an efficient ml decoder for tail biting codes based on circular trap detection tail biting codes are efficient coding techniques to eliminate the rate loss in conventional known tail convolutional codes at a cost of increased complexity in decoders in addition tail biting trellis representation of block codes makes the trellis based maximum likelihood ml decoder desirable for implementation circular viterbi algorithm cva is introduced to decode the tail biting codes for its decoding efficiency however its decoding process suffers from circular traps which degrade the decoding efficiency in this paper we propose an efficient checking rule for the detection of circular traps based on this rule a novel maximum likelihood ml decoding algorithm for tail biting codes is presented on tail biting trellis computational complexity and memory consumption of this decoder are significantly reduced comparing to other available ml decoders such as the two phase ml decoder to further reduce the decoding complexity we propose a new near optimal decoding algorithm based on a simplified trap detection strategy the performance of the above algorithms is validated with simulation

partial orders on b h in this paper we characterize the sets of all b b h such that a b and the sets of all b b h such that b a where a b h is given and

point island dynamics under fixed rate deposition abstract we consider the dynamics of point islands during submonolayer deposition in which the fragmentation of subcritical size islands is allowed to understand asymptotics of solutions we use methods of centre manifold theory and for globalisation we employ results from the theories of compartmental systems and of asymptotically autonomous dynamical systems we also compare our results with those obtained by making the quasi steady state assumption

automorphisms of b h with respect to minus partial order abstract let h be an infinite dimensional hilbert space and b h the algebra of all bounded linear operators on h we discuss possible extensions of the concept of the minus partial order from matrix to operator algebras in particular we show that mitra s unified theory of matrix partial orders based on generalized inverses can be modified in such a way that we get a unified approach to partial orders on b h or even more general algebras and rings then we choose the most natural among possible definitions of minus partial order on b h and describe the structure of corresponding automorphisms

towards a dynamical temperature of finite hamiltonian systems abstract with the aid of numerical simulations of the fermi pasta ulam fpu system we compare the different definitions of dynamical temperature for hamiltonian systems we have shown that each definition gives different values of temperature for a system with a small number of degrees of freedom dof only for systems with a sufficiently large number of dof do all the definitions of dynamical temperature approach the same value

tailbiting codes bounds and search results tailbiting trellis representations of linear block codes with an arbitrary sectionalization of the time axis are studied the notations of regular and irregular tailbiting codes are introduced and their maximal state complexities are lower bounded the asymptotic behavior of the derived bound is investigated furthermore for regular tailbiting codes the product state complexity is lower bounded tables of new tailbiting trellis representations of linear block codes of rates 1 2 1 3 and 1 4 are presented almost all found trellises are optimal in the sense of the new bound on the state complexity and for most codes with nonoptimal trellises there exist time varying trellises which are optimal five of our newly found tailbiting codes are better than the previously known linear codes with the same parameters four of them are also superior to any previously known nonlinear code with the same parameters also more than 40 other quasi cyclic codes have been found that improve the parameter set of previously known quasi cyclic codes

possible physical meaning of the tsallis entropy parameter since the proposal of the tsallis generalized entropy the general explanation of the role played by the parameter q that defines which specific entropy to pick among a whole family remained somewhat partial and tentative although some particular examples were taken into account specifically the purpose of the present paper is to present a rigorous formal derivation of a mathematical expression giving the parameter q in terms of the momentum fluctuations of a stochastic process thus furnishing at least one of its possible physical origins

on the decay rate of discrete time linear delay systems with cone invariance this technical note is concerned with the decay rate constrained stability analysis for linear delay systems that possess cone invariant property in order to capture the decay rate of such systems we introduce a nondecreasing positive function whose reciprocal represents the decay rate under mild assumptions on the growth rate of this function an explicit condition is given to ensure that a cone preserving linear system with unbounded time varying delays is asymptotically stable with a given decay rate as typical cases necessary and sufficient conditions are given to characterize the decay rate when the delay is restricted by a linear sublinear or logarithmic growth rate finally some numerical examples are given to illustrate the effectiveness of the theoretical results

the partial order graph for a zme matrix abstract the spectral projectors for a zme matrix form a partially ordered set with respect to a simple combinatorial relation the relationship between the corresponding partial order graph and the inflation sequence for a set of projectors is investigated those directed graphs that correspond to a partial order graph for a zme matrix are characterized the effect on the partial order due to operations on the set of projectors is studied generalizing a result of schneider and stuart

large assemblies of stochastic oscillators this paper studies the occurrence of stochastic synchronization and phase locking in large assemblies of coupled stochastic oscillators which are modelled as phaseangle stochastic processes attention will be restricted to the case of discrete phaseangle spaces these are technically much simpler than processes over continuous phase spaces and yet show an interesting range of properties stochastic synchronization occurs if the oscillator assembly obeys a large deviation principle and if the deterministic limit dynamics possesses a stable periodic orbit all relevant concepts are reviewed in section section 1 2 and the appendix in section 4 general necessary and sufficient conditions for stochastic synchronization are obtained weak and robust types of synchronization are distinguished a describing function method is formulated which is very convenient for checking the general conditions in concrete examples separate treatments of feedback gain feedback type i e positive or negative and feedback sources lead to investigations of how the occurrence of stochastic synchronization depends on any one of those feedback aspects in a sequence of gradually more realistic models section 3 4b 5a the general results are applied to assemblies of stochastic fireflies the first of these models section 3 is mathematically instructive in that it provides a good example of how the liapunov function character of large deviation rate functions can be exploited to study global properties of the corresponding deterministic limit ode the analysis of firefly assemblies culminates in a proof of stochastic firefly synchronization this result is the precise stochastic analogue of the well known proof of deterministic firefly synchronization given by mirollo strogatz 1990 in section 5 the general results of section 4 are applied to neuronal assemblies particular attention is paid to the dependence of neuronal synchronization on the feedback type that is excitatory or inhibitory signalling we find it natural and instructive to distinguish between external and internal variants of inhibition the latter in particular in the form of graded refractoriness of neurons is shown to be crucial for stochastic synchronization within one neural assembly whereas the former is instrumental for phase locking between distinct assemblies these findings are summarized and sharpened in a number of concrete predictions for real biological networks of neurons except for some topical aspects of large deviation theory reviewed in the appendix the mathematics employed in this paper are straightforward

finite time semistability and consensus for nonlinear dynamical networks this paper focuses on semistability and finite time stability analysis and synthesis of systems having a continuum of equilibria semistability is the property whereby the solutions of a dynamical system converge to lyapunov stable equilibrium points determined by the system initial conditions in this paper we merge the theories of semistability and finite time stability to develop a rigorous framework for finite time semistability in particular finite time semistability for a continuum of equilibria of continuous autonomous systems is established continuity of the settling time function as well as lyapunov and converse lyapunov theorems for semistability are also developed in addition necessary and sufficient conditions for finite time semistability of homogeneous systems are addressed by exploiting the fact that a homogeneous system is finite time semistable if and only if it is semistable and has a negative degree of homogeneity unlike previous work on homogeneous systems our results involve homogeneity with respect to semistable dynamics and require us to adopt a geometric description of homogeneity finally we use these results to develop a general framework for designing semistable protocols in dynamical networks for achieving coordination tasks in finite time

on the minus partial order in control systems abstract in this paper the minus matrix partial order is considered to introduce the concept of minus partial ordered control systems the transmission of the reachability property under this binary relation is investigated furthermore the analysis of compartmental systems leads us to consider block triangular matrices hence the existence and computation of partially ordered matrices having a similar block structure are studied these results are applied to compartmental systems to get via feedback related systems with the same block structure and ordered under the minus partial order

fluctuation of energy in the generalized thermostatistics abstract we calculate the fluctuation of a system s energy in tsallis statistics following the finite heat bath canonical ensemble approach we obtain this fluctuation as the second derivative of the logarithm of the partition function plus an additional term we also find an explicit expression for the relative fluctuation as related to the number of degrees of freedom of the bath and the composite system

realization of continuous time positive linear systems positive linear systems are used in biomathematics economics and other research areas for discrete time positive linear systems part of the realization problem has been solved in this paper the solution of the corresponding problem for continuous time positive linear systems will be presented which can be deduced from that of the discrete time case by a transformation sufficient and necessary conditions for the existence of a positive realization are presented to solve the problem of minimality the solution of the factorization of positive matrices is needed

the star partial order and the eigenprojection at 0 on ep matrices abstract the space of n n complex matrices with the star partial order is considered in the first part of this paper the class of ep matrices is analyzed and several properties related to this order are given in addition some information about predecessors and successors of a given ep matrix is obtained the second part is dedicated to the study of some properties that relate the eigenprojection at 0 with the star and sharp partial orders

star partial order on b h abstract let h be an infinite dimensional complex hilbert space and let b h be the algebra of all bounded linear operators on h in the paper the equivalent definition of the star partial order on b h using selfadjoint idempotent operators is introduced also some properties of the generalized concept of order relations on b h defined with the help of idempotent operators are investigated

composite systems with uncertain couplings of fixed structure scaled riccati equations and the problem of quadratic stability we consider large scale systems consisting of a finite number of separate uncertain subsystems which interact via uncertain couplings of arbitrarily prescribed structure the couplings are viewed as structured perturbations of the block diagonal system representing the collection of the separate nominal subsystems the nominal system we define spectral value sets and stability radii for these time invariant structured perturbations and derive formulas for their computation scaled riccati equations are introduced to obtain explicit formulas for the stability radii with respect to time varying and possibly nonlinear perturbations of the given structure from these we derive necessary and sufficient conditions under which the stability radii with respect to time invariant and time varying perturbations are equal these results are obtained by constructing joint quadratic liapunov functions of optimal robustness with their help we prove necessary and sufficient conditions for quadratic stability and sufficient conditions for the validity of a generalized aizerman conjecture

an updated table of minimum distance bounds for binary linear codes in 1973 helgert and sfinaff published a table of upper and lower bounds on the maximum minimum distance for binary linear error correcting codes up to length 127 this article presents an updated table incorporating numerous improvements that have appeared since then to simplify the updating task the author has developed a computer program that systematically investigates the consequences of each improvement by applying several well known general code construction techniques this program also made it possible to check the original table furthermore it offers a quick and reliable update service for future improvements

special families of matrices a talk in honor of miroslav fiedler abstract this paper is essentially the talk that i delivered in the minisymposium in honor of miroslav fiedler at the 17th ilas meeting in braunschweig germany

technical communique adaptive control for nonlinear nonnegative dynamical systems nonnegative and compartmental models are widespread in engineering systems and life sciences and play a key role in the understanding of these systems in this paper we develop a direct adaptive control framework for nonlinear uncertain nonnegative and compartmental dynamical systems the proposed framework is lyapunov based and guarantees partial asymptotic set point regulation that is asymptotic set point regulation with respect to part of the closed loop system states associated with the plant in addition the adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space

paradigms and puzzles in the theory of dynamical systems a self contained exposition is given of an approach to mathematical models in particular to the theory of dynamical systems the basic ingredients form a triptych with the behavior of a system in the center and behavioral equations with latent variables as side panels the author discusses a variety of representation and parametrization problems in particular questions related to input output and state models the proposed concept of a dynamical system leads to a new view of the notions of controllability and observability and of the interconnection of systems in particular to what constitutes a feedback control law the final issue addressed is that of system identification it is argued that exact system identification leads to the question of computing the most powerful unfalsified model

on sets of elements in rickart rings induced by partial orders abstract let a be a rickart ring and let a 1 be the set of all regular elements in a the set of all a a such that a b are characterized where b a 1 is given and is the minus partial order in case when a is a rickart ring such sets are characterized for the diamond the left star the right star the left sharp and the right sharp partial orders some recent results of mosic et al on partial orders in b h the algebra of all bounded linear operators on a hilbert space h are thus generalized

possible canonical distributions for finite systems with nonadditive energy region des pays de la loire of france 2007 6088 science research fund 07bs105 huaqiao university people s republic of china

central limit behavior of deterministic dynamical systems we investigate the probability density of rescaled sums of iterates of deterministic dynamical systems a problem relevant for many complex physical systems consisting of dependent random variables a central limit theorem clt is valid only if the dynamical system under consideration is sufficiently mixing for the fully developed logistic map and a cubic map we analytically calculate the leading order corrections to the clt if only a finite number of iterates is added and rescaled and find excellent agreement with numerical experiments at the critical point of period doubling accumulation a clt is not valid anymore due to strong temporal correlations between the iterates nevertheless we provide numerical evidence that in this case the probability density converges to a q gaussian thus leading to a power law generalization of the clt the above behavior is universal and independent of the order of the maximum of the map considered i e relevant for large classes of critical dynamical systems

weighted g drazin inverses and a new pre order on rectangular matrices abstract this paper deals with weighted g drazin inverses which is a new class of matrices introduced to extend to the rectangular case g drazin inverses recently considered by wang and liu for square matrices first we define and characterize weighted g drazin inverses next we consider a new pre order defined on complex rectangular matrices based on weighted g drazin inverses finally we characterize this pre order and relate it to the minus partial order and to the weighted drazin pre order

majorization for matrix classes abstract we introduce a new majorization order for classes sets of matrices which generalizes several existing notions of matrix majorization roughly the notion says that every matrix in one class is majorized by some matrix in the other class the motivation to study this majorization concept comes from mathematical statistics and involves the information content in experiments this connection is briefly described we investigate properties of this new order both of algebraic and geometric character in particular we establish results on so called minimal cover classes with respect to the introduced majorization

neural network adaptive control for nonlinear nonnegative dynamical systems nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative these models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous in this paper we develop a full state feedback neural adaptive control framework for adaptive set point regulation of nonlinear uncertain nonnegative and compartmental systems the proposed framework is lyapunov based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains in addition the neural adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space for nonnegative initial conditions

the pointwise feedback relation for linear dynamical systems abstract let and be two m input n dimensional linear dynamical systems over a commutative ring r if is feedback equivalent to then is pointwise feedback equivalent to i e for all prime ideal p of r the systems p and p are feedback equivalent over the residue field k p where p is the natural extension of to k p this paper is devoted to the study of the pointwise feedback relation we characterize when two systems and are pointwise equivalent we show that r is an absolutely flat ring if and only if the feedback relation and the pointwise feedback relation are equivalent the particular case of rings of real valued continuous functions is specially treated

numerical calculation of the energy relative fluctuation for a system in contact with a finite heat bath abstract we have recently shown that the dispersion and the energy square relative fluctuations of a finite system in contact with a finite heat bath depends on the number of degrees of freedom of the system and of the bath in this paper we present numerical simulations which support this result

asymptotic behavior of solutions of nonautonomous neutral dynamical systems abstract this paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator of great importance for their applications to the study of the long term behavior of the trajectories of problems described by this kind of equations such us compartmental systems and neural networks among many others precisely more general admissible initial conditions are included in the study to show that the solutions are asymptotically of the same type as the coefficients of the neutral and non neutral part

dissipative dynamics in a finite chaotic environment relationship between damping rate and lyapunov exponent we consider the energy flow between a classical one dimensional harmonic oscillator and a set of n two dimensional chaotic oscillators which represents the finite environment using linear response theory we obtain an analytical effective equation for the system harmonic oscillator which includes a frequency dependent dissipation a shift and memory effects the damping rate is expressed in terms of the environment mean lyapunov exponent a good agreement is shown by comparing theoretical and numerical results even for environments with mixed regular and chaotic motion resonance between system and environment frequencies is shown to be more efficient to generate dissipation than larger mean lyapunov exponents or a larger number of bath chaotic oscillators

spectral conditions for stability and stabilization of positive equilibria for a class of nonlinear cooperative systems nonlinear cooperative systems associated to vector fields that are concave or subhomogeneous describe well interconnected dynamics that are of key interest for communication biological economical and neural network applications for this class of positive systems we provide conditions that guarantee existence uniqueness and stability of strictly positive equilibria these conditions can be formulated directly in terms of the spectral radius of the jacobian of the system if control inputs are available then it is shown how to use state feedback to stabilize an equilibrium point in the interior of the positive orthant

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

tight bounds on the minimum average weight per branch for rate n 1 n convolutional codes consider a cycle in the state diagram of a convolutional code the average weight per branch of the cycle is equal to the total hamming weight of all labels on the branches divided by the number of branches let w sub 0 be the minimum average weight per branch over all cycles in the state diagram except the zero state self loop of weight zero codes with low w sub 0 result in high bit error probabilities when they are used with either viterbi or sequential decoding hemmati and costello 1980 showed that w sub 0 is upper bounded by 2 sup spl nu 2 3 spl middot 2 sup spl nu 2 1 for a class of 2 1 codes where spl nu denotes the constraint length in the present correspondence it is shown that the bound is valid for a large class of n n 1 codes n spl ges 2 examples of high rate codes with w sub 0 equal to the upper bound are also given hemmati and costello defined a class of codes to be asymptotically catastrophic if w sub 0 approaches zero for large spl nu the class of n n 1 codes constructed by wyner and ash 1963 is shown to be asymptotically catastrophic all codes in the class have minimum possible w sub 0 equal to 1 spl nu

tailbiting codes obtained via convolutional codes with large active distance slopes the slope of the active distances is an important parameter when investigating the error correcting capability of convolutional codes and the distance behavior of concatenated convolutional codes the slope of the active distances is equal to the minimum average weight cycle in the state transition diagram of the encoder a general upper bound on the slope depending on the free distance of the convolutional code and new upper bounds on the slope of special classes of binary convolutional codes are derived moreover a search technique resulting in new tables of rate r 1 2 and rate r 1 3 convolutional encoders with high memories and large active distance slopes is presented furthermore we show that convolutional codes with large slopes can be used to obtain new tailbiting block codes with large minimum distances tables of rate r 1 2 and rate r 1 3 tailbiting codes with larger minimum distances than the best previously known quasi cyclic codes are given two new tailbiting codes also have larger minimum distances than the best previously known binary linear block codes with same size and length one of them is also superior in terms of minimum distance to any previously known binary nonlinear block code with the same set of parameters

stability theory for nonnegative and compartmental dynamical systems with time delay abstract nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations and involve the exchange of nonnegative quantities between subsystems or compartments these models are widespread in biological and physical sciences and play a key role in understanding these processes a key physical limitation of such systems is that transfers between compartments is not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments in this paper we present necessary and sufficient conditions for stability of nonnegative and compartmental dynamical systems with time delay specifically asymptotic stability conditions for linear and nonlinear nonnegative dynamical systems with time delay are established using linear lyapunov krasovskii functionals

a beast for prowling in trees when searching for convolutional codes and tailbiting codes of high complexity it is of vital importance to use fast algorithms for computing their weight spectra which corresponds to finding low weight paths in their code trellises this can be efficiently done by a combined search in both forward and backward code trees a bidirectional efficient algorithm for searching such code trees beast is presented for large encoder memories it is shown that beast is significantly more efficient than comparable algorithms beast made it possible to find new convolutional and tailbiting codes that have larger free minimum distances than the previously best known codes with the same parameters tables of such codes are presented

statistical mechanics of quartic oscillators we study statistical mechanics of quartic oscillator with two degrees of freedom which is known to be chaotic almost everywhere except in a few regions of the parameter range we obtain exact expressions for temperature entropy and distribution functions temperature is also obtained numerically by time averaging the kinetic energy and using equipartition theorem and agrees with our expressions when the system is almost chaotic we further generalize our model to quartic oscillators with n degrees of freedom and exact expressions for thermodynamic quantities are obtained as n standard statistical mechanics results are recovered we also discuss pressure density and equation of state of this system

some orders for operators on hilbert spaces in this paper we present some interesting properties of the diamond left right star and sharp orders for operators on hilbert spaces

allowable spectral perturbations of zme matrices a zme matrix is a matrix a all of whose positive integer powers are z matrices and whose odd powers are irreducible we find a combinatorial partial order on the spectral idempotents of a zme matrix a which determines the allowable spectral perturbations b for which b is again a zme matrix we apply this result to show that under certain restrictions the product of two zme matrices is a zme matrix

generalized entropies from first principles a derivation of power law canonical distributions from first principle statistical mechanics including the exponential distribution as a particular case is presented it is shown that these distributions arise naturally and that the heat capacity of the heat bath is the condition that determines its type as a consequence a physical interpretation for the parameter q of the generalized entropy is given

on the reachable set for third order linear discrete time systems with positive control the case of complex eigenvalues abstract in this paper we study the geometrical properties of the set of reachable states of a single input third order discrete time linear system with positive controls this set is a cone and we give a complete geometrical characterization of this set when the system has a complex conjugate pair of eigenvalues more in detail we give necessary and sufficient conditions for properness and polyhedrality of the cone and provide the number of its edges in terms of eigenvalue locations

dynamically consistent nonstandard finite difference schemes for epidemiological models this work is the numerical analysis and computational companion of the paper by kamgang and sallet j c kamgang g sallet computation of threshold conditions for epidemiological models and global stability of the disease free equilibrium dfe mathematical biosciences 213 2008 1 12 where threshold conditions for epidemiological models and the global stability of the disease free equilibrium dfe are studied we establish a discrete counterpart of the main continuous result that guarantees the global asymptotic stability gas of the dfe for general epidemiological models then we design nonstandard finite difference nsfd schemes in which the metzler matrix structure of the continuous model is carefully incorporated and both mickens rules world scientific singapore 1994 on the denominator of the discrete derivative and the nonlocal approximation of nonlinear terms are used in an innovative way as a result of these strategies our nsfd schemes are proved to be dynamically consistent with the continuous model i e they replicate their basic features including the gas of the dfe the linear stability of the endemic equilibrium ee the positivity of the solutions the dissipativity of the system and its inherent conservation law the general analysis is made detailed for the mseir model for which the nsfd theta method is implemented with emphasis on the computational aspects such as its convergence or local truncation error numerical simulations that illustrate the theory are provided

transit time and age distributions for nonlinear time dependent compartmental systems many processes in nature are modeled using compartmental systems reservoir pool box systems usually they are expressed as a set of first order differential equations describing the transfer of matter across a network of compartments the concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions until now explicit formulas for transit time and age distributions of nonlinear time dependent compartmental systems were not available we compute densities for these types of systems under the assumption of well mixed compartments assuming that a solution of the nonlinear system is available at least numerically we show how to construct a linear time dependent system with the same solution trajectory we demonstrate how to exploit this solution to compute transit time and age distributions in dependence on given start values and initial age distributions furthermore we derive equations for the time evolution of quantiles and moments of the age distributions our results generalize available density formulas for the linear time independent case and mean age formulas for the linear time dependent case as an example we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time dependent input signal which represents fossil fuel additions we derive time dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business as usual scenario

stabilization of positive linear systems we consider stabilization of equilibrium points of positive linear systems which are in the interior of the first orthant the existence of an interior equilibrium point implies that the system matrix does not possess eigenvalues in the open right half plane this allows to transform the problem to the stabilization problem of compartmental systems which is known and for which a solution has been proposed already we provide necessary and sufficient conditions to solve the stabilization problem by means of affine state feedback a class of stabilizing feedbacks is given explicitly

stability of traffic flow networks with a polytree topology we consider global stability of a flow network model for vehicular traffic standard approaches which rely on monotonicity of flow networks for stability analysis do not immediately apply to traffic networks with diverging junctions in this paper we show that the network model nonetheless exhibits a mixed monotonicity property mixed monotonicity allows us to prove global asymptotic stability by embedding the system in a larger system that is monotone

thermodynamical relations for systems in contact with finite heat baths abstract we obtain the relations between macroscopic thermodynamical properties and microscopic ensemble averages of a system in contact with a heat bath which has a finite number of degrees of freedom our approach is based on the geometry of the accessible phase space of the system by using a suitable definition of temperature for such kind of system energy equipartition theorem it is shown that the relations obtained here have the same dependence on the system s partition function z 1 as in boltzmann gibbs statistics

on the fundamental matrix of the inverse of a polynomial matrix and applications to arma representations the fundamental matrix of the inverse of a particular toeplitz structured matrix pencil is used in order to provide an algorithm for the computation of the fundamental matrix of the inverse of a polynomial matrix the dynamical interpretation of this pencil is explored and its fundamental matrix is used to provide closed formulas for the solutions of autoregressive moving average arma representations finally using this pencil the notion of reachability for descriptor state space systems is extended to arma representations

stability and dissipativity theory for discrete time non negative and compartmental dynamical systems non negative and compartmental dynamical systems are derived from mass and energy balance considerations that involve dynamic states whose values are non negative these models are widespread in engineering biomedicine and ecology in this paper we develop several results on stability dissipativity and stability of feedback interconnections of discrete time linear and non linear non negative dynamical systems specifically using linear lyapunov functions we first develop necessary and sufficient conditions for lyapunov stability and asymptotic stability for non negative systems in addition using linear and non linear storage functions with linear supply rates we develop new notions of dissipativity theory for non negative dynamical systems finally these results are used to develop general stability criteria for feedback interconnections of non negative dynamical systems

nontangency based lyapunov tests for convergence and stability in systems having a continuum of equilibria this paper focuses on the stability analysis of systems having a continuum of equilibria two notions that are of particular relevance to such systems are convergence and semistability convergence is the property whereby every solution converges to a limit point that may depend on the initial condition semistability is the additional requirement that all solutions converge to limit points that are lyapunov stable we give new lyapunov function based results for convergence and semistability of nonlinear systems these results do not make assumptions of sign definiteness on the lyapunov function instead our results use a novel condition based on nontangency between the vector field and invariant or negatively invariant subsets of the level or sublevel sets of the lyapunov function or its derivative and represent extensions of previously known stability results involving semidefinite lyapunov functions to illustrate our results we deduce convergence and semistability of the kinetics of the michaelis menten chemical reaction and the closed loop dynamics of a scalar system under a universal adaptive stabilizing feedback controller

tsallis power laws and finite baths with negative heat capacity it is often stated that heat baths with finite degrees of freedom i e finite baths are sources of tsallis distributions for classical hamiltonian systems by using well known fundamental statistical mechanics expressions we rigorously show that tsallis distributions with fat tails are possible only for finite baths with constant negative heat capacity while constant positive heat capacity finite baths yield decays with sharp cutoff with no fat tails however the correspondence between tsallis distributions and finite baths holds at the expense of violating the equipartition theorem for finite classical systems at equilibrium we comment on the implications of the finite bath for the recent attempts towards a q generalized central limit theorem

correction to structure and stability of certain chemical networks and applications to the kinetic proofreading model of t cell receptor signal transduction deals with the theory of structure stability robustness and stabilization for an appealing class of nonlinear systems which arises in the analysis of chemical networks the results given here extend but are also heavily based upon certain previous work by feinberg 1977 1979 1987 1995 and horn and jackson 1972 of which a self contained and streamlined exposition is included the theoretical conclusions are illustrated through an application to the kinetic proofreading model proposed by mckeithan 1995 for t cell receptor signal transduction

some new binary quasi cyclic codes by means of local search techniques five quasi cyclic codes have been found that have a higher minimum distance than known binary linear codes the new codes have parameters 102 17 37 60 20 17 84 21 27 105 21 36 and 100 25 30 also 39 other quasi cyclic codes have been found that improve the parameter sets of previously known quasi cyclic codes twenty four of them give a new and easier description of binary linear codes with best known parameters

active distances for convolutional codes a family of active distance measures for general convolutional codes is defined these distances are generalizations of the extended distances introduced by thommesen and justesen 1983 for unit memory convolutional codes it is shown that the error correcting capability of a convolutional code is determined by the active distances the ensemble of periodically time varying convolutional codes is defined and lower bounds on the active distances are derived for this ensemble the active distances are very useful in the analysis of concatenated convolutional encoders

on relationships between several classes of z matrices m matrices and nonnegative matrices abstract in this paper we establish relationships between several classes of well known matrices and some new classes of matrices we consider matrices whose powers are irreducible z matrices or m matrices these matrices are called zma matrices or mma matrices we establish a relationship between theses classe of matrices and the class of soules matrices moreover we prove that symmetric zma matrices and mma matrices are diagonally congruent to matrices that we call z sums and m sums conversely z sums and m sums are diagonally congruent to zma matrices and mma matrices this relationship exploits the structure of zma matrices and mma matrices and several well known properties of zma matrices follow immediately z sums and m sums are closely related to strictly ultrametric matrices sums we also characterize inverse zma matrices we prove that symmetric inverse zma matrices are diagonally congruent to shifted sums and that shifted sums are diagonally congruent to symmetric inverse zma matrices

woven convolutional codes i encoder properties encoders for convolutional codes with large free distances can be constructed by combining several less powerful convolutional encoders this paper is devoted to constructions in which the constituent convolutional codes are woven together in a manner that resembles the structure of a fabric the general construction is called twill and it is described together with two special cases viz woven convolutional encoders with outer warp and with inner warp the woven convolutional encoders inherit many of their structural properties such as minimality and catastrophicity from their constituent encoders for all three types of woven convolutional codes upper and lower bounds on their free distances as well as lower bounds on the active distances of their encoders are derived

core inverse and core partial order of hilbert space operators abstract the core inverse of matrix is generalized inverse which is in some sense in between the group and moore penrose inverse in this paper a generalization of core inverse and core partial order to hilbert space operator case is presented some properties are generalized and some new ones are proved connections with other generalized inverses are obtained the useful matrix representations of operator and its core inverse are given it is shown that a is less than b under the core partial order if and only if they have specific kind of simultaneous diagonalization induced by appropriate decompositions of hilbert space the relation is also characterized by the inclusion of appropriate sets of generalized inverses the spectral properties of core inverse are also obtained

the dynamical systems approach to differential equations bulletin new series of the american mathematical society volume 11 number 1 july 1984 the dynamical systems approach to differential equations by morris w hirsch 1 this harmony that human intelligence believes it discovers in nature does it exist apart from that intelligence no without doubt a reality completely independent of the spirit which conceives it sees it or feels it is an impossibility a world so exterior as that even if it existed would be forever inaccessible to us but what we call objective reality is in the last analysis that which is common to several thinking beings and could be common to all this common part we will see can be nothing but the harmony expressed by mathematical laws h poincare la valeur de la science p 9 ignorance of the roots of the subject has its price no one denies that modern formulations are clear elegant and precise it s just that it s impossible to comprehend how any one ever thought of them m spivak a comprehensive introduction to differential geometry introduction the mathematical subject we call dynamical systems was fathered by poin care developed sturdily under birkhoff and has enjoyed a vigorous new growth for the last twenty years as i try to show in chapter i it is interesting to look at this mathematical development as the natural outcome of a much broader theme which is as old as science itself the universe is a sytem which changes in time every mathematician has a particular way of thinking about mathematics but rarely makes it explicit yet such perspectives in any particular field can be of great value to nonexperts who must apply the results of the field or who want to learn them in some fields the points of view of its practitioners cluster around several comparatively clearly defined concepts and insights dynamical systems theory is one of them the basic concepts go back to poincare the main thrust of chapters i and ii is to explain rather discursively some of received by the editors december 14 1983 1980 mathematics subject classification primary 00a25 00a99 01a45 01a55 01a60 34a40 34c35 34d10 34d30 35b05 35b35 35b40 35b50 35b30 35k55 54h20 58f25 58f40 58f12 58f10 58d25 58d07 46a40 46e10 47h07 47h20 92a15 92a17 secondary 06f30 35b65 58f13 35j60 46e05 92 03 90 03 90a16 supported in part by national science foundation and institute for advanced study 1984 american mathematical society 0273 0979 84 1 00 25 per page

qualitative theory of compartmental systems dynamic models of many processes in the biological and physical sciences which depend on local mass balance conditions give rise to systems of ordinary differential equations many nonlinear that are called compartmental systems in this paper the authors define compartmental systems specify their relations to other nonnegative systems and discuss examples of applications the authors review the qualitative results on linear and nonlinear compartmental systems including their relation to cooperative systems they review the results for linear compartmental systems and then integrate and expand the results on nonlinear compartmental systems providing a framework for unifying them under a few general theorems in the course of that they complete the solution of a problem posed by bellman and show that closed nonlinear autonomous n compartment systems can show the full gamut of possible behaviors of systems of odes finally to provide additional structure to this study the authors show how to partiti

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

brunovsky s canonical form for linear dynamical systems over commutative rings abstract this paper is devoted to studying the action of the feedback group on linear dynamical systems over a commutative ring r with unit we characterize the class of m input n dimensional reachable linear dynamical systems f g over r that are feedback equivalent to a system c fc gc with brunovsky s canonical form this characterization is obtained in terms of the minors of the matrices g i g fg f i 1 g for 1 i n

positive linear observers for linear compartmental systems linear compartmental systems are mathematical systems that are frequently used in biology and mathematics the inputs states and outputs of such systems are positive because they denote amounts or concentrations of material for linear dynamic systems the observer problem has been solved the purpose of the observer problem is to determine a linear observer such that the state can be approximated the difference between the state and its estimate should converge to zero the interpretation in terms of a physical system requires that an estimate of the state be positive like the state itself in this paper conditions on the system matrices are presented that guarantee that there exists a positive linear observer such that both the error converges to zero and the estimate is positive

some best rate 1 p and rate p 1 p systematic quasi cyclic codes tables of 1 p and rate p 1 p binary quasi cyclic qc codes that extend previously published results are presented many of these codes attain bounds given by t verhoeff 1987 who composed a table of bounds on the maximum possible minimum distance of binary linear codes many of the codes presented meet or improve these bounds a best code is considered to be one which has the largest possible minimum distance for the given code dimensions n and k and class of error correcting codes a good code has the maximum known minimum distance for the class of codes an optimal code is one that achieves the maximum possible minimum distance for a linear code with the same dimensions binary power residue codes are found and used to construct qc codes

quasicanonical gibbs distribution and tsallis non extensive statistics abstract we derive and study quasicanonical gibbs distribution function which is characterized by the thermostat with finite number of particles quasithermostat we show that this naturally leads to tsallis non extensive statistics and thermodynamics with tsallis parameter q is found to be related to the number of particles in the quasithermostat we show that the chi square distribution of fluctuating temperature used recently by beck can be partially understood in terms of normal random momenta of particles in the quasithermostat also we discuss on the importance of the time scale hierarchy and fluctuating probability distribution functions in understanding of tsallis distribution within the framework of kinetics of dilute gas and weakly inhomogeneous systems

a note on asymptotically catastrophic convolutional codes of rate n 1 n convolutional codes with rate r n 1 n n spl ges 2 are defined in terms of their minimal parity check matrices the matrices are represented by a binary vector notation introduced by ytrehus 1992 the upper bounds on spl omega 0 minimum average weight per branch are presented many classes of rate n 1 n convolutional codes are shown to be asymptotically catastrophic

on higher order linear systems reachability and feedback invariants we consider l order linear control systems with coefficients in a commutative ring r the notion of reachability is studied for such systems and it is related to the reachability of the associated linearized system lin we prove that reachability is a pointwise property just as in the case of first order systems the feedback equivalence of l order linear control systems over a commutative ring is also studied we introduce some feedback invariants that generalize the hermida perez sanchezgiralda invariant modules mi to conclude we apply results in order to give classification results in low dimension