brief equivalence of hybrid dynamical models this paper establishes equivalences among five classes of hybrid systems mixed logical dynamical mld systems linear complementarity lc systems extended linear complementarity elc systems piecewise affine pwa systems and max min plus scaling mmps systems some of the equivalences are established under rather mild additional assumptions these results are of paramount importance for transferring theoretical properties and tools from one class to another with the consequence that for the study of a particular hybrid system that belongs to any of these classes one can choose the most convenient hybrid modeling framework

improved algorithm for mixed integer quadratic programs and a computational study in a recent paper 6 we suggested an algorithm for solving complicated mixed integer quadratic programs based on an equivalent formulation that employs a nonsingular transformation of variables the objectives of the present paper are two first to present an improved version of this algorithm which reduces substantially its computational requirements second to report on the results of a computational study with the revised algorithm

grassman path integral solution for a class of triangular type decorated ising models abstract grassman path integral solution is given for a class of two dimensional triangular type decorated ising models canonical ising lattices rectangular triangular and hexagonal enter into this class as the most simple particular cases as a first step the problem is reformulated in terms of a free fermionic field theory the method is based on the mirror factorization principle for the density matrix traditional transfer matrix or combinatorial considerations are not needed the solution exhibits the characteristics free fermionic structure providing the universal logarithmic singularity in the specific heat the symmetries and the critical point behaviour are investigated within the spin polynomial interpretation of the problem some concrete decorated lattices are treated by illustration attention is given to the choice of rational computational devices

phase transitions on fractals iii infinitely ramified lattices for pt ii see ibid vol 17 p 435 1984 in the first two papers of this series the authors considered self similar fractal lattices with a finite order of ramification r in the present paper they study physical models defined on a family of fractals with r infinity in order to characterise the geometry of these systems they need the connectivity q and the lacunarity l in addition to the fractal dimensionality d it is found that discrete symmetry spin models on these lattices undergo a phase transition at tc 0 an approximate renormalisation group scheme is constructed and used to find the dependence of tc and the critical exponents on the geometrical factors they also solve the problem of resistor networks on these fractals and discuss its consequences concerning spin models with continuous symmetry

numerical experience with lower bounds for miqp branch and bound the solution of convex mixed integer quadratic programming miqp problems with a general branch and bound framework is considered it is shown how lower bounds can be computed efficiently during the branch and bound process improved lower bounds such as the ones derived in this paper can reduce the number of quadratic programming qp problems that have to be solved the branch and bound approach is also shown to be superior to other approaches in solving miqp problems numerical experience is presented which supports these conclusions

exact solution of a general two dimensional ising model the partition function abstract the exact partition function per spin is obtained for a two dimensional generalization of the ising model this general model consists of a unitary cell that is repeated throughout the system the unitary cell is made up of spins in t columns and q rows with arbitrary energies between them the exact result is given in terms of certain quantities see section 2 which can be determined for particular cases it is always possible to transform the unit cell in order to obtain a desired given model thus the results for several known models are recovered e g the utiyama and the hexagonal with three different interaction parameters models furthermore explicit results are presented for other models hitherto not reported in the literature as are the general hexagonal with six different interaction parameters the general triangular model with six different interaction parameters and the tetragonal triangular with seven different interaction parameters models

identification of fuzzy relational model and its application to control abstract in the case of control systems where physical mechanisms are not well known due to high complexity and nonlinearity a fuzzy relational model may be useful in this paper we propose a recursive parameter tuning algorithm for the identification of fuzzy relational model for an unknown dynamic system furthermore using the fact that a dynamic system is represented by the relational strength between a few reference input and output fuzzy sets in the fuzzy relational model we construct a control input fuzzy set inducing a desired output fuzzy set by calculating the possibility between the model output and the desired output fuzzy set for the control purpose simulation results show the usefulness of the proposed identification and control algorithms

ferromagnetic phase transitions of inhomogeneous systems modelled by square ising models with diamond type bond decorations abstract the two dimensional ising model defined on square lattices with diamond type bond decorations is employed to study the nature of the ferromagnetic phase transitions of inhomogeneous systems the model is studied analytically under the bond renormalization scheme for an n level decorated lattice the long range ordering occurs at the critical temperature given by the fitting function k b t c j n 1 6410 0 6281 exp 0 5857 n and the local ordering inside n level decorated bonds occurs at the temperature given by the fitting function k b t m j n 1 6410 0 8063 exp 0 7144 n the critical amplitude a sin g n of the logarithmic singularity in specific heat characterizes the width of the critical region and it varies with the decoration level n as a sin g n 0 2473 exp 0 3018 n obtained by fitting the numerical results the cross over from a finite decorated system to an infinite decorated system is not a smooth continuation for the case of infinite decorations the critical specific heat becomes a cusp with the height c n 0 639852 the results are compared with those obtained in the cell decorated ising model

leggett williams norm type fixed point theorems for multivalued mappings this paper presents several norm type versions of the leggett williams fixed point theorem for multivalued maps with nonempty convex compact values

phase transitions on fractals ii sierpinski gaskets for pt i see ibid vol 16 p 1267 1983 the authors construct and investigate a family of fractals which are generalisations of the sierpinski gaskets sgs to all euclidean dimensionalities these fractal lattices have a finite order of ramification and can be considered marginal between one dimensional and higher dimensional geometries physical models defined on them are exactly solvable the authors argue that short range spin models on the sg show no finite temperature phase transitions as examples they solve a few spin models and study the resistor network and percolation problems on these lattices

exact differentiation and sliding mode observers for switched lagrangian systems abstract the main topic of this paper is the problem of constructing observers for switched mechanical systems which includes as a specific case the design of observers based on the high order sliding mode technique the high order sliding mode is used to overcome the chattering phenomena occurring which induce some irrelevant and undesirable phenomena for mechanical systems the proposed approach based on the fliess canonical form also allows observers to give an estimate of the discrete location of the system which indicates the dynamic evolution the convergence of the observers is proved and a stick mass friction system is used to illustrate the efficiency of the proposed hybrid observers

efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form for hybrid systems described by switched linear difference equations linear threshold conditions automata and propositional logic conditions described in mixed logical dynamical form this note describes two algorithms for transforming such systems into an equivalent piecewise affine form where equivalent means that for the same initial conditions and input sequences the trajectories of the system are identical the proposed techniques exploit ideas from mixed integer programming and multiparametric programming

existence and uniqueness theorems for boundary value problems involving reflection of the argument soit f r n r une fonction deux fois continue differentiable g 1 1 r n r n r n une fonction satisfaisant des conditions de caratheodory et e t t dans 1 1 une fonction donnee dans l 1 1 1 r n on etudie des theoremes d existence et d unicite pour des problemes aux valeurs limites suivants 1 x t d gradf x t d g t x t x t e t x 1 x 1 0 2 x t g t x t x t e t x 1 hx 1 0 x 1 kx 1 0 ou h k 0 k h 0 t 1 1

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

spin pair correlation function of the ising model on the brickwork lattice with second neighbor interactions abstract the asymptotic behavior of the spin pair correlation function along an axis is investigated for the ising model on a brickwork lattice with second neighbor interactions it is suggested that some of long range phase predicted by the mean field appriximation arereflected in the asymptotic behavior the ising model on a layered triangular lattice is also treated

fully frustrated ising antiferromagnets at the fractal to euclidean crossover abstract we present a study of the residual entropies of the frustrated ising antiferromagnets in a zero field situated on the sierpinski gasket type of fractals our results render it possible to establish the fractal residual entropy crossover towards wannier s exact value for the euclidean triangular lattice

reentrant phase transition in a particular 3 3 uc two dimensional ising model abstract using the method presented in an earlier paper we obtain the exact partition function per spin l t corresponding to the particular 3 3 unitary cell two dimensional ising model studied by kitatani et al in contrast with these authors that worked with numerical methods we use algebraic procedures to obtain the analytic expression for l t and the exact equation for the critical temperature t c for other values of the interaction parameters we find results for more extensive ranges of the values of the interaction parameters than obtained by kitatani et al we use these results to discuss physical properties of the systems we exhibit an extended range of values for which double reentrancy is found

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

introducing the fuzzy relational hybrid model as a building block for intelligent modeling of hybrid dynamical systems in this paper a novel intelligent modeling framework is introduced for modeling hybrid dynamical systems which may contain both continuous valued and discrete valued dynamics and or signals the proposed modeling framework consists of a fuzzy relational hybrid model frhm structure and an online identification algorithm the frhm structure has some useful properties e g the ability of modeling both hard and soft switchings even simultaneously model transparency in view of knowledge extraction and knowledge embedment and possibility of connecting disjoint models through mathematical operations to construct larger model structures in addition the proposed frhm structure can be used to model a wide variety of hybrid dynamical systems including nonlinear dynamical systems dynamical systems with switchings or logical functions dynamical systems with discrete valued or qualitative inputs and or outputs etc the fuzzy relational hybrid dynamical system is an important product of the proposed modeling structure which in this paper has applied to modeling an asynchronous dc dc buck converter as the case study

phase transitions in regularly diluted 2d ising models with a complicated inherent structure of a lattice cell abstract we analyze the critical point and study the nonuniversal peculiarities occuring in the temperature dependence of the specific heat for a sequence of the exactly solvable highly decorated two dimensional triangular type ferromagnetic ising models with a complicated fractal type inherent structure of elementary cell the lattices are indexed by the decoration parameter n 0 1 2 3 the elementary cell for the n lattice is the n th order lattice approximation of the sierpinski gasket fractal at any finite n there is the second order phase transition indicated by the logarithmic singularity in the specific heat the critical temperature decreases as 4 ln 4 n 1 with increasing decoration the specific heat critical amplitude vanishes as 3 n n ln n 2 as n the basic nonuniversal features observable in the specific heat at strong decoration are the anomalous narrowing of the critical interval and the appearance of a rounded peak above the true t c point these effects are closely related and can both be explained by the above t c local ordering in the local lattice inhomogeneities the mechanism of the above t c local ordering is analyzed the models under discussion can as well be interpreted as the regular bond diluted 2d ising ferromagnets with a hierarchy of the nonmagnetic holes at different scales and varying dilution a comparative discussion on the properties of the regularly and randomly diluted 2d ising ferromagnets is given

mpc for continuous piecewise affine systems abstract a large class of hybrid systems can be described by a max min plus scaling mmps model i e using the operations maximization minimization addition and scalar multiplication first we show that continuous piecewise affine systems are equivalent to mmps systems next we consider model predictive control mpc for these systems in general this leads to nonlinear nonconvex optimization problems we present a new mpc method for mmps systems that is based on canonical forms for mmps functions in case the mpc constraints are linear constraints in the inputs only this results in a sequence of linear optimization problems such that the mpc control can often be computed in a much more efficient way than by just applying nonlinear optimization as was done in previous work

critical exponent γ for a class of directed walks at the fractal to euclidean crossover abstract an exact evaluation of the critical exponent associated with the average number of n step walks of the piecewise directed random walks is presented in the case of the complete family of the sierpinski gasket type of fractals