a basis construction of the extended catalan and shi arrangements of the type a2 abstract in 10 terao proved the freeness of multi coxeter arrangements with constant multiplicities by giving an explicit construction of bases combining it with algebro geometric method yoshinaga proved the freeness of the extended catalan or shi arrangements in 12 however there have been no explicit constructions of the bases for the logarithmic derivation modules of the extended catalan and shi arrangements in this paper we give the first explicit construction of them when the root system is of the type a 2

testing for in finite moments this paper proposes a test to verify whether the th moment of a random variable is finite we use the fact that under general assumptions sample moments either converge to a finite number or diverge to infinity according as the corresponding population moment is finite or not building on this we propose a test for the null that the th moment does not exist since by construction our test statistic diverges under the null and converges under the alternative we propose a randomised testing procedure to discern between the two cases we study the application of the test to raw data and to regression residuals monte carlo evidence shows that the test has the correct size and good power the results are further illustrated through an application to financial data

on the properties of the coefficient of determination in regression models with infinite variance variables abstract we examine the asymptotic properties of the coefficient of determination r 2 in models with stable random variables if the regressor and error term share the same index of stability 2 we show that the r 2 statistic does not converge to a constant but has a nondegenerate distribution on the entire 0 1 interval we provide closed form expressions for the cumulative distribution function and probability density function of this limit random variable and we show that the density function is unbounded at 0 and 1 if the indices of stability of the regressor and error term are unequal we show that the coefficient of determination converges in probability to either 0 or 1 depending on which variable has the smaller index of stability irrespective of the value of the slope coefficient in an empirical application we revisit the fama and macbeth 1973 two stage regression and demonstrate that in the infinite variance case the r 2 statistic of the second stage regression converges to 0 in probability even if the slope coefficient is nonzero we deduce that a small value of the r 2 statistic should not in itself be used to reject the usefulness of a regression model

semi implicit extension of a godunov type scheme based on low mach number asymptotics i one dimensional flow a single scale multiple space scale asymptotic analysis provides detailed insight into the low mach number limit behavior of solutions of the compressible euler equations we use the asymptotics as a guideline for developing a low mach number extension of an explicit higher order shock capturing scheme this semi implicit scheme involves multiple pressure variables large scale differencing and averaging procedures that are discretized versions of standard operations in multiple scales asymptotic analysis advection and acoustic wave propagation are discretized explicitly and upwind and only one scalar elliptic equation is to be solved implicitly at each time step this equation is a pressure correction equation for incompressible flows when the mach number is zero in the low mach number limit the time step is restricted by a courant number based essentially on the maximum flow velocity for moderate and large mach numbers the scheme reduces to the underlying explicit higher order shock capturing algorithm

comparison of nonreflecting outlet boundary conditions for compressible solvers on unstructured grids this paper describes extensions and tests of characteristic methods for outlet boundary conditions in compressible solvers three methods based on the specification of incoming waves using one and multidimensional approximations are extended to unstructured grids they are first compared for weak to strong vortices propagating on low to high speed mean flows through outlet sections a major issue is to determine the mach number to be used in the specification of the transverse terms that must be taken into account in the incoming wave amplitude specifications for the vortex computations results show that the averaged mach number leads to better results than its local value the boundary conditions are then tested in a more complex case the flow around a turbine blade a reference solution using a long distance between the blade trailing edge and the outlet plane is first computed for this solution outlet boundary conditions have almost no effect on the flow around the blade the distance between the trailing edge and the outlet plane is then shortened and the various characteristic treatments are compared in which intense vortices cross the outlet plane results confirm the conclusions obtained on the simple vortex test case

multiderivations of coxeter arrangements let v be an l dimensional euclidean space let g o v be a finite irreducible orthogonal reflection group let be the corresponding coxeter arrangement let s be the algebra of polynomial functions on v for h choose h v such that h ker h for each nonnegative integer m define the derivation module d m ders h s mh the module is known to be a free s module of rank l by k saito 1975 for m 1 and l solomon h terao 1998 for m 2 the main result of this paper is that this is the case for all m moreover we explicitly construct a basis for d m their degrees are all equal to mh 2 when m is even or are equal to m 1 h 2 mi 1 i l when m is odd here m1 ml are the exponents of g and h ml 1 is the coxeter number the construction heavily uses the primitive derivation d which plays a central role in the theory of flat generators by k saito or equivalently the frobenius manifold structure for the orbit space of g some new results concerning the primitive derivation d are obtained in the course of proof of the main result

limit theory for the sample covariance and correlation functions of moving averages abstract document describes a moving average process which have regularly varying tail probabilities with index alpha 0 the limit distribution of the sample covariance function is derived in the case that the process has a finite variance but an infinite variance but an infinite fourth moment furthermore in the infinite variance case 0 alpha 2 the sample correlation function is shown to converge in distribution to the ratio of two independent stable random variables with indices alpha and alpha 2 respectively this result immediately gives the limit distribution for the least squares estimates of the parameters in an autoregressive process author

equivariant multiplicities of coxeter arrangements and invariant bases let a be an irreducible coxeter arrangement and w be its coxeter group then w naturally acts on a a multiplicity m a z is said to be equivariant when m is constant on each w orbit of a in this article we prove that the multi derivation module d a m is a free module whenever m is equivariant by explicitly constructing a basis which generalizes the main theorem of terao 2002 12 the main tool is a primitive derivation and its covariant derivative moreover we show that the w invariant part d a m w for any multiplicity m is a free module over the w invariant subring

simple root bases for shi arrangements abstract in his affirmative answer to the edelman reiner conjecture yoshinaga proved that the logarithmic derivation modules of the cones of the extended shi arrangements are free modules however we know very little about the bases themselves except their existence in this article we prove the unique existence of two distinguished bases which we call the simple root basis plus srb and the simple root basis minus srb they are characterized by nice divisibility properties relative to the simple roots

limit theory for moving averages of random variables with regularly varying tail probabilities let z k infty k infty be iid where the z k s have regularly varying tail probabilities under mild conditions on a real sequence c j j geq 0 the stationary process x n sum infty j 0 c jz n j n geq 1 exists a point process based on x n converges weakly and from this a host of weak limit results for functionals of x n ensue we study sums extremes excedences and first passages as well as behavior of sample covariance functions

coxeter multiarrangements with quasi constant multiplicities we study structures of derivation modules of coxeter multiarrangements with quasi constant multiplicities by using the primitive derivation as an application we show that the characteristic polynomial of a coxeter multiarrangement with quasi constant multiplicity is combinatorially computable

a primitive derivation and logarithmic differential forms of coxeter arrangements let w be a finite irreducible real reflection group which is a coxeter group we explicitly construct a basis for the module of differential 1 forms with logarithmic poles along the coxeter arrangement by using a primitive derivation as a consequence we extend the hodge filtration indexed by nonnegative integers into a filtration indexed by all integers this filtration coincides with the filtration by the order of poles the results are translated into the derivation case

small disturbance asymptotics and the durbin watson and related tests in the dynamic regression model abstract until recently it was thought inappropriate to apply the durbin watson dw test to a dynamic linear regression model because of the lack of appropriate critical values recently inder 1986 used a modified small disturbance distribution sdd to find approximate critical values this paper studies the exact sdd of statistics of the same general form as the dw statistic and suggests some changes to inder s result we show how to calculate true small disturbance critical values and bounds for these critical values that take into account the exogenous regressors our results give a justification for the use of the familiar tables of bounds when the dw test is applied to a dynamic regression model

the durbin watson ratio under infinite variance errors abstract this paper studies the properties of the von neumann ratio for time series with infinite variance our asymptotics cover the null of iid variates and general moving average ma alternatives regression residuals are also considered in the static regression model the durbin watson statistic has the same limit distribution as the von neumann ratio in dynamic models the results are more complex in finite variance models our results specialize to those of the durbin h statistic and equivalent lm test asymptotics some monte carlo results are reported illustrating the effects of infinite variance errors and regressors in finite samples

stable limits for partial sums of dependent random variables let x n be a stationary sequence of random variables whose marginal distribution f belongs to a stable domain of attraction with index alpha 0 alpha 2 under the mixing and dependence conditions commonly used in extreme value theory for stationary sequences nonnormal stable limits are established for the normalized partial sums the method of proof relies heavily on a recent paper by lepage woodroofe and zinn which makes the relationship between the asymptotic behavior of extreme values and partial sums exceedingly clear also an example of a process which is an instantaneous function of a stationary gaussian process with covariance function r n behaving like r n log n rightarrow 0 as n rightarrow infty is shown to satisfy these conditions

primitive filtrations of the modules of invariant logarithmic forms of coxeter arrangements abstract we define primitive derivations for coxeter arrangements which may not be irreducible using those derivations we introduce the primitive filtrations of the module of invariant logarithmic differential forms for an arbitrary coxeter arrangement with an arbitrary multiplicity in particular when the coxeter arrangement is irreducible with a constant multiplicity the primitive filtration was studied in abe and terao 2010 2 which generalizes the hodge filtration introduced by k saito e g saito 2003 6

moment condition tests for heavy tailed time series abstract we develop an asymptotically chi squared statistic for testing moment conditions e m t 0 0 where m t 0 may be weakly dependent scalar components of m t 0 may have an infinite variance and e m t need not exist for any under the alternative score tests are a natural application and in general a variety of tests can be heavy tail robustified by our method including white noise garch affects omitted variables distribution functional form causation volatility spillover and over identification the test statistic is derived from a tail trimmed sample version of the moments evaluated at a consistent plug in t for 0 depending on the test in question and heaviness of tails t may be any consistent estimator including sub t 1 2 convergent and or asymptotically non gaussian ones since t can be assured not to affect the test statistic asymptotically we adapt bootstrap p value occupation time and covariance determinant methods for selecting the trimming fractile in any sample and apply our statistic to tests of white noise omitted variables and volatility spillover we find it obtains sharp empirical size and strong power while conventional tests exhibit size distortions

improved boundary conditions for viscous reacting compressible flows previous studies on physical boundary conditions for flame boundary interactions of an ideal multicomponent compressible gas have neglected reactive source terms in their boundary condition treatments by combining analyses of incompletely parabolic systems with those based on the hyperbolic euler equations a rational set of boundary conditions is determined to address this shortcoming accompanying these conditions is a procedure for implementation into a maltidimensional code in the limits of zero reaction rate or one species the boundary conditions reduce in a predictable way to cases found in the literature application is made to premixed and nonpremixed flames in one and two dimensions to establish efficacy inclusion of source terms in boundary conditions derived from characteristic analysis is essential to avoid unphysical generation of pressure and velocity gradients as well as flow reversals minor deficiencies in the boundary conditions are attributed primarily to the diffusive terms imposing vanishing diffusive boundary normal flux gradients works better than imposing vanishing fluxes but neither is entirely satisfactory

estimating the stable index alpha in order to measure tail thickness a critique stable laws are often fit to outlier prone data and if the index alpha is estimated to be much less than two then the normal law is rejected in favor of an infinite variance stable law this paper derives the theoretical properties of such a procedure when the true distribution is stable the distribution of the m l e of alpha is non regular if alpha 2 when the true distribution is not stable the estimate of alpha is not a robust measure of the rate of decrease of the tail probabilities a more robust procedure is developed and a statistic for describing and comparing the tail shapes of arbitrary samples is proposed