internal deformation of lie algebroids and symplectic realizations given a lie algebroid and a bundle over its base which is endowed with a localizable poisson structure and a flat connection we construct an extended bundle whose dual is endowed with an almost poisson structure that is a quadratic poisson structure when a certain compatibility property is satisfied this new formalism on lie algebroids describes systems with internal degrees of freedom

a survey of exact algorithms for the simple assembly line balancing problem in this survey paper we discuss the development of the simple assembly line balancing problem salbp modifications and generalizations over time present alternate 0 1 programming formulations and a general integer programming formulation of the problem discuss other well known problems related to salbp describe and comment on a number of exact i e optimum seeking methods and present a summary of the reported computational experiences all models discussed here are deterministic i e all input parameters are assumed to be known with certainty and all the algorithms discussed are exact the problem is termed simple in the sense that no mixed models subassembly lines zoning restrictions etc are considered due to the richness of the literature we exclude from discussion here a the inexact i e heuristic approximate algorithms for salpb and b the algorithms for the general assembly line balancing problem including the stochastic models

frictional wear of a thermoelastic beam we present two versions of a mathematical model for the evolution of wear in a thermoelastic beam resulting from frictional contact with a rigid moving surface one version is quasistatic and the other dynamic we show that the quasistatic problem allows for the decoupling of the mechanical and thermal aspects of the process the problem reduces to that of the heat equation with nonlinear and history dependent boundary conditions then the displacements shear stresses and wear can be obtained by quadrature we establish the existence of a local weak solution for the problem and a partial uniqueness result and obtain conditions for the solution s further regularity the dynamic problem consists of the heat equation coupled with the equation of motion and the archard wear equation we prove the existence and uniqueness of the local weak solution of this problem too

integrability of lie brackets in this paper we present the solution to a longstanding problem of differential geometry lie s third theorem for lie algebroids we show that the integrability problem is controlled by two computable obstructions as applications we derive explain and improve the known integrability results we establish integrability by local lie groupoids we clarify the smoothness of the poisson sigma model for poisson manifolds and we describe other geometrical applications

geometric structures as deformed infinitesimal symmetries a general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries specifically this model consists of a lie algebroid equipped with an affine connection compatible with the lie algebroid structure the curvature of this connection vanishes precisely when the structure is locally symmetric this model generalizes cartan geometries a substantial class to the intransitive case simple examples are surveyed and corresponding local obstructions to symmetry are identified these examples include foliations riemannian structures infinitesimal g structures symplectic and poisson structures

on co morphisms of lie pseudoalgebras and groupoids we give a unified description of morphisms and comorphisms of lie pseudoalgebras showing that the both types of morphisms can be regarded as subalgebras of a lie pseudoalgebra called the sum we also provide similar descriptions for morphisms and comorphisms of lie algebroids and groupoids

on integrability of infinitesimal actions we use foliations and connections on principal lie groupoid bundles to prove various integrability results for lie algebroids in particular we show under quite general assumptions that the semi direct product associated to an infinitesimal action of one integrable lie algebroid on another is integrable this generalizes recent results of dazord and nistor

lie algebroid structures on double vector bundles and representation theory of lie algebroids abstract a vb algebroid is essentially defined as a lie algebroid object in the category of vector bundles there is a one to one correspondence between vb algebroids and certain flat lie algebroid superconnections up to a natural notion of equivalence in this setting we are able to construct characteristic classes which in special cases reproduce characteristic classes constructed by crainic and fernandes we give a complete classification of regular vb algebroids and in the process we obtain another characteristic class of lie algebroids that does not appear in the ordinary representation theory of lie algebroids

stability analysis of an optimal balance for an assembly line with fixed cycle time abstract we address the simple assembly line balancing problem minimize the number of stations m for processing n partially ordered operations v 1 2 n within the cycle time c the processing time ti of operation i v and cycle time c are given however during the life cycle of the assembly line the values ti are definitely fixed only for the subset of automated operations v v another subset v v includes manual operations for which it is impossible to fix the exact processing times during the whole life cycle of the assembly line if j v then operation time tj can be different for different cycles of production process for the optimal line balance b of a paced assembly line with vector t t1 t2 tn of the operation times we investigate stability of its optimality with respect to possible variations of the processing times tj of the manual operations j v in particular we derive necessary and sufficient conditions when optimality of the line balance b is stable with respect to sufficiently small variations of the operation times tj j v we show how to calculate the maximal value of independent variations of the processing times of all the manual operations which definitely keep the feasibility and optimality of the line balance b

algebraic constructions in the category of lie algebroids the aim of this paper is to give the first general and abstract treatment of the algebraic properties of lie algebroids the concept of lie algebroid was introduced in 1967 by pradines ls as the basic infinitesimal invariant of a differentiable groupoid the construction of the lie algebroid of a differentiable groupoid is a direct generalization of the construction of the lie algebra of a lie group and 183 described a full lie theory for differentiable groupoids and lie algebroids encompassing many phenomena in the foundations of differential geometry a more detailed account and further references are given in 13 however at this stage the algebraic properties of lie algebroids were not pursued in 13 iii section 2 iv section 11 one of us gave a fairly detailed account of the abstract algebra of lie algebroids over a fixed base lie algebroids are vector bundles with several additional structures and a category of lie algebroids on a given base and morphisms which preserve that base has properties similar to those of the category of lie algebras using this algebra it was demonstrated in 13 that the lie theory of a category of locally trivial differentiable lie groupoids over a fixed base and the corresponding category of transitive lie algebroids over that base is coextensive with the standard theory of connections in principal bundles we now propose to show that the lie functor from the category of all differentiable groupoids over arbitrary bases and arbitrary smooth morphisms to the category of all lie algebroids preserves the basic algebraic constructions known to be possible in the category of differentiable groupoids the main work is to give abstract formulations of the corresponding lie algebroid concepts the groupoid results with which we

representations up to homotopy of lie algebroids we introduce and study the notion of representation up to homotopy of a lie algebroid paying special attention to examples we use representations up to homotopy to define the adjoint representation of a lie algebroid and show that the resulting cohomology controls the deformations of the structure the weil algebra of a lie algebroid is defined and shown to coincide with kalkman s brst model for equivariant cohomology in the case of group actions the relation of this algebra with the integration of poisson and dirac structures is explained in arias abad crainic ann inst fourier

lie algebroid foliations and script e1 m dirac structures we prove some general results about the relation between the 1 cocycles of an arbitrary lie algebroid a over m and the leaves of the lie algebroid foliation on m associated with a using these results we show that a 1 m dirac structure l induces on every leaf f of its characteristic foliation a 1 f dirac structure lf which comes from a precontact structure or from a locally conformal presymplectic structure on f in addition we prove that a dirac structure on m can be obtained from l and we discuss the relation between the leaves of the characteristic foliations of l and

lagrangian reduction by stages for non holonomic systems in a lie algebroid framework the lagrange d alembert equations of a non holonomic system with symmetry can be reduced to the lagrange d alembert poincarequations in a previous contribution we have shown that both sets of equations fall in the category of the so called lagrangian systems on a subbundle of a lie algebroid in this paper we investigate the special case when the reduced system is again invariant under a new symmetry group and so forth via lie algebroid theory we develop a geometric context in which successive reduction can be performed in an intrinsic way we prove that at each stage of the reduction the reduced systems are part of the above mentioned category and that the lie algebroid structure in each new step is the quotient lie algebroid of the previous step we further show that that reduction in two stages is equivalent with direct reduction

the stability radius of an optimal line balance with maximum efficiency for a simple assembly line abstract we consider a simple assembly line balancing problem in which each element of the partially ordered set of assembly operations must be assigned to one element of the set of workstations used for processing the operations an objective is minimizing the product of the number of workstations used in the line balance and the cycle time of the line balance among all admissible line balances an admissible line balance is a partition of all assembly operations into at least two workstations without violating the precedence relations among the assembly operations we assume that during the lifespan of the assembly line the duration of each manual operation may deviate from an initially estimated value while the duration of each automated operation is deterministic we conduct the stability analysis of an optimal line balance first we derive a sufficient and necessary condition for an optimal line balance to be stable second we show that the stability radius of an optimal line balance could be infinitely large we also establish some lower and upper bounds for a finite stability radius third we derive formulae that are needed and develop an algorithm for obtaining the stability radius of an optimal line balance

thermoelastic frictional contact problems modelling finite element approximation and numerical realization abstract in this paper frictional contact including frictional heat generation and heat transfer across the contact interface is studied a model for the behaviour of the contact interface is proposed and combined with the conventional equations of linear thermoelasticity for the bulk material of the contacting bodies a finite element discretization in space and a finite difference discretization in time are introduced and an iterative algorithm is proposed to deal with the coupled thermal mechanical nature of the problem finally several numerical examples are given

stability of an optimal schedule abstract this paper deals with the problem of optimal scheduling n uninterrupted operations on m machines with respect to a regular criterion the stability radius s a for an optimal schedule s relative to the changes in the vector a a 1 a n of durations of operations q 1 n is studied the problem of calculating s a is reduced to the solution of a non linear mathematical programming problem the necessary and sufficient conditions for s a 0 and for s a are given in the case when s is the optimal makespan schedule

integration of twisted dirac brackets given a lie groupoid g over a manifold m we show that multiplicative 2 forms on g relatively closed with respect to a closed 3 form phi on m correspond to maps from the lie algebroid of g into t m satisfying an algebraic condition and a differential condition with respect to the phi twisted courant bracket this correspondence describes as a special case the global objects associated to phi twisted dirac structures as applications we relate our results to equivariant cohomology and foliation theory and we give a new description of quasi hamiltonian spaces and group valued momentum maps

reduction of a symplectic like lie algebroid with momentum map and its application to fiberwise linear poisson structures this paper addresses the problem of developing an extension of the marsden weinstein reduction process to symplectic like lie algebroids and in particular to the case of the canonical cover of a fiberwise linear poisson structure whose reduction process is the analog to cotangent bundle reduction in the context of lie algebroids dedicated to the memory of jerrold e marsden

vector bundles over lie groupoids and algebroids abstract we study vb groupoids and vb algebroids which are vector bundles in the realm of lie groupoids and lie algebroids through a suitable reformulation of their definitions we elucidate the lie theory relating these objects i e their relation via differentiation and integration we also show how to extend our techniques to describe the more general lie theory underlying double lie algebroids and la groupoids

on the existence and uniqueness of steady state solutions in thermoelastic contact with frictional heating existence and uniquness of steady state solutions in thermoelastic contact with frictional heating