on conservation at grid interfaces this paper considers the solution of hyperbolic systems of conservation laws on discontinuous grids in particular we consider what happens to conservation at grid interfaces a procedure is presented to derive conservative difference approximations at the grid interfaces for two dimensional grids which overlap in an arbitrary configuration the same procedures are applied to compute interface formulas for grids which are refined in space and or time and for continuous grids where a switch in the scheme causes the discontinuity

vector bundles and regulous maps let x be a compact nonsingular affine real algebraic variety we prove that every pre algebraic vector bundle on x becomes algebraic after finitely many blowing ups using this theorem we then prove that the stiefel whitney classes of any pre algebraic mathbb r vector bundle on x are algebraic we also derive that the chern classes of any pre algebraic mathbb c vector bundles and the pontryagin classes of any pre algebraic mathbb r vector bundle are blow mathbb c algebraic we also provide several results on line bundles on x

asymptotic independence of multiple wiener ito integrals and the resulting limit laws we characterize the asymptotic independence between blocks consisting of multiple wiener ito integrals as a consequence of this characterization we derive the celebrated fourth moment theorem of nualart and peccati its multidimensional extension and other related results on the multivariate convergence of multiple wiener ito integrals that involve gaussian and non gaussian limits we give applications to the study of the asymptotic behavior of functions of short and long range dependent stationary gaussian time series and establish the asymptotic independence for discrete non gaussian chaoses

the topology of real algebraic sets with isolated singularities in this paper we give a topological classification of real algebraic sets with isolated singularities showing that they are exactly smooth closed manifolds with smooth subpolyhedra crushed to points the question of which topological spaces are homeomorphic to real algebraic sets solutions of polynomial equations in euclidean space has been long studied in 1936 seifert showed that any smooth compact stably parallelizable manifold is diffeomorphic to a component of an algebraic set 121 and in 1952 nash extended this result to all smooth compact manifolds 11 in 1973 tognoli showed that any smooth compact manifold is diffeomorphic to a nonsingular algebraic set 13 so at least compact nonsingular algebraic sets are classified little has been done with singular algebraic sets however since the transversality arguments used by seifert nash and tognoli no longer apply except in some special cases one could use stability of singularities such as kuiper 71 and akbulut 1 used to show certain nonsmoothable pl manifolds are algebraic sets or one could use the projective version of seifert nash tognoli as king did 6 but one could still not hope these techniques would allow even a characterization of isolated singularities to get around this problem we take a cue from hironaka s resolution of singularities 4 the idea is to take a topological resolution of a space if it exists we can apply transversality techniques seifertnash tognoli to the resolved space and then blow down algebraically and end up with the original space as an algebraic set it seems likely that this technique allows one to classify all algebraic sets but in any case we show that it classifies all algebraic sets with isolated singularities in future papers we will use this technique to show for instance that all compact pl manifolds are homeomorphic to real algebraic sets 17 and that 2 dimensional real algebraic sets are topologically characterized as polyhedra satisfying sullivan s even local euler characteristic condition 16

real algebraic morphisms represent few homotopy classes we study the problem of representing homotopy classes of maps between real algebraic varieties of regular maps

on real algebraic morphisms into even dimensional spheres given affine real algebraic varieties x and y let us denote by r x y the set of regular mappings real algebraic morphisms from x into y for definitions and notions of real algebraic geometry see 2 where the theory of real algebraic varieties is treated systematically our aim in this paper is to study the set m x s of regular mappings from affine nonsingular real algebraic varieties x into s the unit sphere ezn 1x2 1 earlier we obtained several results in this direction 3 4 cf also 2 chap 13 in particular it was shown in 4 that given a compact connected nonsingular orientable real algebraic subset x of rp of odd dimension k either each smooth mapping from x to sk is homotopic to a regular mapping or precisely those mappings of even topological degree have this property now we shall study the case of regular mappings into even dimensional spheres strangely enough the situation then is radically different from that mentioned above for odd dimensional spheres for a very large class of compact smooth manifolds of even dimension 2k most algebraic models x of these manifolds have the property that every regular mapping from x into s2k is null homotopic the meaning of most will be made precise later cf remark 1 6 theorem 2 1 example 2 3 this class of manifolds contains all compact co hypersurfaces of r2k 1

on approximating submanifolds by algebraic sets and a solution to the nash conjecture in n nash showed that any compact smooth submanifold m of ir is e isotopic to a union of connected components of a real algebraic variety if n 2 dim m e isotopic just means that there are arbitrarily small smooth isotopies to components of real algebraic varieties for smaller n however he was not able to get such a strong result but conjectured it was still true in w a proof of this conjecture was given which unfortunately had a gap later i and t2 gave correct proofs in the case where n is bigger than roughly 3 dim m 2 among other results in this paper we give a proof of this conjecture of nash in particular we will show

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

analytical pricing of geometric asian power options on an underlying driven by a mixed fractional brownian motion abstract in this paper we study the pricing problem of the continuously monitored fixed and floating strike geometric asian power options in a mixed fractional brownian motion environment first we derive both closed form solutions and mixed fractional partial differential equations for fixed and floating strike geometric asian power options based on delta hedging strategy and partial differential equation method second we present the lower and upper bounds of the prices of fixed and floating strike geometric asian power options under the assumption that both risk free interest rate and volatility are interval numbers finally numerical studies are performed to illustrate the performance of our proposed pricing model

variance change point detection for fractional brownian motion based on the likelihood ratio test abstract fractional brownian motion is one of the main stochastic processes used for describing the long range dependence phenomenon for self similar processes it appears that for many real time series characteristics of the data change significantly over time such behaviour one can observe in many applications including physical and biological experiments in this paper we present a new technique for the critical change point detection for cases where the data under consideration are driven by fractional brownian motion with a time changed diffusion coefficient the proposed methodology is based on the likelihood ratio approach and represents an extension of a similar methodology used for brownian motion the process with independent increments here we also propose a statistical test for testing the significance of the estimated critical point in addition to that an extensive simulation study is provided to test the performance of the proposed method

rigidity and moduli space in real algebraic geometry let r be a real closed field and let x be an affine algebraic variety over r we say that x is universally map rigid umr for short if for each irreducible affine algebraic variety z over r the set of nonconstant rational maps from z to x is finite a bijective map open image in new window from an affine algebraic variety over r to x is called weak change of the algebraic structure of x if it is regular and 1 is a nash map which preserves nonsingular points we prove the following rigidity theorem every affine algebraic variety over r is umr up to a weak change of its algebraic structure let us introduce another notion let y be an affine algebraic variety over r we say that x and y are algebraically unfriendly if all the rational maps from x to y and from y to x are trivial i e zariski locally constant from the preceding theorem we infer that if dim x 1 then there exists a set open image in new window of weak changes of the algebraic structure of x such that for each t s r with t s open image in new window and open image in new window are algebraically unfriendly this result implies the following expected fact for each nonsingular affine algebraic variety x over r of positive dimension the natural nash structure of x does not determine the algebraic structure of x in fact the moduli space of birationally nonisomorphic nonsingular affine algebraic varieties over r which are nash isomorphic to x has the same cardinality of r this result was already known under the special assumption that r is the field of real numbers and x is compact and nonsingular

automatic adaptive grid refinement for the euler equations a method of adaptive grid refinement for the solution of the steady euler equations for transonic flow is presented the algorithm automatically decides where the coarse grid accuracy is insufficient and creates locally uniform refined grids in these regions this typically occurs at the leading and trailing edges the solution is then integrated to steady state using the same integrator flo52 in the interior of each grid the boundary conditions needed on the fine grids are examined and the importance of treating the fine coarse grid interface conservatively is discussed numerical results indicate substantial computational savings for the same solution accuracy can be achieved

on equivalence of likelihood maximization of stochastic block model and constrained nonnegative matrix factorization abstract community structures detection in complex network is important for understanding not only the topological structures of the network but also the functions of it stochastic block model and nonnegative matrix factorization are two widely used methods for community detection which are proposed from different perspectives in this paper the relations between them are studied the logarithm of likelihood function for stochastic block model can be reformulated under the framework of nonnegative matrix factorization despite model equivalence the algorithms employed by the two methods are different preliminary numerical experiments are carried out to compare the behaviors of the algorithms demonstrating that the multiplicative update rules for nmf are more effective

algebraic realization of manifolds with group actions abstract let g be a compact lie group and m a closed smooth g manifold with some restrictions on g or on the isotropy groups of the action we show that m is algebraically realized i e there exists a non singular real algebraic g variety which is equivariantly diffeomorphic to m

1 f behavior in cross correlations between absolute returns in a us market abstract employing detrended fluctuation analysis dfa and detrended cross correlations analysis dcca we analyze auto correlations in the absolute returns for each of 30 dow jones industrial average djia constituents s i and cross correlations in the absolute returns between the djia and each s i we find that each djia member follows the djia in absolute returns since the dcca curve for each pair s i djia i exhibits strong cross correlations with average dcca exponent 1 03 0 04 this value for implies that the power law cross correlations are of the 1 f functional form for the financial firms comprising the djia we also find that the dfa and dcca exponents controlling the duration of firm risk are somewhat larger than the corresponding values for the rest of the us financial industry

stochastic calculus for fractional brownian motion i theory in this paper a stochastic calculus is given for the fractional brownian motions that have the hurst parameter in 1 2 1 a stochastic integral of ito type is defined for a family of integrands so that the integral has zero mean and an explicit expression for the second moment this integral uses the wick product and a derivative in the path space some ito formulae or change of variables formulae are given for smooth functions of a fractional brownian motion or some processes related to a fractional brownian motion a stochastic integral of stratonovich type is defined and the two types of stochastic integrals are explicitly related a square integrable functional of a fractional brownian motion is expressed as an infinite series of orthogonal multiple integrals

non recursive functions knots with thick ropes and self clenching thick hyperspheres we introduce an approach to certain geometric variational problems based on the use of the algorithmic unrecognizability of the n dimensional sphere for n 5 sometimes this approach allows one to prove the existence of infinitely many solutions of a considered variational problem this recursion theoretic approach is applied in this paper to a class of functionals on the space of c1 1 smooth hypersurfaces diffeomorphic to sn in rn 1 where n is any fixed number 5 the simplest of these functionals kv is defined by the formula kv n vol n 1 n r n where r n denotes the radius of injectivity of the normal exponential map for n rn l we prove the existence of an infinite set of distinct locally minimal values of kv on the space of c1 1 smooth topological hyperspheres in rn 1 for any n 5 the functional kv naturally arises when one attempts to generalize knot theory in order to deal with embeddings and isotopies of thick circles and more generally thick spheres into euclidean spaces we introduce the notion of knot with thick rope types the theory of knot with thick rope types turns out to be quite different from the classical knot theory because of the following result there exists an infinite set of non trivial knot with thick rope types in codimension one for every dimension greater than or equal to five

on real algebraic models of smooth manifolds an affine nonsingular real algebraic variety x diffeomorphic to a smooth manifold m is said to be an algebraic model of m the remarkable theorem of nash tognoli asserts that each compact smooth manifold m has an algebraic model 16 or 6 theorem 14 1 10 in fact there exists an infinite family x n of irreducible algebraic models of m such that xt and xj are birationally nonisomorphic for i j 10 cf also 7 for a proof in a special case in view of these results it seems natural and interesting to investigate algebro geometric properties of various algebraic models of a given smooth manifold this paper addresses a few questions of this type for notions and results of real algebraic geometry we refer the reader to the book 6 given a compact affine nonsingular real algebraic variety x denote by h x z 2 the subgroup of hk x z 2 of the homology classes represented by zariski closed fc dimensional algebraic subvarieties of x 6 chapter 11 or 11 let h x z 2 be the image of h k xfz 2 9 d dimx under the poincare duality isomorphism hd k x z 2 h x z 2 although the groups hlg x z 2 are one of the most important invariants of x a sample of applications can be found in 1 2 3 6 8 9 our knowledge of their behavior is still rather limited here we consider the following problem let m be a compact smooth manifold and let g be a subgroup of h m z 2 when are there an algebraic model x of m and a diffeomorphism c x m such that the induced isomorphism p h m z 2 h x z 2

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

on the integral hodge conjecture for real varieties i we formulate the real integral hodge conjecture a version of the integral hodge conjecture for real varieties and raise the question of its validity for cycles of dimension 1 on uniruled and calabi yau threefolds and on rationally connected varieties we relate it to the problem of determining the image of the borel haefliger cycle class map for 1 cycles with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the chow group of 1 cycles of real threefolds new results about these problems are obtained along the way

long range correlation analysis of economic news flow intensity abstract the goal of the paper is to examine the auto correlation properties for time series of the news flow intensity using different methods such as the fluctuation analysis the detrended fluctuation analysis and the detrending moving average analysis empirical findings for news analytics data show the presence of long range correlations for the time series of news intensity data

parameter identification for mixed fractional brownian motions with the drift parameter abstract this paper deals with the problem of estimating the unknown parameters in the drift mixed fractional brownian motion based on discrete sampled observations we construct two different estimators for the drift parameter based on the approximation by random walks of the driving noise and prove the consistency of these two estimators some numerical simulations are also presented to illustrate the performance of these maximum likelihood estimators empirical examples are given to illustrate the potential applications of these proposed estimators

pricing geometric asian power options under mixed fractional brownian motion environment abstract it has been observed that the stock price process can be modeled with driving force as a mixed fractional brownian motion with hurst index h 3 4 whenever long range dependence is possibly present we obtain a closed form expression for the price of a geometric asian option under the mixed fractional brownian motion environment we consider also asian power options when the payoff function is a power function

mixed gaussian processes a filtering approach this paper presents a new approach to the analysis of mixed processes xt bt gt t 0 t xt bt gt t 0 t where btbt is a brownian motion and gtgt is an independent centered gaussian process we obtain a new canonical innovation representation of xx using linear filtering theory when the kernel k s t 2 s tegtgs s t k s t 2 s tegtgs s t has a weak singularity on the diagonal our results generalize the classical innovation formulas beyond the square integrable setting for kernels with stronger singularity our approach is applicable to processes with additional fractional structure including the mixed fractional brownian motion from mathematical finance we show how previously known measure equivalence relations and semimartingale properties follow from our canonical representation in a unified way and complement them with new formulas for radon nikodym densities

algebraic cycles and approximation theorems in real algebraic geometry let af be a compact c manifold a theorem of nash tognoli asserts that m has an algebraic model that is m is diffeomorphic to a nonsingular real algebraic set x let fv afx z 2 denote the subgroup of hk x z 2 of the cohomology classes determined by algebraic cycles of codi mension k on x assuming that m is connected orientable and dim m 5 we prove in this paper that a subgroup g of h2 m z 2 is isomorphic to h x z 2 for some algebraic model x of m if and only if w2 tm is in g and each element of g is of the form w2k for some real vector bundle over m where w2 stands for the second stiefel whitney class a result of this type was previously known for subgroups g of hx m z 2

least informative distributions in maximum q log likelihood estimation abstract we use the maximum q log likelihood estimation for least informative distributions lids in order to estimate the parameters in probability density functions pdfs efficiently and robustly when data include outlier s lids are derived by using convex combinations of two pdfs a convex combination of two pdfs is composed of an underlying distribution and a contamination the optimal criterion is obtained by minimizing the change of maximum q log likelihood function when the data contain small amount of contamination in this paper we make a comparison between ordinary maximum likelihood estimation maximum q log likelihood estimation mqle and lids based on mqle for parameter estimation from data with outliers we derive a new fisher information matrix based on the score function for lid from m function and use it for choice of optimal estimator in the class of mqle the model selection is done by the robust information criteria we test the methods on the real data with outliers and estimate shape and scale parameters of probability distributions as a result we show that the lids based on mqle provide the most robust and efficient estimation of the model parameters

a resolution theorem for homology cycles of real algebraic varieties the theorem is the best possible in the sense that the components of nonsingular algebraic subsets in the conclusion cannot be replaced by nonsingular algebraic subsets see remark 14 it is well known that the topology of the singularities of 7 2 homology cycles is closely related to real algebraic structures on v ak 2 ak3 therefore it is natural to study to what extent general homology cycles differ from the cycles induced by submanifolds the main theorem of this paper implies that all the singularities of homology cycles can be smoothed by a blowing up process this result should be viewed as a homology version of the resolution theorem h the reason this result is not an easy consequence of h is that not all homology cycles of v may be represented by algebraic subsets there are real obstructions e g ak2 even if they were the map resolving them may introduce new bad homology cycles upstairs the result turns out to be a useful device in topologically classifying real algebraic sets ak6 it also gives interesting corollaries in algebraic topology ak2 another result of this paper theorem 4 says that any smooth map f w v between nonsingular algebraic sets can be approximated by a rational map after changing w by a rational diffeomorphism if the homotopy class of f contains a rational representative this strengthens proposition 2 3 of aks for given algebraic sets vcf and w e n m a function f v w is called an entire rational function if f x p x q x where p ir and q ir ir

grid embedding technique using cartesian grids for euler solutions grid embedding techniques are presently applied to the solutions of the euler equations on cartesian grids for the naca 0012 airfoil and the multielement skf1 1 airfoil at transonic speeds based on comparisons with solutions on fine grids it is shown that the present scheme when used in conjunction with the runge kutta time stepping scheme as well as cartesian grids yields reduced memory requirements and a substantial reduction in computational time without loss of accuracy

algebraic models of smooth manifolds in fact we conjecture that such a family can be chosen uncountable in view of this theorem it seems natural and interesting to investigate algebrogeometric properties of various algebraic models of a given smooth manifold let us now describe one of these problems which will be the main object of study in this paper for notions definitions and results of real algebraic geometry we refer the reader to the book 9 given a compact nonsingular real affine algebraic variety x denote by h ig x 7z 2 the subgroup of nk x z 2 of homology classes represented by zariski closed k dimensional algebraic subvarieties of x cf 9 chap 1 1 let h lg x z 2 be the image of h a k x 71 2 d dimx under the poincar6 duality isomorphism hd k x 71 2 o hk x 71 2 these groups h ig x 71 2 are undoubtedly one of the most important invariants of an algebraic variety x still our knowledge of the behavior of h g x 71 2 is rather limited the main open problem is the following

statistical aspects of the fractional stochastic calculus we apply the techniques of stochastic integration with respect to the fractional brownian motion and the gaussian theory of regularity and supremum estimation to study the maximum likelihood estimator mle for the drift parameter of stochastic processes satisfying stochastic equations driven by fractional brownian motion with any level of h o lder regularity any emph hurst parameter we prove existence and strong consistency of the mle for linear and nonlinear equations we also prove that a basic discretized version of the mle is still a strongly consistent estimator