brief observer controller design for cranes via lyapunov equivalence we consider a linearized parameter varying model of a planar crane and show how a controller can be designed following the state feedback stabilization technique for time varying systems proposed by wolovich the resulting closed loop system is equivalent via a lyapunov transformation to a stable time invariant system of assigned eigenvalues we also show that an observer can be designed applying wolovich procedure to the dual system of the plant the proposed procedure leads to the computation of the desired time varying gains for controller and observer in a parameterized form the results of several simulations with data taken from a real container crane are also shown

blow up solutions to a system of nonlinear volterra equations a system of nonlinear volterra integral equations with convolution kernels is considered estimates are given for the blow up time when conditions are such that the solution is known to become unbounded in finite time for two examples that arise in combustion problems numerical estimates of blow up time are presented additionally the asymptotic behavior of the blow up solution in the key limit is established for the power law and exponential nonlinearity cases

a condition for finite blow up time for a volterra integral equation abstract the paper is devoted to the study of the equation u x x 0 x s 1 g u s ds 0 x 0 where g is continuous and nondecreasing some estimates of u and the interval of the existence of a nontrivial solution u are given

operations on fuzzy ideals in this paper we give suitable definitions of the operations of l fuzzy ideals in a ring as intersection addition multiplication and residual division and we prove some fundamental properties of the operations analogous to those that hold for the operations of ordinary ideals see 3

blowing up behavior for a class of nonlinear vies connected with parabolic pdes we study the blowing up behavior of solutions of a class of nonlinear integral equations of volterra type that is connected with parabolic partial differential equations with concentrated nonlinearities we present some analytic results and in the case of the kernel of abel kind with power nonlinearity and fixed initial data we give a numerical approximation by using one point collocation methods by means of the numerical simulations we give the dependence of the blow up time from the parameters of the equation

analysis of explosion for nonlinear volterra equations this survey paper presents some analytical tools for determining the existence of a blow up solution for a wide class of nonlinear volterra integral equations the related phenomenon of quenching has also been investigated using similar techniques in both cases lower and upper bound estimates for the critical time as well as asymptotic solution behavior in the key limit are established this paper surveys recent results in the analysis of such problems and proposes problems for future study

function observer design for a class of linear time varying system this paper presents for the first time a reduced order linear function observer design algorithm for uniformly observable linear time varying systems the resulting observer will have a constant jordan form system matrix with arbitrarily given poles the order reduction of the function observer is also clarified and clearly explained

transforming time varying multivariable systems into block companion canonical forms abstract the problem of transforming a class of linear time varying continuous time systems into controllable and observable block companion canonical forms is considered in terms of system block controllability observability matrix this paper generalizes the results of shieh et al 3 and provides systematic and straightforward algorithms for obtaining block companion canonical forms an example is provided to illustrate this transformation technique

conditions for blow up of solutions of some nonlinear volterra integral equations in this paper we give necessary and sufficient conditions for blow up of solutions for a particular class of nonlinear volterra equations we also give some examples

brief modified stochastic luenberger observers a modified stochastic luenberger observer mslo structure is proposed to recover the optimal performance of the coventional slo for obtaining full state estimates in linear discrete time stochastic systems the optimal mslo omslo which gives the mmse estimates is derived by using the general two stage kalman filter a reduced order form of the omslo is also proposed for systems having singular measurement noises the connection between the omslo and the optimal minimal order observer of leondes and novak is also shown

a new upper estimation for the blow up time of solutions of a volterra integral equation and its application to the modeling of the formation of shear bands abstract the estimation of the blow up time of a class of volterra integral equations of convolution type is studied a new upper estimate of the blow up time expressed in terms of the convergence of a certain integral is found moreover it turns out that the aforementioned upper estimate can be applied to an even more general class of volterra integral equations like the one describing the formation of shear bands in steel

the existence problem for a nonlinear abel equation on the half line abstract we discuss a nonlinear abel equation on the half line c c 0 the basic results provide criteria for the existence of nontrivial everywhere positive solutions they are expressed in terms of the generalized osgood condition

weakly singular gronwall inequalities and applications to fractional differential equations abstract we obtain some new gronwall type inequalities which are applicable to some weakly singular volterra integral equations similar to the ones first studied by d henry the main interest is that we consider cases with a double singularity and we obtain explicit l bounds rather than l 1 bounds furthermore our bounds involve the exponential function and not the mittag leffler function as in some previous works we give applications to some volterra integral equations with a doubly singular kernel that arise from caputo fractional differential equations where as opposed to previous papers we have a singularity in the nonlinearity

a proof of the minimal order observer in 8 it is conjectured that the minimal order observer is p n r 1 for a system with r 1 noise free measurements r 2 noisy measurements and r r 1 r 2 a proof of the existence of the minimal order observer with p n r 1 is given in this note furthermore it is shown that from this minimal order observer one can derive the familiar luenberger observer and kalman filter as two special cases

arbitrary eigenvalue assignments for linear time varying multivariable control systems the problem of eigenvalue assignments for a class of linear time varying multi variable systems is considered using matrix operators and canonical transformations it is shown that a time varying system that is lexicography fixedly controllable can be made via state feedback to be equivalent to a time invariant system whose eigenvalues are arbitrarily assignable a simple algorithm for the design of the state feedback is provided

on fuzzy ideals of a ring 1 abstract the aim of this paper is to study fuzzy ideals of a ring to characterise regular rings and noetherian rings by fuzzy ideals and to determine all fuzzy prime ideals of the ring z of integers

fuzzy maximal radical and primary ideals of a ring we introduce the concepts of fuzzy maximal ideal the fuzzy radical of a fuzzy ideal and fuzzy primary ideal of a ring we show that a fuzzy left right ideal a of a ring r is a fuzzy maximal ideal if and only a 0 1 and a x r a x a 0 is a maximal left right ideal of r we also show that a fuzzy ideal a of a commutative ring r with unity is a fuzzy primary ideal of r if and only a 0 1 a is two valued and a is a primary ideal of r

positive solutions to a nonlinear abel type integral equation on the whole line abstract we consider the existence of positive solutions to the nonlinear integral equation where g is a continuous nondecreasing function such that g 0 0 we show that the equation always has nontrivial solutions and we give a necessary and sufficient condition for the existence of solutions u such that u x we also provide a condition which ensures that all the nontrivial solutions experience the blow up behaviour

design of a state estimator for a class of time varying multivariable systems in this note matrix operators are first introduced to develop a canonical transformation then it shows that a full order state estimator with any eigenvalues can be constructed for linear time varying systems that are uniformly observable and lexicography fixed a simple algorithm is provided to design the state estimator

canonical transformation for a class of time varying multivariable systems this paper concerns the transformation of time varying multivariable systems into canonical structures the study employs differential matrix operators it leads to a systematic and straightforward technique for developing canonical forms for time varying multivariable systems that are uniformly observable and lexicography fixed it shows that canonical forms derived by other authors are special cases of the canonical form of this paper the derived canonical forms are not unique however their structures are controlled by the designer

aspects of the behaviour of solutions of nonlinear abel equations abstract in this paper we study properties about the behaviour uniqueness locally boundedness attracting behaviour etc of positive solutions for nonlinear abel integral equations and we present examples of nonlinear abel integral equations with two nontrivial solutions these examples are related to the existence of nonlocally bounded solutions

fuzzy prime ideals of rings abstract the notions of fuzzy ideal and fuzzy prime ideal of a ring with truth values in a complete lattice satisfying the infinite meet distributive law are introduced which generalize the existing notions with truth values in the unit interval of real numbers a procedure to construct any fuzzy ideal from a family of ideals with certain conditions is established all fuzzy prime maximal ideals of a given ring are determined by establishing a one to one correspondence between fuzzy prime maximal ideals and the pairs p where p is a prime maximal ideal of the ring and is a prime element dual atom in the complete lattice

some results on a galois connection between lattices of l fuzzy ideals in this paper first we present a cl semigroup structure on l fuzzy ideals and conclude that the set of all l fuzzy quasi ideals is a cl monoid with zero then we obtain a galois connection between two cl semigroups of l fuzzy ideals of homomorphic rings finally by using galois connections we give the concepts of contracted and extended l fuzzy ideals and some related results are given

blow up collocation solutions of nonlinear homogeneous volterra integral equations in this paper collocation methods are used for detecting blow up solutions of nonlinear homogeneous volterra hammerstein integral equations to do this we introduce the concept of blow up collocation solution and analyze numerically some blow up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied finally we discuss the relationships between necessary conditions for blow up of collocation solutions and exact solutions

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

comments on on the application of matrix generalized inverses to the design of observers for time varying and time invariant linear systems in this discussion several comments on the eigenvalue assignment algorithm in the above paper are made for the purpose of better illustration and clarity

on functional observers for linear time varying systems the technical note deals with existence conditions of a functional observer for linear time varying systems in the case where the order of the observer is equal to the number of observed variables constructive procedures for the design of such a linear functional observer are deduced from the existence conditions as a specific feature the proposed procedures do not require the solution of a differential sylvester equation some examples illustrate the presented results

nonlinear volterra integral equations and the schroder functional equation we show an interesting connection between a special class of volterra integral equations and the famous schroder equation the basic results provide criteria for the existence of nontrivial as well as blow up solutions of the volterra equation expressed in terms of the convergence of some integrals examples related to volterra equations with power and exponential nonlinearities are presented

a characterization of l fuzzy prime ideals abstract in this paper the concepts of a l fuzzy prime and a l fuzzy completely prime ideal are given and some fundamental lemmas are proved in particular bijections among some of the l fuzzy prime ideals of two homomorphic rings are constructed also a characterization of a l fuzzy prime ideal of a ring is given

design of reduced order state estimators for linear time varying multivariable systems the design of reduced order state estimators for linear time varying multivariable systems is considered employing the concepts of matrix operators and the method of canonical transformations this paper shows that there exists a reduced order state estimator for linear time varying systems that are lexicography fixedly observable in addition the eigenvalues of the estimator can be arbitrarily assigned a simple algorithm is proposed for the design of the state estimator

blow up time for solutions to some nonlinear volterra integral equations the problem of the estimating of a blow up time for solutions of volterra nonlinear integral equation with convolution kernel is studied new estimates lower and upper are found and moreover the procedure for the improvement of the lower estimate is presented main results are illustrated by examples the new estimates are also compared with some earlier ones related to a shear band model

blow up solutions in one dimensional diffusion models abstract a sufficient and necessary condition for the existence of blow up solutions of a certain class of nonlinear volterra integral equations with kernels arising from various diffusion models and with nonlinearities satisfying the condition g 0 0 is given in the form of the so called generalized osgood condition such nonlinearities were not permitted in the original articles of olmstead and roberts where these diffusion models were introduced