dynamic analysis of continuous plane trusses with equidistant supports the natural and forced vibrations of a continuous warren truss resting on equidistant roller supports are studied in the analyses the longitudinal inertial forces are neglected in the equation of motion and the mass of the truss is replaced by two sets of lumped masses at the nodes in the forced vibration case the truss is subjected to transverse harmonic loads acting at the nodes the truss can be considered as an equivalent system with cyclic bi periodicity periodicities due to the repetitive units of the truss and the supports respectively therefore the governing equation for such a system can be uncoupled by applying u transformation twice to form a set of single degree of freedom equations such equations can be used to solve for the natural frequencies of the trusses or their responses due to external excitations typical warren trusses are taken as examples to demonstrate the advantages of the proposed method and the accuracy that can be achieved the response of a truss with six substructures and four supports with a harmonic load acting at the centre node is investigated

bifurcation at infinity in polynomial vector fields abstract we study here the appearance of limit cycles from the equator in polynomial vector fields with no singular points at infinity this bifurcation is a generalized hopf bifurcation from the point at infinity we start with the general theory and then specialize to the particular case of cubic polynomial systems for which we study the simultaneous bifurcation of limit cycles from the origin and from the equator we finally discuss the transformation of a weak focus at infinity into a finite weak focus

dcca cross correlation coefficient quantifying level of cross correlation abstract in this paper a new coefficient is proposed with the objective of quantifying the level of cross correlation between nonstationary time series this cross correlation coefficient is defined in terms of the dfa method and the dcca method the implementation of this cross correlation coefficient will be illustrated with selected time series

the problem of general center focus and bifurcation of limit cycles for a planar system of nine degrees abstract our researches are concerned with a class of planar general equivariant system of nine degrees by making two appropriate transformations of system and calculating focal values carefully we obtain the conditions that the infinity and three elementary focuses 1 2 0 1 2 1 2 1 2 1 2 become four general centers at the same time moreover 20 limit cycles including 15 small limit cycles from three elementary foci and 5 large limit cycles from the infinity can occur under a certain condition what is worth mentioning is that similar conclusions are hardly seen in published papers up till now and our work is completely new

a quintic polynomial differential system with eleven limit cycles at the infinity in this article a recursion formula for computing the singular point quantities of the infinity in a class of quintic polynomial systems is given the first eleven singular point quantities are computed with the computer algebra system mathematica the conditions for the infinity to be a center are derived as well finally a system that allows the appearance of eleven limit cycles in a small enough neighborhood of the infinity is constructed

obtaining eringen s length scale coefficient for vibrating nonlocal beams via continualization method abstract eringen s length scale coefficients e 0 are presented herein for initially stressed vibrating nonlocal beams with various boundary conditions the coefficients are obtained by applying the continualization method to the discrete equations of microstructured beam models when compared to another continualized approach that is based on the pade approximant the proposed continualization method which is based on assuming continuous exponential displacement functions for the discrete displacement field is a more straightforward approach for solution unlike the pade approximant approach this latter method needs no sophisticated mathematical manipulations for obtaining the continuous equation moreover the continualization method allows one to directly solve the discrete governing equations for vibration of microstructured beams in the discrete domain rather than solving an approximated continuous equation obtained via the pade approximant by using this method it is found that e 0 1 12 for the buckling case of beams and e 0 1 6 for the vibration case for any combination of end conditions however the coefficients are not the same in the presence of an initial stress for vibrating beams with different boundary conditions

multifractal detrended cross correlation analysis for two nonstationary signals we propose a method called multifractal detrended cross correlation analysis to investigate the multifractal behaviors in the power law cross correlations between two time series or higher dimensional quantities recorded simultaneously which can be applied to diverse complex systems such as turbulence finance ecology physiology geophysics and so on the method is validated with cross correlated one and two dimensional binomial measures and multifractal random walks as an example we illustrate the method by analyzing two financial time series

dcca and dmca correlations of cryptocurrency markets abstract we examine the serial correlation structure of six liquid cryptocurrencies with a long data record bitcoin dash stellar litecoin monero and ripple with a use of the detrended cross correlation dcca and detrending moving average cross correlation dmca correlation coefficients we find that these cryptocurrencies behave differently from the stock markets which are much closer to the random walk efficient dynamics we further discuss issues connected to strong statements about cryptocurrency markets practical inefficiency

a new correlation coefficient for bivariate time series data abstract the correlation in time series has received considerable attention in the literature its use has attained an important role in the social sciences and finance for example pair trading in finance is concerned with the correlation between stock prices returns etc in general pearson s correlation coefficient is employed in these areas although it has many underlying assumptions which restrict its use here we introduce a new correlation coefficient which takes into account the lag difference of data points we investigate the properties of this new correlation coefficient we demonstrate that it is more appropriate for showing the direction of the covariation of the two variables over time we also compare the performance of the new correlation coefficient with pearson s correlation coefficient and detrended cross correlation analysis dcca via simulated examples

measuring correlations between non stationary series with dcca coefficient abstract in this short report we investigate the ability of the dcca coefficient to measure correlation level between non stationary series based on a wide monte carlo simulation study we show that the dcca coefficient can estimate the correlation coefficient accurately regardless the strength of non stationarity measured by the fractional differencing parameter d for a comparison we also report the results for the standard pearson correlation coefficient the dcca coefficient dominates the pearson coefficient for non stationary series

the multiplicity of the equatorial limit cycle of a class of planar polynomial vector fields abstract in this paper we have investigated the existence and the multiplicity of the equatorial limit cycle for a class of planar vector fields of degree 2 m 1 obtained the necessary and sufficient condition that the equator is a closed orbit and the multiplicity of the equatorial limit cycle of the planar polynomial vector fields is m 1 it is helpful to answer the second part of hilbert s 16th problem

detecting and quantifying cross correlations by analogous multifractal height cross correlation analysis abstract a new algorithm analogous multifractal height cross correlation analysis amf hxa is proposed in this paper our novel method takes into consideration of both the fluctuation information and the sign information in the corresponding cross covariance function numerical tests on artificially simulated series and real world series are performed to demonstrate that our method can accurately detect long range cross correlations for two simultaneously recorded series a new cross correlation coefficient is also defined to quantify the levels of cross correlation between two series

transfer entropy coefficient quantifying level of information flow between financial time series abstract in this paper a new coefficient is proposed with the objective of quantifying the level of information flow between financial time series this transfer entropy coefficient which provides an assessment on the multiscale information flow between measurements is defined in terms of the transfer entropy method and the multiscale method the implementation of this transfer entropy coefficient is illustrated with simulated time series and financial time series examples taken from simulated and financial data demonstrate that the dynamic mechanism of a complex system cannot be detected solely on the basis of transfer entropy of single scale

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

characterization of flow pattern transitions for horizontal liquid liquid pipe flows by using multi scale distribution entropy in coupled 3d phase space abstract horizontal oil water two phase flows often exist in many industrial processes uncovering the dynamic mechanism of the flow pattern transition is of great significance for modeling the flow parameters in this study we propose a method called multi scale distribution entropy msde in a coupled 3d phase space and use it to characterize the flow pattern transitions in horizontal oil water two phase flows firstly the proposed msde is validated with lorenz system and arfima processes interestingly it is found that the msde is dramatically associated with the cross correlations of the coupled time series then through conducting the experiment of horizontal oil water two phase flows the upstream and downstream flow information is collected using a conductance cross correlation velocity probe the coupled cross correlated signals are investigated using the msde method and the results indicate that the msde is an effective tool uncovering the complex dynamic behaviors of flow pattern transitions

quantifying the cross correlations between online searches and bitcoin market abstract in this paper we quantify the cross correlations between google trends and bitcoin market by employing the multifractal detrended cross correlation analysis mf dcca method we find that the change of google trends cgt and bitcoin market i e returns and changes of volume are overall significantly cross correlated based on the cross correlation test in particular the empirical results show that 1 there exist power law cross correlations between cgt and bitcoin returns as well as cgt and changes of volume 2 the cross correlations between cgt and returns have a higher degree of multifractal in the long term and weak multifractal in the short term while the cross correlations between cgt and change of volume show the opposite trend 3 with the rolling window analysis we further find that there is a decrease trend for the cross correlations between cgt and bitcoin returns over time and the cross correlations scaling exponents are less than 0 5 which indicate that they are both anti persistent cross correlated

mixed correlated arfima processes for power law cross correlations abstract we introduce a general framework of the mixed correlated arfima mc arfima processes which allows for various specifications of univariate and bivariate long term memory apart from a standard case when h x y 1 2 h x h y mc arfima also allows for processes with h x y 1 2 h x h y but also for long range correlated processes which are either short range cross correlated or simply correlated the major contribution of mc arfima lies in the fact that the processes have well defined asymptotic properties for h x h y and h x y which are derived in the paper so that the processes can be used in simulation studies comparing various estimators of the bivariate hurst exponent h x y moreover the framework allows for modeling of processes which are found to have h x y 1 2 h x h y

multifractal fourier detrended cross correlation analysis of traffic signals abstract multifractal detrended cross correlation analysis mf dxa has been developed to detect the long range power law cross correlation of considered signals in the presence of non stationarity however crossovers arising from extrinsic periodic trends make the scaling behavior difficult to analyze we introduce a fourier filtering method to eliminate the trend effects and systematically investigate the multifractal cross correlation of simulated and real traffic signals the crossover locations are found approximately corresponding to the periods of underlying trend traffic velocity on one road and flows on adjacent roads show strong cross correlation they also present weak multifractality after periodic trends are removed the traffic velocity and flow are cross correlated in opposite directions which is accordant to their actual evolution

orthogonality condition for a multi span beam and its application to transient vibration of a two span beam abstract this paper treats the orthogonality condition for a multi span beam and its application to forced transient vibration of a two span beam the beam is modeled as a bernoulli euler beam the boundary conditions for the particular case of two span beam are clamped pinned pinned an exact closed form solution is obtained for this problem even though there has been an enormous amount of work on beam vibration most of the studies are conducted on a single span beam there are some studies on the multi span beam vibration however their treatment is rather specialized in terms of the applied loading and the initial conditions none of the studies in the past treats an exact solution for a forced transient vibration of a general two span beam with arbitrary initial conditions and arbitrary forcing functions therefore the solution obtained in this paper is new the key development in the solution is the orthogonality condition for a multi span beam the method of solution developed in this paper establishes a general methodology for the forced transient vibration of a multi span beam the closed form solution obtained in this paper can be used as a benchmark solution for the transient vibration of a two span beam

the inefficiency of cryptocurrency and its cross correlation with dow jones industrial average abstract as a form of cryptocurrency the issue of informational efficiency of bitcoin has received much attention recently we add to the literature by investigating nine forms of cryptocurrencies i e bitcoin ripple ethereum nem stellar litecoin dash monero and verge with a battery of efficiency tests and the empirical results indicate that all these cryptocurrencies are inefficient markets what is more we further construct a value weighted cryptocurrency composite index cci and show that cci and dow jones industrial average are persistently cross correlated

modified multifractal large deviation spectrum based on cid for financial market system abstract we modify the basic roughness grain exponent only available for application of one single series to complexity invariant distance c i d for studying multifractal features between two time series c i d is taken into consideration as a new roughness grain exponent with the large deviation spectrum to detect the similarity and correlation between different stock markets in this work the new method is firstly applied to artificial series in order to test the scale invariance hypothesis with both the legendre spectrum and large deviation spectrum results show that the large deviation spectrum is better in the detection of multifractal analysis between two time series as it exhibit plentiful scaling structures then we investigate the scaling behavior between financial time series so as to test whether there is scale invariance of stock markets in china and the us besides from the values responding to the maximal f in the 5 pair series and the widths of the spectrum a new way of measurement of the similarity and correlation has been found to overcome the limitation of q we then compute the surface area of the large deviation spectrum under each scale and further detect the evolution of the slope by a scaling non scaling criterion which helps in the measurement of scaling behavior moreover the proposed method can give us more information between different markets and distinguish them from different angles

quantifying the range of cross correlated fluctuations using a q l dependent ahxa coefficient abstract recently based on analogous height cross correlation analysis ahxa a cross correlation coefficient l has been proposed to quantify the levels of cross correlation on different temporal scales for bivariate series a limitation of this coefficient is that it cannot capture the full information of cross correlations on amplitude of fluctuations in fact it only detects the cross correlation at a specific order fluctuation which might neglect some important information inherited from other order fluctuations to overcome this disadvantage in this work based on the scaling of the q th order covariance and time delay l we define a two parameter dependent cross correlation coefficient q l to detect and quantify the range and level of cross correlations this new version of q l coefficient leads to the formation of a q l surface which not only is able to quantify the level of cross correlations but also allows us to identify the range of fluctuation amplitudes that are correlated in two given signals applications to the classical arfima models and the binomial multifractal series illustrate the feasibility of this new coefficient q l in addition a statistical test is proposed to quantify the existence of cross correlations between two given series applying our method to the real life empirical data from the 1999 2000 california electricity market we find that the california power crisis in 2000 destroys the cross correlation between the price and the load series but does not affect the correlation of the load series during and before the crisis

statistical test for δρdcca cross correlation coefficient abstract in this paper we propose a new statistical test for d c c a detrended cross correlation coefficient difference a tool to measure contagion interdependence effect in time series of size n at different time scale n for this proposition we analyzed simulated and real time series the results showed that the statistical significance of d c c a depends on the size n and the time scale n and we can define a critical value for this dependency in 90 95 and 99 of confidence level as will be shown in this paper

finite sample properties of power law cross correlations estimators abstract we study finite sample properties of estimators of power law cross correlations detrended cross correlation analysis dcca height cross correlation analysis hxa and detrending moving average cross correlation analysis dmca with a special focus on short term memory bias as well as power law coherency we present a broad monte carlo simulation study that focuses on different time series lengths specific methods parameter setting and memory strength we find that each method is best suited for different time series dynamics so that there is no clear winner between the three the method selection should be then made based on observed dynamic properties of the analyzed series

dcca cross correlation coefficients reveals the change of both synchronization and oscillation in eeg of alzheimer disease patients abstract alzheimer s disease ad is a degenerative disorder of neural system that affects mainly the older population recently many researches show that the eeg of ad patients can be characterized by eeg slowing enhanced complexity of the eeg signals and eeg synchrony in order to examine the neural synchrony at multi scales and to find a biomarker that help detecting ad in diagnosis detrended cross correlation analysis dcca of eeg signals is applied in this paper several parameters namely dcca coefficients in the whole brain dcca coefficients at a specific scale maximum dcca coefficient over the span of all time scales and the corresponding scale of such coefficients were extracted to examine the synchronization respectively the results show that dcca coefficients have a trend of increase as scale increases and decreases as electrode distance increases comparing dcca coefficients in ad patients with healthy controls a decrease of synchronization in the whole brain and a bigger scale corresponding to maximum correlation is discovered in ad patients the change of max correlation scale may relate to the slowing of oscillatory activities linear combination of max dcca coefficient and max correlation scale reaches a classification accuracy of 90 from the above results it is reasonable to conclude that dcca coefficient reveals the change of both oscillation and synchrony in ad and thus is a powerful tool to differentiate ad patients from healthy elderly individuals

multifractal detrended cross correlation analysis of sunspot numbers and river flow fluctuations abstract we use the detrended cross correlation analysis dcca to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators specifically rivers represented by river flow fluctuation for daugava holston nolichucky and french broad rivers the multifractal detrended cross correlation analysis mf dxa shows that there exist some crossovers in the cross correlation fluctuation function versus time scale of the river flow and sunspot series one of these crossovers corresponds to the well known cycle of solar activity demonstrating a universal property of the mentioned rivers the scaling exponent given by dcca for original series at intermediate time scale 12 24 s 130 months is 1 17 0 04 which is almost similar for all underlying rivers at 1 confidence interval showing the second universal behavior of river runoffs to remove the sinusoidal trends embedded in data sets we apply the singular value decomposition svd method our results show that there exists a long range cross correlation between the sunspot numbers and the underlying streamflow records the magnitude of the scaling exponent and the corresponding cross correlation exponent are 0 76 0 85 and 0 30 0 48 respectively different values for scaling and cross correlation exponents may be related to local and external factors such as topography drainage network morphology human activity and so on multifractal cross correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series in addition the empirical relation between scaling exponent derived by dcca and detrended fluctuation analysis dfa h sun h river 2 is confirmed

a new approach to quantify power law cross correlation and its application to commodity markets abstract we proposed a new method detrended moving average cross correlation analysis dmca to detect the power law cross correlation between two correlated non stationary time series by combining detrended cross correlation analysis dcca and detrended moving average dma in order to compare the performance of dmca and dcca in the detection of cross correlation and to estimate the influence of periodic trend we generate two cross correlated time series x i and y i by a periodic two component fractionally autoregressive integrated moving average arfima process then we apply both methods to quantify the cross correlations of the generated series whose theoretical values are already known to us by comparing the results we obtained we find that the performance of this new approach is comparable to dcca with less calculating amounts our method can also reduce the impact of trends furthermore dmca for background and forward moving average case outperforms dcca in more accurate estimation when the analyzed times series are short in length to provide an example we also apply this new method to the time series of the real world data from brent and wti crude oil spot markets to investigate the complex cross market correlation between these commodity markets in all our method is another practical choice to detect the cross correlation between two short period non stationary time series and has potential application to real world problems

dcca cross correlation coefficient with sliding windows approach abstract we have implemented in this paper the dcca cross correlation coefficient d c c a with sliding windows approach to measure cross correlation as a function of time thereby from two non stationary time series a fixed size window will be defined by w and the coefficients d c c a calculated for different time scales 4 n w 4 following this procedure it was possible to set up a cross correlation color map of d c c a which was tested in this paper for a simulated random and an empirical econometric case this new color map with sliding windows shows the time scale and the current time for a cross correlation analysis in this way it is possible to analyze the complete cross correlation between two variables in different areas of knowledge such as economics our case of study

quantifying cross correlation between ibovespa and brazilian blue chips the dcca approach abstract the objective of this paper is to demonstrate the influence of the blue chips companies in the stock market in this we apply the detrended cross correlation coefficient dcca at the sao paulo stock market ibovespa brazil initially we found that there is a positive cross correlation between these companies and the index afterwards we show that the cross correlation coefficient value depends on the time scale and the specific company blue chips thus this type of analysis lets to infer what is the most adherent company with ibovespa also in this paper we analyze in the point of view of dcca the 2008 financial crisis before after altogether the results show that there is more cross correlation between ibovespa index the blue chips after the 2008 crisis

a cubic kolmogorov system with six limit cycles abstract we consider a class of cubic kolmogorov systems we show in particular that a maximum of six small amplitude limit cycles can bifurcate from a critical point in the first quadrant and we discuss the number of invariant lines

optimal portfolio strategy with cross correlation matrix composed by dcca coefficients evidence from the chinese stock market abstract in this paper a new estimator of correlation matrix is proposed which is composed of the detrended cross correlation coefficients dcca coefficients to improve portfolio optimization in contrast to pearson s correlation coefficients pcc dcca coefficients acquired by the detrended cross correlation analysis dcca method can describe the nonlinear correlation between assets and can be decomposed in different time scales these properties of dcca make it possible to improve the investment effect and more valuable to investigate the scale behaviors of portfolios the minimum variance portfolio mvp model and the mean variance mv model are used to evaluate the effectiveness of this improvement stability analysis shows the effect of two kinds of correlation matrices on the estimation error of portfolio weights the observed scale behaviors are significant to risk management and could be used to optimize the portfolio selection

modeling long range cross correlations in two component arfima and fiarch processes we investigate how simultaneously recorded long range power law correlated multivariate signals cross correlate to this end we introduce a two component arfima stochastic process and a two component fiarch process to generate coupled fractal signals with long range power law correlations which are at the same time long range cross correlated we study how the degree of cross correlations between these signals depends on the scaling exponents characterizing the fractal correlations in each signal and on the coupling between the signals our findings have relevance when studying parallel outputs of multiple component of physical physiological and social systems

dynamical mechanism in aero engine gas path system using minimum spanning tree and detrended cross correlation analysis abstract identifying the mutual interaction in aero engine gas path system is a crucial problem that facilitates the understanding of emerging structures in complex system by employing the multiscale multifractal detrended cross correlation analysis method to aero engine gas path system the cross correlation characteristics between gas path system parameters are established further we apply multiscale multifractal detrended cross correlation distance matrix and minimum spanning tree to investigate the mutual interactions of gas path variables the results can infer that the low spool rotor speed n1 and engine pressure ratio epr are main gas path parameters the application of proposed method contributes to promote our understanding of the internal mechanisms and structures of aero engine dynamics

detrended fluctuation analysis as a regression framework estimating dependence at different scales we propose a framework combining detrended fluctuation analysis with standard regression methodology the method is built on detrended variances and covariances and it is designed to estimate regression parameters at different scales and under potential nonstationarity and power law correlations the former feature allows for distinguishing between effects for a pair of variables from different temporal perspectives the latter ones make the method a significant improvement over the standard least squares estimation theoretical claims are supported by monte carlo simulations the method is then applied on selected examples from physics finance environmental science and epidemiology for most of the studied cases the relationship between variables of interest varies strongly across scales

a cubic polynomial system with seven limit cycles at infinity in this paper we study bifurcation of limit cycles at infinity for a class of cubic polynomial system with no singular points at infinity in which the problem for bifurcation of limit cycles from infinity be transferred into that from the origin by computation of singular point values the conditions of the origin correspondingly infinity to be a center and the highest degree fine focus are derived consequently we construct a cubic system which can bifurcate seven limit cycles from infinity when let normal parameters be suitable values the positions of these limit cycles without constructing poincare cycle fields can be pointed out exactly

an analysis of the intrinsic cross correlations between api and meteorological elements using dpcca abstract in order to reveal the intrinsic cross correlations between air pollution index api records and synchronously meteorological elements data the detrended partial cross correlation dpcc coefficients are analyzed using a detrended partial cross correlation analysis dpcca dpcc coefficients for different spatial locations and seasons are calculated and compared the results show that dpcca can uncover intrinsic cross correlations between api and meteorological elements and most of their interactional mechanisms can be explained dpcc coefficients are either positive or negative and vary with spatial locations and seasons with consistently interactional mechanisms more remarkable we find that detrended cross correlation analysis can present the cross correlations between the fluctuations in two nonstationary time series but this cross correlation does not always fully reflect the interactional mechanism for the original time series despite this dpcca is recommended as a comparatively reliable method for revealing intrinsic cross correlations between api and meteorological elements and it can also be useful for our understanding of their interactional mechanisms

a new methodology for local cross correlation between two nonstationary time series abstract to measure the degree of local cross correlation between two nonstationary time series a new approach with a locally weighted pearson correlation coefficient based on a simple locally weighted linear regression model was proposed in this approach a gaussian decay based function is selected as a weighting function an appropriate bandwidth is selected using an alternative criterion some factors influencing the local cross correlation degree including long range exponent estimated by means of a detrended fluctuation analysis dfa and seasonal change in the series are discussed artificial and real world datasets are analyzed the results show that the proposed method can measure the degree of a locally intrinsic cross correlation between two series the contribution of this locally intrinsic cross correlation is attributed to original input excitation sources and dfa scaling exponents the effects of seasonal change with a high frequency in the series on a locally intrinsic cross correlation are significant the effects of a low frequency seasonal change are insignificant a positive local cross correlation between a synchronous wind speed and air pollution index series in nanjing china is observed which is related to externally imported air pollution sources consistent results are obtained by comparing the new method with the detrended cross correlation coefficient d c c a therefore the proposed approach is reliable reasonable and applicable and can examine the degree of the local intrinsic cross correlation between two nonstationary time series

dynamic response of infinite continuous beams subjected to a moving force an exact method this paper describes an exact method for investigating the dynamic response of an infinite uniform beam resting on periodic rolle supports and subjected to a moving force at first an exact solution for a rotationally periodic continous beam subjected to a moving force is obtained by the u transformation and mode method then by a limiting process with the number of spans approaching infinity the result is generalized to give a solution for an infinite continuous beam subjected to a moving force this method will be applicable to the forced vibration analysis of an infinite continuous beam under arbitrary excitation

transverse vibration analysis of plane trusses by analytical method abstract the type of plane truss considered in this paper is the warren truss which is built up with basic units consisting of four sets of bars pin jointed at the nodes and subjected to transverse nodal loads the natural vibration and dynamic response are studied for the simply supported truss with lumped masses at the nodes closed form solutions are deduced by using the u transformation technique which leads to the uncoupling of the governing equations in order to explain the procedure of the present method the response functions for the nodal displacements of a truss subjected to the action of a suddenly applied load at a node are derived it is obvious that the present method is also applicable to the forced vibration analysis of trusses subjected to arbitrary transverse loads applied at the nodes

multifractal detrending moving average cross correlation analysis there are a number of situations in which several signals are simultaneously recorded in complex systems which exhibit long term power law cross correlations the multifractal detrended cross correlation analysis mfdcca approaches can be used to quantify such cross correlations such as the mfdcca based on the detrended fluctuation analysis mfxdfa method we develop in this work a class of mfdcca algorithms based on the detrending moving average analysis called mfxdma the performances of the proposed mfxdma algorithms are compared with the mfxdfa method by extensive numerical experiments on pairs of time series generated from bivariate fractional brownian motions two component autoregressive fractionally integrated moving average processes and binomial measures which have theoretical expressions of the multifractal nature in all cases the scaling exponents h xy extracted from the mfxdma and mfxdfa algorithms are very close to the theoretical values for bivariate fractional brownian motions the scaling exponent of the cross correlation is independent of the cross correlation coefficient between two time series and the mfxdfa and centered mfxdma algorithms have comparative performances which outperform the forward and backward mfxdma algorithms for two component autoregressive fractionally integrated moving average processes we also find that the mfxdfa and centered mfxdma algorithms have comparative performances while the forward and backward mfxdma algorithms perform slightly worse for binomial measures the forward mfxdma algorithm exhibits the best performance the centered mfxdma algorithms performs worst and the backward mfxdma algorithm outperforms the mfxdfa algorithm when the moment order q 0 we apply these algorithms to the return time series of two stock market indexes and to their volatilities for the returns the centered mfxdma algorithm gives the best estimates of h xy q since its h xy 2 is closest to 0 5 as expected and the mfxdfa algorithm has the second best performance for the volatilities the forward and backward mfxdma algorithms give similar results while the centered mfxdma and the mfxdfa algorithms fail to extract rational multifractal nature

bifurcations of limit cycles in a z4 equivariant planar polynomial vector field of degree 7 the present paper intends to explore the number and distribution of limit cycles for a class of perturbed z 4 equivariant planar hamiltonian system of degree 7 the bifurcation theory of planar dynamical systems and the method of detection functions are applied to study the given perturbed system by controlling the perturbation parameters an example of a special perturbed z 4 equivariant vector field having 41 limit cycles is found the distribution of the above 41 limit cycles is also given the results are significant to the study of weaken hilbert s 16th problem and to the acquaintance of the characteristics of higher order equivariant vector fields

cross correlations between volume change and price change in finance one usually deals not with prices but with growth rates r defined as the difference in logarithm between two consecutive prices here we consider not the trading volume but rather the volume growth rate r the difference in logarithm between two consecutive values of trading volume to this end we use several methods to analyze the properties of volume changes r and their relationship to price changes r we analyze 14 981 daily recordings of the standard and poor s s p 500 index over the 59 year period 1950 2009 and find power law cross correlations between r and r by using detrended cross correlation analysis dcca we introduce a joint stochastic process that models these cross correlations motivated by the relationship between r and r we estimate the tail exponent of the probability density function p r r 1 for both the s p 500 index as well as the collection of 1819 constituents of the new york stock exchange composite index on 17 july 2009 as a new method to estimate we calculate the time intervals q between events where r q we demonstrate that q the average of q obeys q q we find 3 furthermore by aggregating all q values of 28 global financial indices we also observe an approximate inverse cubic law

detrended multiple cross correlation coefficient abstract based on the detrended cross correlation coefficient x a x b we propose in this paper to establish a detrended multiple cross correlation coefficient d m c x 2 to be applied in order to quantify the relations between non stationary signals on different time scales this detrended multiple cross correlation coefficient will be the measure of the total association between the dependent variable y with the others i independent variables x it will be the generalization of x a x b for more than two independent variables to validate d m c x 2 we set up a cross correlation table ranging from 0 to 1 and we determined the detrended multiple cross correlation coefficient into simulated and real time series the results of this analysis show that the detrended multiple cross correlation coefficient may be suitable and useful to measure multiple cross correlations as we will see in this paper

multifractal detrended cross correlation analysis of the oil dependent economies evidence from the west texas intermediate crude oil and the gcc stock markets abstract in this paper we firstly investigate the cross correlations between the crude oil market and the six gcc stock markets based on the analysis of the significant statistic q c c m and the cross correlation coefficient we find that the cross correlations between the crude oil market and the six gcc stock markets are all significant employing the method of the mf dfa and mf dxa we further find that the auto correlations of the crude oil market and the six gcc stock markets and cross correlations between them are all the multifractality moreover using the multifractal spectrum we can also verify the multifractal characteristics between the crude oil market and the six gcc stock markets furthermore we use the penalized contrast function to detect the structural break points of the wti oil return series and its conditional volatility and then discuss the cross correlations between the crude oil and the six gcc stock markets in the different phases according to these break points at last we employ the technique of the rolling window to investigate the dynamic of the scaling exponent h x y q in addition we explore the relationship between the cross correlation exponents h x y q and the average scaling exponents h x x q h y y q 2

small limit cycles bifurcating from fine focus points in quartic order z3 equivariant vector fields abstract this paper is concerned with the number of limit cycles for a quartic polynomial z3 equivariant vector fields the system under consideration has a fine focus point at the origin and three fine focus points which are symmetric about the origin by the computation of the singular point values sixteen limit cycles are found and their distributions are studied by using the new methods of bifurcation theory and qualitative analysis this is a new result in the study of the second part of the 16th hilbert problem it gives rise to the conclusion h 4 16 where h n is the hilbert number for the second part of hilbert s 16th problem the process of the proof is algebraic and symbolic as far as know the technique employed in this work is different from more usual ones the calculation can be readily done with using computer symbol operation system such as mathematica

bifurcation at the equator for a class of quintic polynomial differential system abstract the center problem and bifurcation of limit cycles for degenerate singular point and infinity are far from being solved in general in this paper we studied center conditions and bifurcation of limit cycles at the degenerate singular point and infinity the equator in a class of quintic polynomial differential system with two small parameters and eight normal parameters the method is based on two homeomorphic transformations of the infinity and degenerate singular point into linear singular point which allows us to compute the generalized lyapunov constants the singular point quantities for the origin and infinity the center conditions for the degenerate singular point and infinity are derived respectively the limit cycle configurations of 7 2 and 2 6 are obtained under simultaneous perturbation at the origin and infinity as far as we know it is the first time that the bifurcation of limit cycles from a degenerate singular point and infinity simultaneously is studied in planar differential system

the number of limit cycles for a family of polynomial systems in this paper the number of limit cycles in a family of polynomial systems was studied by the bifurcation methods with the help of a computer algebra system e g maple 7 0 we obtain that the least upper bound for the number of limit cycles appearing in a global bifurcation of systems 2 1 and 2 2 is 5n 5 1 1 n 2 for c 0 and n for c 0

uncoupling of dynamic equations for periodic structures abstract this paper is aimed at providing some explanation of the physical meaning and mathematical formulation of the u transformation method which has found many applications in obtaining solutions for structures with periodicity properties the u transformation was first derived from the mode method for rotational periodic structures the dynamic equation for cyclic periodic structures can be uncoupled in the domain of single substructure by u transformation it is then extended to the double u transformation method for structures with cyclic periodicity in two directions however it should be noted that the method may also be applied to some one way or two way linear periodic structures

a polynomial differential system withnine limit cycles at infinity abstract in this article we give a recursive formula to compute the singular point quantities of a class of seventh order polynomial systems the first eleven singular point quantities have been computed with computer algebra system mathematica and the conditions for infinity to be a center have been deduced as well at last we construct a system that allows the appearance of nine limit cycles in the neighborhood of infinity

general center conditions and bifurcation of limit cycles for a quasi symmetric seventh degree system in this paper we study a class of quasi symmetric seventh degree system by making two appropriate transformations of system 3 and calculating general focal values carefully we obtain the conditions that the infinity and the elementary focus 12 0 become centers at the same time moreover 12 limit cycles including 6 small limit cycles from the elementary focus and 6 large limit cycles from the infinity can occur under a certain condition what is worth mentioning is that similar conclusions are less and our work is new in terms of research about quasi symmetric systems up till now

power law correlations in finance related google searches and their cross correlations with volatility and traded volume evidence from the dow jones industrial components abstract we study power law correlations properties of the google search queries for dow jones industrial average djia component stocks examining the daily data of the searched terms with a combination of the rescaled range and rescaled variance tests together with the detrended fluctuation analysis we show that the searches are in fact power law correlated with hurst exponents between 0 8 and 1 1 the general interest in the djia stocks is thus strongly persistent we further reinvestigate the cross correlation structure between the searches traded volume and volatility of the component stocks using the detrended cross correlation and detrending moving average cross correlation coefficients contrary to the universal power law correlations structure of the related google searches the results suggest that there is no universal relationship between the online search queries and the analyzed financial measures even though we confirm positive correlation for a majority of pairs there are several pairs with insignificant or even negative correlations in addition the correlations vary quite strongly across scales

dynamic analysis of a hollow cylinder subject to a dual traveling force imposed on its inner surface abstract the dynamic behavior of a hollow cylinder under a dual traveling force applied to the inner surface is investigated in this study the cylinder is constrained at both the top and bottom surfaces not to move in the length direction but free in other directions and a dual force travels at a constant velocity along the length direction on the inner surface of the hollow cylinder the resulting governing field equations and the associated boundary conditions are ruled by the general hooke s law due to the nature of the field equations proper adjoint system of equations and biorthogonality conditions were derived in a precise and detailed manner to solve these field equations in this study the method of separation of variable is used and the method of fr o benius is employed for the differential equations in the radial direction using the field equations the eigenanalyses on both the original and its adjoint system were performed with great care which results in the eigenfunction sets of both systems the biorthogonality conditions were applied to the field equations to obtain the discretized equation for each mode using the solutions of the discretized equations that account for the boundary forcing terms the critical speed for a dual traveling force for each mode could be computed

bifurcation of limit cycles and pseudo isochronous center at degenerate singular point in a septic system abstract in this literature we are concerned with the bifurcation of limit cycles and pseudo isochronous center conditions at degenerate singular point in a polynomial differential system of degree seven the key contribution of this paper is to give an example of septic system with 8 limit cycles bifurcated from the degenerate singular point and list its pseudo isochronous center conditions

cross correlation analysis between chinese tf contracts and treasury etf based on high frequency data abstract in this paper we investigate the high frequency cross correlation relationship between chinese treasury futures contracts and treasury etf we analyze the logarithmic return of these two price series from which we can conclude that both return series are not normally distributed and the futures markets have greater volatility we find significant cross correlation between these two series we further confirm the relationship using the dcca coefficient and the dmca coefficient we quantify the long range cross correlation with dcca method and we further show that the relationship is multifractal an arbitrage algorithm based on dfa regression with stable return is proposed in the last part

detrending moving average cross correlation coefficient measuring cross correlations between non stationary series abstract in the paper we introduce a new measure of correlation between possibly non stationary series as the measure is based on the detrending moving average cross correlation analysis dmca we label it as the dmca coefficient d m c a with a moving average window length we analytically show that the coefficient ranges between 1 and 1 as a standard correlation does in the simulation study we show that the values of d m c a very well correspond to the true correlation between the analyzed series regardless the non stationarity level dependence of the newly proposed measure on other parameters correlation level moving average window length and time series length is discussed as well

bifurcation of limit cycles at the equator this paper studies center conditions and bifurcation of limit cycles from the equator for a class of polynomial differential system of order seven by converting real planar system into complex system we established the relation of focal values of a real system with singular point quantities of its concomitant system and the recursion formula for the computation of singular point quantities of a complex system at the infinity therefore the first 14 singular point quantities of a complex system at the infinity are deduced by using computer algebra system mathematica what s more the conditions for the infinity of the real system to be a center or 14 degree fine focus are derived respectively a system of order seven that bifurcates 12 limit cycles from the infinity is constructed for the first time

stability and bifurcations of limit cycles of the equator in a class of cubic polynomial systems abstract in this paper we study the appearance of limit cycles from the equator in a class of cubic polynomial vector fields with no singular points at infinity and the stability of the equator of the systems we start by deducing the recursion formula for quantities at infinity in these systems then specialize to a particular case of these cubic systems for which we study the bifurcation of limit cycles from the equator we compute the quantities at infinity with computer algebraic system mathematica 2 2 and reach with relative ease an expression of the first six quantities at infinity of the system and give a cubic system which allows the appearance of six limit cycles in the neighborhood of the equator as far as we know this is the first time that an example of cubic system with six limit cycles bifurcating from the equator is given the technique employed in this work is essentially different from more usual ones the recursion formula we present in this paper for the calculation of quantities at infinity is linear and then avoids complex integrating operations therefore the calculation can be readily done with using computer symbol operation system such as mathematica

dcca cross correlation analysis in time series with removed parts abstract in this paper we analyze the effect of removing pieces in time series with long range memory by dfa method and detrended cross correlation coefficient to achieve this purpose initially simulated time series are produced by arfima process long time dependence from these simulated time series cuts and removals are produced the results show that for up to 50 of removed parts compared to the original time series there is no change in the final results for detrended auto and cross correlations therefore with this paper we show that the dfa method and the detrended cross correlation coefficient are robust for time series analysis even for time series with removed parts this result ensures that these methods can be applied to real time series which in many cases lacks measurement for a variety of reasons and causes

dynamic relationship between chinese rmb exchange rate index and market anxiety a new perspective based on mf dcca abstract this paper employs multifractal detrended cross correlation analysis mf dcca to study the cross correlations between the chinese rmb exchange rate index and market anxiety using data from june 21 2010 to december 28 2018 cross correlation statistics and coefficients verify the existence of cross correlations and the mf dcca method quantitatively confirms the presence of multifractality between the chinese rmb index and market anxiety for both the long and short term the results of the rolling window analysis reveal that cross correlation scaling exponents of the chinese rmb index and market anxiety are sensitive to external shocks

an explicit expression of the first liapunov and period constants with applications in this paper we study systems in the plane having a critical point with pure imaginary eigenvalues and we search for effective conditions to discern whether this critical point is a focus or a center in the case of it being a center we look for additional conditions in order to be isochronous we stress that the essential differences between the techniques used in this work and the more usual ones are basically two the elimination of the integration constants when we consider primitives of functions see also remark 3 2 and the fact that we maintain the complex notation in the whole study thanks to these aspects we reach with relative ease an expression of the first three liapunov constants v3 v5 andv7 and of the first two period ones p2andp4 for a general system as far as we know this is the first time that a general and compact expression ofv7has been given moreover the use of a computer algebra system is only needed in the computation ofv7andp4 these results are applied to give a classification of centers and isochronous centers for certain families of differential equations

the center conditions and bifurcation of limit cycles at the infinity for a cubic polynomial system abstract in this paper the problem of center conditions and bifurcation of limit cycles at the infinity for a class of cubic systems are investigated the method is based on a homeomorphic transformation of the infinity into the origin the first 21 singular point quantities are obtained by computer algebra system mathematica the conditions of the origin to be a center and a 21st order fine focus are derived respectively correspondingly we construct a cubic system which can bifurcate seven limit cycles from the infinity by a small perturbation of parameters at the end we study the isochronous center conditions at the infinity for the cubic system

simultaneous bifurcation of limit cycles from two nests of periodic orbits abstract let z f z be an holomorphic differential equation having a center at p and consider the following perturbation z f z e r z z we give an integral expression similar to an abelian integral whose zeroes control the limit cycles that bifurcate from the periodic orbits of the period annulus of p this expression is given in terms of the linearizing map of z f z at p the result is applied to control the simultaneous bifurcation of limit cycles from the two period annuli of z i z z 2 after a polynomial perturbation

cross correlations between price and volume in chinese gold markets abstract we apply the multifractal detrended cross correlation analysis mf dcca method to investigate the cross correlation behaviors between price and volume in chinese gold spot and futures markets qualitatively we find that the price and volume series are significantly cross correlated using the cross correlation test statistics q c c m and the d c c a coefficients quantitatively by employing the mf dcca analysis we find that there is a power law cross correlation and significant multifractal features between price and volume in gold spot and futures markets furthermore by comparing the multifractality of the original series to the shuffled and surrogated series we find that for the gold spot market the main contribution of multifractality is fat tail distribution for the gold futures market both long range correlations and fat tail distributions play important roles in the contribution of multifractality finally by employing the method of rolling windows we undertake further investigation into the time varying features of the cross correlations between price and volume we find that for both spot and futures markets the cross correlations are anti persistent in general in the short term the cross correlation shows obvious fluctuations due to exogenous shocks while in the long term the relationship tends to be at a metastable level due to the dynamic mechanism

linear recursion formulas of quantities of singular point and applications in this paper we study the algorithm of focus quantities and saddle quantities of a real planar autonomous differential system two linear recursion formulas for computation of quantities of singular point are obtained using the recursion formulas to compute focus quantities or saddle quantities of a real planar autonomous differential system we need only make use of four fundamental operation of arithmetic in the coefficients of the system then avoid complex integrating recursion operations which is necessary in more usual approaches therefore the calculation can be readily done with using computer symbol operation system such as mathematica they are far more practical than more usual approaches from the algorithmic point of view and by which the focus quantities and saddle quantities of a polynomial system can be computed and simplified in a much simpler way as a result of straightforward application we obtain with relative ease the first 8 focus quantities at origin of a cubic system and the sufficient and necessary conditions of integrability in the neighborhood of the origin of this system

dcca cross correlation coefficient differentiation theoretical and practical approaches abstract we propose in this paper to establish a well defined relationship between d f a the long range auto correlation exponent and d c c a the long range cross correlation exponent respectively described by the dfa and dcca methods this relationship will be accomplished theoretically by differentiating the dcca cross correlation coefficient d c c a n also for some specific times series we apply this theory in order to establish its validity

semi analytic solution in the time domain for non uniform multi span bernoulli euler beams traversed by moving loads abstract this paper presents a semi analytic solution of the moving load problem which is of great interest for the analysis of multi span uniform and non uniform beams subjected to moving forces such as high speed trains the solution is based on the response of the structure to a unit load circulating at a constant speed of the train viscous modal damping is considered using bernoulli euler beam elements with variable cross sectional properties the structure is discretized and the mode shapes are computed using standard procedure the moving load is represented by a unitary dirac delta function and the modal loads are obtained in terms of cubic hermitian polynomials this leads in a straightforward manner to the closed form solution for the unit load in the time domain the solution is expressed in terms of 10 coefficients per element and per mode the values of which are independent of the speed of the moving load finally the response to a series of loads is built simply by adding the contribution of each the overall procedure is fast and accurate depending only on the spatial discretization and the time step selected for evaluating the solution without the need of any integration step numerical tests have been included in order to show the efficiency of this technique