existence of positive solutions for various boundary value problems in this paper we afford a concise approach to guarantee the existence of positive solutions for nonlinear second order ordinary differential equations with respect to various boundary conditions

successive iteration of positive solution for a discontinuous third order boundary value problem in this paper we obtain a successively iterative scheme of positive solution for the nonlinear third order two point boundary value problem u q u f t u 0 u 0 a u 1 b u 0 c where f is a caratheodory function f and q satisfy some additional monotone conditions the iterative scheme starts off with zero function and is therefore useful for computation purpose the main tool is monotone iterative technique on banach space moreover the iterative scheme is independent of the existence of lower and upper solutions

existence of positive solutions for non positive higher order bvps abstract we shall provide conditions on non positive function f t u 1 u n 1 so that the boundary value problem has at least one positive solution then we shall apply this result to establish several existence theorems which guarantee the multiple positive solutions

tensor product of modules over a vertex algebra abstract we find a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra we define the notion of vertex bilinear map and provide two algebraic constructions of the tensor product where one of them is of ring theoretical type we show the relation between tensor product and vertex homomorphisms we prove commutativity of the tensor product we also prove associativity of the tensor product of modules under certain necessary and sufficient condition finally we show certain functorial properties of vertex homomorphism and the tensor product

on the existence and nonexistence of positive solutions for nonlinear sturm liouville boundary value problems abstract in this paper the existence and nonexistence results of positive solutions are obtained for sturm liouville boundary value problem p x u q x u f x u x 0 1 a u 0 b p 0 u 0 0 c u 1 d p 1 u 1 0 where p c 1 0 1 q c 0 1 p x 0 q x 0 for x 0 1 f c 0 1 r a b c d 0 are constants and satisfy a b c d 0 the discussion is based on the positivity estimation for the green s function of associated linear boundary value problem and the fixed point index theory in cones

positive solutions of two point boundary value problems for second order differential equations with the nonlinearity dependent on the derivative abstract the existence of positive solutions is established for two point boundary value problems for second order differential equations with the nonlinearity dependent on the derivative l x h x f x x 0 x 1 r 1 1 0 1 0 0 r 2 2 1 2 1 0 where l x p x x q x x conditions are given in terms of the relative behaviors of the quotient f u v u v for u v near 0 and

dual time frequency domain system identification in this paper we obtain the maximum likelihood estimate of the parameters of discrete time linear models by using a dual time frequency domain approach we propose a formulation that considers a reduced rank linear transformation of the available data such a transformation may correspond to different options selection of time domain data transformation to the frequency domain or selection of frequency domain data obtained from time domain samples we use the proposed approach to identify multivariate systems represented in state space form by using the expectation maximisation algorithm we illustrate the benefits of the approach via numerical examples

positive solutions of sub superlinear sturm liouville problems in this paper we introduce the notion of a strict lower upper solution to nonlinear sturm liouville boundary value problems based on the maximum principles we establish a result of leray schauder degree on the ordered intervals induced by the pairs of strict lower and upper solutions applying the result and the fixed point index theory in cones we obtain the global existence results of positive solutions for sub superlinear sturm liouville problems

first and second cohomologies of grading restricted vertex algebras let v be a grading restricted vertex algebra and w a v module we show that for any the first cohomology of v with coefficients in w introduced by the author is linearly isomorphic to the space of derivations from v to w in particular for are equal and can be denoted using the same notation h 1 v w we also show that the second cohomology of v with coefficients in w introduced by the author corresponds bijectively to the set of equivalence classes of square zero extensions of v by w in the case that w v we show that the second cohomology corresponds bijectively to the set of equivalence classes of first order deformations of v

frequency domain system identification using arbitrary signals it is the common conviction that frequency domain system identification suffers from the drawback that it cannot handle arbitrary signals without introducing systematic errors this paper shows that it is possible to deal with nonperiodic signals without any approximation and under the same assumptions as in the time domain by estimating simultaneously some initial conditions and the system model parameters

existence and iteration of positive solutions to a class of sturm liouville like p laplacian boundary value problems abstract this paper deals with the existence and iteration of positive solutions for the following p laplacian differential equation p u t q t f t u t u t 0 t 0 1 subject to the following sturm liouville like four point boundary condition u 0 u 0 u 1 u 0 where 0 1 by applying the monotone iterative technique and without the assumption of the existence of lower and upper solutions we not only obtain the existence of positive solutions for the problems but also establish iterative schemes for approximating the solutions

existence of positive solutions for second order boundary value problem with one parameter abstract in the case of not requiring f t u to be nonnegative by transforming the boundary value problem into the integral equation system and applying the fixed point index theory the author studies the following second order boundary value problem with one parameter u u f t u 0 t 1 u 0 u 1 0 and obtains the results on the existence of its positive solution

multiple positive solutions of some boundary value problems abstract we study the existence of multiple positive solutions of the equations u t u subject to linear boundary conditions we show that there are at least two positive solutions if t u is superlinear at one end point zero or infinity and sublinear at the other applications of these results are provided to yield multiple positive solutions of some elliptic boundary value problems on an annulus

identification of the deterministic part of mimo state space models given in innovations form from input output data the problem of linear multivariable state space model identification from input output data can under the presence of process and measurement noise be solved in a non iterative way when incorporating instrumental variables constructed from both input and output sequences in the recently developed class of multivariable output error state space model class of subspace model identification schemes abstract in this paper we describe two algorithms to identify a linear time invariant finite dimensional state space model from input output data the system to be identified is assumed to be excited by a measurable input and an unknown process tloise and the measurements are disturbed by unknown measurement noise both noise sequences are discrete zero mean white noise the first algorithm gives consistent estimates only for the case where the input also is zero mean white noise while the same result is obtained with the second algorithm without this constraint for the special case where the input signal is discrete zero mean white noise it is explicitly shown that this second algorithm is a special case of the recently developed multivariable output error state space moesp class of algorithms based on instrumental variables the usefulness of the presented schemes is highlighted in a realistic simulation study

cohomology of conformal algebras the notion of a conformal algebra encodes an axiomatic description of the operator product expansion of chiral fields in conformal field theory on the other hand it is an adequate tool for the study of infinite dimensional lie algebras satisfying the locality property the main examples of such lie algebras are those based on the punctured complex plane such as the virasoro algebra and loop lie algebras in the present paper we develop a cohomology theory of conformal algebras with coefficients in an arbitrary module it possesses standards properties of cohomology theories for example it describes extensions and deformations we offer explicit computations for the most important examples

positive solution for singular boundary value problems abstract a sufficient condition for the existence of positive solutions of the nonlinear boundary value problem u t f t u t 0 0 u 0 u 1 0 is constructed where f 0 1 0 0 is continuous f t u is locally lipschitz continuous and f t u u is strictly decreasing in u 0 for each t 0 1

multiplicity results for some second order four point boundary value problems abstract in this paper by using a fixed point theorem of functional type in a cone some new results for the multiplicity of positive solutions of second order four point boundary value problems are obtained the emphasis is put on the nonlinear term involved with the first order derivative

subspace based multivariable system identification from frequency response data two noniterative subspace based algorithms which identify linear time invariant mimo multi input multioutput systems from frequency response data are presented the algorithms are related to the recent time domain subspace identification techniques the first algorithm uses equidistantly in frequency spaced data and is strongly consistent under weak noise assumptions the second algorithm uses arbitrary frequency spacing and is strongly consistent under more restrictive noise assumptions promising results are obtained when the algorithms are applied to real frequency data originating from a large flexible structure

positive solutions to singular system with four point coupled boundary conditions abstract existence of positive solution to a nonlinear singular system with four point coupled boundary conditions of the type x t f t x t y t t 0 1 y t g t x t y t t 0 1 x 0 0 x 1 y y 0 0 y 1 x is established the nonlinearities f g 0 1 0 0 0 are continuous and singular at t 0 t 1 while the parameters satisfy 0 1 0 1 an example is included to show the applicability of our result

multiple solutions of impulsive sturm liouville boundary value problem via lower and upper solutions and variational methods abstract in this paper we prove the existence of multiple solutions for second order sturm liouville boundary value problem l u f x u x 0 1 r 1 u 0 r 2 u 0 where l u p x u q x u is a sturm liouville operator r 1 u u 0 u 0 r 2 u u 1 u 1 the technical approach is fully based on lower and upper solutions and variational methods the interesting point is that the existence of four solutions and seven solutions is given

on the existence of positive solutions for semilinear elliptic equations in the annulus abstract we study the existence of positive radial solutions of u g x u 0 in annuli with dirichlet dirichlet neumann boundary conditions we prove that the problems have positive radial solutions on any annulus if is sublinear at 0 and

a cohomology theory of grading restricted vertex algebras we introduce a cohomology theory of grading restricted vertex algebras to construct the correct cohomologies we consider linear maps from tensor powers of a grading restricted vertex algebra to rational functions valued in the algebraic completion of a module for the algebra instead of linear maps from tensor powers of the algebra to a module for the algebra one subtle complication arising from such functions is that we have to carefully address the issue of convergence when we compose these linear maps with vertex operators in particular for each n in mathbb n we have an inverse system h n m v w m in mathbb z of nth cohomologies and an additional nth cohomology h infty n v w of a grading restricted vertex algebra v with coefficients in a v module w such that h infty n v w is isomorphic to the inverse limit of the inverse system h n m v w m in mathbb z in the case of n 2 there is an additional second cohomology denoted by h 2 frac 1 2 v w which will be shown in a sequel to the present paper to correspond to what we call square zero extensions of v and to first order deformations of v when w v

cohomology of vertex algebras abstract let v be a vertex algebra and m a v module we define the first and second cohomology of v with coefficients in m and we show that the second cohomology h 2 v m corresponds bijectively to the set of equivalence classes of square zero extensions of v by m in the case that m v we show that the second cohomology h 2 v v corresponds bijectively to the set of equivalence classes of first order deformations of v

successive iteration and positive solution for nonlinear second order three point boundary value problems in this paper we study the existence of positive solution for two classes of nonlinear second order three point boundary value problems using some monotone iterative schemes in both cases such schemes start off with known constant functions and therefore are useful to computation purpose

frequency domain subspace system identification using non parametric noise models in the general case of non uniformly spaced frequency domain data and or arbitrarily coloured disturbing noise the frequency domain subspace identification algorithms described in mckelvey akcay and ljung ieee trans automatic control 41 7 1996 960 and van overschee and de moor signal processing 52 2 1996 179 are consistent only if the covariance matrix of the disturbing noise is known this paper studies the asymptotic properties strong convergence convergence rate asymptotic normality strong consistency and loss in efficiency of these algorithms when the true noise covariance matrix is replaced by the sample noise covariance matrix obtained from a small number of independent repeated experiments as an additional result the strong convergence in case of model errors the convergence rate and the asymptotic normality of the subspace algorithms with known noise covariance matrix follows

nonlinear boundary value problems in hilbert spaces abstract in this paper we examine nonlinear two point boundary value problems with sturm liouville type boundary conditions in a hilbert space our technique involves using the topological transversality theorem of a granas which relies on the notions of an essential map and a priori bounds on solutions we obtain existence results for a wide class of problems with our nonlinear term satisfying a bernstein nagumo growth condition

multiple solutions of some boundary value problems with parameters abstract in this paper we study the existence and multiplicity of nontrivial solutions for the following second order dirichlet nonlinear boundary value problem with odd order derivative u t a u t b u t f t u t for all t 0 1 with u 0 u 1 0 where a b r 1 f c 1 0 1 r 1 r 1 by using the morse theory we impose certain conditions on f which are able to guarantee that the problem has at least one nontrivial solution two nontrivial solutions and infinitely many solutions separately

positive solutions of second order boundary value problems with sign changing nonlinear terms abstract in this paper the existence results of positive solutions are obtained for second order boundary value problem u f t u t 0 1 u 0 u 1 0 where f c 0 1 r whose sign may change the proof is based on the fixed point index theory in cones

nontrivial solutions of singular sublinear sturm liouville problems abstract the singular superlinear sturm liouville problems l x h x f x 0 x 1 r 1 1 0 1 0 0 r 2 2 1 2 1 0 are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators where l x p x x q x x and h x is allowed to be singular at both x 0 and x 1 in particular f is not necessary to be nonnegative the existence results of nontrivial solutions and positive solutions are given by means of the topological degree theory

frequency domain subspace identification using frf data from arbitrary signals abstract recently an extension of the frequency domain subspace identification methods was developed that can cope with arbitrary excitation signals and transient effects in this paper the implications of this extended model are investigated for the h 1 estimator it is shown that an extended model makes it possible to start from frequency response functions frfs without suffering from leakage by modelling the initial conditions of each data block used in the averaging procedure of the h 1 estimator in this way the measurements can be averaged in order to reduce both the data set and the noise levels without introducing bias errors caused by leakage phenomena it is shown by both simulations and real life measurements that the presented approach improves the modal parameter estimates and in particular the damping estimates

three positive solutions for second order m point boundary value problems for the second order m point boundary value problemu t f t u 0 0 0 i 1 2 m 2 0 x 1 x 2 x m 2 1 growth conditions are imposed on f which yield the existence of at least three positive solutions by using the leggett williams fixed point theorem the associated green s function for the m point boundary value problem is also given

an application of topological transversality to non positive higher order difference equations in this paper we shall provide sufficient conditions on the non positive function i u 1 u n 1 so that the boundary value problem bvp given by e d nu i m i u i du i d n 2 i 0 and bc d mu 0 0 0 m n 3 a d n 2 0 b d n 1u 0 0 c d n 2u t 1 d d n 1u t 1 0 has at least one positive solution

nonstationary consistency of subspace methods in this paper we study ldquononstationary consistencyrdquo of subspace methods for eigenstructure identification i e the ability of subspace algorithms to converge to the true eigenstructure despite nonstationarities in the excitation and measurement noises note that such nonstationarities may result in having time varying zeros for the underlying system so the problem is nontrivial in particular likelihood and prediction error related methods do not ensure consistency under such situation because estimation of poles and estimation of zeros are tightly coupled we show in turn that subspace methods ensure such consistency our study carefully separates statistical from nonstatistical arguments therefore enlightening the role of statistical assumptions in this story

lie conformal algebra cohomology and the variational complex we find an interpretation of the complex of variational calculus in terms of the lie conformal algebra cohomology theory this leads to a better understanding of both theories in particular we give an explicit construction of the lie conformal algebra cohomology complex and endow it with a structure of a mathfrak g complex on the other hand we give an explicit construction of the complex of variational calculus in terms of skew symmetric poly differential operators

multiple positive solutions of nonlinear two point boundary value problems we improve the results obtained by erbe hu and wang in a recent paper we show that there exist at least two positive solutions of two point boundary value problems under conditions weaker than those used by erbe hu and wang

second and higher order systems of boundary value problems abstract existence results for systems of kth order boundary value problems are presented our analysis is based on a nonlinear alternative of a granas and use of a priori bounds