a connection between normalized coprime factorizations and linear quadratic regulator theory given a transfer matrix described by a minimal state space triple a method is given for computing state space realizations for the numerator and denominator of a normalized stable right coprime factorization for the transfer matrix the method involves the solution of an algebraic riccati equation it allows the use of existing computational state space algorithms in finding normalized stable right coprime factorizations and avoids explicit calculations of spectral factors

on the application of the critical minimum energy subspace method to disordered systems abstract we discuss the recent application to strongly disordered systems of the critical minimum energy subspace crmes method used to limit the energy subspace of the wang landau sampling we compare with our results on the 3d random field ising model obtained by a multi range wang landau simulation over the whole energy range we point out some problems that may arise when applying the crmes scheme to models having a complex free energy landscape

controllability and observability of linear retarded systems in banach spaces abstract controllability and observability are studied for linear retarded systems in a banach space x both the x exact and the x approximate controllability are considered and a number of necessary and sufficient conditions in terms of the coefficient operators and or the fundamental solution are presented various corresponding concepts for observability are introduced and the duality between controllability and observability is clarified an applicable condition for the x approximate controllability and the x observability is established under the assumptions that the control is a finite dimensional one and the system of generalized eigenspaces is projectively complete the condition is stated in terms of eigenvectors and controllers

the random field ising model with an asymmetric trimodal probability distribution the ising model in the presence of a random field is investigated within the mean field approximation based on landau expansion the random field is drawn from the trimodal probability distribution p hi p hi h0 q hi h0 r hi where the probabilities p q r take on values within the interval 0 1 consistent with the constraint p q r 1 asymmetric distribution hi is the random field variable and h0 the respective strength this probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites the current random field ising system displays second order phase transitions which for some values of p q and h0 are followed by first order phase transitions thus confirming the existence of a tricritical point and in some cases two tricritical points also reentrance can be seen for appropriate ranges of the aforementioned variables using the variational principle we determine the equilibrium equation for magnetization solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h0

monte carlo analysis of the critical properties of the two dimensional randomly bond diluted ising model via wang landau algorithm abstract the influence of random bond dilution on the critical properties of the two dimensional ising model on a square lattice with periodic boundary conditions is presented using the monte carlo process with wang landau sampling the lattice linear size is l 20 140 and the concentration of the diluted bonds spans a wide range from weak to strong dilution namely q 0 05 0 1 0 2 0 3 0 4 the respective percolation limit for the square lattice is q c p e r c 0 5 its pure version q 0 has a second order phase transition with vanishing specific heat critical exponent an example of inapplicability of the harris criterion the main effort is focused on the temperature dependence of the specific heat and magnetic susceptibility to estimate the respective maximum values and subsequent pseudocritical temperatures for extracting the relative critical exponents we have also looked at the probability distribution of the susceptibility pseudocritical temperature and specific heat for assessing self averaging the study is carried out in the appropriately restricted but dominant energy subspaces by applying the finite size scaling analysis the critical exponents are estimated the specific heat exponent vanishes the correlation length exponent is equal to one and the critical exponents ratio retains its pure ising model value thus supporting the strong universality hypothesis

brief papers new results in state estimation and regulation an alternative technique to design linear state estimators and regulators is presented this technique is based on transfer matrix considerations the optimal regulator or estimator gain is obtained via spectral factorization and the solution of a simple equation in polynomial matrices this approach provides further insight displays the duality of estimation and control nicely and bridges the state space and frequency domain techniques the resulting design procedure is computationally attractive and particularly simple for system matrices in the observer or controller canonical form

phase behavior under the averaging over disorder realizations abstract effects of the averaging over disorder realizations samples on the phase behavior are analyzed in terms of the mean field approximation for the random field ising model with infinite range interactions it is found that the averaging is equivalent to a drastic modification in the statistics of the quenched variables in its turn this lowers the critical temperature of a second order phase transition or depending on the sampling even suppresses the ordered phase possible first order transitions are shown to be softened by the sample averaging common issues and differences in the interpretation of these effects in the context of the simulation and experimental studies are discussed

spectral factorization and lq optimal regulation for multivariable distributed systems a necessary and sufficient condition is proved for the existence of a bistable spectral factor with entries in the distributed proper stable transfer function algebra x1d49c in the context of distributed multivariable convolution systems with no delays a by product is the existence of a normalized coprime fraction of the transfer function of such a possibly unstable system with entries in the algebra of fractions over x1d49c we next study semigroup state space systems sgb with bounded sensing and control having a transfer function with entries in and consider its standard lq optimal regulation problem having an optimal state feedback operator k0 for a system sgb a formula is given relating any spectral factor of a transfer function coprime fraction power spectral density to k0 a by product is the description of any normalized coprime fraction of the transfer function in terms of k0 finally we describe an alternative way of finding the solution operator k0 of the lq problem using spectral factor

covers and envelopes in grothendieck categories flat covers of complexes with applications abstract in the general setting of grothendieck categories with enough projectives we prove theorems that make possible to restrict the study of the problem of the existence of f covers and envelopes to the study of some properties of the class f we then prove the existence of flat covers and cotorsion envelopes of complexes giving some examples this generalizes the earlier work j algebra201 1998 86 102 and finishes the problem of the existence of flat covers of complexes

lack of self averaging of the specific heat in the three dimensional random field ising model we apply the recently developed critical minimum energy subspace scheme for the investigation of the random field ising model we point out that this method is well suited for the study of this model the density of states is obtained via the wang landau and broad histogram methods in a unified implementation by employing the n fold version of the wang landau scheme the random fields are obtained from a bimodal distribution h i ifmmode pm else textpm fi 2 and the scaling of the specific heat maxima is studied on cubic lattices with sizes ranging from l 4 to l 32 observing the finite size scaling behavior of the maxima of the specific heats we examine the question of saturation of the specific heat the lack of self averaging of this quantity is fully illustrated and it is shown that this property may be related to the question mentioned above

the random field ising model with an asymmetric and anisotropic bimodal probability distribution abstract the ising model in the presence of a random field drawn from the asymmetric and anisotropic trimodal probability distribution p h i p h i h 0 q h i h 0 r h i is investigated the partial probabilities p q r take on values within the interval 0 1 consistent with the constraint p q r 1 asymmetric distribution h i is the random field variable with basic absolute value h 0 strength is the competition parameter which is the ratio between the respective strength of the random magnetic field in the two principal directions z and z and is positive so that the random fields are competing anisotropic distribution this probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites the current random field ising system displays mainly second order phase transitions which for some values of p q and h 0 are followed by first order phase transitions joined smoothly by a tricritical point occasionally two tricritical points appear implying another second order phase transition in addition to these points re entrant phenomena can be seen for appropriate ranges of the temperature and random field for specific values of p and q using the variational principle we write down the equilibrium equation for the magnetization and solve it for both phase transitions and at the tricritical point in order to determine the magnetization profile with respect to h 0 considered as an independent variable in addition to the temperature

relative homological algebra in the category of quasi coherent sheaves abstract in this paper we prove the existence of a flat cover and of a cotorsion envelope for any quasi coherent sheaf over a scheme x o x indeed we prove something more general we define what it is understood by the category of quasi coherent r modules where r is a representation by rings of a quiver q and we prove the existence of a flat cover and a cotorsion envelope for quasi coherent r modules then we use the fact that the category of quasi coherent sheaves on x o x is equivalent to the category of quasi coherent r modules for some q and r to get our result

linear quadratic optimal control of hereditary differential systems infinite dimensional riccati equations and numerical approximations recent theory of infinite dimensional riccati equations is applied to the linear quadratic optimal control problem for hereditary differential systems and it is shown that for most such problems the operator solutions of the riccati equations are of trace class i e nuclear with special attention to trace norm convergence an abstract approximation theory is developed and applied to a particular approximation scheme numerical examples are given problems on both finite and infinite time intervals are studied for both the hereditary system and the approximating systems in the infinite time problem characteristic equations are derived for the closed loop eigenvalues and formulas for the corresponding eigenvectors are given

robust stabilizability of normalized coprime factors the infinite dimensional case the problem of robustly stabilizing a linear system subject to h bounded perturbations in the numerator and the denominator of its normalized left coprime factorization is considered for a class of infinite dimensional systems this class has possible unbounded finite rank input and output operators which include many delay and distributed systems the optimal stability margin is expressed in terms of the solutions of the control and filter algebraic riccati equations

flat covers in abelian and in non abelian categories abstract a general existence theorem for flat covers in e g quasi abelian locally finitely presented categories is obtained from an additive ramsey type theorem in the abelian case it is shown that flat covers always exist applications to categories of separated presheaves or sheaves localizations of bousfield type torsion free classes of finite type and categories of filtered objects or complexes are given

the sherrington kirkpatrick spin glass model in the presence of a random field with a joint gaussian probability density function for the exchange interactions and random fields abstract the magnetic systems with disorder form an important class of systems which are under intensive studies since they reflect real systems such a class of systems is the spin glass one which combines randomness and frustration the sherrington kirkpatrick ising spin glass with random couplings in the presence of a random magnetic field is investigated in detail within the framework of the replica method the two random variables exchange integral interaction and random magnetic field are drawn from a joint gaussian probability density function characterized by a correlation coefficient the thermodynamic properties and phase diagrams are studied with respect to the natural parameters of both random components of the system contained in the probability density the de almeida thouless line is explored as a function of temperature and other system parameters the entropy for zero temperature as well as for non zero temperatures is partly negative or positive acquiring positive branches as h 0 increases

continuity of the spectral factorization on a vertical strip the continuity of the mapping which associates a spectral factor to a spectral density is investigated this mapping can be defined on several classes of spectral densities and spectral factors for the usual largest class of spectral densities i e essential bounded functions on the imaginary axis that are bounded away from zero it is known that this mapping is not continuous it is shown here that for slightly smaller but still generic class the mapping becomes continuous

brief paper lq control design of a class of hyperbolic pde systems application to fixed bed reactor a general linear controller design method for a class of hyperbolic linear partial differential equation pdes systems is presented this is achieved by using an infinite dimensional hilbert state space description with infinite dimensional distributed input and output a state lq feedback operator is computed via the solution of a matrix riccati differential equation in the space variable the proposed method is applied to a fixed bed chemical reactor control problem where one elementary reaction takes place an optimal controller is designed for linearized fixed bed reactor model it is applied to the original nonlinear model and the resulting closed loop stability is analyzed numerical simulations are performed to show the performance of the designed controller

distributed system transfer functions of exponential order o is a real number we construct a transfer function algebra of fractions viz f o for modelling possibly unstable distributed systems such that i fcirc in f o is holomorphic in re s o i e is o stable iff fcirc is o exponentially stable and ii we allow delay in the direct input output transmission of the system this algebra is a a restriction of the algebra b o developed by callier and desoer 1978 1980 a b an extension of the algebra of proper rational functions such that the exponential order properties of the latter transfer functions of lumped systems are maintained the algebra f o can be used for modelling and feedback system design it is shown that standard semigroup systems are better modelled by a transfer function in f o rather than b o

wang landau study of the critical behavior of the bimodal 3d random field ising model we apply the wang landau method to the study of the critical behavior of the three dimensional random field ising model with a bimodal probability distribution for high values of the random field intensity we find that the energy probability distribution at the transition temperature is double peaked suggesting that the phase transition is first order on the other hand the transition looks continuous for low values of the field intensity in spite of the large sample to sample fluctuations observed the double peak in the probability distribution is always present for high fields

baxter wu model in the presence of an external magnetic field abstract in this work we study an unusual phase transition of the baxter wu model in the presence of an external magnetic field the model is pure baxter wu which means that only three spin interactions are taken into account we construct a phase diagram on the temperature field plane based mainly on the singularities of the specific heat these singularities are more clearly observed than those of the magnetic susceptibility which are used in existing works we establish a discontinuity in the critical exponents when the field is changed from zero to negative

on projectivity in locally presentable categories abstract we show that some fundamental results about projectivity classes weakly coreflective subcategories and cotorsion theories can be generalized from r modules to arbitrary locally presentable categories

critical endpoint behavior in an asymmetric ising model application of wang landau sampling to calculate the density of states using the wang landau sampling method with a two dimensional random walk we determine the density of states for an asymmetric ising model with two and three body interactions on a triangular lattice in the presence of an external field with an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite size analyses at and away from the critical endpoint we observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint and the exponents for both divergences agree well with previous theoretical predictions

cartan eilenberg complexes and resolutions abstract we study cartan eilenberg projective injective and flat complexes and show how they can be used to get cartan eilenberg resolutions we argue that every complex has a cartan eilenberg injective envelope then we show that a complex is a cartan eilenberg flat complex if and only if it is the direct limit of finitely generated cartan eilenberg projective complexes

lack of self averaging in random systems liability or asset abstract the study of quenched random systems is facilitated by the idea that the ensemble averages describe the thermal averages for any specific realization of the couplings provided that the system is large enough careful examination suggests that this idea might have a flaw when the correlation length becomes of the order of the size of the system we find that certain bounded quantities are not self averaging when the correlation length becomes of the order of the size of the system this suggests that the lack of self averaging expressed in terms of properly chosen signal to noise ratios may serve to identify phase boundaries this is demonstrated by using such signal to noise ratios to identify the boundary of the ferromagnetic phase of the random field ising system and compare the findings with more traditional measures

elementary varieties and existence of flat covers abstract it is shown that flat covers exist in a wide class of additive categories we call them elementary which behave similar to locally finitely presented grothendieck categories elementary categories have enough finitely presented objects but they need not be locally finitely presented this is related to the existence of pure monomorphisms which are not kernels and the non exactness of direct limits for a module category mod r every class of r modules containing r cogenerates an elementary full subcategory

quadratic optimal control of stable well posed linear systems we consider the infinite horizon quadratic cost minimization problem for a stable time invariant well posed linear system in the sense of salamon and weiss and show that it can be reduced to a spectral factorization problem in the control space more precisely we show that the optimal solution of the quadratic cost minimization problem is of static state feedback type if and only if a certain spectral factorization problem has a solution if both the system and the spectral factor are regular then the feedback operator can be expressed in terms of the riccati operator and the riccati operator is a positive self adjoint solution of an algebraic riccati equation this riccati equation is similar to the usual algebraic riccati equation but one of its coefficients varies depending on the subspace in which the equation is posed similar results are true for unstable systems as we have proved elsewhere

critical energy distribution function of the baxter wu model abstract in this work we examine the critical finite size scaling behavior of the energy probability distribution function and its corresponding binder cumulant at critical point based on the results of monte carlo simulations at zero external magnetic field using the recently developed triangle cluster algorithm we calculate the energy distribution function s exponents and we derive the scaling relations for the energy binder cumulant finally we predict the exact form of the scaled energy distribution function most of our conclusions seem applicable not only to the baxter wu model but also to other ising like models

flat covers of complexes abstract in this article we define and study flat complexes over any ring also we prove that any complex over a commutative noetherian ring with finite krull dimension has a flat cover and a dg flat cover

first order transition features of the triangular ising model with nearest and next nearest neighbor antiferromagnetic interactions abstract we implement a new and accurate numerical entropic scheme to investigate the first order transition features of the triangular ising model with nearest neighbor j nn and next nearest neighbor j nnn antiferromagnetic interactions in ratio r j nn j nnn 1 important aspects of the existing theories of first order transitions are briefly reviewed tested on this model and compared with previous work on the potts model using lattices with linear sizes l 30 40 100 120 140 160 200 240 360 and 480 we estimate the thermal characteristics of the present weak first order transition our results improve the original estimates of rastelli et al and verify all the generally accepted predictions of the finite size scaling theory of first order transitions including transition point shifts thermal and magnetic anomalies however two of our findings are not compatible with current phenomenological expectations the behavior of transition points derived from the number of phases parameter is not in accordance with the theoretically conjectured exponentially small shift behavior and the well known double gaussian approximation does not correctly describe higher correction terms of the energy cumulants it is argued that this discrepancy has its origin in the commonly neglected contributions from domain wall corrections

the random field ising model with asymmetric bimodal probability distribution abstract the ising model in the presence of a random field is investigated within the mean field approximation based on landau expansion the random field is drawn from the bimodal probability distribution p h p h h 0 1 p h h 0 where the probability p assumes any value within the interval 0 1 asymmetric distribution the prevailing transitions are of second order but for some values of p and h 0 first order phase transitions take place for smaller temperatures and higher h 0 thus confirming the existence of a tricritical point also the possible reentrant phenomena in the phase diagram t h 0 plane occur for appropriate values of p and h 0 using the variational principle we determine the equilibrium equation for magnetization and solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h 0

self averaging in many body quantum systems out of equilibrium time dependence of distributions in a disordered system a quantity is self averaging when the ratio between its variance for disorder realizations and the square of its mean decreases as the system size increases here we consider a chaotic disordered many body quantum system and search for a relationship between self averaging behavior and the properties of the distributions over disorder realizations of various quantities and at different timescales an exponential distribution as found for the survival probability at long times explains its lack of self averaging since the mean and the dispersion are equal gaussian distributions however are obtained for both self averaging and non self averaging quantities our studies show also that one can make conclusions about the self averaging behavior of one quantity based on the distribution of another related quantity this strategy allows for semianalytical results and thus circumvents the limitations of numerical scaling analysis which are restricted to few system sizes

approximation and stabilization of distributed systems by lumped systems in this note we study two questions regarding linear time invariant distributed systems namely 1 when can the given system be approximated by a lumped system 2 when can the given system be stabilized by a lumped system in each case we obtain a complete answer to the question in terms of the behaviour of the purely atomic parts of the stable numerator and denominator of the plant

linear state space systems in infinite dimensional space the role and characterization of joint stabilizability detectability several fundamental results from the theory of linear state space systems in finite dimensional space are extended to encompass a class of linear state space systems in infinite dimensional space the results treated are those pertaining to the relationship between input output and internal stability the problem of dynamic output feedback stabilization and the concept of joint stabilizability detectability a complete structural characterization of jointly stabilizable detectable systems is obtained the generalized theory applies to a large class of linear state space systems assuming only that i the evolution of the state is governed by a strongly continuous semigroup of bounded linear operators ii the state space is hilbert space iii the input and output spaces are finite dimensional and iv the sensing and control operators are bounded general conclusions regarding the fundamental structure of control theoretic problems in infinite dimensional space can be drawn from these results