topology of symplectomorphism groups of rational ruled surfaces let m be either s 2 s 2 or the one point blow up cp 2 cp 2 of cp 2 in both cases m carries a family of symplectic forms where 1 determines the cohomology class this paper calculates the rational co homology of the group g of symplectomorphisms of m as well as the rational homotopy type of its classifying space bg it turns out that each group g contains a nite collection kk k 0 of nite dimensional lie subgroups that generate its homotopy we show that these subgroups asymptotically commute i e all the higher whitehead products that they generate vanish as 1 however for each xed there is essentially one nonvanishing product that gives rise to a jumping generator w in h g and to a single relation in the rational cohomology ring h bg an analog of this generator w was also seen by kronheimer in his study of families of symplectic forms on 4 manifolds using seiberg witten theory our methods involve a close study of the space of compatible almost complex structures on m

from taubes currents to almost kahler forms the taubes current is introduced by taubes in j symplectic geom 9 161 250 2011 as an intermediate step to construct almost kahler forms in this paper we prove that an almost complex structures being almost kahler structure in dimension four is the equivalent of the existence of taubes currents precisely we show that taubes currents could be regularized to almost kahler forms up to small perturbations of cohomology classes on any 4 dimensional almost complex manifold m j a similar result is established for higher dimensions under the assumption of almost kahler an application to donaldson s tamed to compatible question is provided

multifractal detrended cross correlation analysis on benchmark cryptocurrencies and crude oil prices abstract in this paper we investigate the cross correlations between three benchmark cryptocurrencies including bitcoin ethereum and ripple and some of the well known crude oils west texas intermediate and brent the data of the study spans from 7 august 2015 to 10 june 2019 we utilized the multifractal detrending moving average cross correlation analysis mf x dma method to examine the multifractal features among data we find that the cross correlations between each pair of time series are significant by using the cross correlation test statistic q c c m analysis and detrended moving average cross correlation analysis dmca coefficient also the cross correlation coefficients d m c a show that the data are positively correlated but the degree of correlation has been elevated by increasing the window intervals v the observed results obtained through the mf x dma method infer the existence of multifractal cross correlations on ten bivariate time series in the study and that the strength of multifractality between ethereum and ripple is the highest followed by the strength of multifractality between wti crude oil and ethereum

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

compatible complex structures on symplectic rational ruled surfaces in this article we study the topology of the spacei of complex structures compatible with a fixed symplectic form using the framework of donaldson by comparing our analysis of the spacei with results of mcduff on the spacej of compatible almost complex structures on rational ruled surfaces we find that i is contractible in this case we then apply this result to study the topology of the symplectomorphism group of a rational ruled surface extending results of abreu and mcduff

detrending moving average algorithm for multifractals the detrending moving average dma algorithm is a widely used technique to quantify the long term correlations of nonstationary time series and the long range correlations of fractal surfaces which contains a parameter ensuremath theta determining the position of the detrending window we develop multifractal detrending moving average mfdma algorithms for the analysis of one dimensional multifractal measures and higher dimensional multifractals which is a generalization of the dma method the performance of the one dimensional and two dimensional mfdma methods is investigated using synthetic multifractal measures with analytical solutions for backward ensuremath theta 0 centered ensuremath theta 0 5 and forward ensuremath theta 1 detrending windows we find that the estimated multifractal scaling exponent ensuremath tau q and the singularity spectrum f ensuremath alpha are in good agreement with the theoretical values in addition the backward mfdma method has the best performance which provides the most accurate estimates of the scaling exponents with lowest error bars while the centered mfdma method has the worse performance it is found that the backward mfdma algorithm also outperforms the multifractal detrended fluctuation analysis the one dimensional backward mfdma method is applied to analyzing the time series of shanghai stock exchange composite index and its multifractal nature is confirmed

crossing of two mobile averages a method for measuring the roughness exponent self affine signals characterized by a defined hurst roughness exponent h can be investigated through mobile averages the density ensuremath rho of crossing points between any two moving averages is a measure of long range power law correlations in the signal the method is compared to the detrended fluctuation analysis we take advantage of our findings in order to propose a practically powerful and accurate technique for determining h and apply it right away to cases with persistent or antipersistent correlations

large time behavior of a generalized oseen evolution operator with applications to the navier stokes flow past a rotating obstacle consider the motion of a viscous incompressible fluid in a 3d exterior domain d when a rigid body mathbb r 3 setminus d moves with prescribed time dependent translational and angular velocities for the linearized non autonomous system l q l r smoothing action near t s as well as generation of the evolution operator t t s t ge s ge 0 was shown by hansel and rhandi j reine angew math 694 1 26 2014 under reasonable conditions in this paper we develop the l q l r decay estimates of the evolution operator t t s as t s rightarrow infty and then apply them to the navier stokes initial value problem

regularity and estimates for j holomorphic discs attached to a maximal totally real submanifold we prove that pseudo holomorphic discs attached to a maximal totally real submanifold inherit their regularity to the boundary from the regularity of the submanifold and of the almost complex structure the proof is based on the computation of an explicit lower bound for the kobayashi metric in almost complex manifolds which also yields explicit estimates of holderian norms of such discs

homotopy equivalence of nearby lagrangians and the serre spectral sequence we construct using relatively basic techniques a spectral sequence for exact lagrangians in cotangent bundles similar to the one constructed by fukaya seidel and smith that spectral sequence was used to prove that exact relative spin lagrangians in simply connected cotangent bundles with vanishing maslov class are homology equivalent to the base a similar result was also obtained by nadler the ideas in that paper were extended by abouzaid who proved that vanishing maslov class alone implies homotopy equivalence in this paper we present a short proof of the fact that any exact lagrangian with vanishing maslov class is homology equivalent to the base and that the induced map on fundamental groups is an isomorphism when the fundamental group of the base is pro finite this implies homotopy equivalence

convergence of yang mills higgs fields in this paper we study the convergence of yang mills higgs ymh fields defined on fiber bundles over riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the underlying surface is allowed to vary we show that away from the nodes the ymh fields converges up to gauge to a smooth ymh field modulo finitely many harmonic spheres while near the nodes where the conformal structure degenerates the ymh fields converges to a pair consisting of a flat connection and a twisted geodesic with potential in particular we generalize the recent compactness results on both harmonic maps from surfaces and twisted holomorphic curves to general ymh fields

fractionally integrated process with power law correlations in variables and magnitudes we propose a new stochastic process de ned by only two parameters 1 and 2 which generates power law correlations or anticorrelations in the variable increments and power law correlations in their magnitudes to account for empirical observations in a range of physical systems to demonstrate the utility of our process we consider the case with power law anticorrelations in the variable increments and power law correlations in their magnitudes to model scaling properties in heartbeat data the parameters 1 and 2 control separately the correlations in the increments and their magnitudes and we nd linear relations between each parameter and the corresponding correlation exponent

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

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

financial multifractality and its subtleties an example of dax abstract detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency deutsche aktienindex data the tail index the renyi exponents based on the box counting algorithm for the graph d q and the generalized hurst exponents h q are computed in parallel for short and daily return times the results indicate a more complicated nature of the stock market dynamics than just consistent multifractal

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

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

the birkhoff lewis fixed point theorem and a conjecture of v i arnold abstract the following conjecture of v i arnold is proved every measure preserving diffeomorphism of the torus t2 which is homologeous to the identity and which leaves the center of mass invariant possesses at least 3 fixed points the proof of this global fixed point theorem does not make use of the generating function technique the theorem is a consequence of the statement that a hamiltonian vector field on a torus t2n which depends periodically on time possesses at least 2n 1 forced oscillations these periodic solutions are are found using the classical variational principle by means of two qualitative statements for general flows a second conjecture of v i arnold proved concerns a birkhoff lewis type fixed point theorem for symplectic maps additional keywords periodic functions variational principles equations reprints author

ruled 4 manifolds and isotopies of symplectic surfaces we study symplectic surfaces in ruled symplectic 4 manifolds which are disjoint from a given symplectic section as a consequence in any symplectic 4 manifold two homologous symplectic surfaces which are c 0 close must be hamiltonian isotopic

are crude oil markets multifractal evidence from mf dfa and mf ssa perspectives abstract in this article we investigated the multifractality and its underlying formation mechanisms in international crude oil markets namely brent and wti which are the most important oil pricing benchmarks globally we attempt to find the answers to the following questions 1 are those different markets multifractal 2 what are the dynamical causes for multifractality in those markets if any to answer these questions we applied both multifractal detrended fluctuation analysis mf dfa and multifractal singular spectrum analysis mf ssa based on the partition function two widely used multifractality detecting methods we found that both markets exhibit multifractal properties by means of these methods furthermore in order to identify the underlying formation mechanisms of multifractal features we destroyed the underlying nonlinear temporal correlation by shuffling the original time series thus we identified that the causes of the multifractality are influenced mainly by a nonlinear temporal correlation mechanism instead of a non gaussian distribution at last by tracking the evolution of left and right half multifractal spectra we found that the dynamics of the large price fluctuations is significantly different from that of the small ones our main contribution is that we not only provided empirical evidence of the existence of multifractality in the markets but also the sources of multifractality and plausible explanations to current literature furthermore we investigated the different dynamical price behaviors influenced by large and small price fluctuations

polyfolds cobordisms and the strong weinstein conjecture abstract we prove the strong weinstein conjecture for closed contact manifolds that appear as the concave boundary of a symplectic cobordism admitting an essential local foliation by holomorphic spheres

solvability of dirac type equations abstract this paper develops a weighted l 2 method for the half dirac equation for dirac bundles over closed riemann surfaces we give a sufficient condition for the solvability of the half dirac equation in terms of a curvature integral applying this to the dolbeault dirac operator we establish an automatic transversality criteria for holomorphic curves in kahler manifolds on compact riemannian manifolds we give a new perspective on some well known results about the first eigenvalue of the dirac operator and improve the estimates when the dirac bundle has a z 2 grading on riemannian manifolds with cylindrical ends we obtain solvability in the l 2 spaces with suitable exponential weights while allowing mild negativity of the curvature

nonlinear structure analysis of carbon and energy markets with mfdcca based on maximum overlap wavelet transform abstract this paper investigates the nonlinear structure between carbon and energy markets by employing the maximum overlap wavelet transform modwt as well as the multifractal detrended cross correlation analysis based on maximum overlap wavelet transform mfdcca modwt based on the modwt multiresolution analysis and the statistic q c c m significance relatively significant cross correlations are obtained between carbon and energy future markets either on different time scales or on the whole the result of the granger causality test indicates bidirectional granger causality between carbon and electricity future markets although the granger causality relationship between the carbon and oil price is not evident the existence of multifractality for the returns between carbon and energy markets is proven with the mfdcca modwt algorithm in addition results of investigating the origin of multifractality demonstrate that both long range correlations and fat tailed distributions play important roles in the contributions of multifractality

l p theory of the navier stokes flow in the exterior of a moving or rotating obstacle in this paper we describe two recent approaches for the lp theory of the navier stokes flow in the exterior of a moving or rotating obstacle

comparative analysis of grey detrended fluctuation analysis methods based on empirical research on china s interest rate market abstract this study empirically compares the development of china s interest rate market in the past decade the yield of shibor market from 2006 to 2016 showed anti persistence and the later five year trend was stronger than that in the previous half period indicating a significantly growing trend of china s interest rate market we perform a comparative analysis of detrended fluctuation analysis dfa detrending moving average dma algorithm and the maximum overlap wavelet transform dfa modwt using grey and original sequences the autoregressive integrated moving average model is adopted to generate set point h sequences results illustrated that 1 for original sequences both the dfa modwt and dma 0 5 shows outstanding performances when the set hurst exponents are 0 6 and 0 7 and 0 8 and 0 9 respectively 2 for grey sequences g dfa performs best among the three methods followed by g dma and g dfa modwt 3 the long range correlation of the original sequences is slightly lower than the set values on the contrary the long range correlation of grey sequences is much higher than the set values thus the grey sequence exerts a strong aggregation effect as it can accumulate the trend of the sequence our results show that the grey sequence can determine the regular pattern from the messy sequence however grey sequences tend to be overly analyzed and misleading when large volumes of data are involved empirical studies confirm that china s interest rate market remains an inefficient market

the informativeness of options trading activities non linear analysis based on mf dcca and granger test abstract using both put call ratio p c and option to stock volume ratio o s as measures of options trading activities this paper investigates the information content of sse 50 etf options we begin by using detrended fluctuation analysis mf dfa method to examine the multifractal properties of p c ratio change series o s ratio change series and etf returns and find that these time series exhibit strong multifractality moreover employing multifractal detrended cross correlation analysis mf dcca we show that there exists strong anti persistent cross correlation between p c ratios and 50 etf returns but no significant cross correlation between o s ratios and 50 etf returns suggesting that p c ratio is more pronounced detecting the information content of options furthermore we use nonlinear granger causality test and show that the granger causality relationships between p c ratio and 50 etf return series is more significant and stronger than that between o s ratio and 50 etf return series our findings imply that p c ratio can better capture the informativeness of options

lp lq estimate of the stokes operator and navier stokes flows in the exterior of a rotating obstacle we consider the motion of a viscous fluid filling the whole three dimensional space exterior to a rotating obstacle with constant angular velocity we develop the l p l q estimates and the similar estimates in the lorentz spaces of the stokes semigroup with rotation effect we next apply them to the navier stokes equation to prove the global existence of a unique solution which goes to a stationary flow as t with some definite rates when both the stationary flow and the initial disturbance are sufficiently small in l3 weak l3 space

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

a c 2 smooth counterexample to the hamiltonian seifert conjecture in r 4 we construct a proper c 2 smooth function on r 4 such that its hamiltonian flow has no periodic orbits on at least one regular level set this result can be viewed as a c 2 smooth counterexample to the hamiltonian seifert conjecture in dimension four

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

the oseen navier stokes flow in the exterior of a rotating obstacle the non autonomous case consider the navier stokes flow past a rotating obstacle with a general time dependent angular velocity and a time dependent outflow condition at infinity sometimes called an oseen condition by a suitable change of coordinates the problem is transformed to an non autonomous problem with unbounded drift terms on a fixed exterior domain r d it is shown that the solution to the linearized problem is governed by a strongly continuous evolution system ft t s gts 0 on l p for 1 p 1 moreover l p l q smoothing properties and gradient estimates of t t s 0 st are obtained these results are the key ingredients to show local in time existence of mild solutions to the full nonlinear problem for pd and initial value in l p

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

price volume multifractal analysis and its application in chinese stock markets abstract an empirical research on chinese stock markets is conducted using statistical tools first the multifractality of stock price return series r i r i ln p t 1 ln p t and trading volume variation series v i v i ln v t 1 ln v t is confirmed using multifractal detrended fluctuation analysis furthermore a multifractal detrended cross correlation analysis between stock price return and trading volume variation in chinese stock markets is also conducted it is shown that the cross relationship between them is also found to be multifractal second the cross correlation between stock price p i and trading volume v i is empirically studied using cross correlation function and detrended cross correlation analysis it is found that both shanghai stock market and shenzhen stock market show pronounced long range cross correlations between stock price and trading volume third a composite index r based on price and trading volume is introduced compared with stock price return series r i and trading volume variation series v i r variation series not only remain the characteristics of original series but also demonstrate the relative correlation between stock price and trading volume finally we analyze the multifractal characteristics of r variation series before and after three financial events in china namely price limits reform of non tradable shares and financial crisis in 2008 in the whole period of sample to study the changes of stock market fluctuation and financial risk it is found that the empirical results verified the validity of r

multifractality attributed to dual central limit like convergence effects abstract multifractals can be defined as fractal systems that express a range of fractal dimensions the origins of multifractality in time series data have conventionally been attributed to fat tailed probability distributions and to long range correlations multifractal sequences can be generated from the eigenvalue deviations of the gaussian unitary and orthogonal ensembles of random matrix theory these deviations can be resolved into component monofractal sequences governed by the tweedie compound poisson distribution a statistical model that expresses a variance to mean power law related to long range correlations fully multifractal descriptions of these deviations can be constructed provided that the parameter of the compound poisson model related to fractal dimension varies in accordance with an asymmetric laplace distribution both the tweedie compound poisson distribution and the asymmetric laplace distribution serve as foci of convergence in limit theorems on independent and identically distributed random variables the hypothesis that multifractal sequences can be attributed to mathematical convergence effects that have as their focus these two statistical models is proposed

decay estimates of gradient of a generalized oseen evolution operator arising from time dependent rigid motions in exterior domains let us consider the motion of a viscous incompressible fluid past a rotating rigid body in three dimensions where the translational and angular velocities of the body are prescribed but time dependent in a reference frame attached to the body we have the navier stokes system with the drift and one half of the coriolis terms in a fixed exterior domain the existence of the evolution operator t t s in the space l q generated by the linearized non autonomous system was proved by hansel and rhandi j reine angew math 694 1 26 2014 and the large time behavior of t t s f in l r for t s rightarrow infty was then developed by hishida math ann 372 915 949 2018 when f is taken from l q with q leqq r the contribution of the present paper concerns such l q l r decay estimates of nabla t t s with optimal rates which must be useful for the study of stability attainability of the navier stokes flow in several physically relevant situations our main theorem completely recovers the l q l r estimates for the autonomous case stokes and oseen semigroups those semigroups with rotating effect in three dimensional exterior domains which were established by hishida and shibata arch ration mech anal 193 339 421 2009 iwashita math ann 285 265 288 1989 kobayashi and shibata math ann 310 1 45 1998 maremonti and solonnikov ann sc norm super pisa 24 395 449 1997 and shibata in amann arendt hieber neubrander nicaise von below eds functional analysis and evolution equations the gunter lumer volume birkhauser basel pp 595 611 2008

strong solutions to the navier stokes equations around a rotating obstacle we study the existence of strong solutions to the three dimensional navier stokes initial boundary value problem in the domain exterior to a rigid body that rotates with constant angular velocity we show that when the initial data u0 are prescribed in an appropriate functional class a strong solution exists at least in some finite time interval moreover the solution exists for all times provided u0 in suitable norm and the magnitude of do not exceed a certain constant depending only on the kinematic viscosity and on the regularity of in this latter case we also show that the velocity field converges to the velocity field of the corresponding steady state solution

l q l r estimates for solutions of the nonstationary stokes equations in an exterior domain and the navier stokes initial value problems inl q spaces

detrended fluctuation analysis on spot and futures markets of west texas intermediate crude oil abstract in this paper we study the auto correlations and cross correlations of west texas intermediate wti crude oil spot and futures return series employing detrended fluctuation analysis dfa and detrended cross correlation analysis dcca scaling analysis shows that for time scales smaller than a month the auto correlations and cross correlations are persistent for time scales larger than a month but smaller than a year the correlations are anti persistent while for time scales larger than a year the series are neither auto correlated nor cross correlated indicating the efficient operation of the crude oil markets moreover for small time scales the degree of short term cross correlations is higher than that of auto correlations using the multifractal extension of dfa and dcca we find that for small time scales the correlations are strongly multifractal while for large time scales the correlations are nearly monofractal analyzing the multifractality of shuffled and surrogated series we find that both long range correlations and fat tail distributions make important contributions to the multifractality our results have important implications for market efficiency and asset pricing models

the homotopy lie algebra of symplectomorphism groups of 3 fold blow ups of the projective plane by a result of kedra and pinsonnault we know that the topology of groups of symplectomorphisms of symplectic 4 manifolds is complicated in general however in all known very specific examples the rational cohomology rings of symplectomorphism groups are finitely generated in this paper we compute the rational homotopy lie algebra of symplectomorphism groups of the 3 point blow up of the projective plane with an arbitrary symplectic form and show that in some cases depending on the sizes of the blow ups it is infinite dimensional moreover we explain how the topology is generated by the toric structures one can put on the manifold our method involve the study of the space of almost complex structures compatible with the symplectic structure and it depends on the inflation technique of lalonde mcduff

existence and classification of overtwisted contact structures in all dimensions we establish a parametric extension h principle for overtwisted contact structures on manifolds of all dimensions which is the direct generalization of the 3 dimensional result from 12 it implies in particular that any closed manifold admits a contact structure in any given homotopy class of almost contact structures

topology of symplectomorphism groups of s 2 s 2 in dimension 4 due to non existence of adequate tools very little is known about the topology of groups of diffeomorphisms for example it is unknown if the group of compactly supported diffeomorphisms of r is connected the situation is much better if one wants to study groups of symplectomorphisms this is due to the existence of powerful tools going by the name of pseudo holomorphic curve techniques and introduced in symplectic geometry by m gromov in his seminal paper of 1985 5 gromov proved in that paper among several other remarkable results the contractibility of the group of compactly supported symplectomorphisms of r with its standard symplectic form dx dy dx dy gromov also studied the following example letm be the symplectic manifold s s 1 0 0 where 0 r and 0 is a standard area form on s with total area equal to 1 denote by g the group of symplectomorphisms of m that act as the identity on h2 s s z gromov proved in 5 that g0 is homotopy equivalent to its subgroup of standard isometries so 3 so 3 he also showed why that would not be true for g with 0 and in 1987 d mcduff 10 constructed explicitly an element of infinite order in h1 g 0 in this paper we will give a more detailed description of g for 0 1 in particular we will prove the following on leave from instituto superior tecnico lisbon portugal partially supported by jnict programas ciencia and praxis fundacao luso americana para o desenvolvimento and a sloan doctoral dissertation fellowship current address school of mathematics institute for advanced study princeton nj 08540 usa e mail abreu math ias edu

the topology of the space of symplectic balls in rational 4 manifolds we study in this paper the rational homotopy type of the space of symplectic embeddings of the standard ball b4 c r4 into 4 dimensional rational symplectic manifolds where c r2 is the capacity of the standard ball of radius r we compute the rational homotopy groups of that space when the 4 manifold has the form m s2 s2 0 0 where 0 is the area form on the sphere with total area 1 and belongs to the interval 1 2 we show that when is 1 this space retracts to the space of symplectic frames for any value of c however for any given 1 2 the rational homotopy type of that space changes as c crosses the critical parameter 1 which is the difference of areas between the two s2 factors we prove moreover that the full homotopy type of that space changes only at that value that is that the restriction map between these spaces is a homotopy equivalence as long as these values of c remain either below or above that critical value the same methods apply to all other values of and other rational 4 manifolds as well the methods rely on two different tools the study of the action of symplectic groups on the stratified space of almost complex structures developed by gromov abreu and mcduff and the analysis of the relations between the group corresponding to a manifold m the group corresponding to its blow up m and the space of symplectic embedded balls in m

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

the navier stokes equations in the weak l n space with time dependent external force abstract we consider the navier stokes equations with time dependent external force either in the whole time or in positive time with initial data with domain either the whole space the half space or an exterior domain of dimension n ge 3 we give conditions on the external force sufficient for the unique existence of small solutions in the weak l n space bounded for all time in particular this result gives sufficient conditions for the unique existence and the stability of small time periodic solutions or almost periodic solutions this result generalizes the previous result on the unique existence and the stability of small stationary solutions in the weak l n space with time independent external force

examples of symplectic structures in this paper we construct symplectic forms tilde omega k k geqq 0 on a compact manifold tilde y which have the same homotopy theoretic invariants but which are not diffeomorphic

periodic fourth order cubic nls local well posedness and non squeezing property abstract in this paper we consider the cubic fourth order nonlinear schrodinger equation 4nls under the periodic boundary condition we prove two results one is the local well posedness in h s t with 1 3 s 0 for the cauchy problem of the wick ordered 4nls the other one is the non squeezing property for the flow map of 4nls in the symplectic phase space l 2 t to prove the former we used the ideas introduced in 36 and 27 and to prove the latter we used the ideas in 8

an existence theorem for the navier stokes flow in the exterior of a rotating obstacle we consider the three dimensional navier stokes initial value problem in the exterior of a rotating obstacle it is proved that a unique solution exists locally in time if the initial velocity possesses the regularity l 1 2 this regularity assumption is the same as that in the famous paper of fujita kato an essential step for the proof is the deduction of a certain smoothing property together with estimates near t 0 of the semigroup which is not an analytic one generated by the operator in the space l 2 where stands for the angular velocity of the rotating obstacle and p denotes the projection associated with the helmholtz decomposition

a relative seidel morphism and the albers map in this note we introduce a relative or lagrangian version of the seidel homomorphism that assigns to each homotopy class of paths in ham m starting at the identity and ending on the subgroup that preserves a given lagrangian submanifold l an element in the floer homology of l we show that these elements are related to the absolute seidel elements by the albers map we also study for later use the effect of reversing the signs of the symplectic structure as well as the orientations of the generators and of the operations on the floer homologies

hamiltonian collapsing of irrational lagrangian submanifolds with small first betti number among the main symplectic invariants of a closed lagrange submanifoldl of the cotangent of n is the tubular radiusr l defined as the smallest tube d r n 1 of n t n in whichl can be pushed by an hamiltonian diffeotopy of n we show here using pseudo holomorphic techniques that such a submanifold cannot collapse if the first betti number ofl is smaller than 3 and if the maslov class ofl does not vanish in other words r l is then strictly positive and one can actually give an explicit lower bound in terms of the liouville and maslov classes ofl