isomorphisms are shown to be exactly those that preserve the rank of all finite rank operators we present some examples of nonspatial isomorphisms and discuss some sufficient conditions on the lattices that ensure that all isomorphisms be spatially implemented the relationship between isomorphisms and derivations of csl algebras is also investigated

some optimal error estimates for piecewise linear finite element approximations it is shown that the ritz projection onto spaces of piecewise linear finite elements is bounded in the sobolev space wl for 2 p oc this implies that for functions in wf n w2 the error in approximation behaves like 0 h in wp for 2 p oo and like 0 h2 in lp for 2 p oo in all these cases the additional logarithmic factor previously included in error estimates for linear finite elements does not occur

numerical technique in plasticity including solution advancement control numerical techniques applied to the consistent formulation of plasticity which is based on convex analysis are investigated for each time step the stress is found as the projection in complementary energy of the elastic stress onto the set of plastically admissible stresses while the velocity field is the extremal of a non quadratic functional explicit formulas for von mises yield criterion with mixed hardening are developed and the nonlinear equations arising from finite element discretization are solved for comparison by a number of newton type iteration procedures with line search and are length control a few numerical examples with proportional and non proportional loading are analyzed

derivations of a class of kadison singer algebras abstract let l be a double triangle lattice of projections in a finite von neumann algebra acting on a separable and complex hilbert space k we show that every derivation from the reflexive algebra determined by l into b k is quasi spatial and automatically continuous we also obtain that every local derivation on the reflexive algebra is a derivation

a few logs suffice to build almost all trees part ii abstract inferring evolutionary trees is an interesting and important problem in biology but one that is computationally difficult as most associated optimization problems are np hard although many methods are provably statistically consistent i e the probability of recovering the correct tree converges to 1 as the sequence length increases the actual rate of convergence for different methods has not been well understood in a recent paper we introduced a new method for reconstructing evolutionary trees called the dyadic closure method dcm and we showed that dcm has a very fast convergence rate dcm runs in o n 5 log n time where n is the number of sequences and so although polynomial the computational requirements are potentially too large to be of use in practice in this paper we present another tree reconstruction method the witness antiwitness method wam wam is faster than dcm especially on random trees and converges to the true tree topology at the same rate as dcm we also compare wam to other methods used to reconstruct trees including neighbor joining possibly the most popular method among molecular biologists and new methods introduced in the computer science literature

a canonical decomposition theory for metrics on a finite set abstract we consider specific additive decompositions d d 1 d n of metrics defined on a finite set x where a metric may give distance zero to pairs of distinct points the simplest building stones are the slit metrics associated to splits i e bipartitions of the given set x while an additive decomposition of a hamming metric into split metrics is in no way unique we achieve uniqueness by restricting ourselves to coherent decompositions that is decompositions d d 1 d n such that for every map f x r with f x f y d x y for all x y x there exist maps f 1 f n x r with f f 1 f n and f i x f i y d i x y for all i 1 n and all x y x these coherent decompositions are closely related to a geometric decomposition of the injective hull of the given metric a metric with a coherent decomposition into a weighted sum of split metrics will be called totally split decomposable tree metrics and more generally the sum of two tree metrics are particular instances of totally split decomposable metrics our main result confirms that every metric admits a coherent decomposition into a totally split decomposable metric and a split prime residue where all the split summands and hence the decomposition can be determined in polynomial time and that a family of splits can occur this way if and only if it does not induce on any four point subset all three splits with block size two

regularity and multigrid analysis for laplace type axisymmetric equations consider axisymmetric equations associated with laplace type operators we establish full regularity estimates in high order kondrat vetype spaces for possible singular solutions due to the non smoothness of the domain and to the singular coefficients in the operator then we show suitable graded meshes can be used in high order finite element methods to achieve the optimal convergence rate even when the solution is singular using these results we further propose multigrid v cycle algorithms solving the system from linear finite element discretizations on optimal graded meshes we prove the multigrid algorithm is a contraction with the contraction number independent of the mesh level numerical tests are provided to verify the theorem

the fourier finite element method for the poisson problem on a non convex polyhedral cylinder we study the poisson problem with zero boundary datum in a finite polyhedral cylinder with a non convex edge applying the fourier sine series to the equation along the edge and by a corner singularity expansion for the poisson problem with parameter we define the edge flux coefficient and the regular part of the solution on the polyhedral cylinder we present a numerical method for approximating the edge flux coefficient and the regular part and show the stability we derive an error estimate and give some numerical experiments

axisymmetric finite element solution of non isothermal parallel plate flow steady non isothermal parallel plate flow of a newtonian fluid with a temperature dependent viscosity is considered the viscosity is modelled by a nahme type law we apply axisymmetric q k finite elements to the coupled nonlinear system to obtain numerical solutions for a wide range of parameters

finite element analysis for the axisymmetric laplace operator on polygonal domains abstract let l r 2 r r 2 z 2 we consider the equation l u f on a bounded polygonal domain with suitable boundary conditions derived from the three dimensional axisymmetric poisson s equation we establish the well posedness regularity and fredholm results in weighted sobolev spaces for possible singular solutions caused by the singular coefficient of the operator l as r 0 and by non smooth points on the boundary of the domain in particular our estimates show that there is no loss of regularity of the solution in these weighted sobolev spaces besides by analyzing the convergence property of the finite element solution we provide a construction of improved graded meshes such that the quasi optimal convergence rate can be recovered on piecewise linear functions for singular solutions the introduction of a new projection operator from the weighted space to the finite element subspace certain scaling arguments and a calculation of the index of the fredholm operator together with our regularity results are the ingredients of the finite element estimates

predictor corrector p and hp versions of the finite element method for poisson s equation in polygonal domains abstract we consider boundary value problems for the poisson equation on polygonal domains with general nonhomogeneous mixed boundary conditions and derive on the one hand explicit extraction formulas for the coefficients of the singularities on the other hand the formulas are used to construct efficient adaptations for the h p and h p versions of the finite element method for the numerical treatment a priori error estimates show that the h version of the finite element algorithm exhibits the same rate of convergence as it is known for problems with smooth solutions however the principal results of the present work are the robust exponential convergence results for the p and h p versions of the finite element method on quasiuniform meshes in fact it is shown that if the input data source term and boundary data are piecewise analytic then with appropriate choices of conforming finite element subspaces v n of dimension n n the p and h p versions of the finite element algorithms on quasiuniform meshes yield approximate solutions u n to the exact solution u that satisfy the estimates u u n h 1 c 1 e b 1 n 2 3 and u u n h 1 c 2 e b 2 n 1 3 respectively several numerical experiments are included to illustrate the practical effectiveness of the proposed algorithms the results show that the theoretical error analyses are attained within the range of engineering accuracy

algebraic isomorphisms and strongly double triangle subspace lattices abstract let d 0 k l m x be a strongly double triangle subspace lattice on a non zero complex reflexive banach space x which means that at least one of three sums k l l m and m k is closed it is proved that a non zero element s of alg d is single in the sense that for any a b alg d either as 0 or sb 0 whenever asb 0 if and only if s is of rank two we also show that every algebraic isomorphism between two strongly double triangle subspace lattice algebras is quasi spatial

mesh refinement and windowing near edges for some elliptic problem the solutions of elliptic problems in three dimensional domains with edges contain singularities in general which influence the order of convergence of the standard finite element method in this paper for some elliptic problem with a special but typical edge singularity function an appropriate local mesh refinement is studied estimates of the rate of convergence with respect to the text l 2 and text w 1 2 norm are proved and moreover bounds of the condition number of the matrix associated with this approximation are derived by means of some error estimates for subdomains the justification of a two step finite element discretization windowing technique is given

analysis of the combined finite element and fourier interpolation we consider lagrange interpolation involving trigonometric polynomials of degree n in one space direction and piecewise polynomials over a finite element decomposition of mesh size h in the other space directions we provide error estimates in non isotropic sobolev norms depending additively on the parametersh andn an application to the convergence analysis of an elliptic problem with some numerical results is given

application of discrete fourier series to the finite element stress analysis of axi symmetric solids this paper describes an efficient formulation based on a discrete fourier series expansion for the analysis of axi symmetric solids subjected to non symmetric loading in contrast to the commonly adopted continuous fourier series approach the discrete fourier series representation has largely overcome problems such as the presence of gibb s phenomenon and the lack of conformity of elements the computational advantage over a fully three dimensional formulation is illustrated finally the method is demonstrated through a finite element study of rigid caissons founded in both elastic and elasto plastic soils

inferring evolutionary trees with strong combinatorial evidence we consider the problem of inferring the evolutionary tree of a set of n species we propose a quartet reconstruction method which specifically produces trees whose edges have strong combinatorial evidence let q be a set of resolved quartets defined on the studied species the method computes the unique maximum subset q of q which is equivalent to a tree and outputs the corresponding tree as an estimate of the species phylogeny we use a characterization of the subset q due to bandelt and dress adv appl math 7 1986 309 343 to provide an o n4 incremental algorithm for this variant of the np hard quartet consistency problem moreover when chosing the resolution of the quartets by the four point method fpm and considering the cavender farris model of evolution we show that the convergence rate of the q method is at worst polynomial when the maximum evolutive distance between two species is bounded we complete these theoretical results by an experimental study on real and simulated data sets the results show that i as expected the strong combinatorial constraints it imposes on each edge leads the q method to propose very few incorrect edges ii more surprisingly the method infers trees with a relatively high degree of resolution

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

kadison singer algebras hyperfinite case a new class of operator algebras kadison singer algebras ks algebras is introduced these highly noncommutative non self adjoint algebras generalize triangular matrix algebras they are determined by certain minimally generating lattices of projections in the von neumann algebras corresponding to the commutant of the diagonals of the ks algebras a new invariant for the lattices is introduced to classify these algebras

on some automorphisms of a class of kadison singer algebras abstract let l be the kadison singer lattice generated by a nontrivial nest n on an infinite dimensional separable hilbert space h and a rank one projection p determined by a separating vector for the von neumann algebra n and alg l be the corresponding kadison singer algebra in this paper we study the problem on the weak density of the subalgebra generated all the rank one operators characterize the single elements in alg l and give the quasi spatiality of an automorphism of alg l depending on whether i has an immediate predecessor in n or not