powering by a table look up and a multiplication with operand modification an efficient method for generating a power of an operand i e x sup p for an operand x and a given p is proposed it is applicable to ps in the form of spl plusmn 2 sup k where k is any integer and of spl plusmn 2 k sub 1 spl plusmn 2 k sub 2 where k sub 1 is any integer and k sub 2 is any nonnegative integer the reciprocal the square root the reciprocal square root the reciprocal square the reciprocal cube and so forth are included the method is a modification of the piecewise linear approximation a power of an operand is generated through a table look up and a multiplication with operand modification the same accuracy is achieved as the piecewise linear approximation the multiplication and an addition required for the piecewise linear approximation are replaced by only one double sized multiplication with a slight modification of the operand and hence one clock cycle may be reduced the required table size is reduced because only one coefficient instead of two has to be stored

levy brownian motion on finite intervals mean first passage time analysis we present the analysis of the first passage time problem on a finite interval for the generalized wiener process that is driven by levy stable noises the complexity of the first passage time statistics mean first passage time cumulative first passage time distribution is elucidated together with a discussion of the proper setup of corresponding boundary conditions that correctly yield the statistics of first passages for these non gaussian noises the validity of the method is tested numerically and compared against analytical formulas when the stability index alpha approaches 2 recovering in this limit the standard results for the fokker planck dynamics driven by gaussian white noise

fractional brownian motion and motion governed by the fractional langevin equation in confined geometries motivated by subdiffusive motion of biomolecules observed in living cells we study the stochastic properties of a non brownian particle whose motion is governed by either fractional brownian motion or the fractional langevin equation and restricted to a finite domain we investigate by analytic calculations and simulations how time averaged observables e g the time averaged mean squared displacement and displacement correlation are affected by spatial confinement and dimensionality in particular we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain the general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality we define the displacement correlation function and find that this quantity shows distinct features for fractional brownian motion fractional langevin equation and continuous time subdiffusion such that it appears an efficient measure to distinguish these different processes based on single particle trajectory data

holonomic and perverse logarithmic d modules abstract we introduce the notion of a holonomic d module on a smooth idealized logarithmic scheme and show that verdier duality can be extended to this context in contrast to the classical case the pushforward of a holonomic module along an open immersion is in general not holonomic we introduce a perverse t structure on the category of coherent logarithmic d modules which makes the dualizing functor t exact on holonomic modules conversely this t exactness characterizes holonomic modules among all coherent logarithmic d modules we also introduce logarithmic versions of the gabber and kashiwara malgrange filtrations

rigid dualizing complex for quantum enveloping algebras and algebras of generalized differential operators abstract in the first part of this article we compute the rigid dualizing complex of a quantum enveloping algebra we consider the generic case and the case of a specialization at a non root of unity this answers a question of yekutieli j pure appl algebra 150 2000 85 in bull soc math france 122 1994 371 and math z 232 1999 367 we generalized d module theory to lie algebroids using these results we compute explicitly the rigid dualizing complex of the algebra of differential operators defined by an affine lie algebroid this generalizes results of yekutieli j pure appl algebra 150 2000 85

measuring the accuracy of rom reciprocal tables we prove that a convenient rom reciprocal table construction algorithm generates tables that minimize the relative error the worst case relative errors realized for such optimally computed k bits in m bits out rom reciprocal tables are then determined for all table sizes 3 spl les k m spl les 12 we next prove the table construction algorithm always generates a k bits in k bits out table with relative errors never any greater than 3 4 2 sup k and more generally with g guard bits that for k g bits out the relative error is never any greater than 2 k 1 1 1 2g 1 to provide for determining extreme case test data and to compute the precision of a reciprocal table without prior construction of the full rom reciprocal table we describe a procedure that requires generation and inspection of only a small portion of such a table to identify input values guaranteed to include the worst case relative errors in the table

parabolic sheaves on logarithmic schemes abstract we show how the natural context for the definition of parabolic sheaves on a scheme is that of logarithmic geometry the key point is a reformulation of the concept of logarithmic structure in the language of symmetric monoidal categories which might be of independent interest our main result states that parabolic sheaves can be interpreted as quasi coherent sheaves on certain stacks of roots

stability and lack of memory of the returns of the hang seng index abstract in this paper we show that the logarithmic returns of the hang seng index from january 2 1987 to november 14 2005 statistically resemble a sequence of independent identically distributed levy stable random variables this is in stark contrast to xiu and jin 2007 39 where long memory farima processes with gaussian noise were suggested as well fitted to the data the lack of memory is checked by using lo s modified r s statistic and a new method of estimation of the memory parameter d which applies the notion of empirical mean squared displacement in order to test stability of the data we employ several statistical tests based on the empirical distribution function finally we also show that the returns possess no conditional heteroscedasticity property thus excluding the arch garch family of processes as possible underlying models

existence theorems for dualizing complexes over non commutative graded and filtered rings abstract in this note we prove existence theorems for dualizing complexes over graded and filtered rings thereby generalizing some results by zhang yekutieli and jorgensen

a unified architecture for the accurate and high throughput implementation of six key elementary functions this paper presents a unified architecture for the compact implementation of several key elementary functions including reciprocal square root and logarithm in single precision floating point arithmetic the proposed high throughput design is based on uniform domain segmentation and curve fitting techniques numerically accurate least squares regression is utilized to calculate the polynomial coefficients the architecture is optimized by analyzing the trade off between the size of the required memory and the precision of intermediate variables to achieve the minimum 23 bit accuracy required for single precision floating point representation the efficiency of the proposed unified data path is demonstrated on a common field programmable gate array

stable non gaussian random processes stochastic models with infinite variance stable random variables on the real line multivariate stable distributions stable stochastic integrals dependence structures of multivariate stable distributions non linear regression complex stable stochastic integrals and harmonizable processes self similar processes chentsov random fields introduction to sample path properties boundedness continuity and oscillations measurability integrability and absolute continuity boundedness and continuity via metric entropy integral representation historical notes and extensions

analytic approach to the problem of convergence of truncated levy flights towards the gaussian stochastic process an analytic expression for characteristic function defining a truncated l evy flight is derived it is shown that the characteristic function yields results in agreement with recent simulations of truncated l evy flights by mantegna and stanley phys rev lett 73 2946 1994 with the analytic expression for the characteristic function the convergence of the l evy process towards the gaussian is demonstrated without simulations in the calculation of first return probability the simulations are replaced by numerical integration using simple quadratures

compactifications of subvarieties of tori we study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non archimedean amoebas these compactifications have many nice properties for example any k boundary divisors intersect in codimension k we consider some examples including m 0 n subset overline m 0 n and more generally log canonical models of complements of hyperplane arrangements and compact quotients of grassmannians by a maximal torus

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

very high radix square root with prescaling and rounding and a combined division square root unit an algorithm for square root with prescaling and selection by rounding is developed and combined with a similar scheme for division since division is usually more frequent than square root the main concern of the combined implementation is to maintain the low execution time of division while accepting a somewhat larger execution time for square root the algorithm is presented in detail including the mathematical development of bounds for the first square root digit and for the scaling factor the proposed implementation is described evaluated and compared with other combined div sqrt units the comparisons show that the proposed scheme potentially produces a significant speed up for division whereas for square root the speed up is small

efficient initial approximation for multiplicative division and square root by a multiplication with operand modification an efficient initial approximation method for multiplicative division and square root is proposed it is a modification of the piecewise linear approximation the multiplication and the addition required for the linear approximation are replaced by only one multiplication with a slight modification of the operand the same accuracy is achieved the modification of the operand requires only a bit wise inversion and a one bit shift and can be implemented by a very simple circuit one clock cycle may be saved because the addition is removed the required table size is also reduced because only one coefficient instead of two has to be stored

parabolic sheaves with real weights as sheaves on the kato nakayama space abstract we define quasi coherent parabolic sheaves with real weights on a fine saturated log analytic space and explain how to interpret them as quasi coherent sheaves of modules on its kato nakayama space this recovers the description as sheaves on root stacks of 5 and 27 for rational weights but also includes the case of arbitrary real weights

models of anomalous diffusion the subdiffusive case abstract the paper discusses a model for anomalous diffusion processes their one point probability density functions p d f are exact solutions of fractional diffusion equations the model reflects the asymptotic behavior of a jump anomalous random walk process with random jump sizes and random inter jump time intervals with infinite means and variances which do not satisfy the law of large numbers in the case when these intervals have a fractional exponential p d f the fractional komogorov feller equation for the corresponding anomalous diffusion is provided and methods of finding its solutions are discussed finally some statistical properties of solutions of the related langevin equation are studied the subdiffusive case is explored in detail the emphasis is on a rigorous presentation which however would be accessible to the physical sciences audience

gelfand kirillov dimension and associated graded modules abstract let s a 0sa be a filtered algebra over a field k and m ma a filtered s module with associated graded module gr m m a m a 1 over gr s s a s a 1 we consider conditions which ensure that gr m and m have the same gelfand kirillov dimension and show that this equality holds in particular if gr s is an affine commutative k algebra

fractional langevin equation we investigate fractional brownian motion with a microscopic random matrix model and introduce a fractional langevin equation we use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath we further compare fractional brownian motion with the fractal time process the respective mean square displacements of these two forms of anomalous diffusion exhibit the same power law behavior here we show that their lowest moments are actually all identical except the second moment of the velocity this provides a simple criterion that enable us to distinguish these two non markovian processes

approximating elementary functions with symmetric bipartite tables this paper presents a high speed method for function approximation that employs symmetric bipartite tables this method performs two parallel table lookups to obtain a carry save borrow save function approximation which is either converted to a two s complement number or is booth encoded compared to previous methods for bipartite table approximations this method uses less memory by taking advantage of symmetry and leading zeros in one of the two tables it also has a closed form solution for the table entries provides tight bounds on the maximum absolute error and can be applied to a wide range of functions a variation of this method provides accurate initial approximations that are useful in multiplicative divide and square root algorithms