conversion and evaluation for two types of parametric surfaces constructed by ntp bases in this paper a new generalized ball basis normalized totally positive ntp basis given by delgado and pena is investigated the conversion formulae between the basis and the bernstein basis are derived we also prove that these formulae not only are valuable for studying the geometric properties such as subdivision of the curves and surfaces constructed by this generalized ball basis but also can improve the computational speed of the bezier curves and surfaces after the bezier surface curve is converted into the generalized ball surface curve the time complexity for evaluation can be reduced from cubic to quadratic of the degree of the surface curve however the intrinsic property such as shape preserving property is not changed so the generalized ball surface and curve have a great future in application of geometric design

q epsilon tensor for quantum and braided spaces the machinery of braided geometry introduced previously is used now to construct the e totally antisymmetric tensor on a general braided vector space determined by r matrices this includes natural q euclidean and q minkowski spaces the formalism is completely covariant under the corresponding quantum group such as soq 4 or soq 1 3 the hodge operator and differentials are also constructed in this approach

spreading of damage in the domany kinzel cellular automaton a mean field approach abstract we present a detailed analytical formulation and a mean field approximation analysis of the spreading of damage in the domany kinzel cellular automaton our results show that the system exhibits a chaotic state besides the frozen and active these results are in agreement with recent numerical simulations also we study the conjugate fields associated to the order parameters of the active and chaotic phases

symplecton for uh sl 2 and representations of slh 2 polynomials of boson creation and annihilation operators which form irreducible tensor operators for jordanian quantum algebra uh sl 2 called h symplecton are introduced and their properties are investigated it is shown that many properties of symplecton for lie algebra sl 2 are extended to h symplecton the h symplecton is also a basis of irreducible representation of slh 2 dual to uh sl 2 as an application of the procedure used to construct h symplecton we construct the representation bases of slh 2 on the quantum h plane

a nonparametric probabilistic approach for quantifying uncertainties in low dimensional and high dimensional nonlinear models summary a nonparametric probabilistic approach for modeling uncertainties in projection based nonlinear reduced order models is presented when experimental data are available this approach can also quantify uncertainties in the associated high dimensional models the main underlying idea is twofold first to substitute the deterministic reduced order basis rob with a stochastic counterpart second to construct the probability measure of the stochastic reduced order basis srob on a subset of a compact stiefel manifold in order to preserve some important properties of a rob the stochastic modeling is performed so that the probability distribution of the constructed srob depends on a small number of hyperparameters these are determined by solving a reduced order statistical inverse problem the mathematical properties of this novel approach for quantifying model uncertainties are analyzed through theoretical developments and numerical simulations its potential is demonstrated through several example problems from computational structural dynamics copyright 2016 john wiley sons ltd

on the concepts of lie and covariant derivatives of spinors i for pt 1 see ibid vol 27 p 1 1994 the framework developed in part i for defining lie and covariant differentiation of spinors is investigated to show its compatibility with tensor calculus the special role played by conformal killing vectors and conformal connections is also determined

error analysis of efficient evaluation algorithms for tensor product surfaces backward stability of the casteljau algorithm and two more efficient algorithms for polynomial tensor product surfaces with interest in cagd is shown the conditioning of the corresponding bases are compared these algorithms are also compared with the corresponding horner algorithm and their higher accuracy is shown a running error analysis of the algorithms is also carried out providing algorithms which calculate a posteriori sharp error bounds simultaneously to the evaluation of the surface without increasing significantly the computational cost

directed compact percolation cluster size and hyperscaling exact recurrence relations are obtained for the length and size distributions of compact directed percolation clusters on the square lattice the corresponding relation for the moment generating function of the length distribution is obtained in closed form whereas in the case of the size distribution only the first three moments are obtained the work is carried out for clusters grown from a seed of arbitrary width on an anisotropic lattice a duality property is shown to exist which relates the moment generating functions on the two sides of the critical curve the moments of both distributions have critical exponents which satisfy a constant gap hypothesis with gap exponents nu 2 and delta 3 corresponding to the scaling length and scaling size respectively the usual hyperscaling relation for directed percolation is found to be invalid for compact clusters and is replaced by delta nu d nu perpendicular to where nu perpendicular to is the exponent corresponding to the cluster width and d is the number of transverse dimensions 1 for the square lattice

characteristic constraint modes for component mode synthesis a technique is presented for reducing the size of a model generated by the craig bampton method craig r r and bampton m c c coupling of substructures for dynamic analyses aiaa journal vol 6 no 7 1968 pp 1313 1319 of component mode synthesis cms an eigenanalysis is performed on the partitions of the cms mass and stiffness matrices that correspond to the so called constraint modes the resultant eigenvectors are referred to as characteristic constraint modes because they represent the characteristic motion of the interface between the component structures when the characteristic constraint modes are truncated a cms model with a highly reduced number of degrees of freedom may be obtained an example of a cantilever plate is considered it is shown that relatively few characteristic constraint modes are needed to yield accurate approximations of the lower natural frequencies furthermore this method yields physical insight into the mechanisms of vibration transmission in complex structures and it provides an excellent framework for the efficient calculation of power flow

quantum group covariant anti symmetrizers tensors vielbein hodge map and laplacian glq n and soq n covariant deformations of the completely symmetric antisymmetric projectors with an arbitrary number of indices are explicitly constructed as polynomials in the braid matrices the precise relation between the completely antisymmetric projectors and the completely antisymmetric tensor is determined adopting the glq n and soq n covariant differential calculi on the corresponding quantum group covariant noncommutative spaces we introduce a generalized notion of vielbein basis or frame based on differential operator valued 1 forms we then give a thorough definition of a soq n covariant bilinear hodge map acting on the bimodule of differential forms on introduce the exterior coderivative and show that the laplacian acts on differential forms exactly as in the undeformed case namely it acts on each component as it does on functions

fluid structure interaction of an elastically mounted slender body at high incidence a numerical study of the fluid structure interaction of an inclined tangent ogive cylinder rigid body mounted on torsion springs that can rotate in the pitching yawing and rolling directions is conducted the body is subjected to three dimensional compressible laminar flow at a reynolds number of 30 000 and a mach number of 0 2 a second order implicit finite difference scheme is employed for the flow equations adapted to a curvilinear coordinate system whereas the coupled structural equations written using an euler angle notation are solved by a fourth order runge kutta method a detailed investigation of two angles of attack 40 deg and 55 deg is described for a fixed body at 40 deg the yaw moment changed smoothly with the location of the circumferential disturbance whereas at 55 deg the yaw moment was characterized by an almost square wave variation behavior with bifurcation points at disturbance circumferential roll angles 90 deg 140 deg and 180 deg for an elastical

phase diagram of a stochastic cellular automaton with long range interactions abstract a stochastic one dimensional cellular automaton with long range spatial interactions is introduced in this model the state probability of a given site at time t depends on the state of all the other sites at time t 1 through a power law of the type 1 r r being the distance between sites for this model reduces to the domany kinzel cellular automaton the dynamical phase diagram is analyzed using monte carlo simulations for 0 we found the existence of two different regimes one for 0 1 and the other for 1 it is shown that in the first regime the phase diagram becomes independent of regarding the frozen active phase transition in this regime a strong evidence is found that the mean field prediction for this model becomes exact a result already encountered in magnetic systems it is also shown that for replicas evolving under the same noise the long range interactions fully suppress the spreading of damage for 0 1

diagnosis of local uncertain modifications in the boundary conditions of a rectangular plate via convex modeling abstract in this study the diagnosis of the boundary conditions is treated as the identification of the adversely affected region on the boundary and estimation of limits on the magnitude of possible change in the stiffness convex models are utilized to represent the degree of uncertainty in the boundary condition modification this means that the diagnosis is actually the identification of the convex model to which the actual boundary stiffness profile belongs as a result the diagnosis is formulated as a discrete multi hypothesis decision problem with attendant formulation of the adaptive termination of this algorithm the generalized bolotin s dynamic edge effect method is employed to determine the approximate natural frequencies and normal modes of elastically supported isotropic uniform rectangular plates employed in the analysis the entire procedure of diagnosis of local modifications is implemented and results of such an identification are reported

braided chains of q deformed heisenberg algebras given m copies of a q deformed weyl or clifford algebra in the defining representation of a quantum group we determine a prescription to embed them into a unique inclusive covariant algebra the different copies are coupled to each other and are naturally ordered into a chain in the case a modified prescription yields an inclusive algebra which is even explicitly covariant where is a symmetry relating the different copies by the introduction of these inclusive algebras we significantly enlarge the class of covariant deformed weyl clifford algebras available for physical applications

construction of triangular dp surface and its application in this paper a new type of bivariate basis on a triangle is presented which is constructed by extending the univariate ntp basis proposed by delgado and pena some algebraic properties and its recursive formulae are given then a new type of surfaces that is called triangular dp surface is defined and its recursive evaluation algorithm is obtained also in the case of low degree its subdivision algorithm and degree elevation algorithm are derived it is shown that this type of surfaces is obviously more advantageous than triangular bezier surface and hence extremely useful for geometric design especially for the situation in which the surface needs to be evaluated quickly

a comprehensive overview of a non parametric probabilistic approach of model uncertainties for predictive models in structural dynamics abstract in structural dynamics a predictive model is constructed by developing a mathematical mechanical model of a designed system in order to predict the response of the real system which is the manufactured system realized from the designed system the mathematical mechanical modelling process of the designed system introduces two fundamental types of uncertainties the data uncertainties and the model uncertainties uncertainties have to be taken into account for improving the predictability of the model model uncertainties cannot be modelled by using the usual parametric probabilistic approach recently a general non parametric probabilistic approach of model uncertainties for dynamical systems has been proposed using the random matrix theory this paper gives a comprehensive overview of this approach in developing its foundations in simple terms and in illustrating all the concepts and the tools introduced in the general theory by using a simple example this paper deals with 1 notions of designed systems real systems mean models as predictive models errors and uncertainties 2 the definition of a simple example in linear elastodynamics 3 a comprehensive overview of the non parametric probabilistic approach of model uncertainties for predictive models in structural dynamics 4 a summary of the random matrix ensembles which are necessary for the non parametric modelling of random uncertainties 5 the estimation of the dispersion parameters of the non parametric probabilistic model using experimental data 6 the method to solve the stochastic equation of the dynamical system with non parametric probabilistic model of random uncertainties 7 a numerical simulation and the validation for the simple example

conjugation in braided c categories and orthogonal quantum groups we consider braided c categories with conjugates and the notion of dimension if the braid is a birman wenzl murakami symmetry then we characterize the compact orthogonal quantum groups

nonparametric stochastic modeling of structures with uncertain boundary conditions coupling between substructures the focus of this investigation is on the formulation and validation of a novel approach for the inclusion of uncertainty in the modeling of the boundary conditions of linear structures and of the coupling between linear substructures this work is particularly relevant to complex structures assembled from simpler substructures as in aerospace applications first a mean structural dynamic model that includes boundary condition coupling flexibility is obtained using classical substructuring concepts the application of the nonparametric stochastic modeling approach to this mean model is next described and thus permits the consideration of both model and parameter uncertainty finally the identification of the two parameters of this stochastic model the mean boundary condition coupling flexibility and the overall level of uncertainty is shown and discussed the methodology is demonstrated on three different structural dynamic models of a rectangular plate and of two different wings

the domany kinzel cellular automaton relaxation time susceptibility and constrained dynamics we use a monte carlo simulation to study new features of the one dimensional domany kinzel cellular automaton ca considering the relaxation process of the magnetization the frozen active order parameter towards its equilibrium value we measure its dynamical critical exponent z also we investigate the effect of p0 not 0 non vanishing external field conjugate to the magnetization on the phase diagram and on the susceptibility finally we introduce constraints in the evolution rule of the domany kinzel ca and study the associated criticality critical surfaces and universality classes

unbraiding the braided tensor product we show that the braided tensor product algebra a1 a2 of two module algebras a1 a2 of a quasitriangular hopf algebra h is isomorphic to the ordinary tensor product a1 a2 provided there exists a realization of h within a1 in other words under this assumption we construct a transformation of generators which decouples a1 a2 i e makes them commuting we apply the theorem to the braided tensor product algebras of two or more quantum group covariant quantum spaces deformed heisenberg algebras and q deformed fuzzy spheres

re entrant behaviour in the domany kinzel cellular automaton we present numerical and analytical results for a special kind of one dimensional probabilistic cellular automaton the so called domany kinzel automaton it is shown that the phase boundary separating the active and the recently found chaotic phase exhibits re entrant behaviour furthermore exact results for the p2 0 line are discussed

quantum groups soq n spq n have q determinants too we construct the q deformed analogue of the completely antisymmetric tensors and the corresponding q determinants detq t for the quantum groups soq n spq n the construction is based on the existence of the volume form in the algebra of exterior forms on the corresponding quantum spaces we show that detq t is central in fun soq n respectively fun sp n is group like under the hopf algebra comultiplication and that its square is 1

gauss lobatto to bernstein polynomials transformation the aim of this paper is to transform a polynomial expressed as a weighted sum of discrete orthogonal polynomials on gauss lobatto nodes into bernstein form and vice versa explicit formulas and recursion expressions are derived moreover an efficient algorithm for the transformation from gauss lobatto to bernstein is proposed finally in order to show the robustness of the proposed algorithm experimental results are reported

from equilibrium spin models to probabilistic cellular automata the general equivalence betweend dimensional probabilistic cellular automata pca and d 1 dimensional equilibrium spin models satisfying a disorder condition is first described in a pedagogical way and then used to analyze the phase diagrams the critical behavior and the universality classes of some automata diagrammatic representations of time dependent correlation functions of pca are introduced two important classes of pca are singled out for which these correlation functions simplify 1 quasi hamiltonian automata which have a current carrying steady state and for which some correlation functions are those of ad dimensional static model pca satisfying the detailed balance condition appear as a particular case of these rules for which the current vanishes 2 linear and more generally affine pca for which the diagrammatics reduces to a random walk problem closely related to d 1 dimensional directed saws both problems display a critical behavior with mean field exponents in any dimension the correlation length and effective velocity of propagation of excitations can be calculated for affine pca as is shown on an explicitd 1 example we conclude with some remarks on nonlinear pca for which the diagrammatics is related to reaction diffusion processes and which belong in some cases to the universality class of reggeon field theory

the euclidean hopf algebra u q e n and its fundamental hilbert space representations the euclidean hopf algebra uq en dual of fun rnq soq 1 n is constructed by realizing it as a subalgebra of the differential algebra diff rnq on the quantum euclidean space rnq in fact the previous realization g fiore commun math phys 169 475 500 1995 of uq 1 so n is extended within diff rnq through the introduction of q derivatives as generators of q translations the fundamental hilbert space representations of uq en turn out to be of highest weight type and rather simple lattice regularized versions of the classical ones the vectors of a basis of the singlet i e zero spin irrep can be realized as normalizable functions on rnq going to distributions in the limit q 1

representation functions for jordanian quantum group slh 2 and jacobi polynomials the explicit expressions of the representation functions d functions for jordanian quantum group slh 2 are obtained by combination of tensor operator technique and drinfeld twist it is shown that the d functions can be expressed in terms of jacobi polynomials as the undeformed d functions can some of the important properties of the d functions for slh 2 such as wigner s product law recurrence relations and rtt type relations are also presented

evidence for a new phase in the domany kinzel cellular automaton we consider a generalized version including anisotropy of the stochastic one dimensional cellular automaton studied by domany and kinzel it recovers wolfram like deterministic cellular automata as particular cases the phase diagram presents three and not two as previously suggested phases which were detected through the numerical study of both the order parameter and the sensitivity to initial conditions the various universality classes are exhibited as well cellular automata ca are totally discrete dynamical systems discrete space discrete time and discrete number of states which find general applications in physics chemistry biology computer science etc with each site noted i is associated a variable cr which can be in k different states cr 0 1 k 1 the dynamics is defined at each time step by rules depending on the values at a previous time of o j associated with a given number of r arbitrary sites called inputs usually one considers regular lattices and the inputs refer to the sites on the local neighborhood only the local rules of a ca may be probabilistic or deterministic and the sites are simultaneously updated thus we recognize the glauber dynamics for example as a special case of a ca however in the more general context of ca the dynamics is not restricted to the usual boltzmann weight and detailed balance therefore ca do not necessarily evolve towards equilibrium thus they can model chemical reactions crystal growth models turbulence biological problems or other nonlinear processes far from thermal equilibrium

random matrix theory for modeling uncertainties in computational mechanics this paper deals with data uncertainties and model uncertainties issues in computational mechanics if data uncertainties can be modeled by parametric probabilistic methods for a given mean model a nonparametric probabilistic approach can be used for modeling model uncertainties the first part is devoted to random matrix theory for which we summarize previous published results and for which two new ensembles of random matrices useful for the nonparametric models are introduced in a second part the nonparametric probabilistic approach of random uncertainties is presented for linear dynamical systems and for nonlinear dynamical systems constituted of a linear part with additional localized nonlinearities in a third part a new method is proposed for estimating the parameters of the nonparametric approach from experiments finally examples with experimental comparisons are given

correlation function studies on the domany kinzel cellular automaton abstract the domany kinzel cellular automaton is a simple and yet very rich model to study phase transitions in nonequilibrium systems this model exhibits three characteristic phases frozen active and chaotic in this paper we discuss the behavior of the equal time two point correlation functions and that of the associated correlation lengths as one crosses the phase boundary both for the frozen active and active chaotic transitions we have investigated in detail how the correlation lengths diverge as one approaches the phase boundary from both sides the divergence of the correlation length coupled with the previous studies on the divergence of the susceptibility suggests that the fluctuation dissipation theorem holds true in the domany kinzel cellular automaton model time dependence of the correlation functions is also discussed

cellular automata and statistical mechanical models we elaborate on the analogy between the transfer matrix of usual lattice models and the master equation describing the time development of cellular automata transient and stationary properties of probabilistic automata are linked to surface and bulk properties respectively of restricted statistical mechanical systems it is demonstrated that methods of statistical physics can be successfully used to describe the dynamic and the stationary behavior of such automata some exact results are derived including duality transformations exact mappings disorder and linear solutions many examples are worked out in detail to demonstrate how to use statistical physics in order to construct cellular automata with desired properties this approach is considered to be a first step toward the design of fully parallel probabilistic systems whose computational abilities rely on the cooperative behavior of their components

duality for the jordanian matrix quantum group we find the hopf algebra dual to the jordanian matrix quantum group as an algebra it depends only on the sum of the two parameters and is split into two subalgebras with three generators and with one generator the subalgebra is a central hopf subalgebra of the subalgebra is not a hopf subalgebra and its co algebra structure depends on both parameters we discuss also two one parameter special cases g h and g h the subalgebra is a hopf algebra and coincides with the algebra introduced by ohn as the dual of the subalgebra is isomorphic to u sl 2 as an algebra but has a nontrivial co algebra structure and again is not a hopf subalgebra of

uncertainty quantification in computational linear structural dynamics for viscoelastic composite structures this paper deals with the analysis of a stochastic reduced order computational model in computational linear dynamics for linear viscoelastic composite structures in the presence of uncertainties the computational framework proposed is based on a recent theoretical work that allows for constructing the stochastic reduced order model using the nonparametric probabilistic approach in the frequency domain the generalized damping matrix and the generalized stiffness matrix of the stochastic computational reduced order model are random matrices due to the causality of the dynamical system these two frequency dependent random matrices are statistically dependent and are linked by a compatibility equation induced by the causality of the system involving a hilbert transform the computational aspects related to the nonparametric stochastic modeling of the reduced stiffness matrix and the reduced damping matrix that are frequency dependent random matrices are presented a dedicated numerical approach is developed for obtaining an efficient computation of the cauchy principal value integrals involved in those equations for which an integration over a broad frequency domain is required a computational analysis of the propagation of uncertainties is conducted for a composite viscoelastic structure in the frequency range it is shown that the uncertainties on the damping matrix have a strong influence on the observed statistical dispersion of the stiffness matrix

the dirac operator on compact quantum groups for the q deformation gq 0 q 1 of any simply connected simple compact lie group g we construct an equivariant spectral triple which is an isospectral deformation of that defined by the dirac operator d on g our quantum dirac operator dq is a unitary twist of d considered as an element of ug cl g the commutator of dq with a regular function on gq consists of two parts one is a twist of a classical commutator and so is automatically bounded the second is expressed in terms of the commutator of the associator with an extension of d we show that in the case of the drinfeld associator the latter commutator is also bounded