nonuniform image motion estimation using kalman filtering this correspondence presents a new pixel recursive algorithm for estimating the nonuniform image motion from noisy measurements the proposed method is performed in two steps first the pixels are examined to identify the detectable moving pixels using a binary hypothesis testing then characterizing the motion of the identified moving pixels in terms of a unitary transformation the motion coefficients are estimated using a kalman filter because the motion vector is typically spatially slowly varying the size of the motion coefficient vector is significantly reduced consequently the proposed kalman filter need only search for the truncated coefficients of the motion field the proposed method is simulated on a computer and results are compared with the algorithm reported by netravali and robbins see bell syst tech j vol 58 no 3 p 631 70 mar 1979

fuzzy vector spaces abstract this paper defines a basis for a fuzzy vector space and its dimension a class of fuzzy vector spaces having dimension is introduced and two standard results from crisp theory are proved for this case namely d i m e1 e2 d i m e1 d i m e2 d i m e1 e2 and rmd i m i m f d i m k e r f the product of two fuzzy vector spaces under certain conditions is also characterised

a sharp version of kahan s theorem on clustered eigenvalues let n times n hermitian matrix a have eigenvalues lambda 1 lambda 2 cdots lambda n and let k times k hermitian matrix h have eigenvalues mu 1 le mu 2 le cdots le mu k and let q be an n times k matrix having full column rank so 1 le k le n it is proved that there exist k eigenvalues lambda i 1 le lambda i 2 le cdots le lambda i k of a such that max 1 le j le k mu j lambda i j le frac c sigma min q aq qh 2 always holds with c 1 where sigma min q is the smallest singular value of q and cdot 2 denotes the biggest singular value of a matrix the inequality was proved for c le sqrt 2 in 1967 by kahan who also conjectured that it should be true for c 1

exclusion theorems and the perturbation analysis of the generalized eigenvalue problem a bauer fike type theorem is proved for the eigenvalue problem ax lambda bx a generalization is then applied to obtain perturbation bounds for clusters of eigenvalues the conditioning of an eigenvalue finite or infinite is proved to be dependent on a jordan type condition number its eigenvector deficiency and the regularity of the matrix pencil a lambda b an example illustrating the perturbation bounds is given

nonuniform image motion estimation in reduced coefficient transformed domains the transformed domain maximum likelihood tdml algorithm for image motion estimation is presented this algorithm finds a solution which maximizes a log likelihood function using a steepest ascent scheme important characteristics of the algorithm are the inclusion of noise in the signal model the consideration of motion as a nonuniform process and calculation of convergence parameters by means of a linear analysis simulation on real image sequences demonstrate the validity of the motion estimator the experiments also verify the validity of the equations presented for the calculation of the convergence parameters additional experiments performed to determine the noise sensitivity of the tdml show that noise resistance can be obtained using a reduced coefficient transform rct tdml algorithm an additional benefit of using an rct with the tdml algorithm is an increase in the speed of the algorithm without significant performance degradation two of the common transforms haar and walsh hadamard are shown to have some interesting properties when utilized with the rct tdml algorithm

on the convergence of the generalized maximum likelihood algorithm for nonuniform image motion estimation the generalized maximum likelihood algorithm is a powerful iterative scheme for waveform estimation this algorithm seeks for the maximum likelihood estimates of the karhunen loeve expansion coefficients of the waveform the search for the maximum is performed by the steepest ascent routine the objective of the paper is to obtain conditions that assure the stability in the mean for frame to frame image motion estimation sufficient conditions are established for the convergence of the algorithm in the absence of noise experimental results are presented that illustrate the behavior of the algorithm in the presence of various noise levels

fuzzy ideals and fuzzy subalgebras of lie algebras abstract a fuzzy idea l of a lie algebra l factors it into a lie algebra l l called a fuzzy quotient lie algebra this fuzzy algebra lie algebra is always a fuzzy partition of l and a fuzzy partition of l will be a fuzzy quotient lie algebra if and only if its associated fuzzy similarity relation is compatible with the lie algebra operations relationship between the operations of the lie algebras l i t and zadeh s extension principle are studied we also study homomorphisms of lie algebras and the relationship between them and fuzzy ideals and fuzzy subalgebras of the domains and the co domains of these homomorphisms finally solvability of fuzzy ideals and studied in defining these solvable fuzzy ideals we use zadeh s extension principle

fuzzy linear and affine spaces abstract elementary properties of fuzzy linear and affine spaces are studied the concept of a basis for a fuzzy linear space is defined and an algorithm for computing a basis when the underlying space is finite dimensional is given

fuzzy partitions and fuzzy quotient rings abstract the cosets of a fuzzy ideal m in a ring a form another ring a m called the fuzzy quotient ring of a and m we show that a m is always a fuzzy partition of a and a fuzzy partition of a will be a fuzzy quotient ring with respect to some fuzzy ideal if and only if its associated fuzzy similarity relation is compatible with the ring operations we also discuss relationships between the two operations of the fuzzy quotient ring a m and the extensions over ia of the two operations of a by zadeh s extension principle we study relationships between the level ring structures of a fuzzy quotient ring and the level relations of its associated fuzzy similarity relations we introduce and study a new notion of the factorization of a ring homomorphism through fuzzy quotients finally a relationship between fuzzy prime ideals and fuzzy similarity relation has been established

the adjoint representation of fuzzy lie algebras the commutator of a lie algebra l is extended by zadeh s extension principle to a product of fuzzy subsets a fuzzy subspace generated by the product of two fuzzy ideals is also a fuzzy ideal this notion of product of fuzzy ideals is used to define the descending central series of a fuzzy ideal nilpotency of fuzzy ideals is introduced using this descending central series fuzzification of the adjoint representation of lie algebras is introduced and some relations between this representation and nilpotent fuzzy ideals are proved finally the killing form in the fuzzy case is defined and some of its properties are studied

structural stability for singular systems a quantitative approach this paper studies the structural stability for singular systems the problem is solved via the matrix perturbation analysis method allowed perturbation regions for structural stability are given

quotients with respect to similarity relations abstract the problem of the quotient w r t a similarity relation is closely related to poincare s paradox and central problems in cluster analysis amazingly this problem remains open for more than 30 years as a generalization of strong m categories we introduce the concept of m valued sets which leads to the definition of the category m set in m set we give a complete solution of the quotient problem

systems of linear interval equations this paper presents theory and methods for computing the exact bounds on the solution of a system of n linear equations in n variables whose coefficients and right hand sides vary in some real intervals finite and iterative methods are given based on results from linear complementarity theory also regularity conditions regularity testing and computing the exact inverse of an interval matrix are dealt with

generalization of the bauer fike theorem the bauer fike theorem for diagonalizable matrices is generalized to cases where i non diagonalizable matrices or ii only part of the spectrum is considered

correspondence theorem for fuzzy ideals abstract the ring r j of cosets of a fuzzy ideal j of a ring r is defined and shown to be isomorphic to a factor ring of r in a natural way if f r r is an epimorphism of rings a one to one order preserving correspondence is established between the fuzzy ideals of r and those of r which are constant on the kernel of f this generalizes the correspondence theorem of non fuzzy ideals

nonuniform image motion estimation from noisy data image motion estimation is viewed as a problem in nonlinear demodulation the motion d x modulates the intensity of the previous frame s x to result in the intensity of the present frame s x d x an iterative algorithm based on the generalized maximum likelihood criterion is developed and implemented to demodulate d x an advantage of this scheme is the incorporation of the covariance function matrix which is specifically useful in the stationary case to determine the integration region alpha sub x simulation demonstrated the ability of the algorithm to deal with cases such as markov 2 motion

intuitionistic fuzzy lie sub superalgebras and intuitionistic fuzzy ideals in this paper the concepts of intuitionistic fuzzy sets are introduced to lie superalgebras intuitionistic fuzzy lie sub superalgebras and intuitionistic fuzzy ideals of lie superalgebras are defined and related properties are investigated as the applications of intuitionistic fuzzy lie sub superalgebras and intuitionistic fuzzy ideals the properties of intuitionistic fuzzy lie sub superalgebras and intuitionistic fuzzy ideals under homomorphisms of lie superalgebras are studied the intuitionistic fuzzy bracket product is also introduced and its characterization is established

fuzzy irreducible ideals in rings abstract in this paper the concept of a fuzzy set is extended by introducing the concept of a fuzzy irreducible ideal in a ring the characteristic function of an irreducible ideal and the level ideals of a fuzzy irreducible ideal are studied the algebraic nature of homomorphic images and preimages of fuzzy irreducible ideals is also examined some other fundamental results pertaining to this concept are discussed

fuzzy cosets and some fuzzy radicals abstract an attempt is made to formulate fuzzy versions of jacobson and prime radicals of a ring certain basic results pertaining to the notions of jacobson and prime radicals of a ring are extended to the fuzzy setting in particular the following is obtained the jacobson radical prime radical of the ring of fuzzy cosets of in r is zero where r is a commutative ring with identity and is the fuzzy jacobson radical fuzzy prime radical of r

perturbation theorems for the generalized eigenvalue problem abstract given a matrix pair z a b the perturbation of its eigenvalues is studied considering two pairs z w as points of the grassman manifold g n 2 n and its eigenvalues as points in g 1 2 the projective complex plane the distance of the spectra measured in the chordal metric in g 1 2 is bounded by some distance of the matrix pairs in g n 2 n analogs of the bauer fike theorem henrici s theorem and the hoffman weilandt theorem are obtained from which the classical results can be derived

fuzzy quotient groups abstract the operation of a group g induces through zadeh s extension principle a semigroup operation on ig we define a fuzzy quotient group of g to be a fuzzy partition of g that is a subsemigroup of ig having a group structure we show that fuzzy quotient groups of g are in one to one correspondence with normal fuzzy subgroups of g and that their associated fuzzy similarity relations are all two sided invariant we study relationships between the level structures of these structures we also give a necessary and sufficient condition for a group homomorphism to factor through fuzzy quotients

nonuniform image motion estimation using the maximum a posteriori principle an iterative scheme for frame to frame motion estimation from a pair of noisy images is established the algorithm is developed by assuming that the karhunen loeve coefficients of the motion vector waveform are zero mean and gaussian random variables following the derivation of the generalized maximum likelihood gml algorithm and invoking the maximum a posteriori map criterion an iterative motion estimator is developed a linear analysis of the algorithm is presented and the convergence of the algorithm is discussed simulation experiments are performed and comparisons are made with the gml algorithm the algorithm reported by a n netravali and j d robbins 1979 and the scheme developed by k p g horn and g g schunck 1981

prime fuzzy ideals over noncommutative rings in this paper we introduce prime fuzzy ideals over a noncommutative ring this notion of primeness is equivalent to level cuts being crisp prime ideals it also generalizes the one provided by kumbhojkar and bapat in 1993 which lacks this equivalence in a noncommutative setting semiprime fuzzy ideals over a noncommutative ring are also defined and characterized as intersection of primes this allows us to introduce the fuzzy prime radical and contribute to establish the basis of a fuzzy noncommutative ring theory

a perturbation bound for the eigenvalues of a singular diagonalizable matrix abstract let a be a singular diagonalizable matrix with group inverse a and let a e be a perturbation of a we show that each eigenvalue of a e is an o a e 2 relative perturbation of a nonzero eigenvalue of a unless it is small enough in magnitude to be treated as an o e 2 perturbation of the zero eigenvalue of a

ill conditioned matrices are componentwise near to singularity for a square matrix normed to 1 the normwise distance to singularity is well known to be equal to the reciprocal of the condition number in this paper we give an elementary and self contained proof for the fact that an ill conditioned matrix is also not far from a singular matrix in a componentwise sense this is shown to be true for any weighting of the componentwise distance in other words for matrix inversion ill conditioned means nearly ill posed in the normwise and also in the componentwise sense

a sharp version of bauer fike s theorem in this paper we present a sharp version of bauer fike s theorem we replace the matrix norm with its spectral radius or sign complex spectral radius for diagonalizable matrices 1 norm and norm for non diagonalizable matrices we also give the applications to the pole placement problem and the singular system

perron frobenius theory for complex matrices abstract the purpose of this paper is to present a unified perron frobenius theory for nonnegative for real not necessarily nonnegative and for general complex matrices the sign real spectral radius was introduced for general real matrices this quantity was shown to share certain properties with the perron root of nonnegative matrices in this paper we introduce the sign complex spectral radius again this quantity extends many properties of the perron root of nonnegative matrices to general complex matrices various characterizations will be given and many open problems remain

rough ideals under relations associated to fuzzy ideals in this paper we deal with the theory of rough ideals started in davvaz 2004 we show that the approximation spaces built from an equivalence relation compatible with the ring structure i e associated to a two sided ideal are too naive in order to develop practical applications we propose the use of certain crisp equivalence relations obtained from fuzzy ideals these relations make available more flexible approximation spaces since they are enriched with a wider class of rough ideals furthermore these are fully compatible with the notion of primeness semiprimeness the theory is illustrated by several examples of interest in engineering and mathematics

fuzzy linear spaces over valued fields abstract the concept of fuzzy linear spaces was introduced by nanda 3 the purpose of the present paper is to introduce some further concepts such as convex fuzzy sets etc in fuzzy linear spaces over any valued field

fast enclosure for all eigenvalues in generalized eigenvalue problems a fast method for enclosing all eigenvalues in generalized eigenvalue problems email protected is proposed firstly a theorem for enclosing all eigenvalues which is applicable even if a is not hermitian and or b is not hermitian positive definite is presented next a theorem for accelerating the enclosure is presented the proposed method is established based on these theorems numerical examples show the performance and property of the proposed method as an application of the proposed method an efficient method for enclosing all eigenvalues in polynomial eigenvalue problems is also sketched