minimal locally linearly dependent spaces of operators abstract let s be an n dimensional minimal locally linearly dependent space of operators acting between vector spaces u and v we obtain the sharp lower bound and the sharp upper bound for dim s u and give a complete description of those minimal locally linearly dependent spaces at which the upper bound is attained

reflexivity defect of kernels of the elementary operators of length 2 abstract let x be a finite dimensional complex vector space we give an explicit formula for the reflexivity defect of the kernel of an arbitrary elementary operator of length 2 i e an elementary operator of the form t a 1 tb 1 a 2 tb 2 t l x where a 1 a 2 and b 1 b 2 are linearly independent

one dimensional dynamics in locally heated liquid layers recent results on one dimensional patterns in locally heated experiments are presented a fluid layer is heated locally by a nearly one dimensional heater and subjected to both horizontal and vertical temperature gradients depending on the fluid depth and on the temperature difference established across the layer different convective regimes appear when a very small temperature gradient is applied a basic convective state appears it consists of two big rolls parallel to the heater and filling the convective cell a primary instability in the homogeneous basic flow gives rise to a one dimensional cellular stationary pattern for higher values of the control parameters time dependent patterns appear through a secondary instability various regimes are analyzed oscillations traveling waves and alternating patterns the hydrodynamic characteristics of these patterns are provided local temperature measurements allows to describe the physical mechanisms responsible for the instabilities the similarities and discrepancies of the experimental data with some theoretical models are provided

ldb division algebras abstract an ldb division algebra is a triple a in which and are regular bilinear laws on the finite dimensional non zero vector space a such that x x y is a scalar multiple of y for all vectors x and y of a this algebraic structure has been recently discovered in the study of the critical case in meshulam and semrl s estimate of the minimal rank in non reflexive operator spaces in this article we obtain a constructive description of all ldb division algebras over an arbitrary field together with a reduction of the isotopy problem to the similarity problem for specific types of quadratic forms over the given field in particular it is shown that the dimension of an ldb division algebra is always a power of 2 and that it belongs to 1 2 4 8 if the characteristic of the underlying field is not 2

reflexivity properties of t 0 a construction is given of a reflexive operator t acting on a separable hilbert space h with the property that the direct sum t 0 fails to be reflexive this construction is then used to provide solutions to several other problems which have been studied concerning the direct sum splitting of operator algebras scott brown s technique the theory of bitriangular operators and parareflexivity

reflexivity defect of spaces of linear operators abstract for a finite dimensional linear subspace s l v w and a positive integer k the k reflexivity defect of s is defined by rd k s dim ref k s s where ref k s is the k reflexive closure of s we study this quantity for two dimensional spaces of operators and for single generated algebras and their commutants

variance of operators and derivations abstract the variance of a bounded linear operator a on a hilbert space h at a unit vector is defined by d a a 2 a 2 we show that two operators a and b have the same variance at all vectors h if and only if there exist scalars c with 1 such that b a 1 or a is normal and b a 1 further if a is normal then the inequality d b d a holds for some constant and all unit vectors if and only if b f a for a lipschitz function f on the spectrum of a variants of these results for c algebras are also proved where vectors are replaced by pure states we also study the related inequalities b x x b a x x a supposed to hold for all x b h or for all x b h n and all n n we consider the connection between such inequalities and the range inclusion d b b h d a b h where d a and d b are the derivations on b h induced by a and b if a is subnormal we study these conditions in particular in the case when b is of the form b f a for a function f

separating vectors and reflexivity abstract there is a close connection between separating vectors and reflexivity but the existence of a separating vector does not guarantee reflexivity this paper clarifies the relation we first find that every subspace of linear transformations whose dimension is less than the cardinality of the scalar field and having a disjoint pair of separating vectors is algebraically reflexive then we refine the result and conclude that a finite dimensional subspace of operators having a two dimensional subspace of separating vectors is algebraically reflexive if its scalar field is algebraically closed examples are provided to show that these results are sharp an application of the first result shows that finite dimensional spaces of operators of large rank are reflexive

prediction condensed models adapted to the nonlinear structures in time domain abstract this paper deals with a method to study closely the stationary solution of nonlinear dynamic systems in time domain this method is based on the exploitation of karhunen loeve decomposition with or without parametric modifications as well as on the characteristics of localized nonlinearities with the application of this method at first on linear models initially condensed by karhunen loeve the predictions of nonlinear responses can be obtained rapidly this method is adapted to a condensed linear model used in the first optimization procedure of the nonlinear dynamic behaviour this robust basis will be used as condensation basis of the modified model local per zone which leads to a prediction of vibratory responses of complex structures modified and affected by localized nonlinearities

locally linearly dependent operators and reflexivity of operator spaces we obtain two results on the existence of large subspaces of operators of small rank in locally linearly dependent spaces of operators as a consequence we obtain an upper bound for the rank of operators belonging to a minimal locally linearly dependent space of operators it has been known that the only obstruction to the reflexivity of a finite dimensional operator space comes from the operators with small ranks our results improve known bounds on the minimal rank that guarantees the reflexivity

secondary instability of one dimensional cellular patterns a gap solition black solition and breather analogy abstract ten years ago a normal form theory for the generic secondary instabilities of one dimensional cellular patterns has been rigorously derived close to the secondary bifurcation threshold the aim of this paper is to show that some experimental observations of localized patterns previously unexplained can be understood if one slightly modifies the former theory in order to take into account a linearly damped eigenmode with particular symmetry property the model we develop involving a huge number of unknown parameters turns out to be quite unsatisfactory from a computational point of view but we get round this difficulty by developing a strong analogy with the well known problem of the propagation of a nonlinear wave in a periodic medium with this analogy in mind localized solutions of our model similar to the usual conservative breather gap or black soliton are numerically obtained and compared with the experimental observations with quite a good qualitative agreement

sous espaces invariants d un operateur nilpotent sur un espace de banach resume soit a un operateur lineaire continu nilpotent sur un espace de banach reel ou complexe nous montrons que pour tout sous espace invariant separable m de a il existe un commutant de a dont l image est dense dans m

reflexivite d une extension d un operateur normal par un operateur nilpotent let t be an extension of a one to one normal operator a by a nilpotent operator n in this paper we calculate the defect of reflexivity of t we give a necessary and sufficient condition to insure the reflexivity of such extensions in particular it is shown that t is reflexive when n is reflexive

solitary dilation waves in a circular array of liquid columns abstract solitary dilation waves and self sustained oscillations optical mode are observed in a one dimensional pattern of liquid columns produced in the pouring of a liquid film from a solid ceiling a new experiment carried out on a circular fountain allows us to achieve periodic boundary conditions and thus to observe free propagation of the dilation waves in an infinite medium measurements of the drift and group velocities of the dilation waves and of the optical pulsation are presented as functions of the flow rate in addition starting from qualitative observations and order of magnitude estimates we build a discrete model of non linear dynamics in this system in which dissipation is compensated by an external energy supply transient drop formation this model allows us to recover the appearance of the optical mode induced by a wavelength increase and predicts the focusing of this mode into a localized kink traveling at a constant speed along the column array the kink structure is reminiscent of the dilation waves observed experimentally both the model and experiment support a relationship between the wave velocity and the oscillation frequency similar to that observed by michalland and rabaud in the printer s instability

dynamics of defects and traveling waves in an interfacial finger pattern we present the results of an experimental study of one dimensional traveling finger patterns dominated by source and sink defects the system studied is a driven fluid air interface and the traveling wave state arises via a subcritical bifurcation we analyze space time images of the patterns to obtain the amplitude and local wave number of the left and right going traveling waves near the defects we determine the width of the defects and find that the width of the sinks does not vary significantly with distance above the bifurcation over the range of our experiments while the source width increases as the bifurcation is approached from above we also observe both localized depressions or enhancements in wave amplitude and periodic modulations of the pattern amplitude and wave number

localized phenomena during spatio temporal intermittency in directional viscous fingering in the directional viscous fingering instability the interface can evolve from a basic steady state to chaos by spatio temporal intermittency one essential feature of such a transition is that the chaotic domains appear by a contamination process of the steady phase this mechanism is investigated here and it is shown that contamination occurs by two localized structures dilatation waves and pairs of static asymmetric cells these two structures suggest an elastic behaviour of the pattern

some counterexamples in nonselfadjoint algebras in this note a construction is given of a special operator t on hilbert space a free variable in this construction is a weakly closed subspace ty of operators by appropriate choice of j we give counterexamples to several well known

a modal superposition method for non linear structures the dynamic response of multi degree of freedom mdof non linear structures is usually determined by the numerical integration of equations of motion this is computationally very costly for steady state response analysis in this study a powerful and economical method is developed for the harmonic response analysis of non linear structures in this method the equations of motion are first converted into a set of non linear algebraic equations and then the number of equations to be solved is reduced by employing linear modes of the system the resulting coupled algebraic equations are solved iteratively the concept of the pseudo receptance matrix is introduced in calculating the steady state response it is shown that the reduction in computational time can be considerable as very accurate results can be obtained by using only a limited number of modes several example problems are solved in order to illustrate the performance of the method effects of higher modes and higher harmonic components of the response are discussed in detail in order to illustrate the accuracy and speed of the method suggested the results obtained by applying the so called iterative modal method are compared with those obtained by the newmark method which is used as a classical time domain analysis technique

on the minimal rank in non reflexive operator spaces over finite fields let u and v be vector spaces over a field k and s be an n dimensional linear subspace of l u v the space s is called algebraically reflexive whenever it contains every linear map g u v such that for all x u there exists f s with g x f x a theorem of meshulam and semrl states that if s is not algebraically reflexive then it contains a non zero operator of rank at most 2n 2 provided that k has more than n 2 elements in the present article we prove that the provision on the cardinality of the underlying field is unnecessary to do so we demonstrate that the above result holds for all finite fields

range compatible homomorphisms on matrix spaces abstract let k be a commutative field and u and v be finite dimensional vector spaces over k let s be a linear subspace of the space l u v of all linear operators from u to v a map f s v is called range compatible when f s im s for all s s obvious examples of such maps are the evaluation maps s s x with x u in this article we classify all the range compatible group homomorphisms on s provided that codim l u v s 2 dim v 3 unless k has cardinality 2 and codim l u v s 2 dim v 3 under those assumptions it is shown that the linear range compatible maps are the evaluation maps and the above upper bound on the codimension of s is optimal for this result to hold as an application we obtain new sufficient conditions for the algebraic reflexivity of an operator space and with the above conditions on the codimension of s we give an explicit description of the range restricting and range preserving homomorphisms on s

closed form solutions of weakly nonlinear multi degree of freedom systems with single nonlinear element abstract in this study a new method which provides closed form expressions for the frequency domain solutions of multi degree of freedom systems is introduced the method is applicable for a multi degree of freedom system with a single weak nonlinear element using this method a multi degree of freedom system with a single nonlinear element can be put into a form such that solution of the linear part of the system along with the solution of a single nonlinear equation gives the nonlinear system response the analytic solution of this nonlinear scalar equation is provided for cubic stiffness and coulomb damping cases the proposed approach is implemented on case studies of systems with cubic stiffness and dry friction elements the results show that the method is accurate and completely eliminates the need for an iterative solution hence significant time savings can be obtained for large systems the lack of need for iteration makes the method ideal for large finite element models with a single nonlinear element

reflexivity algebraic reflexivity and linear interpolation introduction this paper was motivated by a discovery that most finite dimensional subalgebras of b h for h an infinite dimensional hilbert space are reflexive with the only obstructions to reflexivity being finite rank considerations proofs section 2 do not depend on multiplicative structure nor on topology so extend to linear subspaces of transformations in an abstract setting abstract reflexivity has been studied in 3 4 7 primarily for singly generated algebras reflexivity properties can be interpreted as linear interpolation properties and we shall adopt this point of view the results of section 2 extend in section 3 to algebraic reflexivity counterparts for countably generated algebraically linear subspaces of bounded linear transformations acting on a banach space as consequences in section 4 we obtain generalizations of two single operator results one is a multivariate version of the result due to kaplansky 10 theorem 15 that a bounded locally algebraic operator acting on a banach space is algebraic the other is a multivariate version of the result due to douglas and foias 5 for hilbert space and to hadwin 7 for a general banach space extending work of fillmore 6 that a bounded non algebraic operator acting on a banach space is topologically algebraically reflexive in section 5 we give an application kindly suggested by d hadwin concerning joint strong similarity orbits of n tupules of operators we wish to thank e azoff k davidson j erdos d hadwin j kraus c lance and a sourour for conversations and some correspon

reflexivity and hyperreflexivity of operator spaces abstract in this paper we show that if s is an n dimensional subspace of l v such that every nonzero transformation of s has rank greater than or equal to 2 n 1 then s is algebraically reflexive if s is an n dimensional subspace of b h such that every nonzero transformation of s has rank greater than or equal to 2 n 1 then s is hyperreflexive we also consider how to construct some new hyperreflexive subspaces

reflexive binormal operators abstract this paper initiates a study of the problem of which binormal operators on a hilbert space are reflexive for a certain important class of binormal operators a simple measure theoretic characterization is given for reflexivity