robust comparative statics of risk changes the standard method for establishing the comparative statics of risk changes in optimization problems has been confined to comparing unique interior solutions relying on strong assumptions about payoff functions and decision variables we propose a simple and intuitive approach that hinges on considerably weaker assumptions merging insights from the monotone comparative statics literature with insights from the risk apportionment literature we show that the ranking of simple lottery pairs is all that is needed for establishing the comparative statics of risk changes we use this approach to analyze the comparative statics of nth degree stochastic dominance shifts in a general setting with one and with multiple decision variables and we show how these results can be applied to generalize the classical theories of precautionary saving self protection and others this paper was accepted by james smith decision analysis

an isogeometric collocation approach for bernoulli euler beams and kirchhoff plates abstract in this paper iga collocation methods are for the first time introduced for the solution of thin structural problems described by the bernoulli euler beam and kirchhoff plate models in particular a precise description of the proposed methods of the relevant implementation details and of the strategy to efficiently deal with different combinations of boundary conditions is given finally several numerical experiments confirm that the proposed formulations represent an efficient and geometrically flexible tool for the simulation of thin structures

risk vulnerability and the tempering effect of background risk we examine in this paper a new natural restriction on utility functions namely that adding an unfair background risk to wealth makes risk averse individuals behave in a more risk averse way with respect to any other independent risk this concept is called risk vulnerability it is equivalent to the condition that an undesirable risk can never be made desirable by the presence of an independent unfair risk moreover under risk vulnerability adding an unfair background risk reduces the demand for risky assets risk vulnerability generalizes the concept of properness individually undesirable independent risks are always jointly undesirable introduced by pratt and zeckhauser 1987 it implies that the two first derivatives of the utility function are concave transformations of the original utility function under decreasing absolute risk aversion a sufficient condition for risk vulnerability is local properness i e r r r where r is the arrow pratt coefficient of absolute risk aversion

integrability and the painleve property for low dimensional systems we examine a system described by two first order nonlinear differential equations from the point of view of integrability the singularity analysis in the complex time plane is used to investigate the painleve property which according to the ablowitz ramani segur conjecture is a prerequisite for integrability for infinite dimensional systems we show that for such low dimensional systems the painleve analysis is still a most useful guide but integrable cases also exist which do not possess the painleve property

generic predation in age structure predator prey models in this paper we use analytical tools based in the painleve analysis and bifurcation theory to offer stable predator prey models with age structure such models account for within species and the approach is based at the level of individual organisms we analyze the type of theoretical predation that a system requires to have real solutions where only poles as singularities are allowed and also to have periodic solutions the main feature sought is the coexistence of the interacting populations

partial tensor decomposition for decoupling isogeometric galerkin discretizations abstract system matrix assembly for isogeometric i e spline based discretizations of partial differential equations is more challenging than for classical finite elements due to the increased polynomial degrees and the larger and hence more overlapping supports of the basis functions the global tensor product structure of the discrete spaces employed in isogeometric analysis can be exploited to accelerate the computations using sum factorization precomputed look up tables and tensor decomposition we generalize the third approach by considering partial tensor decompositions we show that the resulting new method preserves the global discretization error and that its computational complexity compares favorably to the existing approaches moreover the numerical realization simplifies considerably since it relies on standard techniques from numerical linear algebra

optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis abstract we continue the study initiated in hughes et al 2010 in search of optimal quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis these rules are optimal in the sense that there exists no other quadrature rule that can exactly integrate the elements of the given spline space with fewer quadrature points we extend the algorithm presented in hughes et al 2010 with an improved starting guess which combined with arbitrary precision arithmetic results in the practical computation of quadrature rules for univariate non uniform splines up to any precision explicit constructions are provided in sixteen digits of accuracy for some of the most commonly used uniform spline spaces defined by open knot vectors we study the efficacy of the proposed rules in the context of full and reduced quadrature applied to two and three dimensional diffusion reaction problems using tensor product and hierarchically refined splines and prove a theorem rigorously establishing the stability and accuracy of the reduced rules

development of a mixed displacement stress formulation for the analysis of elastoplastic structures under small strains application to a locking free nurbs based solid shell element abstract in this paper we develop a general framework for the extension of mixed displacement stress types of formulations to elastoplastic problems under small strains the difficulty with such formulations is that contrary to the more usual mixed methods used for incompressible materials plasticity which involves the deviatoric part of the stress is affected by the static unknown thus the plastic flow is not governed by displacement induced strains alone the approach followed in this paper consists in choosing the total elastic stress as the static unknown of the mixed formulation then one determines a strain field which is used as input for the plastic projection we applied this formalism to the mixed nurbs based solid shell element of bouclier et al 2013 2015 which led to an efficient extension of the element into the elastoplastic domain we were able to verify the ability of this element to overcome shell locking problems through several test cases involving a plastic flow rule with linear isotropic strain hardening

a fully locking free isogeometric approach for plane linear elasticity problems a stream function formulation in this paper we study plane incompressible elastic problems by means of a stream function formulation such that a divergence free displacement field can be computed from a scalar potential the numerical scheme is constructed within the framework of nurbs based isogeometric analysis and we take advantage of the high continuity guaranteed by nurbs basis functions in order to obtain the displacement field from the potential differentiation as a consequence the obtained numerical scheme is automatically locking free in the presence of the incompressibility constraint a discontinuous galerkin approach is proposed to deal with multiple mapped possibly multiply connected domains extensive numerical results are provided to show the method capabilities 2007 elsevier b v all rights reserved

fast formation and assembly of finite element matrices with application to isogeometric linear elasticity abstract recently a new formation and assembly strategy was proposed in 1 which resulted in significant speedups in the formation and assembly time of the galerkin mass matrix in isogeometric analysis the strategy relies on three key ingredients 1 assembly row by row instead of element by element and an efficient formation strategy based on 2 sum factorization and 3 weighted quadrature that is applied to each specific row of the matrix compared to traditional element procedures applied to three dimensional problems the computational complexity is lowered from o p 9 per degree of freedom to o p 4 where p is the order of polynomials this is close to the theoretical minimum of o p 3 attained by for example collocation consequently this type of formation and assembly scales favorably with polynomial degree which opens the way for high order isogeometric analysis employing k refinement that is use of maximally smooth higher order splines in this work we discuss various important details for the practical implementation of the weighted quadrature formation strategy proposed in 1 specifically we extend the weighted quadrature scheme to accurately integrate the elements of the stiffness matrix in linear elasticity and propose a means of distributing quadrature points for non uniform mixed continuity spline spaces furthermore we discuss efficient access and assignment into the prevalent sparse matrix data structures namely compressed sparse row csr and compressed sparse column csc in particular row by row or column by column assembly allows matrix rows or columns respectively to be formed contiguously in the storage order of the sparse matrix thereby minimizing the memory overhead and eliminating the addition assignment operation on sparse matrices several three dimensional benchmark problems illustrate the efficiency and efficacy of the proposed formation and assembly technique applied to isogeometric linear elasticity we show that the accuracy of full gauss quadrature is maintained while the computational burden of forming the matrix equations is significantly reduced

duality and unified analysis of discrete approximations in structural dynamics and wave propagation comparison of p method finite elements with k method nurbs we study the discretization behavior of classical finite element and nurbs approximations on problems of structural vibrations and wave propagation we find that on the basis of equal numbers of degrees of freedom and bandwidth nurbs have superior approximation properties in fact we observe that the high mode behavior of classical finite elements is divergent with the order of approximation a surprisingly negative result on the other hand nurbs offer almost spectral approximation properties and all modes converge with increasing order of approximation

necessary and sufficient conditions for finite time singularities in ordinary differential equations abstract this paper gives a theorem which provides necessary and sufficient conditions for the existence of a real finite value of the independent variable at which the general solution of a certain class of ordinary differential equations diverges to infinity this class is a large subset of the set of all autonomous non linear polynomial ordinary differential equation these conditions involve the asymptotic form of the local series representation for the general solutions around the singularities and can be checked algorithmically

algebraic multilevel preconditioning in isogeometric analysis construction and numerical studies abstract we present algebraic multilevel iteration amli methods for isogeometric discretization of scalar second order elliptic problems the construction of coarse grid operators and hierarchical complementary operators are given moreover for a uniform mesh on a unit interval the explicit representation of b spline basis functions for a fixed mesh size h is given for p 2 3 4 and for c 0 and c p 1 continuity the presented methods show h and almost p independent convergence rates supporting numerical results for convergence factor and iterations count for amli cycles v linear w nonlinear w are provided numerical tests are performed in two dimensions on square domain and quarter annulus and in three dimensions on quarter thick ring

an unfitted hp adaptive finite element method based on hierarchical b splines for interface problems of complex geometry generating finite element discretizations with direct interface parameterizations constitutes a considerable computational expense in case of complex interface geometries the paper at hand introduces a b spline finite element method which circumvents parameterization of interfaces and offers fast and easy meshing irrespective of the geometric complexity involved its core idea is the adaptive approximation of discontinuities by hierarchical grid refinement which adds several levels of local basis functions in the close vicinity of interfaces but unfitted to their exact location so that a simple regular grid of knot span elements can be maintained numerical experiments show that an hp refinement strategy which simultaneously increases the polynomial degree of the b spline basis and the levels of refinement around interfaces achieves exponential rates of convergence despite the presence of discontinuities it is also demonstrated that the hierarchical b spline fem can be used to transfer the recently introduced finite cell concept to geometrically nonlinear problems its computational performance imposition of unfitted boundary conditions and fast hierarchical grid generation are illustrated for a set of benchmark problems in one two and three dimensions and the advantages of the regular grid approach for complex geometries are demonstrated by the geometrically nonlinear simulation of a voxel based foam composite

isogeometric schwarz preconditioners for linear elasticity systems isogeometric schwarz preconditioners are constructed and analyzed for both compressible elasticity in primal formulation and almost incompressible elasticity in mixed formulation these preconditioners require the solution of local elasticity problems on overlapping subdomains forming a decomposition of the problem domain and the solution of a coarse elasticity problem associated with the subdomain coarse mesh an h analysis of the preconditioner for the primal formulation of compressible elasticity yields an optimal convergence rate bound that is scalable in the number of subdomains and is linear in the ratio between subdomain and overlap sizes extensive numerical experiments in 2d and 3d confirm this theoretical bound and show that an analogous bound holds for the mixed formulation of almost incompressible elasticity the numerical tests also show the good preconditioner performance with respect to the polynomial degree p and regularity k of the isogeometric basis functions as well as with respect to the presence of discontinuous elastic coefficients in composite materials and to domain deformation

integrability and singularity structure of predator prey system the extended ars ablowitz ramani and segur algorithm is introduced to characterize a dynamical system as painleve or otherwise to that end it is required that the formal series the laurent series logarithmic algebraic psi series about a movable singularity are shown to converge in the deleted neighborhood of the singularity the determinations thus obtained are compared with those following from the method of painleve an attempt is made to relate the structure of solutions about a movable singularity with that of first integrals when they exist all these ideas are illustrated by a comprehensive analysis of the general two dimensional predator prey system

a class of utility functions containing all the common utility functions this paper presents a class of utility functions class a that contains all of the utility functions commonly used for mathematical modeling the class consisting of those utility functions whose derivatives alternate in sign a simple representation via mixtures of exponential utilities is provided for this class which is both mathematically convenient and conducive to functional operations a connection with laplace transforms and the resultant implications for preference relations aggregation and utility assessment are discussed

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

overlapping schwarz methods for isogeometric analysis we construct and analyze an overlapping schwarz preconditioner for elliptic problems discretized with isogeometric analysis the preconditioner is based on partitioning the domain of the problem into overlapping subdomains solving local isogeometric problems on these subdomains and solving an additional coarse isogeometric problem associated with the subdomain mesh we develop an h analysis of the preconditioner showing in particular that the resulting algorithm is scalable and its convergence rate depends linearly on the ratio between subdomain and overlap sizes for fixed polynomial degree p and regularity k of the basis functions numerical results in two and three dimensional tests show the good convergence properties of the preconditioner with respect to the isogeometric discretization parameters h p k number of subdomains n overlap size and also jumps in the coefficients of the elliptic operator

weak dirichlet boundary conditions for wall bounded turbulent flows abstract in turbulence applications strongly imposed no slip conditions often lead to inaccurate mean flow quantities for coarse boundary layer meshes to circumvent this shortcoming weakly imposed dirichlet boundary conditions for fluid dynamics were recently introduced in y bazilevs t j r hughes weak imposition of dirichlet boundary conditions in fluid mechanics comput fluids 36 2007 12 26 in the present work we propose a modification of the original weak boundary condition formulation that consistently incorporates the well known law of the wall to compare the different methods we conduct numerical experiments for turbulent channel flow at reynolds number 395 and 950 in the limit of vanishing mesh size in the wall normal direction the weak boundary condition acts like a strong boundary condition accordingly strong and weak boundary conditions give essentially identical results on meshes that are stretched to better capture boundary layers however on uniform meshes that are incapable of resolving boundary layers weakly imposed boundary conditions deliver significantly more accurate mean flow quantities than their strong counterparts hence weakly imposed boundary conditions present a robust technique for flows of industrial interest where optimal mesh design is usually not feasible and resolving boundary layers is prohibitively expensive our numerical results show that the formulation that incorporates the law of the wall yields an improvement over the original method

lie symmetries and invariants of the lotka volterra system in this paper we use the lie symmetry method for finding rational and transcendental symmetry transformations and invariants for the 3d lotka volterra system

connection between the existence of first integrals and the painleve property in two dimensional lotka volterra and quadratic systems taking advantage of the considerable amount of work done in the search for first integrals invariants for the two dimensional lotka volterra system and the quadratic system lvs and qs we compare the relations needed to exhibit invariants one for the lvs at least three for the qs to the two conditions of the painleve test index and compatibility we find that eventually restricting the invariants to those which are analytic all exponents integers and thereby adding new constraints these constraints always coalesce with the two painleve conditions we conclude that straightforward application of the painleve test picks up only these simple analytic invariants and that possession of the painleve property is too strong a condition for the existence of the invariants

dominance conditions for multivariate utility functions stochastic dominance conditions are given for n variate utility functions when k variate risk aversion is assumed for k 1 2 n these conditions are expressed through a comparison of distribution functions as in the well known univariate case and through a comparison of random variables defined on the same probability space

painleve analysis and normal forms theory nonlinear vector fields have two important types of singularities the fixed points in phase space and the time singularities in the complex plane the first singularities are locally analyzed via normal form theory whereas the second ones are studied by the painleve analysis in this paper normal form theory is used to describe the solutions around their complex time singularities to do so a transformation mapping the local series around the singularities to the local series around a fixed point of a new system is introduced regular normal form theory is then used in this new system it is shown that a vector field has the painleve property only if the associated system is locally linearizable around its fixed points a problem analogous to the classical problem of the center moreover the connection between partial and complete integrability and the structure of local series around both types of singularities are established a new proof of the convergence of the local psi series is given and an explicit method to prove the existence of finite time blow up manifold in phase space is presented

elicitation of multiattribute value functions through high dimensional model representations monotonicity and interactions abstract this work addresses the early phases of the elicitation of multiattribute value functions proposing a practical method for assessing interactions and monotonicity we exploit the link between multiattribute value functions and the theory of high dimensional model representations the resulting elicitation method does not state any a priori assumption on an individual s preference structure we test the approach via an experiment in a riskless context in which subjects are asked to evaluate mobile phone packages that differ on three attributes

effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear deformable beams with varying curvature and torsion abstract we present a displacement based and a mixed isogeometric collocation iga c formulation for free form three dimensional shear deformable beams with high and rapidly varying curvature and torsion when such complex shapes are concerned the approach used to build the iga geometric model becomes relevant although iga c has been so far successfully applied to a wide range of problems the effects that different parameterization and knot placement techniques may have on the accuracy of collocation based formulations is still an unexplored field to fill this gap primal and mixed formulations are used combining two parameterization methods chord length and equally spaced with two knot placement techniques uniformly spaced and de boor with respect to the space varying frenet local frame we derive the strong form of the governing equations in a compact form through the definition of two matrix operators conveniently used to perform first and second order derivatives of the vector fields involved in the formulations this approach is very efficient and easy to implement within a collocation based scheme several challenging numerical experiments allow to test the different considered parameterizations and knot placement techniques revealing in particular that with the primal formulation an equally spaced parameterization is definitively the most recommended choice and it should always be used with an approximation degree of at least p 6 although some caution must be adopted when very high jacobians and small curvatures occur the same holds for the mixed formulation with the difference that p 4 is enough to yield accurate results

extended isogeometric boundary element method xibem for two dimensional helmholtz problems isogeometric analysis is a topic of considerable interest in the field of numerical analysis the boundary element method bem requires only the bounding surface of geometries to be described this makes non uniform rational b splines nurbs which commonly describe the bounding curve or surface of geometries in cad software appear to be a natural tool for the approach this isogeometric analysis bem igabem provides accuracy benefits over conventional bem schemes due to the analytical geometry provided by nurbs when applied to wave problems it has been shown that enriching bem approximations with a partition of unity basis in what has become known as the pu bem allows highly accurate solutions to be obtained with a much reduced number of degrees of freedom this paper combines these approaches and presents an extended isogeometric bem xibem which uses partition of unity enriched nurbs functions this new approach provides benefits which surpass those of both the igabem and the pu bem two numerical examples are given a single scattering cylinder and a multiple scatterer made up of two capsules and a cylinder

rotation free isogeometric analysis of an arbitrarily curved plane bernoulli euler beam abstract the present study elucidates linear static analysis for plane beam structures using the isogeometric approach a novel methodology for rotation free analysis of an arbitrarily curved bernoulli euler beam in the convective frame of reference is derived in detail the full degeneration of a 3d continuum beam to a 1d line has been presented and a fully applicable isogeometric finite element has been obtained the driving force behind developing the present research has been the derivation of the nurbs based isogeometric analysis which will enable an elegant formulation of the plane bernoulli euler beams being a function only of the global rectangular cartesian coordinates the verification and accuracy of the research are obtained via a thorough comparison between theory finite element analyses and relevant examples from literature an excellent agreement of results is achieved and usefulness for academic and practical purposes alike are proved the effects of the hpk refinements are illuminated and it is observed that the convergences for the most variables and refinement techniques are not monotonic a special attention is paid to the influence of the product of maximum curvature and thickness of beam on the accuracy of the solution the limits of applicability of the present approach are defined for a few specific types of analyses the derived formulation is geometrically exact and appropriate for the analysis of strongly curved bernoulli euler beams

efficient quadrature for nurbs based isogeometric analysis abstract we initiate the study of efficient quadrature rules for nurbs based isogeometric analysis a rule of thumb emerges the half point rule indicating that optimal rules involve a number of points roughly equal to half the number of degrees of freedom or equivalently half the number of basis functions of the space under consideration the half point rule is independent of the polynomial order of the basis efficient rules require taking into account the precise smoothness of basis functions across element boundaries several rules of practical interest are obtained and a numerical procedure for determining efficient rules is presented we compare the cost of quadrature for typical situations arising in structural mechanics and fluid dynamics the new rules represent improvements over those used previously in isogeometric analysis

adaptive isogeometric analysis by local h refinement with t splines isogeometric analysis based on non uniform rational b splines nurbs as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space which renders a purely local refinement impossible this paper demonstrates how this difficulty can be overcome by using t splines instead t splines allow the introduction of so called t junctions which are related to hanging nodes in the standard fem obeying a few straightforward rules rectangular patches in the parameter space of the t splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry furthermore it is shown how state of the art a posteriori error estimation techniques can be combined with refinement by t splines numerical examples underline the potential of isogeometric analysis with t splines and give hints for further developments

multiattribute utility satisfying a preference for combining good with bad an important challenge in multiattribute decision analysis is the choice of an appropriate functional form for the utility function we show that if a decision maker prefers more of any attribute to less and prefers to combine good lotteries with bad as opposed to combining good with good and bad with bad her utility function should be a weighted average a mixture of multiattribute exponential utilities mixex utility in the single attribute case mixex utility satisfies properties typically thought to be desirable and encompasses most utility functions commonly used in decision analysis in the multiattribute case mixex utility implies aversion to any multivariate risk risk aversion with respect to any attribute decreases as that attribute increases under certain restrictions such risk aversion also decreases as any other attribute increases and a multivariate one switch property is satisfied one of the strengths of mixex utility is its ability to represent cases where utility independence does not hold but mixex utility can be consistent with mutual utility independence and take on a multilinear form an example illustrates the fitting of mixex utility to preference assessments

variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows we present an les type variational multiscale theory of turbulence our approach derives completely from the incompressible navier stokes equations and does not employ any ad hoc devices such as eddy viscosities we tested the formulation on forced homogeneous isotropic turbulence and turbulent channel flows in the calculations we employed linear quadratic and cubic nurbs a dispersion analysis of simple model problems revealed nurbs elements to be superior to classical finite elements in approximating advective and diffusive processes which play a significant role in turbulence computations the numerical results are very good and confirm the viability of the theoretical framework

functional anova ultramodularity and monotonicity applications in multiattribute utility theory abstract utility function properties as monotonicity and concavity play a fundamental role in reflecting a decision maker s preference structure these properties are usually characterized via partial derivatives however elicitation methods do not necessarily lead to twice differentiable utility functions furthermore while in a single attribute context concavity fully reflects risk aversion in multiattribute problems such correspondence is not one to one we show that tsetlin and winkler s multivariate risk attitudes imply ultramodularity of the utility function we demonstrate that geometric properties of a multivariate utility function can be successfully studied by utilizing an integral function expansion functional anova the necessary and sufficient conditions under which monotonicity and or ultramodularity of single attribute functions imply the monotonicity and or ultramodularity of the corresponding multiattribute function under additive preferential and mutual utility independence are then established without reliance on the utility function differentiability we also investigate the relationship between the presence of interactions among the attributes of a multiattribute utility function and the decision maker s multivariate risk attitudes

on certain new integrable second order nonlinear differential equations and their connection with two dimensional lotka volterra system in this paper we consider a second order nonlinear ordinary differential equation of the form x k1 x2 x k2 k3x x k4x3 k5x2 k6x 0 where ki s i 1 2 6 are arbitrary parameters by using the modified prelle singer procedure we identify five new integrable cases in this equation besides two known integrable cases namely i k2 0 k3 0 and ii k1 0 k2 0 k5 0 among these five four equations admit time dependent first integrals and the remaining one admits time independent first integral from the time independent first integral nonstandard hamiltonian structure is deduced thereby proving the liouville sense of integrability in the case of time dependent integrals we either explicitly integrate the system or transform to a time independent case and deduce the underlying hamiltonian structure we also demonstrate that the above second order ordinary differential equation is intimately related to the two dimensional lotka volterra system from the integrable parametric choices of the above non