spatio temporal spectral analysis by eigenstructure methods this paper presents new algorithms for estimating the spatio temporal spectrum of the signals received by a passive array the algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals they allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems simulation results that illustrate the performance of the new algorithms are presented

positive linear maps and spreads of matrices ii abstract it is shown how positive linear maps can be used to obtain lower bounds for spreads of normal matrices some known results and some new ones are obtained in this way

some inequalities for central moments of matrices abstract in this paper we shall study non commutative central moment inequalities with a focus on whether the commutative bounds are tight in the non commutative case as well we prove that the answer is affirmative for the fourth central moment and several particular results are given in the general case as an application we shall present some lower estimates of the spread of hermitian and normal matrices as well

interactions among periodic waves and solitary waves for a higher dimensional system the general variable separated approach is successfully extended to the 2 1 dimensional physical model and we obtain a universal formula involving arbitrary number of variable separated functions because of the existence of the arbitrary functions in the universal formula many new types of structures of periodic waves for example the periodic periodic interaction waves periodic kink interaction waves periodic peakon interaction waves periodic compacton interaction waves periodic foldon interaction waves etc are investigated both analytically and graphically some novel features or interesting behaviours are revealed

singularity analysis and localized coherent structures in 2 1 dimensional generalized korteweg de vries equations in this article a singularity structure analysis of a 2 1 dimensional generalized korteweg de vries equation studied originally by boiti et al admitting a weak lax pair is carried out and it is proven that the system satisfies the painleve property its bilinear form is constructed in a natural way from the p analysis and then it is used to generate multidromion solutions exponentially decaying solutions in all directions the same analysis can be extended to construct the multidromion solutions of the generalized nizhnik novikov veselov nnv equation from which the nnv equation follows as a special case

on the number of signals resolvable by a uniform linear array an algebraic limitation on the maximum number of directions of arrival of plane waves that can be resolved by a uniform linear sensor array is studied achievable lower and upper bounds are derived on that number as a function of the number of elements in the array number of snapshots and the rank of the source sample correlation matrix the signals are assumed narrow band and of identical and known center frequency the results are also applicable in the coherent signal case and when directions of arrival are estimated from few snapshots while in the multiple snapshot case the lower bounds coincide with known asymptotic results the upper bounds indicate the potential for resolving more signals than by present methods of array processing

bounds for the spectrum of normal matrices abstract let a be a normal matrix with eigenvalues 1 2 n and let denote the smallest disc containing these eigenvalues we give some inequalities relating the center and radius of to the entries in a when applied to hermitian matrices our results give lower bounds on the spread maxij i j of a when applied to positive definite hermitian matrices they give lower bounds on the kantorovich ratio maxij i j i j

characterization of birkhoff james orthogonality the birkhoff james orthogonality is a generalization of hilbert space orthogonality to banach spaces we investigate this notion of orthogonality when the banach space has more structures we start by doing so for the banach space of square matrices moving gradually to all bounded operators on any hilbert space then to an arbitrary c algebra and finally a hilbert c module

2 1 dimensional compacton solutions with and without completely elastic interaction properties taking the 2 1 dimensional broer kaup kupershmidt system as a simple example some special types of 2 1 dimensional compacton solutions are constructed it is shown that there is quite rich interaction behaviour between two travelling compactons for some types of compactons the interactions among them may not be completely elastic for some others the interactions are completely elastic there is no phase shift for the interactions of the 2 1 dimensional compactons discussed in this paper

variance bounds with an application to norm bounds for commutators abstract murthy and sethi m n murthy v k sethi sankhya ser b 27 1965 201 210 gave a sharp upper bound on the variance of a real random variable in terms of the range of values of that variable we generalise this bound to the complex case and more importantly to the matrix case in doing so we make contact with several geometrical and matrix analytical concepts such as the numerical range and introduce the new concept of radius of a matrix we also give a new and simplified proof for a sharp upper bound on the frobenius norm of commutators recently proven by bottcher and wenzel a bottcher d wenzel the frobenius norm and the commutator linear algebra appl 429 2008 1864 1885 and point out that at the heart of this proof lies exactly the matrix version of the variance we have introduced as an immediate application of our variance bounds we obtain stronger versions of bottcher and wenzel s upper bound

localized solutions with chaotic and fractal behaviours in a 2 1 dimensional dispersive long wave system it is known that in high dimensions there exist abundant localized excitations such as dromions lumps ring soliton solutions and so on in this paper the possible chaotic and fractal localized structures are revealed for the 2 1 dimensional dispersive long wave equation the chaotic and fractal dromion and lump patterns of the model are constructed by some types of lower dimensional chaotic and fractal patterns

a new general type of solitary wave of a 2 1 dimensional system using the extended homogeneous balance method ehbm and variable separation approach vsa an exact variable separation excitation of a 2 1 dimensional system is derived based on the derived excitation a new general type of solitary wave i e semifolded solitary waves and semifoldons sfsws is defined and studied we investigate the behaviours of the interactions for the semifolded localized structures and find that the interactions possess some novel and interesting features

some inequalities for positive linear maps it has long been known that an analogue of jensen s inequality holds for positive unital linear maps on matrix algebras provided that instead of ordinary convex functions one restricts to matrix convex functions we show that this restriction is not necessary in the case of 2 2 matrices a noncommutative analogue of the variance is studied and a basic inequality with several applications is established

localized excitations of the 2 1 dimensional sine gordon system the 2 1 dimensional sine gordon system is investigated via a generalized bilinear operator representation plateau basin bowl and saddle type ring solitons are thereby constructed it is indicated how iterated moutard transformations may be employed to extend the range of the method

interactions of solitary waves under the conditions of the 3 1 dimensional kadomtsev petviashvilli equation using an extended mapping method with a linear variable separation process a new family of the exact solutions of the 3 1 dimensional kadomtsev petviashvilli kp equation was derived by applying the solitary wave solutions this paper studied some newly localized excitations and the interactions of various solitary waves under the conditions of the 3 1 dimensional kp equation

orthogonality of matrices and some distance problems abstract if a and b are matrices such that a zb a for all complex numbers z then a is said to be orthogonal to b we find necessary and sufficient conditions for this to be the case some applications and generalisations are also discussed

on the inverse scattering problem on branching graphs the inverse scattering problem on branching graphs is studied the definition of the schrodinger operator on such graphs is discussed the operator is defined with real potentials with finite first momentum and using special boundary conditions connecting values of the functions at the vertices it is shown that in general the scattering matrix does not determine the topology of the graph the potentials on the edges and the boundary conditions uniquely

lower bounds for the spread of a matrix a characterization of the spread of a normal matrix is used to derive several simple lower bounds for the spread comparisons are then made with several known bounds

wavefield modeling and array processing iii resolution capacity for pt ii see ibid vol 42 no 10 p 2560 1994 we use here the wavefield modeling formalism in order to derive some fundamental limitations on the performance of passive arrays we first derive upper bounds on both the ideal and effective resolution capacities and show that the effective resolution capacity is bounded by the effective rank of the relevant sampling matrix i e is determined by the array structure we then study how the resolution capacity is affected when the sources are constrained to lie within an angular sector we also look at the case where the source spectra are known a priori to be flat and show that contrary to the common opinion if the array satisfies the spectral sampling condition the effective wideband resolution capacity is bounded by the same bound as the narrowband one we conclude by examining the interesting phenomenon of resonance in arrays we show that these resonances far from being mathematical artifacts can manifest quite dramatically in the performance of arrays

positive linear maps and perturbation bounds of matrices abstract we show how positive unital linear maps can be used to obtain lower bounds for the maximum distance between the eigenvalues of two normal matrices some related bounds for the spread and condition number of hermitian matrices are also discussed here

localized excitations in 2 1 dimensional systems by means of a special variable separation approach a common formula with some arbitrary functions has been obtained for some suitable physical quantities of various 2 1 dimensional models such as the davey stewartson ds model the nizhnik novikov veselov nnv system asymmetric nnv equation asymmetric ds equation dispersive long wave equation broer kaup kupershmidt system long wave short wave interaction model maccari system and a general n m component ablowitz kaup newell segur akns system selecting the arbitrary functions appropriately one may obtain abundant stable localized interesting excitations such as the multidromions lumps ring soliton solutions breathers instantons etc it is shown that some types of lower dimensional chaotic patterns such as the chaotic chaotic patterns periodic chaotic patterns chaotic line soliton patterns chaotic dromion patterns fractal lump patterns and fractal dromion patterns may be found in higher dimensional soliton systems the interactions between the traveling ring type soliton solutions are completely elastic the traveling ring solitons pass through each other and preserve their shapes velocities and phases some types of localized weak solutions peakons are also discussed especially the interactions between two peakons are not completely elastic after the interactions the traveling peakons also pass through each other and preserve their velocities and phases however they completely exchange their shapes

characterizations and lower bounds for the spread of a normal matrix abstract the spread of an n n matrix a with eigenvalues 1 n is defined by spr a max j k j k we prove that if a is normal then spr a max x ax y ay x y c n x y 1 max x ay y ax x y c n x y 1 re x y 0 max x ay y ax x y c n x y 1 x y 0 max spr z a z a 2 z c z 1 2 max x a 2 x x ax 2 x a ax x ax 2 1 2 x c n x 1 we also present several lower bounds for spr a given by these characterizations

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

modal decomposition signal subspace algorithms a new method of estimating the locations of multiple wide band emitters arriving at an array of sensors is presented in this paper the wide band emitter location problem is treated as a separable multidimensional spectrum estimation problem by modal decomposition of the estimated spectral factor or spectral density matrix at the poles of the emitters this modal decomposition method extends conventional sinusoidal separation approaches to wide band emitters several methods of modal decomposition are presented and the signal subspace approach of schmidt 2 and su and morf 3 4 is extended and applied to the decomposed spectral residues for determination of emitter locations the method is asymptotically exact and provides the capability to resolve correlated or even coherent emitters

on the cramer rao bound for direction finding of correlated signals in this paper we present compact closed form formulas for the cramer rao bound corresponding to the joint estimation of the directions of arrival the signal covariance matrix and the noise variance using these formulas we investigate the effect of signal correlation on the achievable accuracy of direction finding system in a correlated signal environment as expected estimation accuracy decreases with increasing correlation magnitude we observe that under certain conditions small aperture high correlation magnitude correlation phase has a strong effect on doa estimation accuracy

wavefield modeling and array processing i spatial sampling we introduce the concept of wavefield modeling and study its relationship to array professing and direction finding we show how the output of an array can be written as the product of a wavefield independent sampling matrix and an array independent coefficient vector using this decomposition we derive the conditions under which the array output may be linearly interpolated to give the array output of a different array within a desired accuracy we proceed to show under what conditions the array output may be linearly interpolated to give the value of the wavefield over a continuous manifold as a result we also derive conditions under which the array manifold may be linearly transformed between frequencies finally we treat the case where the sources are known to be limited to specific possibly disjoint angular sectors of arbitrary shape and show how the sampling matrix can in this case be replaced by a modified sampling matrix of lower rank this result yields a straightforward extension of the formalism presented in this paper to the ease of limited angular sectors in two companion papers we use wavefield modeling to derive practical algorithms and bounds on the performance of arrays