a progressive simultaneous iteration solution for dynamic element vibration analysis development and employment of dynamic elements can result in substantial gain in solution convergence for vibration analysis when compared with the usual finite element discretization efficient solution of the associated quadratic matrix eigenproblem is crucial in achieving a superior and relatively economical solution this paper first describes a novel eigensolution of the quadratic matrix equation by a progressive simultaneous iteration method free vibration analysis results of a rectangular prestressed membrane are next presented in detail that provides an assessment of relative solution convergence and computing expenses of the two idealization procedures

emd based refined composite multiscale entropy analysis of complex signals abstract multiscale entropy mse is an effective method to measure the complexity of signals from complex systems which has been applied to various fields successfully however mse may yield an inaccurate estimate of entropy and induce undefined entropy as the coarse graining procedure reduces the length of data considerably at large scales refined composite multiscale entropy rcmse is then developed to solve this problem however trends superimposed in signals may significantly affect the complexity measurement thus we introduce an empirical mode decomposition based rcmse called emd rcmse to first eliminate such effects of trends and then measure the complexity of signals it is validated from simulated signals and has good estimation in addition this method is also applied to study the complexity of traffic signals and we obtain some interesting results 1 traffic signals are more complex than the results showing from rcmse mse 2 weekday and weekend patterns different combination of trends greatly affect the results 3 complexity indices change with time at each day due to the degree of human activities

refined generalized multiscale entropy analysis for physiological signals abstract multiscale entropy analysis has become a prevalent complexity measurement and been successfully applied in various fields however it only takes into account the information of mean values first moment in coarse graining procedure then generalized multiscale entropy mse n considering higher moments to coarse grain a time series was proposed and mse 2 has been implemented however the mse 2 sometimes may yield an imprecise estimation of entropy or undefined entropy and reduce statistical reliability of sample entropy estimation as scale factor increases for this purpose we developed the refined model rmse 2 to improve mse 2 simulations on both white noise and 1 f noise show that rmse 2 provides higher entropy reliability and reduces the occurrence of undefined entropy especially suitable for short time series besides we discuss the effect on rmse 2 analysis from outliers data loss and other concepts in signal processing we apply the proposed model to evaluate the complexity of heartbeat interval time series derived from healthy young and elderly subjects patients with congestive heart failure and patients with atrial fibrillation respectively compared to several popular complexity metrics the results demonstrate that rmse 2 measured complexity a decreases with aging and diseases and b gives significant discrimination between different physiological pathological states which may facilitate clinical application

on the phase space approach to complexity we elaborate in some detail on a new phase space approach to complexity due to y c zhang we show in particular that the connection between maximal complexity and power law noise or correlations can be derived from a simple variational principle for a 1d signal we find 1 f noise in accordance with zhang

operator monotone functions jacobi operators and orthogonal polynomials abstract we reveal a connection between operator monotone functions and orthogonal polynomials especially we express an operator monotone function with a jacobi operator and show that it is a limit of rational operator monotone functions further we prove that the principal inverse of an orthogonal polynomial is operator monotone and hence it has a holomorphic extension to the open upper half plane namely a pick function or nevanlinna function

a method based on the tsallis entropy for characterizing threshold channel bank profiles abstract as a stable channel forms a point is reached when particles shift to motion threshold threshold channel as such the most common challenges related to alluvial channels include the variation in the transverse bank slope s t and channel geometric profile formation the present study introduces a novel reliable method of estimating the transverse slope distribution of stable channel bank profiles in different hydraulic conditions by using the tsallis entropy concept accordingly an equation for calculating s t and subsequently the vertical boundary level of bank profiles is presented based on the principle of maximum entropy the threshold channel bank profile features are defined according to the probability density function and cumulative density function to adjust the general form of the tsallis entropy for this specific engineering problem an extensive detailed study of lagrange multipliers is carried out and a wide range of observational data are used to determine the tsallis entropy model accuracy in measuring the s t of stable channel banks the results indicate that the tsallis entropy model is capable of detecting the ascending trend governing the profiles of stable channel banks in different hydraulic conditions this model exhibits excellent predictive performance with a mean absolute relative error mare of 0 265 and a coefficient of determination r 2 of 0 975 the proposed tsallis entropy based equation can be used to predict river morphology changes for river management plans

least squares element method for boundary eigenvalue problems linear and non linear boundary eigenvalue problems are discretized by a new finite element like method the reason for the new construction principle is the non linear dependence of the dynamic stiffness element matrix on an eigenparameter the dynamic stiffness element matrix is evaluated for a fixed number of parameters and is then elementwise replaced by a polynomial in the eigenparameter by solving least squares problems a fast solver is introduced for the resulting non linear matrix eigenvalue problem it consists of a combination of bisection method and inverse iteration the superiority of the newconstructionprinciple in comparison with the finite or dynamic element method is demonstrated finally for some numerical examples

inverse functions of polynomials and orthogonal polynomials as operator monotone functions we study the operator monotonicity of the inverse of every polynomial with a positive leading coefficient let p n n o be a sequence of orthonormal polynomials and p n the restriction of p n to a n where a n is the maximum zero of p n then p 1 n and the composite p n 1 o p 1 n are operator monotone on 0 furthermore for every polynomial p with a positive leading coefficient there is a real number a so that the inverse function of p t a p a defined on 0 oo is semi operator monotone that is for matrices a b 0 p a a p a 2 p b a p a 2 implies a 2 b 2

a subspace forward iteration method for solving the quadratic eigenproblem associated with the fde formulation this paper presents the development of an efficient and numerically stable algorithm for accurately computing the eigensolutions of the quadratic real symmetric eigenproblem arising in the finite dynamic element fde formulation closely related to the subspace forward iteration method the proposed scheme is well suited to extracting the lowest natural frequencies and associated mode shapes of large practical eigenproblems takes full advantage of the banded configuration of the stiffness inertia and dynamic correction matrices involved in the eigenproblem and ensures a monotonic convergence from above to the required eigenpairs a shifting technique for convergence acceleration and an eigenpair verification scheme are also presented numerical examples are shown demonstrating the excellent performance of the solution procedure

modified multiscale entropy for short term time series analysis abstract multiscale entropy mse is a prevalent algorithm used to measure the complexity of a time series because the coarse graining procedure reduces the length of a time series the conventional mse algorithm applied to a short term time series may yield an imprecise estimation of entropy or induce undefined entropy to overcome this obstacle the modified multiscale entropy mmse was developed the coarse graining procedure was replaced with a moving average procedure and a time delay was incorporated for constructing template vectors in calculating sample entropy for conducting short term time series analysis this study shows that the mmse algorithm is more reliable than the conventional mse

operator inequalities from a general theorem to concrete inequalities abstract the aim of this paper is to give a method to extract concrete inequalities from a general theorem which is established by making use of majorization relation between functions by this method we can get a lot of inequalities among others we extend furuta inequality as follows let f i g j be positive operator monotone functions on 0 and put k t t r 0 f 1 t r 1 f m t r m h t t p 0 g 1 t p 1 g n t p n where p 0 1 and r i 0 p j 0 then 0 a c b implies for 0 1 r 0 p r 0 with p p 0 p n k c 1 2 h a k c 1 2 k c 1 2 h c k c 1 2 k c 1 2 h b k c 1 2 moreover we show log c 1 2 e a c 1 2 log c 1 2 e c c 1 2 log c 1 2 e b c 1 2 provided c is invertible we also refer to operator geometric mean

numerical formulation for a higher order plane finite dynamic element the paper describes the development of an eight node plane rectangular finite dynamic element and presents detailed descriptions of the associated numerical formulation involving the higher order dynamic correction terms pertaining to the related stiffness and inertia matrices numerical test results of free vibration analyses are presented in detail for the newly developed eight node element and also the corresponding four node element in order to make a clear comparison of the relative efficiencies of the corresponding finite element and dynamic element procedures such results indicate a superior pattern of solution convergence of the presently developed dynamic element

effect of extreme data loss on long range correlated and anticorrelated signals quantified by detrended fluctuation analysis detrended fluctuation analysis dfa is an improved method of classical fluctuation analysis for nonstationary signals where embedded polynomial trends mask the intrinsic correlation properties of the fluctuations to better identify the intrinsic correlation properties of real world signals where a large amount of data is missing or removed due to artifacts we investigate how extreme data loss affects the scaling behavior of long range power law correlated and anticorrelated signals we introduce a segmentation approach to generate surrogate signals by randomly removing data segments from stationary signals with different types of long range correlations the surrogate signals we generate are characterized by four parameters i the dfa scaling exponent alpha of the original correlated signal u i ii the percentage p of the data removed from u i iii the average length mu of the removed or remaining data segments and iv the functional form p l of the distribution of the length l of the removed or remaining data segments we find that the global scaling exponent of positively correlated signals remains practically unchanged even for extreme data loss of up to 90 in contrast the global scaling of anticorrelated signals changes to uncorrelated behavior even when a very small fraction of the data is lost these observations are confirmed on two examples of real world signals human gait and commodity price fluctuations we further systematically study the local scaling behavior of surrogate signals with missing data to reveal subtle deviations across scales we find that for anticorrelated signals even 10 of data loss leads to significant monotonic deviations in the local scaling at large scales from the original anticorrelated to uncorrelated behavior in contrast positively correlated signals show no observable changes in the local scaling for up to 65 of data loss while for larger percentage of data loss the local scaling shows overestimated regions with higher local exponent at small scales followed by underestimated regions with lower local exponent at large scales finally we investigate how the scaling is affected by the average length probability distribution and percentage of the remaining data segments in comparison to the removed segments we find that the average length mu r of the remaining segments is the key parameter which determines the scales at which the local scaling exponent has a maximum deviation from its original value interestingly the scales where the maximum deviation occurs follow a power law relationship with mu r whereas the percentage of data loss determines the extent of the deviation the results presented in this paper are useful to correctly interpret the scaling properties obtained from signals with extreme data loss

chebyshev filtering lanczos process in the subspace iteration method bathe s basic algorithm of subspace iteration for the solution of the symmetric eigenvalue problem is improved by including a chebyshev filtering mechanism to obtain satisfactory convergence for the largest eigenvalues a shifting strategy is adopted the shift factor is approximately computed by the lanczos process

development of a solid hexahedron finite dynamic element this paper presents the pertinent details of a newly developed solid rectangular hexahedron finite dynamic element involving the derivation of the higher order stiffness and inertia dynamic correction matrices numerical results of a test case are also presented which indicate that adoption of the dynamic elements significantly improves the solution convergence when compared with the related performance of the corresponding finite elements

on some operator inequalities a real valued continuous function f 2 defined on a finite or infinite interval of the real line is said to be operator monotone if for any pair of bounded selfadjoint operators a b on an infinite dimensional hilbert space a b implies f a f b here f a and f b are defined according to the usual functional calculus and refers to the order relation induced by the cone of positive semi definite operators operator monotony is quite a restrictive condition in fact for p 0 the function f 2 2 p is operator monotone on the half line 0 c if and only if 0 1 the function f 2 2 p possesses some property akin to operator monotony in this direction furuta i 3 recently observed that if r 0 p 0 q 1 satisfies 1 2r q p 2r then a b 0 implies a tp 2 q arbpa r l if p 2r and q 2 the requirement is automatically satisfied hence a p ap 2bpap 2 i 2 whenever a b 0 when a is invertible this means that

a method for solving high order real symmetric eigenvalue problems a new method for solving structural dynamics problems has been proposed by the author in a separate paper 1 this method of solution produces a high order real symmetric eigenvalue problem of the form a b 2c 3d u 0 an algorithm for solving such an eigenvalue problem using simultaneous iteration is presented in this paper methods of accelerating the convergence and reducing the amount of computation are also described a numerical example is given in which the algorithm is used to calculate the eigenvalues and eigenvectors of a framed structure

operator monotone functions which are defined implicitly and operator inequalities the function t 0 1 is operator monotone on 0 t this is known as the lowner heinz inequality however not too many examples of concrete operator monotone functions are known so far we will systematically seek operator monotone functions which are defined implicitly this investigation is new and our method seems to be powerful we will actually find a family of operator monotone functions which includes t 0 1 moreover by constructing one parameter families of operator monotone functions we will get many operator inequalities especially we will extend the furuta inequality and the exponential inequality of ando

multiscale entropy analysis of complex physiologic time series there has been considerable interest in quantifying the complexity of physiologic time series such as heart rate however traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long range correlations this paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics we introduce a method to calculate multiscale entropy mse for complex time series we find that mse robustly separates healthy and pathologic groups and consistently yields higher values for simulated long range correlated noise compared to uncorrelated noise

majorization and some operator monotone functions abstract let h t be a non decreasing function on i and k t an increasing function on j then h is said to be majorized by k if k a k b implies h a h b f t is operator monotone by definition if f t is majorized by t by making use of this majorization we will show that t a t b t r a r t 1 r b 1 r is operator monotone on 0 for 0 a b and for 0 r 1 the special case of a b 1 is the theorem due to petz hasegawa

a new majorization between functions polynomials and operator inequalities let p be the set of all non negative operator monotone functions defined on 0 and put p 1 h h 1 p then p p 1 p 1 and p 1 p 1 p 1 for a function h t and a strictly increasing function h we write

some results on strongly operator convex functions and operator monotone functions abstract this paper concerns three classes of real valued functions on intervals operator monotone functions operator convex functions and strongly operator convex functions strongly operator convex functions were previously treated in 3 and 4 where operator algebraic semicontinuity theory or operator theory were substantially used in this paper we provide an alternate treatment that uses only operator inequalities or even just matrix inequalities we show also that if t 0 is a point in the domain of a continuous function f then f is operator monotone if and only if f t f t 0 t t 0 is strongly operator convex using this and previously known results we provide some methods for constructing new functions in one of the three classes from old ones we also include some discussion of completely monotone functions in this context and some results on the operator convexity or strong operator convexity of f when f is operator convex or strongly operator convex

acceleration of subspace iteration an algorithm is presented and discussed which gives 40 per cent reduction in the cost of the basic subspace iteration for eigenvalues

mixed matrix operator inequalities we will show that if 0 a b c and s s t t 1 then a s bs t ct implies that ar 2 s bss t cst ar 2 ar 2 s bts t ctt ar 2 s r t r fort 1 t s 0 r 0 and a1 r ar 2 s bts t ctt ar 2 1 r t r fort 1 r 0 these are the extensions of inequalities shown by t furuta proc amer math soc 101 1987 85 111 1991 511 moreover we will give an inequality say mixed inequality which includes the above inequalities and the inequality due to hansen pedersen math ann 258 1982 229

a new approach to the dynamic analysis of structures using fixed frequency dynamic stiffness matrices the dynamic analysis of structures by the standard finite element method introduces additional inaccuracies into the solution which are not present when the method is used for static analyses these inaccuracies can arise from two sources i the element formulation and ii the reduction of the size of the matrices by a static condensation i e using the guyan method1 2 the errors in both cases are caused by neglecting frequency dependent terms in the functions relating the displacements at any point in the structure to the displacements at certain fixed points i e nodes in the element formulation and masters in the condensation a new method of solution is proposed in this paper in which the frequency dependent terms are retained implicitly by using dynamic stiffness matrices defined at a number of fixed frequencies the dynamic stiffness matrices may be condensed efficiently to a relatively small number of master degrees of freedom using a front solution algorithm the final stage in the solution uses these matrices to synthesize a high order eigenvalue problem a method of solving such an eigenvalue problem of arbitrary order is described in a separate paper 3 numerical examples are given to show the accuracy and efficiency of the proposed method compared with conventional methods of solution