structural complexity of disordered surfaces analyzing the porous silicon sfm patterns abstract this paper introduces a relative structural complexity measure for the characterization of disordered surfaces numerical solutions of 2d 1 kpz equation and scanning force microscopy sfm patterns of porous silicon samples are analyzed using this methodology the results and phenomenological interpretation indicate that the proposed measure is efficient for quantitatively characterize the structural complexity of disordered surfaces and interfaces observed and or simulated in nano micro and ordinary scales

pole assignment robustness in a specified disk abstract a sufficient condition is proposed to guarantee robust pole location within a specified circular region for a linear uncertain system the explicit bounds on linear time invariant perturbations with highly structured information are obtained under these allowable highly structured perturbations both stability robustness and certain performance robustness will thus be ensured the merit of the proposed new approach is demonstrated by a given example where the results achieved are much better than the ones reported recently

a representation for the drazin inverse of block matrices with a singular generalized schur complement abstract consider a 2 2 block complex square matrix m a b c d where a and d are square matrices suppose that i aa d b o and c i aa d o where a d is the drazin inverse of a the representations of the drazin inverse m d have been studied in the case where the generalized schur complement s a ca d b is either zero or nonsingular in this paper we develop a representation under certain conditions for m d when s is singular and group invertible moreover this formula includes the case where s o or nonsingular a numerical example is given to illustrate the result

a note on the representation for the drazin inverse of 2 2 block matrices abstract in this note we consider representations of the drazin inverse of 2 2 block matrices under conditions weaker than those used in recent papers on the subject in particular in d s djordjevic p s stanimirovic on the generalized drazin inverse and generalized resolvent czechoslovak math j 51 126 2001 617 634 r hartwig x li y wei representations for the drazin inverse of 2 2 block matrix siam j matrix anal appl 27 2006 757 771

block representations of the generalized drazin inverse abstract under specific conditions we develop new formulae for the generalized drazin inverse of a block matrix in banach algebras also we present necessary and sufficient conditions for the existence and the expression of the group inverse of a block matrix

a note on the representations for the drazin inverse of 2 2 block matrices abstract in 1979 campbell and meyer proposed the problem of finding a formula for the drazin inverse of a 2 2 matrix m a b c d in terms of its various blocks where the blocks a and d are required to be square matrices special cases of the problems have been studied in particular a representation of the drazin inverse of m denoted by md has recently been obtained under the assumptions that c i aad b o and a i aad b o together with the condition that the generalized schur complement d cadb be either nonsingular or zero we derive an alternative representation for md under the same assumptions but with the condition on the schur complement in the hypothesis replaced by the condition that r caa d n b n d where r and n are the range and null space of a matrix

a new conservative swift hohenberg equation and its mass conservative method abstract the swift hohenberg sh energy functional has been widely used to study pattern formation the l 2 and h 1 gradient flows for the sh energy functional are the sh and phase field crystal pfc equations respectively the sh equation is of lower order in space than the pfc equation but does not conserve the total mass furthermore when the sh energy functional does not have the cubic nonlinearity the sh equation unlike the pfc equation only shows striped patterns even for various parameter values in this study we introduce a new mass conservative sh equation by using a lagrange multiplier in order to solve the conservative sh equation that is an integro partial differential equation we propose operator splitting methods that are shown analytically to inherit the mass conservation numerical examples including standard tests in the pfc equation are presented to show the applicability of the proposed framework

singular perturbation modelling of continuous and discrete physical systems the major shortcoming of the singular perturbation theory preventing its application to practical problems is that the system described by state equations is seldom given in the singularly perturbed form this paper presents a systematic procedure which converts the state equations of a large scale time invariant system to singularly perturbed form assuming that such a classification is possible this is accomplished by appropriate scaling and grouping of the state variables into slow and fast groups while retaining as many physical state variables as possible in the new state description an improved slow fast grouping of the states can result by allowing linear combination of certain available physical variables as new state variables several examples are given to illustrate the method

some additive results on drazin inverse some additive perturbation results for drazin inverses are given in particular a formula is given for the drazin inverse of a sum of two matrices when one of the products of these matrices vanishes some special applications of this are also considered

representation for the generalized drazin inverse of block matrices in banach algebras abstract several representations of the generalized drazin inverse of a block matrix with a group invertible generalized schur complement in banach algebra are presented

characterization of the spatio temporal patterns in the osmosedimentation process abstract in the present work we investigate the problem of pattern formation by fluid flow and mass transport in a viscous binary fluid mixture under osmosedimentation we perform a numerical investigation of these patterns using spatial computational operators r2 r computed from the spatial mass distribution field over time our main goal is to determine different dynamical regimes through analysis of the complex patterns arising from the osmosedimentation process the results show that the pattern formation dynamics in the osmosedimentation process can be well characterized by means of these computational operators

on the drazin inverse of block matrices and generalized schur complement in this paper we give an additive result for the drazin inverse with its applications we obtain representations for the drazin inverse of a 2x2 complex block matrix having generalized schur complement s d ca db equal to zero or nonsingular several situations are analyzed and recent results are generalized r e hartwig x li y wei representations for the drazin inverse of a 2x2 block matrix siam j matrix anal appl 27 3 2006 757 771

characterization and computation for the bound e in linear time variantsingularly perturbed systems abstract this paper gives a complete solution to the bound problem in a linear time invariant singularly perturbed system a criterion is presented to determine the existence of the bound

robust stability of singularly perturbed discrete delay systems this paper presents new sufficient conditions for the robust stability of singularly perturbed discrete systems subjected to multiple delayed perturbations for a given spl epsi spl isin 0 spl epsi sub 0 where spl epsi sub 0

a semi analytical fourier spectral method for the swift hohenberg equation abstract the swift hohenberg sh equation has been widely used as a model for the study of pattern formation the sh equation is a fourth order nonlinear partial differential equation and cannot generally be solved analytically therefore computer simulations play an essential role in understanding of nonequilibrium processing the aim of this paper is to present first and second order semi analytical fourier spectral methods as an accurate and efficient approach for solving the sh equation the methods are based on the operator splitting method and are to split the sh equation into linear and nonlinear subequations the linear and nonlinear subequations have closed form solutions in the fourier and physical spaces respectively the methods are simple to implement and computationally cheap to achieve high order time accuracy numerical experiments are presented demonstrating the accuracy and efficiency of proposed methods

representations for the drazin inverse of 2 2 block operator matrix with singular schur complement abstract in this paper we present formulae for the drazin inverse of 2 2 block operator matrix with generalized schur complement being drazin invertible moreover necessary and sufficient conditions for the existence as well as the expressions for the group inverse are obtained

finite mode analysis of the generalized kuramoto sivashinsky equation abstract we present numerical results concerning a five mode truncation of the equation u t uu x u xxx u xx u xxxx 0 subject to periodic boundary conditions we find that for large the system evolves from most initial conditions into a final state consisting of one or two traveling pulses depending on the initial condition and horizontal periodicity this is due to a region of simultaneous stability of the first two branches that bifurcate from the trivial solution an additional two pulse traveling wave which does not bifurcate from u 0 is also present

on the analysis of spatiotemporally chaotic data abstract common problems encountered when dealing with spatially extended systems in extensive chaos regimes are discussed from the point of view of the experimentalist it is argued that both local and global probes are insufficient and potentially misleading and that the space time evolution of at least one variable even with low local resolution should be accessible in order to estimate the possibly large scale coherence in spatiotemporal chaos regimes

gradient pattern analysis of swift hohenberg dynamics phase disorder characterization abstract in this paper we analyze the onset of phase dominant dynamics in a uniformly forced system the study is based on the numerical integration of the swift hohenberg equation and adresses the characterization of phase disorder detected from gradient computational operators as complex entropic form cef the transition from amplitude to phase dynamics is well characterized by means of the variance of the cef phase component

formulas for the drazin inverse of special block matrices properties of the drazin inverse of the matrix f iie0 with e square are investigated based on this approach it is obtained an explicit formula for the drazin inverse of matrices of the form a ip tquv t where u v p and q are nxk the representation for a d is given in terms of kxk matrices involving the individual blocks under some conditions some special cases are also analyzed

representations for the drazin inverse of the sum p q r s and its applications abstract let p q r and s be complex square matrices and m p q r s a quadruple p q r s is called a pseudo block decomposition of m if pq qp 0 ps sq qr rp 0 and r d s d 0 where r d and s d are the drazin inverses of r and s respectively we investigate the problem of finding formulae for the drazin inverse of m the explicit representations for the drazin inverses of m and p q r are developed under some assumptions as its application some representations are presented for 2 2 block matrices a b 0 c and a b d c where the blocks a and c are square matrices several results of this paper extend the well known representation for the drazin inverse of a b 0 c given by hartwig and shoaf meyer and rose in 1977 an illustrative example is given to verify our new representations

a note on the drazin inverse of an anti triangular matrix abstract in this paper we give formulae for the generalized drazin inverse m d of an anti triangular matrix m under some conditions moreover some particular cases of these results are also considered