arma models their kronecker indices and their mcmillan degree this paper highlights some difficulties with the use of arma models with leading unit coefficient matrix in system identification it is shown that the mcmillan degree of such models is not in any easy way related to the row degrees of the polynomial factors of the arma model a rank test is given for the mcmillan degree of such models and it is shown that this degree will generically be a multiple of the dimension of the observation vector

on linearization of hyperbolic equations using differential invariants abstract in this paper we consider the general class of hyperbolic equations u x t f x t u u x u t we use equivalence transformations to derive differential invariants for this class and for two subclasses then we employ these invariants to construct equations that can be linearized via local mappings further applications of the differential invariants are given

subcriticality and gaugeability of the schrodinger operator we investigate a schrodinger operator 2 v in r d d 3 with a potential v in the class k d satisfying a similar kato condition at infinity and prove an equivalence theorem connecting various conditions on subcriticality strong positivity and gaugeability of the operator

enhanced group analysis and conservation laws of variable coefficient reaction diffusion equations with power nonlinearities a class of variable coefficient 1 1 dimensional nonlinear reaction diffusion equations of the general form f x ut g x unux x h x um is investigated different kinds of equivalence groups are constructed including ones with transformations which are nonlocal with respect to arbitrary elements for the class under consideration the complete group classification is performed with respect to convenient equivalence groups generalized extended and conditional ones and with respect to the set of all local transformations usage of different equivalences and coefficient gauges plays the major role for simple and clear formulation of the final results the corresponding set of admissible transformations is described exhaustively then using the most direct method we classify local conservation laws some exact solutions are constructed by the classical lie method

second order differential invariants of a family of diffusion equations an equivalence transformation algebra for a class of nonlinear diffusion equations is found after having obtained the second order differential invariants with respect to we get some results which allow us to linearize a subclass of the equations considered

positive solutions and large time behaviors of schrodinger semigroups simon s problem let h v where v is a multiplication operator by a real valued function v x on rn which is uniformly holder continuous and 1 x 2 2 v x l rn for some 4 the relationship between existence of positive solutions with growth conditions of hg 0 and asymptotic behaviors as t of e th is established using it b simon s problem for h on r2 is solved

singular invariant equation for the 1 1 fokker planck equation semi invariants for the linear parabolic equations with two independent variables time variable t and space variable x and one dependent variable u are derived under the transformation of the independent variables by using the infinitesimal method we also obtain the joint invariant equation for the above mentioned equation under equivalence transformation in fact we prove a necessary and sufficient condition for a 1 1 parabolic equation to be reducible via a local equivalence transformation to the one dimensional classical heat equation this result provides practical criteria for reduction finally examples of 1 1 fokker planck equations from applications are given to verify the results obtained

invariants of two and three dimensional hyperbolic equations abstract we consider linear hyperbolic equations of the form u t t i 1 n u x i x i i 1 n x i x 1 x n t u x i t x 1 x n t u t u x 1 x n t u we derive equivalence transformations which are used to obtain differential invariants for the cases n 2 and n 3 motivated by these results we present the general results for the n dimensional case it appears at least for n 2 that this class of hyperbolic equations admits differential invariants of order one but not of order two we employ the derived invariants to construct interesting mappings between equivalent equations

criticality and the λ property for elliptic equations abstract let l denote a nonnegative second order elliptic expression defined on c 0 and let l be an associated self adjoint operator l is said to have the property in iff l for some fixed positive function and any c 0 l is termed subcritical iff a generalized green s function may be defined for l in various applications of these and closely related concepts may be found in the literature it is the main purpose of this article to show that l is subcritical iff l has the property several corollaries and an example are given as consequences of this equivalence

autoregressive models of singular spectral matrices this paper deals with autoregressive ar models of singular spectra whose corresponding transfer function matrices can be expressed in a stable ar matrix fraction description d 1 q b with b a tall constant matrix of full column rank and with the determinantal zeros of d q all stable i e in q 1 q c to obtain a parsimonious ar model a canonical form is derived and a number of advantageous properties are demonstrated first the maximum lag of the canonical ar model is shown to be minimal in the equivalence class of ar models of the same transfer function matrix second the canonical form model is shown to display a nesting property under natural conditions finally an upper bound is provided for the total number of real parameters in the obtained canonical ar model which demonstrates that the total number of real parameters grows linearly with the number of rows in w q

the properties of the parameterization of armax systems and their relevance for structural estimation and dynamic specification armax systems in structural specification are considered topological and geometric properties of the parameter space and of the parameterization which are important for the properties of the estimators regardless of their special form are investigated and the specification of the maximum lag lengths is discussed

invariants and canonical forms for systems structural and parametric identification the basic definitions regarding invariant functions and canonical forms for an equivalence relation on a generic set are first recalled with reference to observable state space models and to the equivalence relation induced by a change of basis it is then shown how the image of a complete set of independent invariants for the considered equivalence relation can be used to parametrize a subset of canonical forms in the given set then the set of polynomial input output models of the type p z y t q z u t and the equivalence relation induced by the premultiplication of p and q by a unimodular matrix are considered and canonical forms parametrized by a complete set of independent invariants introduced since the two sets of canonical forms share common sets of complete independent invariants very simple algebraical links between state space and input output canonical forms can be deduced the previous results are used to design efficient algorithms solving the problem of the canonical structural and parametric realization and identification of generic input output sequences generated by a linear discrete time invariant multivariable system the results obtained in the identification of a real process are then reported

large time behavior of the lp norm of schrodinger semigroups abstract letv 0 v c0 rv with v 3 be such that h 1 2 v 0 but for any e 0 1 2 1 e v is not positive we determine the exact rate of divergence of the norm of e th as a map from l to l a number of related problems are discussed

on positive solutions of second order elliptic equations stability results and classification soit p un operateur uniformement elliptique d ordre 2 defini dans un domaine cr n soit p le cone convexe de toutes les solutions positives de l equation pu 0 dans on etudie les proprietes generales de p pour p et generaux

criticality and ground states for second order elliptic equations abstract let p be a second order elliptic operator in a domain r n suppose that p admits a positive minimal green function g p in it is the main purpose of this paper to prove that if w c is a small perturbation of p in then max w x 0 min w x 0 t u u g p outside a compact set in

general results on the mcmillan degree and the kronecker indices of arma and mfd models this paper shows that the mcmillan degree of general arma and mfd models is equal to the pole zero excess of the matrix consisting of the polynomial factors furthermore the left kronecker indices are equal to the row degrees of this matrix if and only if it is row reduced and irreducible for left coprime arma and mfd models the mcmillan degree and the left kronecker indices are related to the determinantal degree and the row degrees of a suitable submatrix of the polynomial factors under certain necessary and sufficient conditions this information can even be inferred from the denominator matrices in the arma and mfd models finally a rank test is presented for actually computing the mcmillan degree of left coprime arma and mfd models

linearization of third order ordinary differential equations by point and contact transformations we present here the solution of the problem on linearization of third order ordinary differential equations by means of point and contact transformations we provide in explicit forms the necessary and sufficient conditions for linearization the equations for determining the linearizing point and contact transformations as well as the coefficients of the resulting linear equations

differential invariants for systems of linear hyperbolic equations in this paper we consider a general class of systems of two linear hyperbolic equations motivated by the existence of the laplace invariants for the single linear hyperbolic equation we adopt the problem of finding differential invariants for the system we derive the equivalence group of transformations for this class of systems the infinitesimal method which makes use of the equivalence group is employed for determining the desired differential invariants we show that there exist four differential invariants and five semi invariants of first order applications of systems that can be transformed by local mappings to simple forms are provided

properties of the parametrization of monic arma systems abstract some properties of the parametrization of multi input multi output monic arma systems with prescribed column degrees are considered in particular we give a minimal cover for the set of transfer functions corresponding to all arma systems in terms of this parametrization we investigate the relation between the kronecker indices and the prescribed column degrees and we investigate the boundary of a certain parameter space and of the corresponding set of transfer functions

on form preserving point transformations of partial differential equations new identities are presented relating arbitrary order partial derivatives of and for the general point transformation these identities are used to study the nature of those point transformations which preserve the general form of a wide class of 1 1 partial differential equations these results facilitate the search for point symmetries both discrete and continuous lie and assist the search for point transformations which reduce equations to canonical but similar form a simple test for the existence of hodograph type transformations between equations of similar form is given

new results on group classification of nonlinear diffusion convection equations using a new method and additional conditional and partial equivalence transformations we performed group classification in a class of variable coefficient 1 1 dimensional nonlinear diffusion convection equations of the general form f x ut d u ux x k u ux we obtain new interesting cases of such equations with the density f localized in space which have non trivial invariance algebra exact solutions of these equations are constructed we also consider the problem of investigation of the possible local transformations for an arbitrary pair of equations from the class under consideration i e of describing all the possible partial equivalence transformations in this class

on critical and subcritical sturm liouville operators we study critical and subcritical sturm liouville operators k 1 ddx p ddx v in l2 a b k dx a b r defined as friedrichs extensions under most general conditions on k p and v in particular we prove the equivalence of the notions of criticality as introduced by simon and murata for an important class of potentials v