optimality conditions for linear programming problems with fuzzy coefficients the optimality conditions for linear programming problems with fuzzy coefficients are derived in this paper two solution concepts are proposed by considering the orderings on the set of all fuzzy numbers the solution concepts proposed in this paper will follow from the similar solution concept called the nondominated solution in the multiobjective programming problem under these settings the optimality conditions will be naturally elicited

static and dynamic stability results for a class of three dimensional configurations of kirchhoff elastic rods we analyze the dynamical stability of a naturally straight inextensible and unshearable elastic rod under tension and controlled end rotation within the kirchhoff model in three dimensions the cases of clamped boundary conditions and isoperimetric constraints are treated separately we obtain explicit criteria for the static stability of arbitrary extrema of a general quadratic strain energy we exploit the equivalence between the total energy and a suitably defined norm to prove that local minimizers of the strain energy under explicit hypotheses are stable in the dynamic sense due to liapounov we also extend our analysis to damped systems to show that static equilibria are dynamically stable in the liapounov sense in the presence of a suitably defined local drag force

towards a classification of euler kirchhoff filaments euler kirchhoff filaments are solutions of the static kirchhoff equations for elastic rods with circular cross sections these equations are known to be formally equivalent to the euler equations for spinning tops this equivalence is used to provide a classification of the different shapes a filament can assume explicit formulas for the different possible configurations and specific results for interesting particular cases are given in particular conditions for which the filament has points of self intersection self tangency vanishing curvature or when it is closed or localized in space are provided the average properties of generic filaments are also studied they are shown to be equivalent to helical filaments on long length scales

on the theory of wave propagation in anisotropic plates a theoretical framework is developed which describes wave propagation in infinite homogeneous elastic plates of unrestricted anisotropy the approach exploits the propagator matrix which is the exponential of the fundamental elasticity matrix underlying stroh9s formalism of anisotropic elastodynamics the matrices of plate impedance and admittance are introduced and their analytical properties are established which appear fruitful for computing and analysing the plate wave spectra on this basis the dispersion equation can be cast into the form of a real equation involving the monotonic function whose zeros and poles are the wave velocities in a given plate subjected to different boundary conditions traction free or clamped faces it is proved that three fundamental wave branches exist for any orientation of wave propagation in an anisotropic plate with traction free faces and that those branches are missing if one or both faces are clamped the intrinsic symmetry of the wave motion in an arbitrary plate is revealed the general formalism is applied to elaborate the long wavelength low frequency approximation for a thin free plate of unrestricted anisotropy the frequency dispersive wave velocities displacements and tractions at the onset of the fundamental wave branches are derived explicitly the conditions for the extreme velocity values and some other useful universal connections are determined for an arbitrary thin plate and exemplified for specific anisotropy cases

formulation of general possibilistic linear programming problems for complex industrial systems the current models and methods for plp are usually restricted on some special types and usually the same type of possibilistic distribution this paper focuses on linear programming problems with general possibilistic resources grplp and linear programming problems with general possibilistic objective coefficients goplp by introducing some new concepts of the largest most possible point the smallest most possible point the most optimistic point and the most possible decision a new approach for formulating possibilistic constraints through general possibilistic resources and a satisfactory solution method will be discussed in this paper a most possible decision method for grplp and a dual approach for goplp will be proposed for solving complex industrial decision problems

balancing torques in membrane mediated interactions exact results and numerical illustrations torques on interfaces can be described by a divergence free tensor which is fully encoded in the geometry this tensor consists of two terms one originating in the couple of the stress the other capturing an intrinsic contribution due to curvature in analogy to the description of forces in terms of a stress tensor the torque on a particle can be expressed as a line integral along a contour surrounding the particle interactions between particles mediated by a fluid membrane are studied within this framework in particular torque balance places a strong constraint on the shape of the membrane symmetric two particle configurations admit simple analytical expressions which are valid in the fully nonlinear regime in particular the problem may be solved exactly in the case of two membrane bound parallel cylinders this apparently simple system provides some flavor of the remarkably subtle nonlinear behavior associated with membrane mediated interactions

sensitivity analysis in fuzzy linear fractional programming problem abstract in this paper a linear fractional programming problem where the numerator or denominator or both of the objective function are fuzzy in nature is first converted to an equivalent fuzzy linear programming problem sensitivity analysis of the problem thus formulated is illustrated with the help of a numerical example

fuzzy shortest path problems incorporating interactivity among paths abstract this paper deals with a shortest path problem on a network in which a fuzzy number instead of a real number is assigned to each arc length such a problem is ill posed because each arc cannot be identified as being either on the shortest path or not therefore based on the possibility theory we introduce the concept of degree of possibility that an arc is on the shortest path every pair of distinct paths from the source node to any other node is implicitly assumed to be noninteractive in the conventional approaches this assumption is unrealistic and involve inconsistencies to overcome this drawback we define a new comparison index between the sum of fuzzy numbers by considering interactivity among fuzzy numbers an algorithm is presented to determine the degree of possibility for each arc on a network finally this algorithm is evaluated by means of large scale numerical examples consequently we can find this approach is efficient even for real world practical networks

the fourier transform of tubular densities we consider the fourier transform of tubular volume densities with arbitrary axial geometry and possibly twisted internal structure this density can be used to represent among others magnetic flux or the electron density of biopolymer molecules we consider tubes of both finite radii and unrestricted radius when there is overlap of the tube structure the net density is calculated using the super position principle the fourier transform of this density is composed of two expressions one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater which must have density overlap this expression can accommodate an asymmetric density distribution and a tube structure which has non uniform twisting in addition we give several simpler expressions for isotropic densities densities of finite radius densities which decay at a rate sufficient to minimise local overlap and finally individual surfaces of the tube manifold these simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first order ode s

duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables linear programming problems with trapezoidal fuzzy variables fvlp have recently attracted some interest some methods have been developed for solving these problems by introducing and solving certain auxiliary problems here we apply a linear ranking function to order trapezoidal fuzzy numbers then we establish the dual problem of the linear programming problem with trapezoidal fuzzy variables and hence deduce some duality results in particular we prove that the auxiliary problem is indeed the dual of the fvlp problem having established the dual problem the results will then follow as natural extensions of duality results for linear programming problems with crisp data finally using the results we develop a new dual algorithm for solving the fvlp problem directly making use of the primal simplex tableau this algorithm will be useful for sensitivity or post optimality analysis when using primal simplex tableaus

a dual approach to solve the fuzzy linear programming problem abstract a concept of fuzzy objective based on the fuzzification principle is presented in accordance with this concept the fuzzy linear mathematical programming problem is easily solved a relationship of duality among fuzzy constraints and fuzzy objectives is given the dual problem of a fuzzy linear programming problem is also defined

duality in fuzzy linear programming with possibility and necessity relations a class of fuzzy linear programming flp problems with fuzzy coefficients based on fuzzy relations is introduced the concepts of feasible and a b maximal and minimal solutions are defined the class of crisp classical lp problems can be embedded into the class of flp ones moreover for flp problems a new concept of duality is introduced and the weak and strong duality theorems are derived the introduced concepts and results are illustrated and discussed on a simple numerical example

analytical expression of elastic rods at equilibrium under 3d strong anchoring boundary conditions abstract a general purpose method is presented and implemented to express analytically one stationary configuration of an ideal 3d elastic rod when the end to end relative position and orientation are imposed the mechanical equilibrium of such a rod is described by ordinary differential equations and parametrized by six scalar quantities when one end of the rod is anchored the analytical integration of these equations lead to one unique solution for given values of these six parameters when the second end is also anchored six additional nonlinear equations must be resolved to obtain parameter values that fit the targeted boundary conditions we find one solution of these equations with a zero finding algorithm by taking initial guesses from a grid of potential candidates we exhibit the symmetries of the problem which reduces drastically the size of this grid and shortens the time of selection of an initial guess the six variables used in the search algorithm forces and moments at one end of the rod are particularly adapted due to their unbounded definition domain more than 850 000 tests are performed in a large region of configurational space and in 99 9 of cases the targeted boundary conditions are reached with short computation time and a precision better than 10 5 we propose extensions of the method to obtain many solutions instead of only one using numerical continuation or starting from different initial guesses

a sextic formalism for three dimensional elastodynamics of cylindrically anisotropic radially inhomogeneous materials elasticity of arbitrary cylindrically anisotropic radially inhomogeneous media is considered the system of six first order ordinary differential equations describing time harmonic cylindrical waves propagating along the cylinder axis is obtained the matrix of the system coefficients has a specific algebraic symmetry underlying the structure of the formalism the matricant solution in the form of the peano expansion is discussed the wentzel kramers brillouin approximation is derived algebraic features of the solution are analysed and their physical content is elucidated the dispersion equation for waves in a hollow cylinder with free or clamped lateral surfaces is formulated in terms of the impedance admittance matrices their analytical properties are established which are useful for analysis of the resulting frequency spectrum the theory is extended to anisotropic radially inhomogeneous piezoelectric cylinders for which the octet generalization of the formalism is developed and studied

fuzzy stochastic linear programming survey and future research directions in many real life problems one has to base decision on information which is both fuzzily imprecise and probabilistically uncertain although consistency indexes providing a union nexus between possibilistic and probabilistic representation of uncertainty exist there are no reliable transformations between them this calls for new paradigms for incorporating the two kinds of uncertainty into mathematical models fuzzy stochastic linear programming is an attempt to fulfill this need it deals with modelling and problem solving issues related to situations where randomness and fuzziness co occur in a linear programming framework in this paper we provide a survey of the essential elements methods and algorithms for this class of linear programming problems along with promising research directions being a survey the paper includes many references to both give due credit to results in the field and to help readers obtain more detailed information on issues of interest

evaluation of eigenfunctions from compound matrix variables in non linear elasticity ii sixth order systems we show how the compound matrix method can be extended to give eigenfunctions as well as eigenvalues to bifurcation problems in non linear elasticity the non trivial boundary conditions create some difficulties and we find that sixth order systems for elasticity problems will require a shooting method for two functions of two unknown parameters over and above the calculations required for comparable problems in fluids

on the problem of possibilistic optimization abstract this paper is a continuation on the author s investigation on possibilistic optimization problems which are considered from general methodological positions of possibility theory and managing uncertainty as well to tackle optimization tasks under uncertainty a calculus for possibilities is developed leading to classic and interval valued optimization

duality theory in fuzzy mathematical programming problems with fuzzy coefficients in this paper the notions of subgradient subdifferential and differential with respect to convex fuzzy mappings are investigated which provides the basis for the fuzzy extremum problem theory we consider the problems of minimizing or maximizing a convex fuzzy mapping over a convex set and develop the necessary and or sufficient optimality conditions furthermore the concept of saddle points and minimax theorems under fuzzy environment is discussed the results obtained are used to formulate the lagrangian dual of fuzzy programming under certain fuzzy convexity assumptions kkt conditions for fuzzy programming are derived and the perturbed convex fuzzy programming is considered finally these results are applied to fuzzy linear programming and fuzzy quadratic programming

bector chandra type duality in fuzzy linear programming with exponential membership functions in this paper we study a pair of fuzzy primal dual linear programming problems and calculate duality results using an aspiration level approach we use an exponential membership function which is in contrast to the earlier works that relied on a linear membership function as the fuzzy environment causes a duality gap we investigate how choosing the exponential membership function impacts this gap this issue is particularly important for fuzzy linear programming where in general the primal and dual objective values may not be bounded

nonlinear euler buckling the buckling of hyperelastic incompressible cylindrical tubes of arbitrary length and thickness under compressive axial load is considered within the framework of nonlinear elasticity analytical and numerical methods for bifurcation are developed using the exact solution of wilkes for the linearized problem within the stroh formalism using these methods the range of validity of the euler buckling formula and its first nonlinear corrections are obtained for third order elasticity the values of the geometric parameters tube thickness and slenderness where a transition between buckling and barrelling is observed are also identified

asymptotic bifurcation solutions for compressions of a clamped nonlinearly elastic rectangle transition region and barrelling to a corner like profile in the two experiments by beatty and his coauthors on the compressions of elastic rectangles bars it was found that there is a transition region of the aspect ratio which separates buckling from b

fuzzy optimization an appraisal abstract this paper takes a general look at core ideas that make up the burgeoning body of fuzzy mathematical programming emphasizing the methodological view although fuzzy mathematical programming has enjoyed a rapidly increasing acceptance within the scientific community some technical hurdles exist to hinder a unanimity reasons for this as well as possible ways for improvement are also discussed

development and evaluation of a micro macro algorithm for the simulation of polymer flow a micro macro algorithm for the calculation of polymer flow is developed and numerically evaluated the system being solved consists of the momentum and mass conservation equations from continuum mechanics coupled with a microscopic based rheological model for polymer stress standard finite element techniques are used to solve the conservation equations for velocity and pressure while stochastic simulation techniques are used to compute polymer stress from the simulated polymer dynamics in the rheological model the rheological model considered combines aspects of reptation network and continuum models two types of spatial approximation are considered for the configuration fields defining the dynamics in the model piecewise constant and piecewise linear the micro macro algorithm is evaluated by simulating the abrupt planar die entry flow of a polyisobutylene solution described in the literature the computed velocity and stress fields are found to be essentially independent of mesh size and ensemble size while there is some dependence of the results on the order of spatial approximation to the configuration fields close to the die entry comparison with experimental data shows that the piecewise linear approximation leads to better predictions of the centerline first normal stress difference finally the computational time associated with the piecewise constant spatial approximation is found to be about 2 5 times lower than that associated with the piecewise linear approximation this is the result of the more efficient time integration scheme that is possible with the former type of approximation due to the pointwise incompressibility guaranteed by the choice of velocity pressure finite element

duality in fuzzy multi criteria and multi constraint level linear programming a parametric approach this paper presents a parametric approach for duality in fuzzy multi criteria and multi constraint level linear programming mc2lp which extends fuzzy linear programming approaches first the mc2 simplex method is used to solve the crisp prima dual mc2lp pair and then through these crisp formulations separate membership functions are constructed for fuzzy primal and dual program by considering the corresponding primal and dual decisions for each program a set of fuzzy potential solutions is determined in terms of the membership function and the related optimal solution with a certain range of decision parameters finally using the primal and dual membership functions a fuzzy weak duality function is obtained for any pair of primal and dual fuzzy potential solutions

on the eversion of compressible elastic cylinders we consider the eversion problem for compressible hyperelastic isotropic thick walled cylinders we give a new strain energy function for a highly compressible material that admits an exact solution to the problem with point wise end conditions previously only averaged loads could be accounted for secondly we investigate the bifurcation problem for a wide range of material models we find qualitively similar results to those obtained for incompressible materials while thin walled cylinders can be everted into other right circular cylinders if the wall thickness exceeds some critical value bifurcation into non cylindrical shapes is possible

water quality management with imprecise information abstract the application of fuzzy set and possibility theories for the representation of imprecise information in water quality management problems is investigated imprecision is associated with fuzziness which is non statistical in nature and refers to the absence of sharp boundaries in the information imprecise parameters in water quality decision making can be represented by possibility distributions defining maximum achievable probabilities the corresponding possibilistic programming problem is viewed as an alternative to the stochastic one where the parameters are modeled as fuzzy variables instead of random variables the possibilistic problem can be solved through a succession of classical linear programs the resulting possibility distributions of the objective value provide a possibilistic assessment of the risk based on possibility levels

optimisation problems as decision problems the case of fuzzy optimisation problems abstract the importance that decision making problems and optimisation problems have today in all aspects of life is beyond all doubt despite that importance both problems tend to be thought of as following different routes when they have in fact a symbiotic relation here we consider the different decision problems that arise when different kinds of information and framework of behaviour are considered and we explore the corresponding optimisation problems that can be derived for searching the best possible decision we explore the case where fuzzy mathematical programming problems are obtained as well as other new ones in the fuzzy context

three models of fuzzy integer linear programming abstract in this paper we study some models for dealing with fuzzy integer linear programming problems which have a certain lack of precision of a vague nature in their formulation we present methods to solve them with either fuzzy constraints or fuzzy numbers in the objective function or fuzzy numbers defining the set of constraints these methods are based on the representation theorem and on fuzzy number ranking methods

extendability of kirchhoff elastic rods in complete riemannian manifolds the kirchhoff elastic rod is a classical mathematical model of equilibrium configurations of thin elastic rods and is defined to be a solution of the euler lagrange equations associated to the energy with the effect of bending and twisting we consider the initial value problem for the euler lagrange equations in a riemannian manifold in a previous paper the author proved the existence and uniqueness of global solutions of the initial value problem in the case where the ambient space is a space form in the present paper we extend this result to the case where the ambient space is a general complete riemannian manifold this implies that an arbitrary kirchhoff elastic rod of finite length in a complete riemannian manifold extends to that of infinite length

on the dynamics of rods in the theory of kirchhoff and clebsch we discuss here the dynamical equations of a theory of elastic rods that is due to kmcm ioff 1 2 and cl bsc 3 4 this properly invariant theory is applicable to motions in which the strains relative to an undistorted configuration remain small although rotations may be large it is constructed to be a first order theory i e a theory that is complete to within an error of order two in an appropriate dimensionless measure of thickness curvature twist and extension in a first order theory of thin rods one can treat the rod as inextensible and we do so here at the outset thus at each time t the arc length parameter s for the axial curve t is employed as a material coordinate i e a parameter whose value at a material point is constant in time and not only the resultant of the shearing forces on a cross section but also the tension in the rod are reactive quantities not given by constitutive equations consider for a moment a rod that is naturally prismatic and dynamically symmetric i e a rod that in an undistorted stress free configuration is a cylinder whose directrix although not necessarily a circle bounds a figure with equal principal moments of inertia a motion of the rod is said to be planar and twist flee i e a motion of pure flexure if it is such that t lies at all times in a fixed plane which contains a principal axis of inertia of each cross section for such a motion we employ a fixed cartesian coordinate system on and for consistency with a discussion of more general motions to be given later in this paper we call the abscissa z and the ordinate x we may write fz s t fx s t for the z and x components of the resultant force f at time t on the cross section with arc length coordinate s the motion of the rod may be described by giving the z x coordinates of the points on t as functions of s and t with o s t the counterclockwise angle from the z axis to the tangent of t at s we have

classifications of ideal 3d elastica shapes at equilibrium we investigate the equilibrium configurations of the ideal 3d elastica i e inextensible unshearable isotropic uniform and naturally straight and prismatic rods with linear elastic constitutive relations infinite solution trajectories are expressed analytically and classified in terms of only three parameters related to physical quantities orientation of sections and mechanical loading are also well described analytically with these parameters detailed analysis of solution trajectories yields two main results first all particular trajectories are completely characterized and located in the space of these parameters second a general geometric structure is exhibited for every ideal 3d elastic rod where the trajectory winds around a core helix in a tube shaped envelope this remarkable structure leads to a classification of the general case according to three properties called chirality components in addition the geometry of the envelope provides another characterization of the ideal 3d elas

the energy spectrum of a twisted flexible string under elastic relaxation a full investigation of the energy spectrum of a twisted flexible string under elastic relaxation is presented and discussed in detail for the first time new polynomial expressions for critical energy states are derived and the whole spectrum of critical states minima maxima and inflexion points of the elastic energy is found and discussed in relation to superhelicity and elastic characteristics of the string the study is carried out in the context of the theory of linear elasticity and the thin rod approximation the relaxation mechanism is studied by using conservation of linking difference by the formula delta lk wr delta tw we show how specific geometric quantities such as pitch angle writhe and twist contributions as well as physical quantities such as torsional and bending energy depend on superhelicity given by the specific linking difference and elastic characteristics of the string given by bending and torsional rigidity these quantities expressed per unit length are examined and compared at each critical energy state starting from a supertwisted configuration we show that the string relaxes by twist reduction through two different intermediate helical states which correspond to different local minima to reach the lowest minimum energy state in a supercoiled configuration the case of a generic kink formation and consequent passage through an inflexional configuration is then examined and new expressions for the energy change in the vicinity of the inflexion point are derived

the equivalence of the class of rivlin sawyers equations and a class of stochastic models for polymer stress this paper establishes the precise relationship between the macroscopic class of factorized rivlin sawyers equations and a class of microscopic based stochastic models the former is a well established and popular class of rheological models for polymeric fluids while the latter is a more recently introduced class of rheological models which combines aspects of network and reptation theory with aspects of continuum mechanic models it is shown that the two models are equivalent in a defined sense under certain unrestrictive assumptions the first part of the proof gives the functional relationship between the linear viscoelastic memory function of the rivlin sawyers model and the probability density for creation times of random variables in the stochastic model the main part of the proof establishes the relationship between the strain descriptions in each model by showing that the difference in corresponding strain expressions can be made arbitrarily small using the appropriate weighted norm from spectral approximation theory

duality theorems and saddle point optimality conditions in fuzzy nonlinear programming problems based on different solution concepts under a general setting of partial ordering defined on the set of all fuzzy numbers the duality theorems and saddle point optimality conditions in fuzzy nonlinear programming problems based on two solution concepts for primal problem and three solution concepts for dual problem are derived in this paper those solution concepts are inspired by the nondominated solution concept employed in multiobjective programming problems since the ordering among fuzzy numbers introduced in this paper is a partial ordering not a total ordering we also provide a concept of fuzzy scalar inner product for fuzzy numbers then the fuzzy valued lagrangian function and the fuzzy valued lagrangian dual function are proposed via the concept of fuzzy scalar product under these settings the dual problem is formulated and the objective function of this dual problem is a point to set fuzzy valued function in this case three solution concepts for dual problem are proposed the duality theorems and saddle point optimality conditions can be naturally elicited based on these three solution concepts

finite amplitude elastic waves propagating in compressible solids the paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials including the possibility of dissipation the dissipative term chosen is similar to the classical stress tensor describing a stokesian fluid and is commonly used in nonlinear acoustics the aim of this research is to derive the corresponding general equations of motion valid for any possible form of the strain energy function and to investigate the possibility of obtaining some general and exact solutions to these equations by reducing them to a set of ordinary differential equations then the reductions can lead to some exact closed form solutions for special classes of materials here the examples of the hadamard blatz ko and power law strain energy densities are considered as well as fourth order elasticity the solutions derived are in a time space separable form and may be interpreted as generalized oscillatory shearing motions and generalized sinusoidal standing waves by means of standard methods of dynamical systems theory some peculiar properties of waves propagating in compressible materials are uncovered such as for example the emergence of destabilizing effects these latter features exist for highly nonlinear strain energy functions such as the relatively simple power law strain energy but they cannot exist in the framework of fourth order elasticity

new method for solving fuzzy transportation problems with lr flat fuzzy numbers transportation problems have various applications in logistics and supply chains for reducing costs in real life situations the parameters of transportation problems may not be known precisely because of uncontrollable factors herein we propose a new method for solving fuzzy transportation problems ftps in which the transportation costs and supply and demand are represented by non negative lr flat fuzzy numbers the ftp is converted into four transportation problems which are solved using standard transportation simplex algorithms the advantages of the proposed method over existing methods are discussed in the context of two application examples the results show that the proposed method is simpler and computationally more efficient than existing methods in the literature

duality theorems in fuzzy mathematical programming problems based on the concept of necessity the fuzzy valued lagrangian function for the fuzzy mathematical programming problem via the concept of the fuzzy scalar inner product is proposed a solution concept of fuzzy optimization problems which is essentially similar to the notion of pareto solution in multiobjective programming problems is also introduced by ranking the fuzzy numbers using the necessity indices under these settings the weak and strong duality theorems can be elicited we show that the primal and dual fuzzy mathematical programming problems have no duality gap under suitable convexity assumptions for fuzzy valued functions

analysis of structure in fuzzy linear programs abstract fuzzy linear programming problems are analyzed within the fuzzy set context to uncover redundancies infeasibilities variables whose values are fixed and implied bounds on rows and columns applications include pre analysis of perturbed constraint matrices and post optimization analysis fuzzy linear programming problems

fuzzy boolean programming problems with fuzzy costs a general study abstract this paper deals with boolean linear programming problems involving coefficients in the objective function as fuzzy numbers in the study of these problems different approaches can be proposed to use ranking fuzzy numbers methods and fuzzy preference relations obtaining auxiliary classical boolean programming problems and to use the representation theorem obtaining a convex set with extreme points defined by the lower or upper bound of the a level sets of the fuzzy coefficients and consequently an auxiliary interval boolean programming problem in this paper we develop and link the different approaches

a discrete mechanics approach to the cosserat rod theory part 1 static equilibria a theory of discrete cosserat rods is formulated in the language of discrete lagrangian mechanics by exploiting kirchhoff s kinetic analogy the potential energy density of a rod is a function on the tangent bundle of the configuration manifold and thus formally corresponds to the lagrangian function of a dynamical system the equilibrium equations are derived from a variational principle using a formulation that involves null space matrices in this formulation no lagrange multipliers are necessary to enforce orthonormality of the directors noether s theorem relates first integrals of the equilibrium equations to lie group actions on the configuration bundle so called symmetries the symmetries relevant for rod mechanics are frame indifference isotropy and uniformity we show that a completely analogous and self contained theory of discrete rods can be formulated in which the arc length is a discrete variable ab initio in this formulation the potential energy density is defined directly on pairs of points along the arc length of the rod in analogy to veselov s discrete reformulation of lagrangian mechanics a discrete version of noether s theorem then identifies exact first integrals of the discrete equilibrium equations these exact conservation properties confer the discrete solutions accuracy and robustness as demonstrated by selected examples of application

the solution and duality of imprecise network problems duality properties have been investigated by many researchers in the recent literature they are introduced in this paper for a fully fuzzified version of the minimal cost flow problem which is a basic model in network flow theory this model illustrates the least cost of the shipment of a commodity through a capacitated network in terms of the imprecisely known available supplies at certain nodes which should be transmitted to fulfil uncertain demands at other nodes first we review on the most valuable results on fuzzy duality concepts to facilitate the discussion of this paper by applying hukuhara s difference approximated and exact multiplication and wu s scalar production we exhibit the flow in network models then we use combinatorial algorithms on a reduced problem which is derived from fully fuzzified mcfp to acquire fuzzy optimal flows to give duality theorems we utilize a total order on fuzzy numbers due to the level of risk and realize optimality conditions for providing some efficient combinatorial algorithms finally we compare our results with the previous worthwhile works to demonstrate the efficiency and power of our scheme and the reasonability of our solutions in actual decision making problems

applications of fuzzy set theory to mathematical programming mathematical programming is one of the areas to which fuzzy set theory has been applied extensively primarily based on bellman and zadeh s model of decision in fuzzy environments models have been suggested which allow flexibility in constraints and fuzziness in the objective function in traditional linear and nonlinear programming in integer and fractional programming and in dynamic programming these models in turn have been used to offer computationally efficient approaches for solving vector maximum problems this paper surveys major models and theories in this area and offers some indication on future developments which can be expected

pressuring shearing torsion and extension of a circular tube or bar of cylindrically anisotropic material one of the novel features of the present paper is that we have written the equation of equilibrium and the stress strain law of an inhomogeneous anisotropic linear elastic material in a compact form for cylindrical coordinate system using matrix notation for a two dimensional deformation the result resembles stroh s sextic formalism in a rectangular coordinate system we then consider the material to be cylindrically anisotropic it means that the elastic stiffnesses referred to a cylindrical coordinate system are constants the problem of a circular tube subjected to a uniform normal stress and shearing stresses at the inner and outer surfaces of the tube is studied also studied are the axial extension and torsion of the tube unlike isotropic materials for which the applied normal stress or shear stress induces only the normal or shear stress all three displacement components and most of the six stress components are nonzero for general anisotropic materials this is particularly interesting for the uniform axial extension of the tube for an isotropic material the stress 33 is the only non zero and uniform stress inside the tube for a cylindrically anisotropic material the stresses rr and 3 are also non zero moreover they depend on r and are not uniform a solid cylinder or a cylinder with a pin hole is a special case of a tube it is shown that for the loads mentioned above including the axial extension the stress may be unbounded at the pinhole

interactive fuzzy linear programming abstract in this study an interactive fuzzy linear programming approach is investigated to improve the flexibility and robustness of linear programming lp technique this paper provides a practical modelling method which is a symmetric integration of zimmermann s werners s vergegay s and chanas s fuzzy lp approaches and additionally provides a decision support system for solving a specific domain of practical lp problems the interactive concept provides a learning process about the system whereby the decision maker can learn to recognize good solutions relative importance of factors in the system and then design a high productivity system instead of optimizing a given system this interactive fuzzy lp system provides integration oriented adaptation and learning features by considering all the possibilities of a specific domain of lp problems which are integrated in logical order using an if then rule

nonlinear dynamics of filaments i dynamical instabilities abstract the kirchhoff model provides a well established mathematical framework to study both computationaly and theoretically the dynamics of thin filaments within the approximations of linear elasticity theory the study of static solutions to these equations has a long history and the usual approach to describing their instabilities is to study the time dependent version of the kirchhoff model in the euler angle frame here we study the linear stability of the full time independent equations by introducing a new are length preserving perturbation scheme as an application we consider the instabilities of various stationary solutions such as the planar ring and straight rod subjected to twisting perturbations this scheme gives a direct proof of the existence of dynamical instabilities and provides the selection mechanism for the shape of unstable filaments

geometrical equilibrium of curves a showcase of helical numerical solutions in this work we plot loop configurations that minimize energy functionals depending on geometrical invariants of the loop itself in particular we consider a family of functionals including curvature and torsion terms both linear and quadratic such that their combinations produce geometrical invariants in 1 noether s theorem was advantageously used to identify the constants of integration of the euler lagrange equations describing the equilibrium of loops for this family of energy functionals those authors demonstrated the integrability of these functionals by means of quadratures in this work we follow that approach to realize numeric calculations and to show plots of numerical solutions of the relevant equations for equilibrium of loops as these were presented but not studied in 1 we then show as the main result of this work a representative catalogue of such solutions in euclidean three dimensional space

the fuzzy shortest path problem and its most vital arcs abstract the shortest path problem is to find the shortest distance between two specified nodes in a network an arc is called a single most vital arc in the network if its removal from the network results in the greatest increase in the shortest distance the availability of arcs plays a key role in network problems the most vital arcs problems provide a means by which the importance of arc s availability can be measured in the traditional shortest path problem the arc lengths are assumed to be crisp numbers in this paper we consider the case that the arc lengths are fuzzy numbers in particular we derive the membership function of the shortest distance by using a fuzzy linear programming approach based on this result we then propose an algorithm for finding the single most vital arc in a network

fuzzy capital rationing model in this paper we study the fuzzification of weingartner s pure capital rationing model and its analysis we develop a primal dual pair based on t norm t conorm relation for the constraints and objective function for a fully fuzzified pure capital rationing problem except project selection variables we define the a interval under which the weak duality is proved we perform sensitivity analysis for a change in a budget level or in a cash flow level of a non basic as well as a basic variable we analyze the problem based on duality and complementary slackness results we illustrate the proposed model by computational analysis and interpret the results

solving the boundary value problem for finite kirchhoff rods the kirchhoff model describes the statics and dynamics of thin rods within the approximations of the linear elasticity theory in this paper we develop a method based on a shooting technique to find equilibrium configurations of finite rods subjected to boundary conditions and given load parameters the method consists in making a series of small changes on a trial solution satisfying the kirchhoff equations but not necessarily the boundary conditions by linearizing the differential equations around the trial solution we are able to push its end point to the desired position step by step the method is also useful to obtain configurations of rods with fixed end points but different mechanical parameters such as tension components of the moment or inhomogeneities

karush kuhn tucker conditions for interval and fuzzy optimization in several variables under total and directional generalized differentiability abstract we extend the interval and fuzzy gh differentiability to consider interval and fuzzy valued functions of several variables and to include directional gh differentiability the proposed setting is more general than the existing definitions in the literature and allows a unified view of total and direction gh differentiability and for the computation of partial gh derivatives directional gh derivative and level wise gh differentiability in the fuzzy valued case a concept of gh differential is then deduced and its values are used to define an abstract local tangency property for a gh differentiable function similar to the well known tangency between a differentiable function and its tangent plane the proposed new setting allows an analysis of conditions for local optimality dominance with respect to interval and level wise partial orders well known in the literature in terms of directional gh derivatives including concepts of local convexity and to formulate kkt like conditions for non dominated solutions in constrained optimization problems