numerical methods for the estimation of multifractal singularity spectra on sampled data physical variables in scale invariant systems often show chaotic turbulent like behavior commonly associated to the existence of an underlying fractal or multifractal structure however the assessment of multifractality over experimental discretized data requires of appropriate methods and to establish criteria to measure the confidence degree on the estimates in this paper we have evaluated the quality of different techniques used for multifractal analysis we have tested four different techniques the moment m method the wavelet transform modulus maxima wtmm method the gradient modulus wavelet projection gmwp method and the gradient histogram gh method which are used to estimate the singularity spectra of multifractal signals the test consists in analyzing synthetic multifractal 1d signals with given multifractal spectrum we have compared the results studying the sensibility of each method to the length of the series size of the ensemble and type of spectrum our results show that gmwp method is the one attaining the best performance providing reliable estimates which can be improved when the statistics is increased all the other methods are affected by problems such as the linearization of the right tail of the spectrum and some of them are very demanding in data

a note on the representation and approximation of the outer inverse at s 2 of a matrix a in this note we present a unified representation and an approximation theorem for the outer inverse a t s 2 of a matrix a which is the matrix x satisfying xax x r x t n x s based on the new approximation theorem we can develop several expressions and computational procedures for the generalized inverse a t s 2 which improve the recent work on this topic

multifractal analysis of chinese stock volatilities based on the partition function approach abstract we have performed a detailed multifractal analysis on the 1 min volatility of two indexes and 1139 stocks in the chinese stock markets based on the partition function approach the partition function q s scales as a power law with respect to the box size s the scaling exponents q form a nonlinear function of q statistical tests based on bootstrapping show that the extracted multifractal nature is significant at the 1 significance level the individual securities can be well modeled by the p model in turbulence with p 0 40 0 02 based on the idea of ensemble averaging including quenched and annealed average we treat each stock exchange as a whole and confirm the existence of multifractal nature in the chinese stock markets

splitting based on the outer inverse of matrices in this paper we introduce a conception on the splitting of a matrix a which is based on the outer inverse of the matrix a it will be evidence that splittings early are the special cases several necessary and sufficient conditions to endure the convergence of the fixed pointed system generated by the splitting are also induced

scaling in currency exchange we study the scaling behavior in currency exchange rates our results suggest that they satisfy scaling with an exponent close to 0 5 but that it differs qualitatively from that of a simple random walk indeed price variations cannot be considered as independent variables and subtle correlations are present furthermore we introduce a novel statistical analysis for economic data which makes the physical properties of a signal more evident and eliminates the systematic effects of time periodicity

index splitting for the drazin inverse and the singular linear system abstract an index splitting of a singular matrix a for the drazin inverse and its relative iterations for the minimal p norm solution of the singular linear system ax b b r a k k ind a are presented some convergence criteria are also given and a method is developed for constructing the index splitting of matrix a

multifractal behavior of the korean stock market index kospi abstract we investigate multifractality in the korean stock market index kospi the generalized qth order height height correlation function shows multiscaling properties there are two scaling regimes with a crossover time around t c 40 min we consider the original data sets and the modified data sets obtained by removing the daily jumps which occur due to the difference between the closing index and the opening index to clarify the origin of the multifractality we also smooth the data through convolution with a gaussian function after convolution we observe that the multifractality disappears in the short time scaling regime t t c but remains in the long time scaling regime t t c regardless of whether or not the daily jumps are removed we suggest that multifractality in the short time scaling regime is caused by the local fluctuations of the stock index but the multifractality in the long time scaling regime appears to be due to the intrinsic trading properties such as herding behavior information outside the market the long memory of the volatility and the nonlinear dynamics of the stock market

innovation based on gaussian elimination to compute generalized inverse at s 2 abstract in this paper we execute elementary row and column operations on the partitioned matrix g a g g g 0 into i s 0 0 0 0 0 a t s 2 to compute generalized inverse a t s 2 of a given complex matrix a where g is a matrix such that r g t and n g s the total number of multiplications and divisions operations is t m n s 2 m n 2 4 m s 1 2 n s m s n s m n s and the upper bound of t m n s is less than 6 m n 2 3 2 n 3 1 2 n 2 when n m a numerical example is shown to illustrate that this method is correct

existence of a periodic solution for some partial functional differential equations with infinite delay abstract this paper deals with the existence of periodic solutions for some partial functional differential equations with infinite delay we suppose that the linear part is nondensely defined and satisfies the hille yosida condition in the nonlinear case we give several criteria to ensure the existence of a periodic solution in the nonhomogeneous linear case we prove the existence of a periodic solution under the existence of a bounded solution

the iterative methods for computing the generalized inverse at s 2 of the bounded linear operator between banach spaces in this paper we present the iterative methods for computing the generalized inverse a t s 2 over banach spaces and also for computing the generalized drazin inverses of banach algebra elements moreover we estimate the error bounds of the iterative methods for approximating a t s 2

iterative methods for computing generalized inverses abstract in this article we extend the method of yong lin chen yong lin chen iterative methods for computing the generalized inverses a t s 2 of a matrix a appl math comput 75 2 3 1996 207 222 to infinite dimensional settings precisely we construct an iterative method for computing outer generalized inverses of operators on banach spaces and also for computing the generalized drazin inverse of banach algebra elements

a class of linear partial neutral functional differential equations with nondense domain abstract we consider a system of linear partial neutral functional differential equations with nondense domain a natural generalized notion of solutions is provided by the integral solutions we derive a variation of constants formula which allows us to transform the integral solutions of the neutral equation to solutions of an abstract volterra integral equation the basic existence and uniqueness results are given and the solutions are shown to generate an integrated semigroup

ultimate boundedness and periodicity for some partial functional differential equations with infinite delay abstract in this work we study the existence of periodic solutions for some partial functional differential equation with infinite delay we assume that the linear part is not necessarily densely defined and satisfies the known hille yosida condition firstly we give some estimates of the solutions secondly we prove that the poincare map is condensing which allows us to prove the existence of periodic solutions when the solutions are ultimately bounded

scale invariant distribution and multifractality of volatility multipliers in stock markets abstract the statistical properties of the multipliers of the absolute returns are investigated using 1 min high frequency data of financial time series the multiplier distribution is found to be independent of the box size s when s is larger than some crossover scale providing direct evidence of the existence of scale invariance in financial data the multipliers with base a 2 are well approximated by a normal distribution and the most probable multiplier scales as a power law with respect to the base a we unravel that the volatility multipliers possess multifractal nature which is independent of construction of the multipliers that is the values of s and a

scaling characteristics in the taiwan stock market some statistical tools including histogram spectral analysis and fractal theory were used on the daily taiwan stock price index tspi from 1987 to 2002 to examine the possible scale invariant behavior and the clustering characteristics in taiwan stock market it was found that the tspi data exhibited the characteristic of right skewed frequency distribution the long term memory and the possibility of scale invariance were roughly identified through the analysis of autocorrelation and power spectrum respectively the monofractal analysis was then performed by the box counting method scale invariance was clearly found in the time series and the box dimension was shown to be a decreasing function of the threshold index level implying multifractal characteristics i e the low and high regions scale differently to test this hypothesis the time series were transferred into a useful compact form through the multifractal formalism namely the q q and f plots the analysis confirmed the existence of multifractal characteristics in the investigated time series the origin of multifractal phenomena in taiwan stock market might be interpreted in terms of the multiplicative cascade process of stock market information

free electron gas in the apollonian network multifractal energy spectrum and its thermodynamic fingerprints we study the free electron gas in an apollonian network within the tight binding framework the scale free and small world character of the underlying lattice is known to result in a quite structured energy spectrum with deltalike singularities gaps and minibands after an exact numerical diagonalization of the corresponding adjacency matrix of the network with a finite number of generations we employ a scaling analysis of the moments of the density of states to characterize its multifractality and report the associated singularity spectrum the fractal nature of the energy spectrum is also shown to be reflected in the thermodynamic behavior by logarithmic modulations on the temperature dependence of the specific heat the absence of chiral symmetry of the apollonian network leads to distinct thermodynamic behaviors due to electrons and holes thermal excitations

iterative methods for computing generalized inverses and splittings of operators abstract in this paper we consider an iterative method for computing generalized inverses of linear operators based on splittings of operators thus the result from yong lin chen xue yuan tan computing generalized inverses of matrices by iterative methods based on splitting of matrices appl math comp 163 2005 309 325 is extended to infinite dimensional settings

representation and approximation of the outer inverse at s 2 of a matrix a abstract in this paper we establish a basic representation and a representation theorem for the outer inverse a t s 2 of a matrix a which is the matrix x satisfying xax x r x t and n x s we develop several specific representations and iterative methods for a t s 2 we show that this representation includes many of the traditional generalized inverses and outer inverses and the relation of our results to these outer inverses will be explored

computing generalized inverses of matrices by iterative methods based on splittings of matrices in this paper we study the iterative methods for computing the generalized inverses of the form a 2 t s we prove the result that if a has the splitting a m n and if the generalized inverses a 2 t s and m 2 t s exist then the iterationx j 1 m 2 t snx j m 2 t sconverges to a 2 t s for any x 0 if and only ift t s s email protected 2 t sn 1 or equivalently m 2 t email protected 2 t sn 1 the splitting a m n is called t s splitting of a if m satisfies email protected s c m where t and s are subspaces of c n and c m respectively with dimt dims we also present a specific method to construct convergent t s splitting of a apply these two results to the most of commonly used generalized inverses such as a a d a d w a h k we can get criteria of convergence for the corresponding iterations many old and new splittings and specific choice of the related convergent splittings

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

computing the outer and group inverses through elementary row operations abstract a new method based on elementary row operations for computing the outer inverse of a given constant matrix is presented when this method is applied to matrices of index one a new expression for the group inverse is derived through this expression a more efficient method for computing the group inverse of the square matrix a of order n with rank r 0 725 n is developed

periodic solutions for a class of neutral functional differential equations with infinite delay abstract in this paper we study the existence and uniqueness of periodic solutions of the nonlinear neutral functional differential equation with infinite delay of the form d d t x t 0 g s x t s d s a t x t x t f t x t in the process we use the fundamental matrix solution of x t a t u t x t and construct appropriate mappings where u c r r n is an periodic function then we employ matrix measure and the leray schauder fixed point theorem to show the existence of periodic solutions of this neutral differential equation in the special case where g s u 0 and a t x a t some sufficient conditions which ensure the uniform stability and global attractivity of a unique periodic solution are derived

coarse graining and self similarity of price fluctuations abstract we propose a new approach for analyzing price fluctuations in their strongly correlated regime ranging from minutes to months this is done by employing a self similarity assumption for the magnitude of coarse grained price fluctuation or volatility the existence of a cramer function the characteristic function for self similarity is confirmed by analyzing real price data from a stock market we also discuss the close interrelation among our approach the scaling of moments method and the multifractal approach for price fluctuations

iterative methods for the drazin inverse of a matrix with a complex spectrum iterative methods for the drazin inverse of a square matrix with a real spectrum have been developed recently these methods are generalized in the case of matrices with complex spectra semiiterative method for the drazin inverse is also discussed numerical examples are given to illustrate the theoretic results

a characterization and representation of the generalized inverse a 2 t s and its applications abstract this paper presents an explicit expression for the generalized inverse a 2 t s based on this we established the characterization the representation theorem and the limiting process for a 2 t s as an application we estimate the error bound of the iterative method for approximating a 2 t s

the hyperpower iteration revisited the hyperpower method is generalized by inseting an idempotent matrix p it is shown that most of the iterations that can be used for computing generalized inverses can be recast in this form by suitable choice of the idempotent the limit or the initial values the convergence behavior of bqk is analyzed and the results are applied to give a detailed investigation of this iteration

power law of quiet time distribution in the korean stock market abstract we report the quiet time probability distribution of the absolute return in the korean stock market index we define the quiet time as a time interval during the absolute return of the stock index that are above a threshold r c through an exponential bin plot we observe that the quiet time distribution qtd shows power law behavior p f t t for a range of threshold values the quiet time distribution has two scaling regimes separated by the crossover time t c 200 min the power law exponents of the quiet time distribution decrease when the return time t increases in the late time regime t t c the power law exponents are independent of the threshold within the error bars for the fixed return time the scaled qtd is characterized by a scaling function such as p f t 1 t f t t where the scaling function f x x 2 and t is the average quiet time the scaling exponents 2 depend on the return time t and are independent of the threshold r c the average quiet time follows the power law such as t r c where the exponents depend on the return time t

the representation and approximation for the generalized inverse at s 2 we present a unified representation theorem for the generalized inverses a t s 2 which are 2 or outer inverses having the prescribed range t and null space s specific expressions and computational procedures for the generalized inverses a t s 2 can be uniformly derived

existence and continuous dependence results for nonlinear differential inclusions with infinite delay this paper is concerned with nonlinear functional differential inclusions with infinite delay in banach spaces using tools involving the measure of noncompactness and multi valued fixed point theory existence and continuous dependence results are obtained for integral solutions without the assumption of compactness on the associated nonlinear semigroup

scaling and correlation in financial time series we discuss the results of three recent phenomenological studies focussed on understanding the distinctive statistical properties of nancial time series i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to very drastic events such as the crash of 19 october 1987 sometimes referred to as black monday the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier by as much as 8 orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by 3 orders of magnitude from 1 min up to approximately 10 days ii correlations in nancial time series while price uctuations themselves have rapidly decaying correlations the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power law persisting for several months iii volatility and trading activity we quantify the relation between trading activity measured by the number of transactions nt and the price change gt for a given stock over a time interval t t t we nd that nt displays long range power law correlations in time which leads to the interpretation that the long range correlations previously found for jgtj are connected to those of nt c 2000 elsevier science b v all rights reserved

an algorithm for the characterization of time series based on local regularity abstract the pointwise holder exponent describes the local regularity of a function this description is particularly applicable to complex time series representing natural phenomena that exhibit statistical self similarity where the scaling exponent fluctuates from point to point in this work an algorithm is proposed for the estimation of both global and local scaling exponents of time series the technique is based on scaled window variance method and its practical implementation relies on the convolution operation the proposed algorithm is an attractive alternative to existing techniques because of its simplicity and computational efficiency the accuracy of the algorithm is verified by application on synthetic signals with a prescribed time evolution of holder exponents case studies are presented in the fields of fluid dynamics room acoustics and machinery diagnostics

probability distribution function and multiscaling properties in the korean stock market abstract we consider the probability distribution function pdf and the multiscaling properties of the index and the traded volume in the korean stock market we observed the power law of the pdf at the fat tail region for the return volatility the traded volume and changes of the traded volume we also investigate the multifractality in the korean stock market we consider the multifractality by the detrended fluctuation analysis mfdfa we observed the multiscaling behaviors for index return traded volume and the changes of the traded volume we apply mfdfa method for the randomly shuffled time series to observe the effects of the autocorrelations the multifractality is strongly originated from the long time correlations of the time series

an iterative method for solving general restricted linear equations the newton iterative method for computing outer inverses with prescribed range and null space is used in the non stationary richardson iterative method to develop an iterative method for solving general restricted linear equations starting with any suitably chosen initial iterate our method generates a sequence of iterates converging to the solution the necessary and sufficient conditions for the convergence along with the error bounds are established the applications of the iterative method for solving some special linear equations are also discussed a number of numerical examples are worked out they include singular square rectangular randomly generated rank deficient matrices full rank matrices and a set of singular matrices given in matrix computation toolbox mctoolbox with the condition numbers ranging from order 1016 to 1050 the mean cpu time mct and the error bounds are the performance measures used our results when compared with the results obtained by chen 1997 leads to substantial improvement in terms of both computational speed and accuracy

an efficient computation of generalized inverse of a matrix abstract we propose a hyperpower iteration for numerical computation of the outer generalized inverse of a matrix which achieves 18th order of convergence by using only seven matrix multiplications per iteration loop this yields a high efficiency index for that computational task the algorithm has a relatively mild numerical instability and we stabilize it at the price of adding two extra matrix multiplications per iteration loop this implies an efficiency index that exceeds the known record for numerically stable iterations for this task which means substantial acceleration of the long standing algorithms for an important problem of numerical linear algebra our numerical tests cover a variety of examples in the category of generalized inverses such as drazin case rectangular case and preconditioning of linear systems the test results are in good accordance with our formal study

multifractality in stock indexes fact or fiction abstract multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes including hsi szsc s p 500 and nasdaq to check whether the indexes instead of the returns possess multifractality we find that the mass exponent q is linear and the singularity q is close to 1 for all trading days and all indexes furthermore we find strong evidence showing that the scaling behaviors of the original data sets cannot be distinguished from those of shuffled time series hence the so called multifractality in the intraday stock market indexes is merely an illusion

boundedness and stability for cohen grossberg neural network with time varying delays abstract in this paper a model is considered to describe the dynamics of cohen grossberg neural network with variable coefficients and time varying delays uniformly ultimate boundedness and uniform boundedness are studied for the model by utilizing the hardy inequality combining with the halanay inequality and the lyapunov functional method some new sufficient conditions are derived for the model to be globally exponentially stable the activation functions are not assumed to be differentiable or strictly increasing moreover no assumption on the symmetry of the connection matrices is necessary these criteria are important in signal processing and the design of networks

full rank representation of generalized inverse at s 2 and its application in this paper we introduce a full rank representation of the generalized inverse a t s 2 of a given complex matrix a which is based on an arbitrary full rank decomposition of g where g is a matrix such that r g t and n g s using this representation we introduce the minor of the generalized inverse a t s 2 as a special case of the minor a determinantal representation of the generalized inverse a t s 2 is obtained as an application we use an example to demonstrate that this representation is correct

microcanonical multifractal formalism a geometrical approach to multifractal systems part i singularity analysis multifractal formalism in the microcanonical framework has proved to be a valuable approach to understand and analyze complex signals typically associated with natural phenomena in scale invariant systems in this paper we discuss the multifractal microcanonical formalism in a comprehensive unified way including new theoretical proofs and validation tests on real signals so completing some known gaps in the foundations of this theory we also review the latest advances and describe the present perspectives in this field some technical details on the implementation of involved algorithms and relevant open issues are also discussed

periodic solutions of infinite delay evolution equations abstract for a t and f t x y t periodic in t we consider the differential equation with infinite delay in a general banach space x u t a t u t f t u t u t t 0 u s s s 0 0 1 where the resolvent of the unbounded operator a t is compact and f is continuous in its variables and ut s u t s s 0 we first show that the poincare operator given by p ut i e t units along the unique solution u determined by the initial function is a condensing operator with respect to kuratowski s measure of non compactness in a phase space cg and then derive periodic solutions from bounded solutions by using sadovskii s fixed point theorem this extends the study of deriving periodic solutions from bounded solutions to infinite delay differential equations in general banach spaces

application of the microcanonical multifractal formalism to monofractal systems the design of appropriate multifractal analysis algorithms able to correctly characterize the scaling properties of multifractal systems from experimental discretized data is a major challenge in the study of such scale invariant systems in the recent years a growing interest for the application of the microcanonical formalism has taken place as it allows a precise localization of the fractal components as well as a statistical characterization of the system in this paper we deal with the specific problems arising when systems that are strictly monofractal are analyzed using some standard microcanonical multifractal methods we discuss the adaptations of these methods needed to give an appropriate treatment of monofractal systems

bounded and periodic solutions of infinite delay evolution equations abstract for a t and f t x y t periodic in t we consider the following evolution equation with infinite delay in a general banach space x 0 1 u t a t u t f t u t u t t 0 u s s s 0 where the resolvent of the unbounded operator a t is compact and ut s u t s s 0 by utilizing a recent asymptotic fixed point theorem of hale and lunel 1993 for condensing operators to a phase space cg we prove that if solutions of eq 0 1 are ultimate bounded then eq 0 1 has a t periodic solution this extends and improves the study of deriving periodic solutions from boundedness and ultimate boundedness of solutions to infinite delay evolution equations in general banach spaces it also improves a corresponding result in j math anal appl 247 2000 627 644 where the local strict boundedness is used

the multifractal structure of contrast changes in natural images from sharp edges to textures we present a formalism that leads naturally to a hierarchical description of the different contrast structures in images providing precise definitions of sharp edges and other texture components within this formalism we achieve a decomposition of pixels of the image in sets the fractal components of the image such that each set contains only points characterized by a fixed strength of the singularity of the contrast gradient in its neighborhood a crucial role in this description of images is played by the behavior of contrast differences under changes in scale contrary to naive scaling ideas where the image is thought to have uniform transformation properties field 1987 each of these fractal components has its own transformation law and scaling exponents a conjecture on their biological relevance is also given

projected iterative algorithms with application to multicomponent transport abstract we investigate projected iterative algorithms for solving constrained symmetric singular linear systems we discuss the symmetry of generalized inverses and investigate projected standard iterative methods as well as projected conjugate gradient algorithms using a generalization of stein s theorem for singular matrices we obtain a new proof of keller s theorem we also strengthen a result from neumann and plemmons about the spectrum of iteration matrices as an application we consider the linear systems arising from the kinetic theory of gases and providing transport coefficients in multicomponent gas mixtures we obtain low cost accurate approximate expressions for the transport coefficients that can be used in multicomponent flow models typical examples for the species diffusion coefficients and the volume viscosity are presented

reconstructing images from their most singular fractal manifold real world images are complex objects difficult to describe but at the same time possessing a high degree of redundancy a previous on the statistical properties of natural images reveals that natural images can be viewed through different partitions which are essentially fractal in nature one particular fractal component related to the most singular sharpest transitions in the image seems to be highly informative about the whole scene we show how to decompose the image into their fractal components we see that the most singular component is related to but not coincident with the edges of the objects present in the scenes we propose a new simple method to reconstruct the image with information contained in that most informative component we see that the quality of the reconstruction is strongly dependent on the capability to extract the relevant edges in the determination of the most singular set we discuss the results from the perspective of coding proposing this method as a starting point for future developments

method of elementary transformation to compute moore penrose inverse method of elementary transformation to compute moore penrose inverse is given by applying the rank equalities of matrix the inheritable properties of moore penrose inverse on rank are also discussed

on the perturbation and subproper splittings for the generalized inverse at s 2 of rectangular matrix a abstract in this paper the perturbation and subproper splittings for the generalized inverse at s 2 the unique matrix x such that xax x r x t and n x s are considered we present lower and upper bounds for the perturbation of at s 2 convergence of subproper splittings for computing the special solution at s 2 b of restricted rectangular linear system ax b x t are studied for the solution at s 2 b we develop a characterization therefore we give a unified treatment of the related problems considered in literature by ben israel berman hanke neumann plemmons etc

a random process for the construction of multiaffine fields abstract we define a random process for the construction of multiaffine fields given the scaling exponents for the structure functions the difference with analogous processes for positive defined multifractal measures is stressed in particular our methods can be used for the study of the scaling laws exhibited by the velocity field in three dimensional fully developed turbulence we also discuss the probability distribution functions for the increments of the signal in the scaling range

iterative methods for computing the generalized inverses a 2 t s of a matrix a abstract in this paper the iterative methods for computing the generalized inverse a t s 2 the unique matrix x such that xax x r x t and n x s are established and the iterative methods for computing many important generalized inverses of matrices such as a a mn a d a a d w a l 1 a l and ap l are constructed

perturbation bounds for the generalized inverse at s 2 with respect to the frobenius norm abstract in this paper we present the perturbation bounds and the relative error bound of the generalized inverse a t s 2 with respect to the frobenius norm and apply the results to the relative errors of the solution of the general restricted linear equation

long term correlations and multifractal nature in the intertrade durations of a liquid chinese stock and its warrant abstract the intertrade duration of equities is an important financial measure characterizing trading activities it is defined as the waiting time between successive trades of an equity using the ultrahigh frequency data of a liquid chinese stock and its associated warrant we perform a comparative investigation of the statistical properties of their intertrade duration time series the distributions of the two equities can be better described by the shifted power law form than the weibull form and their scaled distributions do not collapse onto a single curve although the intertrade durations of the two equities have very different magnitude their intraday patterns exhibit very similar shapes both detrended fluctuation analysis dfa and detrending moving average analysis dma show that the 1 min intertrade duration time series of the two equities are strongly correlated in addition both multifractal detrended fluctuation analysis mfdfa and multifractal detrending moving average analysis mfdma unveil that the 1 min intertrade durations possess multifractal nature however the difference between the two singularity spectra of the two equities obtained from the mfdma is much smaller than that from the mfdfa

further results on iterative methods for computing generalized inverses in this paper we reconsider the iterative method x k x k email protected i ax k 1 k 1 2 email protected email protected 0 for computing the generalized inverse a t s 2 over banach spaces or the generalized drazin inverse a d of a banach algebra element a reveal the intrinsic relationship between the convergence of such iterations and the existence of a t s 2 or a d and present the error bounds of the iterative methods for approximating a t s 2 or a d moreover we deduce some necessary and sufficient conditions for iterative convergence to a t s 2 or a d

local existence and stability for some partial functional differential equations with infinite delay we study the existence regularity and stability of solutions for some partial functional dierential equations with infinite delay we assume that the linear part is not necessarily densely defined and satisfies the hille yosida condition on a banach space x the nonlinear term takes its values in space larger than x namely the extrapolated favard class of the extrapolated semigroup corresponding to the linear part our approach is based on the theory of the extrapolation spaces

empirical evidences of a common multifractal signature in economic biological and physical systems abstract recent developments in microcanonical multifractal formalism have lead to a sensible improvement in the numerical techniques for the determination of the multifractal characteristics of real signals with the aid of these techniques we have found empirical evidence of a common multifractal signature in six very different systems ranging from stock market time series to sea surface temperature records these systems are not only found to be multifractal but their singularity spectra are coincident we propose an explanation of this striking coincidence in terms of a cascade process and analyze its consequences

preconditionings and splittings for rectangular systems recently eiermann marek and niethammer have shown how to applysemiiterative methods to a fixed point systemx tx c which isinconsistent or in whichthe powers of the fixed point operator t have no limit to obtain iterative methods which converge to some approximate solution to the fixed point system in view of their results we consider here stipulations on apreconditioning qax qb of the systemax b and separately on asplitting a m n which lead to fixed point systems such that with the aid of a semiiterative method the iterative scheme converges to a weighted moore penrose solution to the systemax b we show in several ways that to obtain a meaningful limit point from a semiiterative method requires less restrictions on the splittings or the reconditionings than those which have been required in the classical picard iterative method see e g the works of berman and plemmons berman and neumann and tanabe we pay special attention to the case when the weighted moore penrose solution which is sought is the minimal norm least squares solution toax b

multifractal detrended cross correlation analysis of foreign exchange and sensex fluctuation in indian perspective abstract the manuscript studies autocorrelation and cross correlation of sensex fluctuations and forex exchange rate in respect to indian scenario multifractal detrended fluctuation analysis mfdfa and multifractal detrended cross correlation analysis mfdxa were employed to study the correlation between the two series it was observed that the two series are strongly cross correlated the change of degree of cross correlation with time was studied and the results are interpreted qualitatively

new proofs of two representations and minor of generalized inverse a 2 t s abstract in this paper we prove the limit representation for the generalized inverse a t s 2 of a given complex matrix a in a simpler way then using this representation two known results the generalized inverse a t s 2 as an analogs of convex combination with the minor of adja and the representation of the minor of the generalized inverse a t s 2 were derived anew as a special case of the minor a determinantal representation of the generalized inverse a t s 2 is obtained

generalized hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series a nonlinear dynamics approach can be used in order to quantify complexity in written texts as a first step a one dimensional system is examined two written texts by one author lewis carroll are considered together with one translation into an artificial language i e esperanto are mapped into time series their corresponding shuffled versions are used for obtaining a baseline two different one dimensional time series are used here one based on word lengths lts the other on word frequencies fts it is shown that the generalized hurst exponent h q and the derived f curves of the original and translated texts show marked differences the original texts are far from giving a parabolic f function in contrast to the shuffled texts moreover the esperanto text has more extreme values this suggests cascade model like with multiscale time asymmetric features as finally written texts a discussion of the difference and complementarity of mapping into a lts or fts is presented the fts f curves are more opened than the lts ones

multifractal geometry in stock market time series it has been recently noticed that time series of returns in stock markets are of multifractal multiscaling character in that context multifractality has been always evidenced by its statistical signature i e the scaling exponents associated to a related variable however a direct geometrical framework much more revealing about the underlying dynamics is possible in this paper we present the techniques allowing the multifractal decomposition we will show that there exists a particular fractal component the most singular manifold msm which contains the relevant information about the dynamics of the series it is possible to reconstruct the series at a given precision from the msm we analyze the dynamics of the msm which shows revealing features about the evolution of this type of series