geometry of exclusion principles in discrete systems abstract using an n species system of difference equations with very general density dependent growth functions we prove that weak dominance and invariance gives the exclusion of all the n 1 dominated species in the system this result is applied to very specific competition models an example of coexistence in a competition model with no invariance is studied a notion of strong dominance is developed in a general setting and shown to imply exclusion of the n 1 dominated species an example of a competition model illustrating that weak dominance plus invariance does not imply strong dominance is given

structural optimization a new dual method using mixed variables a new and powerful mathematical programming method is described which is capable of solving a broad class of structural optimization problems the method employs mixed direct reciprocal design variables in order to get conservative first order approximations to the objective function and to the constraints by this approach the primary optimization problem is replaced with a sequence of explicit subproblems each subproblem being convex and separable it can be efficiently solved by using a dual formulation an attractive feature of the new method lies in its inherent tendency to generate a sequence of steadily improving feasible designs examples of application to real life aerospace structures are offered to demonstrate the power and generality of the approach presented

stress constrained shape and topology optimization with fixed mesh a b spline finite cell method combined with level set function abstract in this paper we develop an efficient and flexible design method that integrates the b spline finite cell method b spline fcm and the level set function lsf for stress constrained shape and topology optimization any structure of complex geometry is embedded within an extended regular and fixed eulerian mesh no matter how the structure is optimized high order b spline shape functions are further implemented to ensure precisions of stress analysis and sensitivity analysis meanwhile level set functions i e implicit functions are used to enable topological changes of the considered structure through smooth boundary variations involved parameters rather than the conventional discrete form of lsf are directly taken as design variables to facilitate the numerical computing process to be specific the lsf is constructed by means of r functions that incorporate cubic splines as implicit functions to offer flexibilities for shape optimization within the framework of fixed mesh while the compactly supported radial basis functions cs rbfs are employed as implicit functions for stress constrained topology optimization it is shown the proposed fcm lsf method is a convenient approach that makes it possible to calculate stress and stress sensitivities with high precision representative examples of shape and topology optimization with and without stress constraints are solved with success demonstrating the advantages of the fcm lsf method

creation operators and algebraic bethe ansatz for the elliptic quantum group eτ η so3 we define the elliptic quantum group e so3 and the transfer matrix corresponding to its simplest highest weight representation we use the bethe ansatz method to construct the creation operators as polynomials of the lax matrix elements expressed through a recurrence relation we give common eigenvectors and eigenvalues of the family of commuting transfer matrices

review of options for structural design sensitivity analysis part 1 linear systems the paper reviews options for structural design sensitivity analysis including global finite differences continuum derivatives discrete derivatives and computational or automated differentiation the objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency computational cost and implementation options and effort linear static analysis and transient dynamic analysis are reviewed in a separate appendix special attention is paid to the semi analytical method a future paper will address design sensitivity analysis in nonlinear structural problems

global stability of discrete competition model abstract this is a study of global stability of a competition model governed by difference equations it is shown that positive equilibrium of the model is globally stable if the competition matrix is diagonally dominant and the constants defining the intraspecific competition are less than or equal to 1 in the two dimensional case a different type of sufficient conditions for the global stability is established which relaxes the restriction on the constants defining the intraspecific competition

topology optimization with closed b splines and boolean operations abstract in this work free form curves of closed b splines cbs are introduced as basic design primitives to realize structural topology optimization in the way of shape optimization unlike the existing density and level set methods the cbs takes full advantage of its parametric form for the design deformability and flexibility with a few number of design variables and its implicit form for boolean operations of the structural topology accounting for any overlapping merging and separation of different cbs no matter how geometric complexities of the cbs and the design domain are the cbs is implemented within the computing framework of finite cell method fcm so that structural analysis and topology optimization can efficiently be carried out using the fixed mesh typical examples are tested to demonstrate the effectiveness and generality of the proposed method in dealing with engineering design problems

shape optimal design using b splines abstract shape optimal design of an elastic structure is formulated using a design element technique it is shown that bezier and b spline curves typical of the cad philosophy are well suited to the definition of design elements complex geometries can be described in a very compact way by a small set of design variables and a few design elements because of the b splines flexibility it is no longer necessary to piece design elements together in order to agree with the shape complexity nor to restrict the shape variations moreover the additional optimization constraints that are most often needed to avoid unrealistic designs when the shape variables are the nodal coordinates of a finite element mesh are automatically taken into account in the new formulation an analytical derivation of the sensitivity analysis will be established giving rise to numerical efficiency it will be seen that the resulting optimization problem does not involve highly nonlinear functions with respect to the shape variables so that simple mathematical programming algorithms can be applied to solve it some numerical examples are offered to demonstrate the power and generality of the new approach presented in this paper

towards simultaneous reduction of both input and output spaces for interactive simulation based structural design abstract engineering design problems generally involve a high dimensional input space of design variables yielding an output space by means of costly high fidelity evaluations in order to decrease the overall cost reduced order models for the output space such as proper orthogonal decomposition pod and proper generalized decomposition pgd are an active area of research however little research has been conducted into alleviating the problems associated with a high dimensional input space in addition to higher dimensionality being an impediment to efficient design by itself complex shapes involve a high number of explicit implicit constraints restricting the design space geometric parameterization methods in traditional cad present difficulties in expressing these constraints leading to a high failure rate and the generation of inadmissible shapes in this paper we propose a simultaneous meta modeling protocol for both input and output spaces we perform a reparametrization of the input space using constrained shape interpolation by introducing the concept of an manifold of admissible meshed shapes the output space is reduced using constrained proper orthogonal decomposition by simultaneously using meta modeling for both spaces we facilitate interactive design space exploration for the purpose of design the proposed approach is applied to the industrial problem of designing a car engine intake port

explicit constraint approximation forms in structural optimization part 1 analyses and projections abstract an analytical study of several alternative forms of constraint approximation relevant to problems in structural design is presented limitations of the existing forms of the constraint approximations are stated and methods are outlined to improve them a new generalized form of constraint approximation is proposed for optimal design problems with and without design variable linking a power form of constraint approximation is derived for bending types of finite elements having nonlinear size stiffness relationships a detailed analysis to determine the relative effectiveness of the various forms is included a rating guideline is proposed to quantify the characteristics of chosen approximations or family of approximations on grounds of accuracy and of conservatism of remaining feasible

algebraic bethe ansatz for the elliptic quantum group eτ η a2 2 we implement the bethe ansatz method for the elliptic quantum group e a2 2 the bethe creation operators are constructed as polynomials of the lax matrix elements expressed through a recurrence relation we also give the eigenvalues of the family of commuting transfer matrices defined in the tensor product of fundamental representations

shape optimization of dirichlet boundaries based on weighted b spline finite cell method and level set function abstract this paper addresses extended shape optimization problems where structural supports i e dirichlet boundaries and free boundaries are simultaneously optimized unlike traditional fem the weighted b spline finite cell method fcm is applied as structural analysis tool and combined with the level set function lsf to take into account dirichlet boundary condition dbc automatically through penalization of the displacement field the proposed shape optimization method achieves a comprehensive integration of fixed grid b spline shape function and level set function as both the structure and dirichlet boundaries are described in the form of lsf any modification of dirichlet boundaries can be made in a straightforward way as easily as free boundaries by changing continuous design variables meanwhile the computing accuracy is ensured within the framework of fixed grid owing to the quadtree refinements of boundary cells stress related shape optimization problems are finally solved to demonstrate the merit and validity of the proposed optimization method in dealing with shape optimization of dirichlet boundaries

stress constrained topology optimization with free form design domains abstract this paper aims at dealing with realistic and challenging design problems of stress constrained topology optimization with free form design domains first the concept of level set function lsf based modelers is introduced to transform this kind of problems into the boolean conjunction operation of a topology variation modeler tvm onto a free form design domain modeler fddm such an operation is mathematically realized by means of the so called r functions in the form of implicit lsfs within this framework topology optimization problems are classified into two general cases depending upon the existence of non designable solid feature analytical sensitivity analysis formulas are further derived compared with the existing level set based method the important sensitivity property of design domain preserving makes it possible to avoid automatically the boundary violation of the design domain caused by the zero level set movement and both the topology and boundary shape of the free form design domain can be simultaneously optimized second the implementation of the finite cell method fcm ensures the stress computing accuracy in the fixed mesh due to the use of high order shape functions and adaptive integration scheme the combination of the active set strategy and the dynamic aggregation technique also reduces the number of local stress constraints greatly finally representative examples are presented to illustrate the conveniences and effectiveness of the proposed method

singularities of n fold integrals of the ising class and the theory of elliptic curves we introduce some multiple integrals that are expected to have the same singularities as the singularities of the n particle contributions n to the susceptibility of the square lattice ising model we find the fuchsian linear differential equation satisfied by these multiple integrals for n 1 2 3 4 and only modulo some primes for n 5 and 6 thus providing a large set of possible new singularities of n we discuss the singularity structure for these multiple integrals by solving the landau conditions we find that the singularities of the associated odes identify up to n 6 with the leading pinch landau singularities the second remarkable obtained feature is that the singularities of the odes associated with the multiple integrals reduce to the singularities of the odes associated with a finite number of one dimensional integrals among the singularities found we underline the fact that the quadratic polynomial condition 1 3w 4w2 0 that occurs in the linear differential equation of 3 actually corresponds to a remarkable property of selected elliptic curves namely the occurrence of complex multiplication the interpretation of complex multiplication for elliptic curves as complex fixed points of the selected generators of the renormalization group namely isogenies of elliptic curves is sketched most of the other singularities occurring in our multiple integrals are not related to complex multiplication situations suggesting an interpretation in terms of motivic mathematical structures beyond the theory of elliptic curves

elliptic quantum groups and ruijsenaars models we construct symmetric and exterior powers of the vector representation of the elliptic quantum groupse sln the corresponding transfer matrices give rise to various integrable difference equations which could be solved in principle by the nested bethe ansatz method in special cases we recover the ruijsenaars systems of commuting difference operators

geometric stability conditions for higher order difference equations is a higher order or delay autonomous difference equation if the order m is a fixed positive integer larger than 1 the real valued function f is assumed continuous on r and x x g r are the initial values in 1ym 0 addition to the fact that discretizations of scalar differential equations result in equations of type 1 direct applications of difference equations of order greater than 1 date back to more than half a century ago and nowadays these equations are increasingly encountered in both social and w x w x natural sciences see 4 and 6 for some applications and additional references a solution x of f x x s x is a fixed point or equilibrium of eq 1 like its differential analogs 1 can be and often is translated into a first order vector equation the instability or the asymptotic stability of x may then be determined by linearizing the associated vector function

shape design optimization of hyperelastic structures using a meshless method ashapedesignoptimizationprocedureforhyperelasticstructuresisdevelopedusing ameshlessmethodforanalysis and a continuum based design sensitivity analysis dsa method the meshless method greatly reduces the mesh distortion or entanglement encountered in using the e nite element method for large deformation nonlinear analysis and structural shape design optimization the dsa method of grindeanu et al grindeanu i chang k h choi k k and chen j s design sensitivity analysis of hyperelastic structures using a meshless method aiaa journal vol 36 no 4 1998 pp 618 627 is extended by using a pressure projection method to avoid volumetric locking for nearly incompressible materials without the need for large support sizes for the meshless shape functions and to reduce the cpu time the lagrange multiplier method is used to impose the essential boundary conditions an engine mount is employed as an example to demonstrate the feasibility of the proposed optimization method the mass is minimized subject to constraints on hydrostatic pressure and stiffness characteristics of the component the design velocity e elds corresponding to theshape design parameters are obtained using the design sensitivity analysis and optimization tool shape design optimization is carried out using the modie ed feasible direction of the design optimization tool

a physics based parameterization method for shape optimization a physical approach is presented to provide shape modification of nurbs curve the movement of the control polygon of nurbs is simulated by a physical frame structure and the curve deformation is then carried out through changes of the mode coordinates which are derived from the eigenvectors of the finite element equations of the physical frame system the shape of the design boundaries is described by a linear combination of the mode shape vectors based on the presented design variable representation and p version finite element analysis an integrated approach to structural shape optimization is discussed a method is developed that enables the description of the shape to be adaptively refined during the shape optimization process numerical examples are used to demonstrate the applicability of this approach to structural shape optimization

a unified parametric design approach to structural shape optimization this paper presents a general parametric design approach for 2 d shape optimization problems this approach has been achieved by integrating practical design methodologies into numerical procedures it is characterized by three features i automatic selection of a minimum number of shape design variables based on the cad geometric model ii integration of sequential convex programming algorithms to solve equality constrained optimization problems iii efficient sensitivity analysis by means of the improved semi analytical method it is shown that shape design variables can be either manually or systematically identified with the help of equality constraints describing the relationship between geometric entities numerical solutions are performed to demonstrate the applicability of the proposed approach a discussion of the results is also given

the gervais neveu felder equation and the quantum calogero moser systems we quantize the spin calogero moser model in ther matrix formalism the quantumr matrix of the model is dynamical thisr matrix has already appeared in gervais neveu s quantization of toda field theory and in felder s quantization of the knizhnik zamolodchikov bernard equation

on representations of the elliptic quantum group e τ η sl 2 we describe representation theory of the elliptic quantum groupe sl 2 it turns out that the representation theory is parallel to the representation theory of the yangiany sl 2 and the quantum loop group u q widetilde sl 2 we introduce basic notions of representation theory of the elliptic quantum groupe sl 2 and construct three families of modules evaluation modules cyclic modules one dimensional modules we show that under certain conditions any irreducible highest weight module of finite type is isomorphic to a tensor product of evaluation modules and a one dimensional module we describe fusion of finite dimensional evaluation modules in particular we show that under certain conditions the tensor product of two evaluation modules becomes reducible and contains an evaluation module in this case the imbedding of the evaluation module into the tensor product is given in terms of elliptic binomial coefficients we describe the determinant element of the elliptic quantum group representation theory becomes special ifn m l wheren m l are integers we indicate some new features in this case

exclusion principles for density dependent discrete pioneer climax models abstract the ultimate dynamical result of an undisturbed pioneer climax model is assumed by experimental scientists to be the exclusion of the pioneer species examples that illustrate stable coexistence in a pioneer climax model with no isolated positive equilibria are given sufficient conditions are developed and used to confirm the pioneer exclusion in discrete pioneer climax models other situations are possible in such models in particular a mutual exclusion principle is established as a mathematical theorem

an approximation concepts approach to shape optimal design abstract in the past much of the work done in structural optimization consisted in resizing the members of fixed configuration models in that case a powerful design procedure has now emerged which is based on the coordinate use of explicit high quality approximations of the behavior constraints and dual methods of mathematical programming there is however a large class of problems for which the main degrees of freedom for the designer correspond to the shape of the structure itself the main objectives of this paper are to recall briefly a convenient geometric representation in which the boundaries of the structure are represented by bezier or b spline curves and then to discuss the choice of optimization algorithm it is shown that cost efficient methods for structural sizing may be advantageously extended to shape optimal design problems different approximation schemes are tested and a new general optimization algorithm is presented that combines mixed approximations and dual methods many large scale applications are treated to demonstrate the generality and the efficiency of the new formulation finally considerations are given about an integrated approach including cad computer codes and finite element optimization software