classification of rotational special weingarten surfaces of minimal type in mathbb s 2 times mathbb r and mathbb h 2 times mathbb r in this paper we classify the complete rotational special weingarten surfaces in mathbb s 2 times mathbb r and mathbb h 2 times mathbb r i e rotational surfaces in mathbb s 2 times mathbb r and mathbb h 2 times mathbb r whose mean curvature h and extrinsic curvature ke satisfy h f h2 ke for some function f in mathcal c 1 0 infty such that f 0 0 and 4x f x 2 1 for any x 0 furthermore we show the existence of non complete examples of such surfaces

multifractal properties of the indian financial market abstract we investigate the multifractal properties of the logarithmic returns of the indian financial indices bse nse by applying the multifractal detrended fluctuation analysis the results are compared with that of the us s p 500 index numerically we find that q th order generalized hurst exponents h q and q change with the moments q the nonlinear dependence of these scaling exponents and the singularity spectrum f show that the returns possess multifractality by comparing the mf dfa results of the original series to those for the shuffled series we find that the multifractality is due to the contributions of long range correlations as well as the broad probability density function the financial markets studied here are compared with the binomial multifractal model bmfm and have a smaller multifractal strength than the bmfm

multifractal property of chinese stock market in the csi 800 index based on mf dfa approach abstract csi 800 index consists of csi 500 index and csi 300 index aiming to reflect the performance of stocks with large mid and small size of china a share market in this paper we analyze the multifractal structure of chinese stock market in the csi 800 index based on the multifractal detrended fluctuation analysis mf dfa method we find that the fluctuation of the closing logarithmic returns have multifractal properties the shape and width of multifractal spectrum are depended on the weighing order q more interestingly we observe a bigger market crash in june august 2015 than the one in 2008 based on the local hurst exponents the result provides important information for further study on dynamic mechanism of return fluctuation and whether it would trigger a new financial crisis

on the topology and index of minimal surfaces we show that for an immersed two sided minimal surface in r 3 there is a lower bound on the index depending on the genus and number of ends using this we show the nonexistence of an embedded minimal surface in r 3 of index 2 as conjectured by choe cho90 moreover we show that the index of an immersed two sided minimal surface with embedded ends is bounded from above and below by a linear function of the total curvature of the surface

the topology and geometry of embedded surfaces of constant mean curvature where ai p and a2 p are the principal curvatures of m at p when h is constant m is called a surface of constant mean curvature a surface is said to have finite type if it is homeomorphic to a closed surface with a finite number of points removed an important problem in classical differential geometry is the classification of properly embedded finite type surfaces m of constant mean curvature in r if m is a closed embedded surface of constant mean curvature then it follows from alexandrov 1 that m must be a round sphere the classical examples of properly embedded surfaces with zero mean curvature are the plane the helicoid and the catenoid surfaces of zero mean curvature are usually called minimal surfaces the remaining classical examples of properly embedded surfaces of constant mean curvature were found by delaunay 4 the delaunay surfaces are surfaces of revolution recently hoffman and meeks 6 7 have found examples of properly embedded minimal surfaces which are homeomorphic to closed surfaces of positive genus with 3 points removed callahan hoffman and meeks 3 have found other examples with more ends an annular end e of properly embedded surface in r 3 is a properly embedded annulus e in m where e is homeomorphic to s x 0 1 when m has finite type then every end of m is annular hoffman and meeks have developed a theory to deal with global problems concerning the geometry of properly embedded minimal surfaces m and in particular they show that most annular ends of m converge at infinity in r to a flat plane or to the end of a catenoid recently n kapouleas 8 in his thesis has shown that for every positive integer k 2 there exists a properly embedded surface m of finite type with nonzero mean curvature and with k ends he also has constructed highergenus examples as in the case of minimal surfaces the annular ends of a properly embedded surface of nonzero constant mean curvature have a special geometry and play an important role in global theorems

embedded minimal surfaces with an infinite number of ends we prove the existence of an infinite family of periodic properly embedded minimal surfaces with an infinite number of annular ends 25 refs 29 figs

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

multifractal detrended cross correlation analysis of carbon and crude oil markets abstract the complex dynamics between carbon and crude oil markets have been an increasingly interesting area of research in this paper we try to take a fresh look at the cross correlations between carbon and crude oil markets as well as their dynamic behavior employing multifractal detrended cross correlation analysis first we find that the return series of carbon and crude oil markets are significantly cross correlated second we confirm the existence of multifractality for the return series of carbon and crude oil markets by the multifractal detrended fluctuation analysis third based on the multifractal detrended cross correlation analysis we find the existence of power law cross correlations between carbon and crude oil markets the cross correlated behavior of small fluctuations is found to be more persistent than that of large fluctuations at last some relevant discussions and implications of the empirical results are presented

ill posed problems with unbounded operators abstract let a be a linear closed densely defined unbounded operator in a hilbert space assume that a is not boundedly invertible if eq 1 a u f is solvable and f f then the following results are provided problem f u a u f 2 u 2 has a unique global minimizer u for any f u a a a i 1 f there is a function lim 0 0 such that lim 0 u y 0 where y is the unique minimal norm solution to 1 a priori and a posteriori choices of are given dynamical systems method dsm is justified for eq 1

index one minimal surfaces in spherical space forms abstract we prove that orientable index one minimal surfaces in spherical space forms with large fundamental group have genus at most two this confirms a conjecture of r schoen for an infinite class of 3 manifolds

on the growth of supersolutions of nonlinear pde s on exterior domains abstract we obtain a comparison principle on annuli with catenoid like functions for supersolutions of non linear elliptic pdes over exterior domains in a non positively curved manifold with a pole this result is applied to get an upper estimate on the growth of such supersolutions and in particular of exterior graphs of non negative mean curvature

research on the relationship between the multifractality and long memory of realized volatility in the sseci abstract we examine the multifractal properties of the realized volatility rv and realized bipower variation rbv series in the shanghai stock exchange composite index sseci by using the multifractal detrended fluctuation analysis mf dfa method we find that there exist distinct multifractal characteristics in the volatility series the contributions of two different types of source of multifractality namely fat tailed probability distributions and nonlinear temporal correlations are studied by using the unit root test we also find the strength of the multifractality of the volatility time series is insensitive to the sampling frequency but that the long memory of these series is sensitive

the calabi yau conjectures for embedded surfaces in this talk i will discuss the proof of the calabi yau conjectures for embedded surfaces this is joint work with bill minicozzi cm9 the calabi yau conjectures about surfaces date back to the 1960s much work has been done on them over the past four decades in particular examples of jorge xavier from 1980 and nadirashvili from 1996 showed that the immersed versions were false we will show here that for embedded surfaces i e injective immersions they are in fact true their original form was given in 1965 in ca where e calabi made the following two conjectures about minimal surfaces see also s s chern page 212 of ch conjecture 1 prove that a complete minimal hypersurface in r must be unbounded calabi continued it is known that there are no compact minimal submanifolds of r or of any simply connected complete riemannian manifold with sectional curvature 0 a more ambitious conjecture is conjecture 2 a complete minimal hypersurface in r has an unbounded projection in every n 2 dimensional flat subspace

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

the spaces of index one minimal surfaces and stable constant mean curvature surfaces embedded in flat three manifolds it is proved that the spaces of index one minimal surfaces and stable constant mean curvature surfaces with genus greater than one in non fixed flat three manifolds are compact in a strong sense given a sequence of any of the above surfaces we can extract a convergent subsequence of both the surfaces and the ambient manifolds in the ck topology these limits preserve the topological type of the surfaces and the affine diffeomorphism class of the ambient manifolds some applications to the isoperimetric problem are given

the space of embedded minimal surfaces of fixed genus in a 3 manifold v fixed genus this paper is the fifth and final in a series on embedded minimal surfaces following our earlier papers on disks we prove here two main structure theorems for itnonsimply connected embedded minimal surfaces of any given fixed genus the first of these asserts that any such surface without small necks can be obtained by gluing together two oppositely oriented double spiral staircases the second gives a pair of pants decomposition of any such surface when there are small necks cutting the surface along a collection of short curves after the cutting we are left with graphical pieces that are defined over a disk with either one or two sub disks removed a topological disk with two sub disks removed is called a pair of pants both of these structures occur as different extremes in the two parameter family of minimal surfaces known as the riemann examples

constant mean curvature graphs on exterior domains of the hyperbolic plane we prove an existence result for non rotational constant mean curvature ends in mathbb h 2 times mathbb r where mathbb h 2 is the hyperbolic real plane the value of the curvature is h in big 0 frac 1 2 big we use schauder theory and a continuity method for solutions of the prescribed mean curvature equation on exterior domains of mathbb h 2 we also prove a fine property of the asymptotic behavior of the rotational ends introduced by sa earp and toubiana

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

groetsch s representation of moore penrose inverses and ill posed problems in hilbert c modules abstract the explicit representation lim 0 1 t t 1 t for the moore penrose inverse of an operator t between hilbert spaces has been given by c w groetsch 1975 6 we obtain his formula for the moore penrose inverse of an unbounded operator between hilbert c modules ill posed problems with unbounded operator between hilbert c modules are also discussed

complete embedded minimal surfaces of finite total curvature we will survey what is known about minimal surfaces s r 3 which are complete embedded and have finite total curvature int s k da infty the only classically known examples of such surfaces were the plane and the catenoid the discovery by costa 14 15 early in the last decade of a new example that proved to be embedded sparked a great deal of research in this area many new examples have been found even families of them as will be described below the central question has been transformed from whether or not there are any examples except surfaces of rotation to one of understanding the structure of the space of examples

modified detrended fluctuation analysis based on empirical mode decomposition for the characterization of anti persistent processes abstract detrended fluctuation analysis dfa is a simple but very efficient method for investigating the power law long term correlations of non stationary time series in which a detrending step is necessary to obtain the local fluctuations at different timescales we propose to determine the local trends through empirical mode decomposition emd and perform the detrending operation by removing the emd based local trends which gives an emd based dfa method similarly we also propose a modified multifractal dfa algorithm called an emd based mfdfa the performance of the emd based dfa and mfdfa methods is assessed with extensive numerical experiments based on fractional brownian motion and multiplicative cascading process we find that the emd based dfa method performs better than the classic dfa method in the determination of the hurst index when the time series is strongly anticorrelated and the emd based mfdfa method outperforms the traditional mfdfa method when the moment order q of the detrended fluctuations is positive we apply the emd based mfdfa to the 1 min data of shanghai stock exchange composite index and the presence of multifractality is confirmed we also analyze the daily austrian electricity prices and confirm its anti persistence

the effects of common risk factors on stock returns a detrended cross correlation analysis abstract in this paper we investigate the cross correlations between fama and french three factors and the return of american industries on the basis of cross correlation statistic test and multifractal detrended cross correlation analysis mf dcca qualitatively we find that the return series of fama and french three factors and american industries were overall significantly cross correlated based on the analysis of a statistic quantitatively we find that the cross correlations between three factors and the return of american industries were strongly multifractal and applying mf dcca we also investigate the cross correlation of industry returns and residuals we find that there exists multifractality of industry returns and residuals the result of correlation coefficients we can verify that there exist other factors which influence the industry returns except fama three factors

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

unbounded elements affiliated with c algebras and non compact quantum groups the affiliation relation that allows to include unbounded elements operators into thec algebra framework is introduced investigated and applied to the quantum group theory the quantum deformation of the two fold covering of the group of motions of euclidean plane is constructed a remarkable radius quantization is discovered it is also shown that the quantumsu 1 1 group does not exist on thec algebra level for real value of the deformation parameter

stationary isothermic surfaces and uniformly dense domains we establish a relationship between stationary isothermic surfaces and uniformly dense domains a stationary isothermic surface is a level surface of temperature which does not evolve with time a domain in the n dimensional euclidean space r n is said to be uniformly dense in a surface r n of codimension 1 if for every small r 0 the volume of the intersection of with a ball of radius r and center x does not depend on x for x we prove that the boundary of every uniformly dense domain which is bounded or whose complement is bounded must be a sphere we then examine a uniformly dense domain with unbounded boundary and we show that the principal curvatures of satisfy certain identities the case in which the surface coincides with is particularly interesting in fact we show that if the boundary of a uniformly dense domain is connected then i if n 2 it must be either a circle or a straight line and ii if n 3 it must be either a sphere a spherical cylinder or a minimal surface we conclude with a discussion on uniformly dense domains whose boundary is a minimal surface

predictability of multifractal analysis of hang seng stock index in hong kong in this paper the daily hang seng index in hong kong stock market is studied by multifractal analysis the main parameter of multifractal spectra used is f which can be used to characterize the ratio of number of highest index moments to that of lowest ones the dependence of today s gain probability g and the day s index increase probability n with f of the previous 3 days are studied it is found that g and n can reach 70 80 at the large positive f region and can be very close to 20 at the big negative f region the predictability decreases with the increasing number of the previous days

ep modular operators and their products abstract we study first ep modular operators on hilbert c modules and then we provide necessary and sufficient conditions for the product of two ep modular operators to be ep these enable us to extend some results of koliha 2000 13 for an arbitrary c algebra and the c algebras of compact operators

inhomogeneous scaling behaviors in malaysian foreign currency exchange rates in this paper we investigate the fractal scaling behaviors of foreign currency exchange rates with respect to malaysian currency ringgit malaysia these time series are examined piecewise before and after the currency control imposed in 1st september 1998 using the monofractal model based on fractional brownian motion the global hurst exponents are determined using the r s analysis the detrended fluctuation analysis and the method of second moment using the correlation coefficients the limitation of these monofractal analyses is discussed the usual multifractal analysis reveals that there exists a wide range of hurst exponents in each of the time series a new method of modelling the multifractal time series based on multifractional brownian motion with time varying hurst exponents is studied

an embedded genus one helicoid there exists a properly embedded minimal surface of genus one with a single end asymptotic to the end of the helicoid this genus one helicoid is constructed as the limit of a continuous one parameter family of screw motion invariant minimal surfaces also asymptotic to the helicoid that have genus equal to one in the quotient

multifractal analysis of hang seng index in hong kong stock market abstract in this paper the daily hang seng index in hong kong stock market is analyzed by multifractal the correlation of the parameters of the multifractal spectra with the variation of close return z is studied statistically it is found that the amount of the variation of return is correlated with the amount of of that day the increase or decrease of the return is related to the positive or negative value of f the gain probability and the increasing day s probability can be higher than 70 at the larger f region and be lower than 20 at the more negative region

power law and multiscaling properties of the chinese stock market abstract we investigate the cumulative probability density function pdf and the multiscaling properties of the returns in the chinese stock market by using returns data adjusted for thin trading we find that the distribution has power law tails at shorter microscopic timescales or lags however the distribution follows an exponential law for longer timescales furthermore we investigate the long range correlation and multifractality of the returns in the chinese stock market by the dfa and mfdfa methods we find that all the scaling exponents are between 0 5 and 1 by dfa method which exhibits the long range power law correlations in the chinese stock market moreover we find by mfdfa method that the generalized hurst exponents h q are not constants which shows the multifractality in the chinese stock market we also find that the correlation of shenzhen stock market is stronger than that of shanghai stock market

the classical theory of minimal surfaces we present here a survey of recent spectacular successes in classical minimal surface theory we highlight this article with the theorem that the plane the helicoid the catenoid and the one parameter family frtgt2 0 1 of riemann minimal examples are the only complete properly embedded minimal planar domains in r 3 the proof of this result depends primarily on work of colding

the product of operators with closed range in hilbert c modules abstract suppose t and s are bounded adjointable operators with close range between hilbert c modules then ts has closed range if and only if ker t ran s is an orthogonal summand if and only if ker s ran t is an orthogonal summand moreover if the dixmier or minimal angle between ran s and ker t ker t ran s is positive and ker s ran t is an orthogonal summand then ts has closed range

forecasting volatility in shanghai and shenzhen markets based on multifractal analysis abstract this paper analyzes the multifractality in shanghai and shenzhen stock markets using multifractal spectrum analysis and multifractal detrended fluctuation analysis we find that the main source of multifractality is long range correlations of large and small fluctuations then we introduce a multifractal volatility measure mv and find that by taking mv as daily conditional volatility the simulated series displayed similar stylized facts to the original daily return series by capturing the dynamics of mv using the arfima model we find that the out of sample forecasting performance of the arfima mv model is better than some garch class models and the arfima rv model under some criteria of loss function

minimal hypersurfaces with bounded index we prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index and volume if the ambient dimension is greater than three in a riemannian manifold m n g 3 le n le 7 can degenerate loosely speaking our results show that embedded minimal hypersurfaces with bounded index behave qualitatively like embedded stable minimal hypersurfaces up to controlled errors several compactness finiteness theorems follow from our local picture

entire solutions of the allen cahn equation and complete embedded minimal surfaces of finite total curvature in r 3 we consider minimal surfaces m which are complete embedded and have finite total curvature in mathbb r 3 and bounded entire solutions with finite morse index of the allen cahn equation delta u f u 0 in mathbb r 3 here f w with w bi stable and balanced for instance w u frac 1 4 1 u 2 2 we assume that m has m ge 2 ends and additionally that m is non degenerate in the sense that its bounded jacobi fields are all originated from rigid motions this is known for instance for a catenoid and for the costa hoffman meeks surface of any genus we prove that for any small alpha gt 0 the allen cahn equation has a family of bounded solutions depending on m 1 parameters distinct from rigid motions whose level sets are embedded surfaces lying close to the blown up surface m alpha alpha 1 m with ends possibly diverging logarithmically from m alpha we prove that these solutions are l infty non degenerate up to rigid motions and find that their morse index coincides with the index of the minimal surface our construction suggests parallels of de giorgi conjecture for general bounded solutions of finite morse index

triply periodic constant mean curvature surfaces abstract given a closed flat 3 torus n for each h 0 and each non negative integer g we obtain area estimates for closed surfaces with genus g and constant mean curvature h embedded in n this result contrasts with the theorem of traizet 31 who proved that every flat 3 torus admits for every positive integer g with g 2 connected closed embedded minimal surfaces of genus g with arbitrarily large area

the asymptotic behavior of properly embedded minimal surfaces of finite topology while advances have been made in recent years in the study of properly embedded minimal surfaces of finite topology in r3 3 5 8 9 11 12 13 23 progress has depended in an essential manner on the special structure of such surfaces with finite total curvature a properly immersed minimal surface with finite total curvature is conformally a compact riemann surface punctured in a finite number of points and its gauss map extends to the compact surface as a meromorphic function 22 in particular all the topological ends are conformally equivalent to a punctured disk and there is a well defined limit tangent plane at each end outside of a sufficiently large compact set such an end is a multisheeted graph over the limit tangent plane and if the end is embedded it is asymptotic to either a plane or a half catenoid see e g schoen 24 for a survey of results on properly immersed surfaces of finite total curvature see 9 1 without the assumption of finite total curvature these results are not true in general as an indication of the relative lack of information consider that it is unknown whether or not the helicoid is the only simply connected minimal surface that is properly embedded and nonplanar a question raised by osserman the helicoid has infinite total curvature and a single annular end if a surface has finite topology then all of its ends are annular any general theory of properly embedded minimal surfaces of finite topology must include an understanding of the behavior of these ends in this paper we prove

efficiency and multifractality analysis of csi 300 based on multifractal detrending moving average algorithm abstract we apply the multifractal detrending moving average mfdma to investigate and compare the efficiency and multifractality of 5 min high frequency china securities index 300 csi 300 the results show that the csi 300 market becomes closer to weak form efficiency after the introduction of csi 300 future we find that the csi 300 is featured by multifractality and there are less complexity and risk after the csi 300 index future was introduced with the shuffling surrogating and removing extreme values procedures we unveil that extreme events and fat distribution are the main origin of multifractality besides we discuss the knotting phenomena in multifractality and find that the scaling range and the irregular fluctuations for large scales in the f q s vs s plot can cause a knot

multifractal detrended fluctuation analysis of sheep livestock prices in origin abstract the multifractal detrended fluctuation analysis mf dfa is used to verify whether or not the returns of time series of prices paid to farmers in original markets can be described by the multifractal approach by way of example 5 weekly time series of prices of different breeds slaughter weight and market differentiation from 2000 to 2012 are analyzed results obtained from the multifractal parameters and multifractal spectra show that the price series of livestock products are of a multifractal nature the hurst exponent shows that these time series are stationary signals some of which exhibit long memory merino milk fed in seville and segurena paschal in jaen short memory merino paschal in cordoba and segurena milk fed in jaen or even are close to an uncorrelated signals merino paschal in seville mf dfa is able to discern the different underlying dynamics that play an important role in different types of sheep livestock markets such as degree and source of multifractality in addition the main source of multifractality of these time series is due to the broadness of the probability function instead of the long range correlation properties between small and large fluctuations which play a clearly secondary role

a schoen theorem for minimal surfaces in h 2 r abstract in this paper we prove that a complete minimal surface immersed in h 2 r with finite total curvature and two ends each one asymptotic to a vertical geodesic plane must be a horizontal catenoid moreover we give a geometric description of minimal ends of finite total curvature in h 2 r we also prove that a minimal complete end e with finite total curvature is properly immersed and that the gaussian curvature of e is locally bounded in terms of the geodesic distance to its boundary

positive semi definite matrices of adjointable operators on hilbert c modules abstract let a be a c algebra h k be two hilbert a modules and b be an adjointable operator from h to k in this paper we prove that the moore penrose inverse of b exists if and only if b has closed range in addition some known results about the moore penrose inverses acting on hilbert spaces as well as in c algebras are extended in the context of hilbert c modules as an application a characterization of positive semi definite matrices of adjointable operators with respect to an orthogonal pair of a hilbert c module is given

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

scaling in the norwegian stock market the main objective of this paper is to investigate the validity of the much used assumptions that stock market returns follow a random walk and are normally distributed for this purpose the concepts of chaos theory and fractals are applied two independent models are used to examine price variations in the norwegian and us stock markets the first model used is the range over standard deviation or r s statistic which tests for persistence or antipersistence in the time series both the norwegian and us stock markets show significant persistence caused by long run memory components in the series in addition an average non periodic cycle of four years is found for the us stock market these results are not consistent with the random walk assumption the second model investigates the distributional scaling behaviour of the high frequency price variations in the norwegian stock market the results show a remarkable constant scaling behaviour between different time intervals this means that there is no intrinsic time scale for the dynamics of stock price variations the relationship can be expressed through a scaling exponent describing the development of the distributions as the time scale changes this description may be important when constructing or improving pricing models such that they coincide more closely with the observed market behaviour the empirical distributions of high frequency price variations for the norwegian stock market is then compared to the levy stable distribution with the relevant scaling exponent found by using the r s and distributional scaling analysis good agreement is found between the levy profile and the empirical distribution for price variations less than 6 standard deviations covering almost three orders of magnitude in the data for probabilities larger than 6 standard deviations there seem to be an exponential fall off from the levy profile in the tails which indicates that the second moment may be finite

long range correlation and predictability of chinese stock prices abstract it is well known that the price time series of an efficient market display a brownian motion in such a case the best prediction of a future price is the last known price thus no arbitrage is possible a real market is however possibly not perfectly efficient in this paper we apply an error back propagation neural network to tick by tick high frequency time series of chinese a share stock prices and try to predict their future values the performance of the predictions varies largely for different stocks in order to seek for the dependence of the performance we study the long range correlation lrc of the data by the conventional detrended fluctuation analysis dfa and its generalization the multifractal detrended fluctuation analysis mfdfa clear relevance between the performance and the lrc is observed the prediction is particularly good when the time series are strongly anti persistent

some uniqueness and nonexistence theorems for embedded minimal surfaces thanks to the works of callahan costa hoffman karcher meeks rosenberg wei etc see for example 1 2 3 5 8 11 12 16 20 we dispose now of a large number of properly embedded minimal surfaces in the euclidean space ir other than the classical examples all those surfaces can be viewed as minimal surfaces with finite total curvature properly embedded in complete flat three manifolds the most basic invariants associated to a surface of this type are its topology and its periodicity it is an interesting problem to decide if the simplest examples like the catenoid the helicoid the scherk s surfaces or the riemann example can be characterized in terms of some of these invariants in the non periodic case there are two important uniqueness theorems in this direction the first one obtained by schoen 17 characterizes the catenoid as the only complete minimal surface embedded

descriptions of partial isometries on hilbert c modules abstract partial isometries and moore penrose inverses of bounded adjointable operators on hilbert c modules are investigated it is shown that a contraction between hilbert c modules is a partial isometry if and only if it possesses a contractive moore penrose inverse a bounded adjointable operator t is a partial isometry if and only if its bounded transform is 2 1 2 t

the classification of complete minimal surfaces with total curvature greater than 12 we classify complete orientable minimal surfaces with finite total curvature 87r introduction the classification of complete minimal surfaces with finite total curvature in r3 has been an important problem in the classical differential geometry some basic properties of these surfaces were studied by r osserman see 8 9 who showed the first nontrivial result about this subject concretely he characterized the catenoid and enneper surface as the unique complete orientable minimal surfaces of total curvature 47 however until recent years no more relevant results have been obtained w h meeks 6 gave the classification of nonorientable complete minimal surfaces with total curvature greater than 87 this paper is concerned with the total classification of orientable complete minimal surfaces with total curvature 87 chen and gackstatter 1 discovered the first example of a complete minimal surface properly of genus 1 see theorem 1 the picture of chen gackstatter surface is obtained by joining a handle on enneper s surface this genus one minimal surface has total curvature 87 and no other examples of such surfaces were found so it is expected that no other genus one orientable minimal surface of total curvature 87 does exist in this paper we give a proof of this fact more precisely we prove that chen gackstatter surface is the only genus one orientable complete minimal surface with finite total curvature 87 of course it is not difficult to find genus zero minimal surfaces with total curvature 8i a geometrically interesting example described by jorge and meeks 5 is the trinoid this surface has three embedded catenoid ends moreover its normal vectors at these ends are placed symmetrically in an equator of s2 received by the editors april 27 1990 and in revised form july 20 1990 1980 mathematics subject classification 1985 revision primary 53a10 research partially supported by dgicyt grant ps87 01 15 c03 02

supercooperation in evolutionary games on correlated weighted networks in this work we study the behavior of classical two person two strategies evolutionary games on a class of weighted networks derived from barabasi albert and random scale free unweighted graphs using customary imitative dynamics our numerical simulation results show that the presence of link weights that are correlated in a particular manner with the degree of the link end points leads to unprecedented levels of cooperation in the whole games phase space well above those found for the corresponding unweighted complex networks we provide intuitive explanations for this favorable behavior by transforming the weighted networks into unweighted ones with particular topological properties the resulting structures help us to understand why cooperation can thrive and also give ideas as to how such supercooperative networks might be built

multifractal properties of chinese stock market in shanghai abstract in this article we apply three methods of multifractal analysis partition function method singular spectrum method and multifractal detrended fluctuation analysis method to analyze the closing index fluctuations of shanghai stock market during the past seven years we have found that shanghai stock market has weak multifractal features and there are long range power law correlations between index series the shapes of singular spectrums do not change with time scales and their strengths weaken when the scales shorten but when the orders of partition function increase the strengths of multifractal increase the singular spectrums become rougher and the general hurst exponents decrease these results provide solid and important values for further study on the dynamic mechanism of stock market price fluctuation

long range correlations and nonstationarity in the brazilian stock market abstract we report an empirical study of the ibovespa index of the sao paulo stock exchange in which we detect the existence of long range correlations to analyze our data we introduce a rescaled variant of the usual detrended fluctuation analysis that allows us to obtain the hurst exponent through a one parameter fitting we also compute a time dependent hurst exponent h t using 3 year moving time windows in particular we find that before the launch of the collor plan in 1990 the curve h t remains in general well above 1 2 while afterwards it stays close to 1 2 we thus argue that the structural reforms set off by the collor plan has lead to a more efficient stock market in brazil we also suggest that the time dependence of the ibovespa hurst exponent could be described in terms of a multifractional brownian motion

a costa hoffman meeks type surface in mathbb h 2 times mathbb r we show the existence in the space 2 x of a family of embedded minimal surfaces of genus 1 k and finite total extrinsic curvature with two catenoidal type ends and one middle planar end the proof is based on a gluing procedure

the space of complete minimal surfaces with finite total curvature as lagrangian submanifold the space m of nondegenerate properly embedded minimal surfaces in r3 with finite total curvature and fixed topology is an analytic lagrangian submanifold of cn where n is the number of ends of the surface in this paper we give two expressions one integral and the other pointwise for the second fundamental form of this submanifold we also consider the compact boundary case and we show that the space of stable nonflat minimal annuli that bound a fixed convex curve in a horizontal plane having a horizontal end of finite total curvature is a locally convex curve in the plane c mathematics subject classification 53a10 53c42

constant mean curvature surfaces with boundary on a sphere in this article we study the shape of a compact surface of constant mean curvature of euclidean space whose boundary is contained in a round sphere we consider the case that the boundary is prescribed or that the surface meets the sphere with a constant angle we study under what geometric conditions the surface must be spherical our results apply in many scenarios in physics where in absence of gravity a liquid drop is deposited on a round solid ball and the air liquid interface is a critical point for area under all variations that preserve the enclosed volume