on the multifractal nature of fully developed turbulence and chaotic systems it is generally argued that the energy dissipation of three dimensional turbulent flow is concentrated on a set with non integer hausdorff dimension recently in order to explain experimental data it has been proposed that this set does not possess a global dilatation invariance it can be considered to be a multifractal set the authors review the concept of multifractal sets in both turbulent flows and dynamical systems using a generalisation of the beta model

fractional calculus and continuous time finance ii the waiting time distribution we complement the theory of tick by tick dynamics of financial markets based on a continuous time random walk ctrw model recently proposed by scalas et al 4 and we point out its consistency with the behaviour observed in the waiting time distribution for bund future prices traded at liffe london

the disappearance of causality at small scale in almost commutative manifolds this paper continues the investigations of noncommutative ordered spaces put forward by one of the authors these metaphoric spaces are defined dually by the so called isocones which generalize to the noncommutative setting the convex cones of order preserving functions in this paper we will consider the case of isocones inside almost commutative algebras of the form c m af with m a compact metrizable space we will give a family of isocones in such an algebra with the property that every possible isocone is contained in exactly one member of the family we conjecture that this family is in fact a complete classification a hypothesis related with the noncommutative stone weierstrass conjecture we also obtain that every isocone in c m af with af noncommutative induces an order relation on m with the property that every point in m lies in a neighbourhood of incomparable points thus if the causal order relation on spacetime is induced by an isocone in an almost commutative but not commutative alg

optimized schwarz methods without overlap for the helmholtz equation the classical schwarz method is a domain decomposition method to solve elliptic partial differential equations in parallel convergence is achieved through overlap of the subdomains we study in this paper a variant of the schwarz method which converges without overlap for the helmholtz equation we show that the key ingredients for such an algorithm are the transmission conditions we derive optimal transmission conditions which lead to convergence of the algorithm in a finite number of steps these conditions are however nonlocal in nature and we introduce local approximations which we optimize for performance of the schwarz method this leads to an algorithm in the class of optimized schwarz methods we present an asymptotic analysis of the optimized schwarz method for two types of transmission conditions robin conditions and transmission conditions with second order tangential derivatives numerical results illustrate the effectiveness of the optimized schwarz method on a model problem and on a problem from industry

fractional calculus and continuous time finance in this paper we present a rather general phenomenological theory of tick by tick dynamics in financial markets many well known aspects such as the levy scaling form follow as particular cases of the theory the theory fully takes into account the non markovian and non local character of financial time series predictions on the long time behaviour of the waiting time probability density are presented finally a general scaling form is given based on the solution of the fractional diffusion equation

optimal solutions of numerical interface conditions in fluid structure thermal analysis abstract this paper presents major and new results in the numerical treatment of conjugate heat transfer problems the stability analysis of a 1d implicit model problem for heat transfer between a fluid and a solid is performed in the traditional finite volume fluid finite element solid configuration the interface stability study is carried out according to the godunov ryabenkii theory normal mode analysis two interface boundary conditions are studied first the commonly used dirichlet robin algorithm is described in detail and to the best of our knowledge the exact expression of an optimal coupling coefficient is formulated for the first time it is shown that this optimal coefficient is the best choice in terms of stability and convergence rate the effect and impact on stability of various solid data are also discussed in the last section of this paper the same stability analysis is carried out for a general robin robin interface condition and an optimal relationship between the two coupling parameters is also provided no stability restrictions are introduced by these optimal interface treatments and some noteworthy expressions are provided

a non overlapping optimized schwarz method for the heat equation with non linear boundary conditions and with applications to de icing abstract when simulating complex physical phenomena such as aircraft icing or de icing several dedicated solvers often need to be strongly coupled in this work a non overlapping schwarz method is constructed with the unsteady simulation of de icing as the targeted application to do so optimized coupling coefficients are first derived for the one dimensional unsteady heat equation with linear boundary conditions and for the steady heat equation with non linear boundary conditions the choice of these coefficients is shown to guarantee the convergence of the method using a linearization of the boundary conditions the method is then extended to the case of a general unsteady heat conduction problem the method is tested on simple cases and the convergence properties are assessed theoretically and numerically finally the method is applied to the simulation of an aircraft electrothermal de icing problem in two dimensions

a stable and accurate partitioned algorithm for conjugate heat transfer abstract we describe a new partitioned approach for solving conjugate heat transfer cht problems where the governing temperature equations in different material domains are time stepped in an implicit manner but where the interface coupling is explicit the new approach called the champ scheme conjugate heat transfer advanced multi domain partitioned is based on a discretization of the interface coupling conditions using a generalized robin mixed condition the weights in the robin condition are determined from the optimization of a condition derived from a local stability analysis of the coupling scheme the interface treatment combines ideas from optimized schwarz methods for domain decomposition problems together with the interface jump conditions and additional compatibility jump conditions derived from the governing equations for many problems i e for a wide range of material properties grid spacings and time steps the champ algorithm is stable and second order accurate using no sub time step iterations i e a single implicit solve of the temperature equation in each domain in extreme cases e g very fine grids with very large time steps it may be necessary to perform one or more sub iterations each sub iteration generally increases the range of stability substantially and thus one sub iteration is likely sufficient for the vast majority of practical problems the champ algorithm is developed first for a model problem and analyzed using normal mode theory the theory provides a mechanism for choosing optimal parameters in the mixed interface condition a comparison is made to the classical dirichlet neumann dn method and where applicable to the optimized schwarz os domain decomposition method for problems with different thermal conductivities and diffusivities the champ algorithm outperforms the dn scheme for domain decomposition problems with uniform conductivities and diffusivities the champ algorithm performs better than the typical os scheme with one grid cell overlap the champ scheme is also developed for general curvilinear grids and cht examples are presented using composite overset grids that confirm the theory and demonstrate the effectiveness of the approach

power law for the calm time interval of price changes abstract in this paper we describe a newly discovered statistical property of time series data for daily price changes we investigated quantitatively the calm time intervals of price changes for 800 companies listed in the tokyo stock exchange and for the nikkei 225 index in the 27 year period from january 1975 to december 2001 a calm time interval is defined as the interval between two successive price changes above a fixed threshold we found that the calm time interval distribution of price changes obeys a power law decay furthermore we show that the power law exponent monotonically decreases with respect to the threshold

a hilbert bundle characterization of hilbert c modules the category of hilbert c modules over a given c algebra is shown to be equivalent to a certain simply described category of hilbert bundles i e continuous fields of hilbert spaces over the space of pure states of the c algebra with the zero functional adjoined

modeling heart rate variability in healthy humans a turbulence analogy many complex systems share similar statistical characteristics in this letter a turbulence analogy is proposed for the long term heart rate variability of healthy humans based on such an analogy the equivalence of an inertial range is found and a cascade model which captures the statistical properties of the heart rate data is given

optimized schwarz waveform relaxation for advection reaction diffusion equations in two dimensions optimized schwarz waveform relaxation methods have been developed over the last decade for the parallel solution of evolution problems they are based on a decomposition in space and an iteration where only subproblems in space time need to be solved each subproblem can be simulated using an adapted numerical method for example with local time stepping or one can even use a different model in different subdomains which makes these methods very suitable also from a modeling point of view for rapid convergence however it is important to use effective transmission conditions between the space time subdomains and for best performance these transmission conditions need to take the physics of the underlying evolution problem into account the optimization of these transmission conditions leads to mathematically hard best approximation problems of homographic functions we study in this paper in detail the best approximation problem for the case of linear advection reaction diffusion equations in two spatial dimensions we prove comprehensively best approximation results for transmission conditions of robin and ventcel higher order type which can also be used in the various limits for example for the heat equation since we include in our analysis a positive low frequency limiter both in space and time we give for each case closed form asymptotic values for the parameters which can directly be used in implementations of these algorithms and which guarantee asymptotically best performance of the iterative methods we finally show extensive numerical experiments including cases not covered by our analysis for example decompositions with cross points we use q1 finite element discretizations in space and forward and backward euler discretizations in time other discretization could also have been considered since all our analysis is at the continuous level and in all cases we measure performance corresponding to our analysis

the distribution of low variability periods in human heartbeat dynamics abstract we study the long term dynamics of the short time variability level of human heart rate an aspect which is not addressed by the traditional methods of non linear time series analysis the length distribution of low variability periods in human heartbeat dynamics typically follows a multi scaling power law the values of the scaling exponents are personal characteristics and depend on the daily habits of the subjects though the distribution function of the low variability periods as a whole discriminates efficiently between several heart pathologies

transition probabilities of normal states determine the jordan structure of a quantum system let x1d516 m1 x1d516 m2 be a bijection not assumed affine nor continuous between the sets of normal states of two quantum systems modelled on the self adjoint parts of von neumann algebras m1 and m2 respectively this paper concerns with the situation when preserves or partially preserves one of the following three notions of transition probability on the normal state spaces the transition probability pu introduced by uhlmann rep math phys 9 273 279 1976 the transition probability pr introduced by raggio lett math phys 6 233 236 1982 and an asymmetric transition probability p0 as introduced in this article it is shown that the two systems are isomorphic i e m1 and m2 are jordan isomorphic if preserves all pairs with zero uhlmann respectively raggio or asymmetric transition probability in the sense that for any normal states and we have p 0 if and only if p 0 where p stands for pu respectively pr or p0 furthermore as an extension of wi

a characteristic time scale in dollar yen exchange rates abstract here we analyze tick data of yen dollar exchange using random walk methods we find that there exists a characteristic time scale approximately at 10 min according to the results at time scales shorter than 10 min the market exhibits anti persistence meaning that it self organizes so as to restore a given tendency for time scales longer than 10 min the market approaches a behavior appropriate to pure brownian motion

complements to various stone weierstrass theorems for c algebras and a theorem of shultz j glimm s stone weierstrass theorem states that ifa is ac algebra p a is the set of pure states ofa andb is ac subalgebra which separates overline p a cup left 0 right thenb a we show that ifb is ac subalgebra ofa andx an element ofa such that any two elements of overline p a cup left 0 right which agree onb agree also onx thenx b similar complements are given to other stone weierstrass theorems a theorem of f shultz states that ifx a the enveloping von neumann algebra ofa and ifx x x andxx are uniformly continuous onp a 0 then there is an element ofa which agrees withx onp a we show that the hypotheses onx x andxx can be dropped

optimized schwarz methods optimized schwarz methods are a new class of schwarz methods with greatly enhanced convergence properties they converge uniformly faster than classical schwarz methods and their convergence rates dare asymptotically much better than the convergence rates of classical schwarz methods if the overlap is of the order of the mesh parameter which is often the case in practical applications they achieve this performance by using new transmission conditions between subdomains which greatly enhance the information exchange between subdomains and are motivated by the physics of the underlying problem we analyze in this paper these new methods for symmetric positive definite problems and show their relation to other modern domain decomposition methods like the new finite element tearing and interconnect feti variants

properties of low variability periods in financial time series abstract properties of low variability periods in the time series are analysed the theoretical approach is used to show the relationship between the multi scaling of low variability periods and multi affinity of the time series it is shown that this technically simple method is capable of revealing more details about time series than the traditional multi affine analysis we have applied this scaling analysis to financial time series a number of daily currency and stock index time series the results show a good scaling behaviour for different model parameters the analysis of high frequency usd eur exchange rate data confirmed the theoretical expectations

scaling analysis of multi variate intermittent time series abstract the scaling properties of the time series of asset prices and trading volumes of stock markets are analysed it is shown that similar to the asset prices the trading volume data obey multi scaling length distribution of low variability periods in the case of asset prices such scaling behaviour can be used for risk forecasts the probability of observing next day a large price movement is super universally inversely proportional to the length of the ongoing low variability period finally a method is devised for a multi factor scaling analysis we apply the simplest two factor model to equity index and trading volume time series

probability of large movements in financial markets abstract based on empirical financial time series we show that the silence breaking probability follows a super universal power law the probability of observing a large movement is inversely proportional to the length of the on going low variability period such a scaling law has been previously predicted theoretically r kitt j kalda physica a 353 2005 480 assuming that the length distribution of the low variability periods follows a multi scaling power law

an overlapping schwarz algorithm for almost incompressible elasticity overlapping schwarz methods are extended to mixed finite element approximations of linear elasticity which use discontinuous pressure spaces the coarse component of the preconditioner is based on a low dimensional space previously developed for scalar elliptic problems and a domain decomposition method of iterative substructuring type i e a method based on nonoverlapping decompositions of the domain while the local components of the preconditioner are based on solvers on a set of overlapping subdomains a bound is established for the condition number of the algorithm which grows in proportion to the logarithm of the number of degrees of freedom in individual subdomains and essentially to the third power of the relative overlap between the overlapping subdomains and which is independent of the poisson ratio as well as jumps in the lame parameters across the interface between the subdomains a positive definite reformulation of the discrete problem makes the use of the standard preconditioned conjugate gradient method straightforward numerical results which include a comparison with problems of compressible elasticity illustrate the findings

pure states as a dual object for c algebras we consider the set of pure states of ac algebra as a uniform space equipped with transition probabilities and orientation and show that the pure states with this structure determine thec algebra up to isomorphism

on factorial states of operator algebras results for the factorial state space of a c algebra a which are analogous to results of glimm ann of math 72 1960 216 244 73 1961 572 612 tomiyama and takesaki tohoku math j 2 13 1961 498 523 for the pure state space it is shown that a is prime if and only if the type i factorial states are dense in the state space it follows that every factorial state is a w limit of type i factorial states the factorial state space of a von neumann algebra is determined and it is shown that if a is unital and acts non degenerately on a hilbert space then the factorial state space of the generated von neumann algebra restricts precisely to the factorial state space of a it is shown that the set of factorial states is w compact if and only if a is unital liminal and has hausdorff primitive ideal space

strategy for investments from zipf law s abstract we have applied the zipf method to extract the exponent for seven financial indices dax ftse djia nasdaq sp hang seng and nikkei 225 after having translated the signals into a text based on two letters we follow considerations based on the signal hurst exponent and the notion of a time dependent zipf law and exponent in order to implement two simple investment strategies for such indices we show the time dependence of the returns

statistical properties of share volume traded in financial markets we quantitatively investigate the ideas behind the often expressed adage it takes volume to move stock prices and study the statistical properties of the number of shares traded q deltat for a given stock in a fixed time interval deltat we analyze transaction data for the largest 1000 stocks for the two year period 1994 95 using a database that records every transaction for all securities in three major us stock markets we find that the distribution p q deltat displays a power law decay and that the time correlations in q deltat display long range persistence further we investigate the relation between q deltat and the number of transactions n deltat in a time interval deltat and find that the long range correlations in q deltat are largely due to those of n deltat our results are consistent with the interpretation that the large equal time correlation previously found between q deltat and the absolute value of price change g deltat related to volatility are largely due to n deltat