aspects of three dimensional constrained delaunay meshing presented in this paper are the theoretical aspects of node addition to a non convex multiboundary mesh of tetrahedral elements as used in finite element modelling the method used is derived from watson1 and shenton and cendes2 and is extended to deal with node addition on inter material boundaries several situations are identified that result in an illegal insertion polyhedron ip these could be caused by the constrained nature of the mesh adjacent objects with different material properties or degenerate node configurations a new delaunay algorithm is described that checks for illegal cases of the ip and then corrects them this checking relies on the consistent ordering of the element nodes it is shown that a particular type of illegal ip can easily be identified and corrected using this technique the delaunay algorithm is then applied to automatic mesh generation and modification to the basic delaunay algorithm is described so that previously meshed edges and faces of the current object being meshed are not deleted during the addition of subsequent nodes this protection method only becomes viable by recognizing the node ordering sense of the ip faces

delaunay versus max min solid angle triangulations for three dimensional mesh generation the delaunay triangulation has been used in several methods for generating finite element tetrahedral meshes in three dimensional polyhedral regions other types of three dimensional triangulations are possible such as a triangulation satisfying a local max min solid angle criterion in this paper we present experimental results to show that max min solid angle triangulations are better than delaunay triangulations for finite element tetrahedral meshes since the former type of triangulations contains tetrahedra of better shape than the latter type we also describe how mesh points are generated and triangulated in our tetrahedral mesh generation method

brownian motion on the hyperbolic plane and selberg trace formula abstract we will show that the relation of the heat kernels for the schrodinger operators with uniform magnetic fields on the hyperbolic plane h 2 the maass laplacians and for the schrodinger operators with morse potentials on r is given by means of a one dimensional fourier transform in the framework of stochastic analysis where the brownian motion on h 2 plays an important role by using this relation we will give the explicit forms of the green functions as a typical related problem we will discuss the selberg trace formula the close relation of the trace formula with the corresponding classical mechanics will also be discussed

reliability of automatic 3d mesh generation abstract this paper considers issues critical to ensuring the reliability of automatic three dimensional mesh generators building on basic concepts from geometric modeling consideration is given to i the definition and assurance of a valid finite element mesh ii the use of topological adjacency information to improve the reliability and efficiency of a meshing process and iii how the geometric approximations used during the construction of a geometric model must be explicitly considered if the mesh generator s reliability is to be ensured

polyanalytic relativistic second bargmann transforms we construct coherent states through special superpositions of eigenstates of the relativistic isotonic oscillator in each superposition the coefficients are chosen to be l2 eigenfunctions of a weight maass laplacian on the poincare disk which are associated with the eigenvalue 4m 1 m m z 0 1 2 for each nonzero m the associated coherent states transform constitutes the m true polyanalytic extension of a relativistic version of the second bargmann transform whose integral kernel is expressed in terms of a special appel kampe de feriet s hypergeometric function the obtained results could be used to extend the known semi classical analysis of quantum dynamics of the relativistic isotonic oscillator

graded tetrahedral finite element meshes vertices in the body centred cubic bcc lattice are used to create a tetrahedral spatial decomposition with this spatial decomposition an octree approach is combined with delaunay triangulations to decompose solids into tetrahedral finite element meshes solids must have their surfaces triangulated and the vertices in the triangulation are finite element nodes local densities of interior tetrahedra are controlled by the densities of surface triangles accuracy of the decomposition into finite elements depends on the accuracy of the surface triangulation which can be constructed with state of the art computer aided design systems

three dimensional unstructured mesh generation part 1 fundamental aspects of triangulation and point creation abstract the present paper introduces an alternative approach for delaunay triangulation in which the triangulation is mapped from an equivalent convex hull in a higher dimension furthermore some fundamental aspects of a point creation algorithm for unstructured mesh generation have been addressed based on numerical experiments a point spacing tensor and point insertion criterion have been introduced aiming to deal with anisotropic meshes

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

solid elements with rotational degrees of freedom part ii tetrahedron elements this is the first of a two part paper on three dimensional finite elements with rotational degrees of freedom dof part i introduces an 8 node solid hexahedron element having three translational and three rotational dof per node the corner rotations are introduced by transformation of the midside translational dof of a 20 node hexahedron element the new element produces a much smaller effective band width of the global system equations than does the 20 node hexahedron element having midside nodes a small penalty stiffness is introduced to augment the usual element stiffness so that no spurious zero energy modes are present the new element passes the patch test and demonstrates greatly improved performance over elements of identical shape but having only translational dof at the corner nodes

super ricci flows for metric measure spaces abstract we introduce the notions of super ricci flows and ricci flows for time dependent families of metric measure spaces x d t m t t i the former property is proven to be stable under suitable space time versions of mgh convergence uniformly bounded families of super ricci flows are compact in the spirit of the synthetic lower ricci bounds of lott sturm villani for static metric measure spaces the defining property for super ricci flows is the dynamic convexity of the boltzmann entropy ent m t regarded as a functions on the time dependent geodesic space p x w t t i for ricci flows in addition a nearly dynamic concavity of the boltzmann entropy is requested alternatively super ricci flows will be studied in the framework of the calculus of bakry emery ledoux and equivalence to gradient estimates will be derived for both notions of super ricci flows also enforced versions involving an upper dimension bound n will be presented

tetrahedral mesh generation in convex primitives this paper presents a method for generating tetrahedral meshes in three dimensional primitives given a set of closed and convex polyhedra having non zero volume and some mesh controlling parameters the polyhedra are automatically split to tetrahedra satisfying the criteria of standard finite element meshes the algorithm tries to generate elements close to regular tetrahedra by maximizing locally the minimum solid angles associated to a set of a few neighbouring tetrahedra the input parameters define the size of the tetrahedra and they can be used to increase or decrease the discretization locally all the new nodes which are not needed to describe the geometry are generated automatically

manifolds with positive curvature operators are space forms the ricci flow was introduced by hamilton in 1982 h1 in order to prove that a compact three manifold admitting a riemannian metric of positive ricci curvature is a spherical space form in dimension four hamilton showed that compact four manifolds with positive curvature operators are spherical space forms as well h2 more generally the same conclusion holds for compact four manifolds with 2 positive curvature operators che recall that a curvature operator is called 2 positive if the sum of its two smallest eigenvalues is positive in arbitrary dimensions huisken hu described an explicit open cone in the space of curvature operators such that the normalized ricci flow evolves metrics whose curvature operators are contained in that cone into metrics of constant positive sectional curvature hamilton conjectured that in all dimensions compact riemannian manifolds with positive curvature operators must be space forms in this paper we confirm this conjecture more generally we show the following

geometry based fully automatic mesh generation and the delaunay triangulation one approach to fully automatic mesh generation in two and three dimensions is to generate and triangulate a set of points within and on the boundary of a geometry using the properties of the delaunay triangulation because the point data generate mesh topology of greater dimension it is necessary to insure topological compatibility and perform classification of the resulting mesh with respect to the original geometry necessary and sufficient conditions for classification of mesh topology on three dimensional planar geometry are given as well as a discussion of the more complex case of curved geometry this paper also presents conditions to insure topological compatibility along with techniques for identifying and resolving cases of incompatibility

correlation functions of the nonstationary quantum singular oscillator the exact density matrix elements and the correlation functions of the one dimensional non stationary singular oscillator the potential u x t omega 2 t x2 2 g x2 excited from the thermodynamic equilibrium states are obtained generating functions for rho nm and also for transition probabilities are constructed

integrability of difference calogero moser systems a general class of n particle difference calogero moser systems with elliptic potentials is introduced besides the step size and two periods the hamiltonian depends on nine coupling constants we prove the quantum integrability of the model for n 2 and present partial results for n 3 in degenerate cases rational hyperbolic or trigonometric limit the integrability follows for arbitrary particle number from previous work connected with the multivariable q polynomials of koornwinder and macdonald liouville integrability of the corresponding classical systems follows as a corollary limit transitions lead to various well known models such as the nonrelativistic calogero moser systems associated with classical root systems and the relativistic calogero moser system

the relativistic linear singular oscillator exactly solvable model of the linear singular oscillator in the relativistic configurational space is considered we have found wavefunctions and energy spectrum for the model under study it is shown that they have the correct non relativistic limits

a hierarchical approach to automatic finite element mesh generation a point based two stage hierarchical method for automatic finite element mesh generation from a solid model is presented given the solid model of a component and the required nodal density distribution nodes are generated according to the hierarchy vertex edge face and solid at the vertices nodes are established naturally nodes on the edges faces and inside the solid model are generated by recursive subdivision the nodes are then connected to form a valid and well conditioned finite element mesh of tetrahedron elements using modified delaunay triangulation checks are conducted to ensure the compatibility of geometry and topology between the solid model and the mesh

a combined octree delaunay method for fully automatic 3 d mesh generation fully automatic three dimensional mesh generation is a fundamental requirement for automating the numerical solution of partial differential equations two techniques in particular the octree and delaunay approaches have been used towards this end a method that combines both approaches to fully automatic mesh generation is presented here the resulting algorithm provides the linear growth rate and divide and conquer approach of the octree method with the simplicity and optimal properties of the delaunay triangulation

a simple difference realization of the heisenberg q algebra a realization of the heisenberg q algebra whose generators are first order difference operators on the full real line is discussed herein the eigenfunctions of the corresponding q oscillator hamiltonian are given explicitly in terms of the q 1 hermite polynomials the nonuniqueness of the measure for these q oscillator states is also studied

delaunay triangulation in computational fluid dynamics abstract a method which utilises the delaunay criterion is described by which computational grids consisting of assemblies of triangles or tetrahedra can be constructed an algorithm is briefly outlined to construct the triangulation and its dual the voronoi diagram issues related to how to construct boundary conforming grids from such a triangulation are addressed and details are presented of how grid points within the domain can be generated automatically the point generation algorithm utilises either the given boundary point distribution or for grid adaption a background mesh computational aspects of constructing the triangulation in both 2 and 3 dimensions are covered examples of meshes and flow computations for a range of aerospace geometries are presented

suq 1 1 and the relativistic oscillator it is shown that the generalization of the quantum harmonic oscillator to the case of the relativistic configurational space is a q oscillator the corresponding group of dynamical symmetry is the quantum group suq 1 1 the deformation parameter being q e omega omega 0 where omega 0 4mc2 and omega is a frequency of the oscillator the deformed creation and annihilation operators are finite difference ones the corresponding deformation of the heisenberg weyl group and new coherent states are also considered

the covariant linear oscillator and generalized realization of the dynamical su 1 1 symmetry algebra an exactly solvable problem for the finite difference schrodinger equation in the relativistic configurational space is considered the appropriate finite difference generalization of the factorization method is developed the theory of new special functions the relativistic hermite polynomials in which the solutions are expressed is constructed

uq covariant oscillators and vertex operators uq sl 2 covariant bose and fermi oscillators are studied systematically and applied to constructing vertex operators and uq invariant blocks for qp 1 p 2 3 a p2 dimensional unitary fock space representation of the bose oscillator algebra a q is constructed this representation does not allow however for the construction of all uq invariant blocks associated with an indecomposable representation of uq an extension of a is needed in this case which involves operators creating states of q spin projection p 2 from the fock vacuum the extended algebra only has infinite dimensional indefinite metric space representations an algebraic notion of trace is introduced provided q2 1 in the bose case this allows the introduction of a family of in general mixed uq invariant temperature states such that the vacuum expectation value appears in the zero temperature limit

the ricci flow under almost non negative curvature conditions we generalize most of the known ricci flow invariant non negative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time as an illustration of the contents of the paper we prove that metrics whose curvature operator has eigenvalues greater than 1 can be evolved by the ricci flow for some uniform time such that the eigenvalues of the curvature operator remain greater than c here the time of existence and the constant c only depend on the dimension and the degree of non collapsedness we obtain similar generalizations for other invariant curvature conditions including positive biholomorphic curvature in the kahler case we also get a local version of the main theorem as an application of our almost preservation results we deduce a variety of gap and smoothing results of independent interest including a classification for non collapsed manifolds with almost non negative curvature operator and a smoothing result for singular spaces coming from sequences of manifolds with lower curvature bounds we also obtain a short time existence result for the ricci flow on open manifolds with almost non negative curvature without requiring upper curvature bounds

the algebra of two dimensional generalized chebyshev koornwinder oscillator in the previous works of borzov and damaskinsky chebyshev koornwinder oscillator theor math phys 175 3 765 772 2013 and ladder operators for chebyshev koornwinder oscillator in proceedings of the days on diffraction 2013 the authors have defined the oscillator like system that is associated with the two variable chebyshev koornwinder polynomials we call this system the generalized chebyshev koornwinder oscillator in this paper we study the properties of infinite dimensional lie algebra that is analogous to the heisenberg algebra for the chebyshev koornwinder oscillator we construct the exact irreducible representation of this algebra in a hilbert space of functions that are defined on a region which is bounded by the steiner hypocycloid the functions are square integrable with respect to the orthogonality measure for the chebyshev koornwinder polynomials and these polynomials form an orthonormalized basis in the space the generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators h h

generalised coherent states and group representations on hilbert spaces of analytic functions using the example for the group su 1 1 the author obtains the basis functions of a hilbert space of analytic functions from the perelomov 1972 definition of generalised coherent states the lie algebra in this space has the form of a holstein primakoff representation appropriate for su 1 1

unitary transformation approach to the cyclic evolution of su 1 1 and su 2 time dependent systems and geometrical phases using the time dependent unitary transformation instead of the invariant operator the solutions of su 1 1 and su 2 time dependent quantum systems are obtained it is shown that the evolution operator is decomposed into the product form of two unitary operators in such a way that one of them has the same periodicity as the hamiltonian and the other correspond to the floquet operator which gives the cyclic states and their associated phases over one period of the evolution the non adiabatic berry s or aharonov anandan phases are determined totally by such a unitary transformation

the clebsch gordan coefficients of the three dimensional lorentz algebra in the parabolic basis starting from the oscillator representation of the three dimensional lorentz algebra so 2 1 we build a lie algebra of second order differential operators which realizes all series of self adjoint irreducible representations the choice of the common self adjoint extention over a two chart function space determines whether they lead to single or multivalued representations over the corresponding lie group the diagonal operator defining the basis is the parabolic subgroup generator the direct product of two such algebras allows for the calculation of all clebsch gordan coefficients explicitly as solutions of schrodinger equations for poschl teller potentials over one d d two d c or three c c charts all coefficients are given in terms of up to two 2f1 hypergeometric functions

a relativistic model of the n dimensional singular oscillator an exactly solvable n dimensional model of the quantum isotropic singular oscillator in the relativistic configurational space is proposed it is shown that through the simple substitutions the finite difference equation for the n dimensional singular oscillator can be reduced to the similar finite difference equation for the relativistic isotropic three dimensional singular oscillator we have found the radial wavefunctions and energy spectrum of the problem and constructed a dynamical symmetry algebra

ricci flows with unbounded curvature we show that any noncompact riemann surface admits a complete ricci flow g t t in 0 infty which has unbounded curvature for all t in 0 infty

linearly and nonlinearly transforming fields on homogeneous spaces of the 4 1 de sitter group scalar functions on the homogeneous spaces hr of the de sitter group g so 4 1 are studied where the spaces hr are of the form g k with k being a subgroup of the lorentz group h so 3 1 contained in so 4 1 the spaces hr can be regarded as fiber bundles er er g h h k with the base v 4 g h being a space of constant negative curvature characterized by a fundamental length parameter r 4 1 de sitter space and the fiber s h k being a homogeneous space of the lorentz group the action of g on the spaces er is a linear action on v4 and a nonlinear action on s where the latter action is defined by a generalized wigner rotation a gauge theory based on the 4 1 de sitter group is investigated with matter represented in terms of a generalized wave function x y with x u4 riemann cartan space time v 4 and y s which is defined as a map from a cross section on the bundle e e u4 f er g so 4 1 over space time u4 with fiber f er g k and structural group g so 4 1 into the complex numbers th

on the rogers szego polynomials an orthogonality relation on the full real line for the rogers szego polynomials is discussed it is argued that fourier transformation with the standard exponential kernel exp ixy relates the rogers szego and stieltjes wigert functions

recurrence relations for radial wavefunctions for the nth dimensional oscillators and hydrogenlike atoms we present a general procedure for finding recurrence relations of the radial wavefunctions for nth dimensional isotropic harmonic oscillators and hydrogenlike atoms

deforming the metric on complete riemannian manifolds soit m g ij x une variete de riemann a n dimensions complete non compacte de tenseur de complexe riemannien r ijkl satisfaisant r ijkl 2 k 0 sur m ou 0 0 dependant seulement de n et de k 0 telle que l equation d evolution g ij x t t 2r ij x t sur m g ij x o g ij x x m ait une solution lisse g ij x t 0 pour un temps court 0 t t u k 0 et satisfait l estimation suivante pour un entier m 0 il existe des constantes c m 0 dependant seulement de n m et k 0 telles que sup x m v m r ijkl x t 2 c m t m 0 t t u k 0

darboux transformations of coherent states of the time dependent singular oscillator darboux transformation of both barut girardelo and perelomov coherent states for the time dependent singular oscillator is studied in either case a measure that realizes the resolution of the identity operator in terms of coherent states is found and a corresponding holomorphic representation is constructed for the particular case of the free particle moving with the fixed value of the square of angular momentum equal to 2 it is shown that the barut giriardelo coherent states are more localized at the initial time moment while the perelomov coherent states are more stable with respect to time evolution it is also illustrated that darboux transformation may keep unchanged this different time behaviour

delaunay s mesh of a convex polyhedron in dimension d application to arbitrary polyhedra this paper presents a method for creating a delaunay triangulation connected to a set of specified points the theoretical aspect is recalled for an arbitrary dimension and the method is discussed in order to derive a practical approach valid for dimensions 2 and 3 which is simple robust and well adapted to computation convex polyhedral and arbitrary polyhedral situations are introduced

exact solutions for the general nonstationary oscillator with a singular perturbation three linearly independent hermitian invariants for the nonstationary generalized singular oscillator so are constructed and their complex linear combination is diagonalized the constructed family of eigenstates contains as subsets all previously obtained solutions for the so and includes all robertson and schrodinger intelligent states for the three invariants it is shown that the constructed analogues of the su 1 1 group related coherent states for the so minimize the robertson and schrodinger uncertainty relations for the three invariants and for every pair of them simultaneously the squeezing properties of the new states are briefly discussed