interaction of diffusion and boundary conditions on considere le systeme d equations paraboliques u t d u f u x d u n e x u 0 x ou u r n r n n 3 est un ouvert borne de frontiere lisse d diag d 1 d n e diag e 1 e n chaque d j 0 est constant e j r est continu e j 0 j 1 2 n et e 0 est constant pour f e fixe on etudie comment le flot defini ci dessus depend des parametres d

on the distribution of saliency detecting salient structures is a basic task in perceptual organization saliency algorithms typically mark edge points with some saliency measure which grows with the length and smoothness of the curve on which these edge points lie here we propose a modified saliency estimation mechanism that is based on probabilistically specified grouping cues and on curve length distributions in this framework the shashua and ullman saliency mechanism may be interpreted as a process for detecting the curve with maximal expected length generalized types of saliency naturally follow we propose several specific generalizations e g gray level based saliency and rigorously derive the limitations on generalized saliency types we then carry out a probabilistic analysis of expected length saliencies using ergodicity and asymptotic analysis we derive the saliency distributions associated with the main curves and with the rest of the image we then extend this analysis to finite length curves using the derived distributions we derive the optimal threshold on the saliency for discriminating between figure and background and bound the saliency based figure from ground performance

improved convergence towards generalized euler mascheroni constant we propose new simple sequences approximating the euler mascheroni constant and its generalization which converge faster towards their limits than those considered by detemple d w detemple a quicker convergence to euler s constant am math monthly 100 5 1998 468 470 sintamarian a sintamarian a generalization of euler s constant numer algorithms 46 2 2007 141 151 and vernescu a vernescu a new accelerate convergence to the constant of euler gazeta matem ser a bucharest xvii xcvi 4 1999 273 278

the generalized basis reduction algorithm let fx be a convex function defined in rn which is symmetric about the origin and homogeneous of degree 1 and let l be the lattice of integers zn a definition of a reduced basis b1 bn of the lattice with respect to the distance function f is presented and we describe an algorithm which yields a reduced basis in polynomial time for fixed n in the special case in which the bodies x fx t are ellipsoids the definition of a reduced basis is identical with that given by lenstra lenstra and lovasz 1982 and the algorithm is the well known basis reduction algorithm we show that the basis vector b1 in a reduced basis is an approximation to a shortest nonzero lattice point with respect to f and relate the basis vectors bi to minkowski s successive minima the results lead to an algorithm for integer programming which executes in polynomial time for fixed n but which avoids the ellipsoidal approximations required by lenstra s algorithm we also discuss the properties of a korkine zolotarev basis for the lattice

on the complexity of familiar functions and numbers this paper examines low complexity approximations to familiar functions and numbers the intent is to suggest that it is possible to base a taxonomy of such functions and numbers on their computational complexity a central theme is that traditional methods of approximation are often very far from optimal while good or optimal methods are often very far from obvious for most functions provably optimal methods are not known however the gap between what is known and what is possible is often small a considerable number of open problems are posed and a number of related examples are presented

an algorithm for multiple precision floating point multiplication we present an algorithm for multiple precision floating point multiplication the conventional algorithms based on the fast fourier transform fft multiply two n bit numbers to obtain a 2n bit result in multiple precision floating point multiplication we need only the returned result whose precision is equal to the multiple precision floating point number we show that the overall arithmetic operations for fft based multiple precision floating point multiplication are reduced by decomposition of the full length multiplication into shorter length multiplication

ramanujan formula for the generalized stirling approximation abstract the aim of this paper is to improve ramanujan s formula for approximation of the factorial function starting from burnside s formula in contradistinction with the classical formula that starts from stirling s formula

can one measure the temperature of a curve the entropy of a plane curve is defined in terms of the number of intersection points with a random line the gibbs distribution which maximizes the entropy enables one to define the temperature of the curve at 0 temperature the curve reduces to a straight segment at high temperature the curve is somewhat chaotic and behaves like a perfect gas we attempt to show that thermodynamic formalism can be used for the study of plane curves the curves we discuss have finite length unlike mandelbrot s fractal curves 1 yet we feel our approach to the mathematics is not far from his

constructing exact symmetric informationally complete measurements from numerical solutions recently several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements sic povms or sics and algebraic number theory these conjectures relate the sics to their minimal defining algebraic number field testing or sharpening these conjectures requires that the sics are expressed exactly rather than as numerical approximations while many exact solutions of sics have been constructed previously using grobner bases this method has probably been taken as far as is possible with current computer technology except in special cases where there are additional symmetries here we describe a method for converting high precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the galois symmetries of an sic using this method we have calculated 69 new exact solutions including nine new dimensions where previously only numerical solutions were known which more than triples the number of known exact solutions in some cases the solutions require number fields with degrees as high as 12 288 we use these solutions to confirm that they obey the number theoretic conjectures and address two questions suggested by the previous work

multiple correction and continued fraction approximation abstract the main aim of this paper is to further develop a multiple correction method formulated in a previous work 6 as applications we find a kind of hybrid type finite continued fraction approximations in two cases of landau constants and lebesgue constants in addition we refine the previous results of lu 29 and xu and you 48 for the euler mascheroni constant

isoperimetric phase transitions of two dimensional droplets we consider two dimensional assemblies of particles governed by hamiltonians depending on the area and the perimeter of their convex hull provided the hamiltonian is quadratically homogeneous in the coordinates we find an exact formula for the free energy phase transitions resulting from the competition between area and perimeter can easily be produced and explicitly dealt with we illustrate those features by a simple example undergoing a second order transition

the droplet in the tube a case of phase transition in the canonical ensemble we consider the 2 dimensional ising model with ferromagnetic nearest neighbour interaction at inverse temperature lets n t be the total magnetization inside ann n square box per be the gibbs state in with periodic b c andm be the spontaneous magnetization we show the existence of the limit psi varrho mathop lim limits n to infty left frac 1 beta n right ln mu lambda per s n n varrho for m provided is large enough it turns out that the quantity is closely related to the wulf construction and the dependence of the function on is singular

a class of integral approximations for the factorial function we introduce stirling s formula in a more general class of approximation formulas to extend the integral representation of liu z liu a new version of the stirling formula tamsui oxf j math sci 23 4 2007 389 392 finally an accurate approximation for the factorial function is established

non negative solutions of the evolution p laplacian equation initial traces and cauchy problem when 1 p 2 from the introduction we continue here the investigation initiated earlier by us trans amer math soc 314 1989 no 1 187 224 concerning the solvability of the cauchy problem and the existence of initial traces for nonnegative weak solutions of the nonlinear evolution equation 1 ut div du p 2 du 0 in st rn 0 t 0 2 both in terms of results and techniques the main difference stems from the fact that unlike solutions in the case p 2 solutions of 1 are not in general locally bounded

special values of multiple polylogarithms historically the polylogarithm has attracted specialists and non specialists alike with its lovely evaluations much the same can be said for euler sums or multiple harmonic sums which within the past decade have arisen in combinatorics knot theory and high energy physics more recently we have been forced to consider multidimensional extensions encompassing the classical polylogarithm euler sums and the riemann zeta function here we provide a general framework within which previously isolated results can now be properly understood applying the theory developed herein we prove several previously conjectured evaluations including an intriguing conjecture of don zagier

systems of p laplacian differential inclusions with large diffusion abstract in this paper we consider coupled systems of p laplacian differential inclusions and we prove under suitable conditions that a homogenization process occurs when diffusion parameters become arbitrarily large in fact we obtain that the attractors are continuous at infinity on l 2 l 2 topology with respect to the diffusion coefficients and the limit set is the attractor of an ordinary differential problem

on the rapid computation of various polylogarithmic constants we give algorithms for the computation of the d th digit of certain transcendental numbers in various bases these algorithms can be easily implemented multiple precision arithmetic is not needed require virtually no memory and feature run times that scale nearly linearly with the order of the digit desired they make it feasible to compute for example the billionth binary digit of log 2 or on a modest work station in a few hours run time

the constructive membership problem for discrete two generator subgroups of sl2 r abstract we describe a practical algorithm to solve the constructive membership problem for discrete two generator subgroups of sl 2 r or psl 2 r this algorithm has been implemented in magma for groups defined over real algebraic number fields

adjoint transform overconvexity and sets of constant width the properties of the adjoint transform associating to a set the in tersection of all disks of given radius centered in the set are systematically in vestigated in particular its relationship with the overconvex the parallelisation and completion of sets sets conjugate by the transform can be characterised in a new way as the union or the intersection of all completions of the reference body new relationships satisfied by their areas and perimeters are derived two applications in problems of random intersection of disks are finally treated

abstract reaction diffusion systems with nonlocal initial conditions abstract we prove some sufficient conditions for the existence and global uniform asymptotic stability of c 0 solutions for a class of nonlinear delay reaction diffusion systems subjected to nonlocal initial conditions some applications to a specific reaction diffusion system are included

unbiased estimation in line intercept sampling summary a theory for unbiased estimation of the total of arbitrary particle characteristics in line intercept sampling for transects of fixed and of random length is presented this theory unifies present lineintercept sampling results examples are given and variance estimation is discussed 1 introduction and literature review line intercept sampling lis is a method of sampling particles in a region whereby roughly a particle is sampled if a chosen line segment called a transect intersects the particle it has the advantage over quadrat sampling in that there is no need to delineate the quadrats and determine which objects are in each quadrat examples of the economics of lis versus quadrat sampling can be found in canfield 1941 bauer 1943 warren and olsen 1964 and bailey 1970 the particles may represent plants shrubs tree crowns nearly stationary animals animal dens or signs roads logs forest debris particles on a microscope slide particles in a plane section of a rock or metal sample etc in early biological applications sampling with a transect appears to have been a purposivesampling technique for studying how vegetation varies with changing environment with the transect running perpendicular to the zonation weaver and clements 1929 in the study of range vegetation canfield 1941 incorporated random placement of the transect and by taking the proportion of the sampled transect intercepted by the vegetation obtained an unbiased estimator of coverage that is the ratio of the area covered by the vegetation to the area of the region of interest however he did not prove the unbiasedness of this estimator canfield called this method the line interception method he also discussed such design questions as how many lines of what length are required and whether or not the area of interest should be stratified bauer 1943 compared transect sampling to quadrat sampling in an area of dense chapparal vegetation and in a laboratory experiment he concluded that transect sampling deserves much wider use mcintyre 1953 investigated the possibility of using data on intercept lengths in order to estimate not only coverage but also density that is the ratio of the number of particles to the area of the region of interest he was able to do this for populations which consisted of particles that were all magnifications of a known shape lucas and seber 1977 presented and proved the unbiasedness of estimators of particle density and coverage for arbitrarily shaped and located particles when the transect is randomly placed their estimator of coverage is the same as that of canfield 1941 eberhardt 1978 reviewed three transect methods for use in ecological sampling lis and two methods line transect sampling and strip transect sampling in which the particles are points and the probability of observing a particle is a function of its perpendicular distance

interaction of localized large diffusion and boundary conditions abstract in this paper we derive the limiting pdes for parabolic problems where localized large diffusion touches the boundary of the domain hence the limit problem reflects the interaction of large diffusion and boundary conditions the limit problem is a pde coupled with a system of odes through some nonlocal terms we study the well posedness and dissipativity of the nonstandard limit problem as well as the continuity of the dynamics as diffusion becomes large

some singular moduli for q 3 in an earlier paper in this journal the authors derived the equations which transform the hilbert modular function field for q v3 when the arguments are multiplied by 1 v 3 1 x these equations define a complex v2 but we concentrate on special diagonal curves on which the values of some of the singular moduli can be evaluated numerically by using the psos algorithm in this way the ring class fields can be evaluated for the forms q2 2ta q2 where a 1 2 3 6 and t 0 these last results are based partly on conjectures supported here by numerical evidence

lattice sums arising from the poisson equation in recent times attention has been directed to the problem of solving the poisson equation either in engineering scenarios computational or in regard to crystal structure theoretical herein we study a class of lattice sums that amount to poisson solutions namely the n dimensional forms by virtue of striking connections with jacobi function values we are able to develop new closed forms for certain values of the coordinates rk and extend such analysis to similar lattice sums a primary result is that for rational x y the natural potential 2 x y is where a is an algebraic number various extensions and explicit evaluations are given such work is made possible by number theoretical analysis symbolic computation and experimental mathematics including extensive numerical computations using up to 20 000 digit arithmetic

new formulae of bbp type with different moduli abstract inspired by a method used by bellard in 1997 we establish a trigonometric expansion for the function arctan a x 1 and then utilize this expansion to derive numerous bbp type formulae that converge in most cases to well known irrational constants

numerical results on relations between fundamental constants using a new algorithm un vecteur de nombres reels x x 1 x 2 x n possede une relation entiere s il existe des entiers a 1 differents de zero tel que a 1 x 1 a 2 x 2 a n x n 0 l auteur decrit dans cet article un algorithme qui permet de trouver une telle relation il est plus efficace en termes de temps de calcul et de precision numerique que des precedents et il a ete implemente sur des ordinateurs de grande vitesse utilisant de l arithmetique multiprecision a l aide de ces programmes plusieurs resultats numeriques sur des constantes mathematiques ont ete generalises

continuity of the flows and upper semicontinuity of global attractors for ps x laplacian parabolic problems abstract in this work we prove continuity of solutions with respect to initial conditions and exponent parameters and we prove upper semicontinuity of a family of global attractors for one dimensional problems of the form u s t x u s x p s x 2 u s x b u s where b is a globally lipschitz map p s p in l i i c d and p 2 constant as s goes to infinity

on the microscopic validity of the wulff construction and of the generalized young equation for a large class of 1 1 dimensional interfaces of the solid on solid type we prove on a microscopic basis the validity of the wulff construction and of the generalized young equation which gives the contact angle of a sessile drop on a wall our proof relies on a new method to treat random walks with a finite number of global constraints

existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditions in this paper we provide a sufficient condition for the existence of c0 solutions for a class of nonlinear functional differential evolution equation of the form u t au t f t t r f t f t u t ut t r u t g u t t 0 where x is a real banach space a is the infinitesimal generator of a nonlinear compact semigroup f r x c 0 d a x is a nonempty convex and weakly compact valued multi function and g cb d a c 0 d a

existence and upper semicontinuity of pullback attractors for non autonomous p laplacian parabolic problems abstract we study the asymptotic behavior of parabolic p laplacian problems of the form u t t div d t u t p 2 u t u t p 2 u t b t u t in a bounded smooth domain in r n where n 1 p 2 d l t with 0 d t x m a e in t 0 and for each 0 we have d s x d t x c s t for all x s t t for some positive constants and c moreover d d 1 in l t as 1 we prove that for each 0 the evolution process of this problem has a pullback attractor and we show that the family of pullback attractors behaves upper semicontinuously at 1

multiprecision arithmetic using fast hartley transforms in this paper we describe a method to perform multiprecision multiplication using fast hartley transforms we improve this method further by eliminating bit reversal permutations

a note on p laplacian parabolic problems in rn abstract in this work we study the asymptotic behavior of parabolic p laplacian problems of the form u t div d u p 2 u a u p 2 u b u in l 2 r n where n 1 p 2 d l r n m d x 0 a e in r n 0 b l 2 r n l 2 r n is a globally lipschitz map and a r n r is a non negative continuous function we prove under suitable assumptions on a the existence of a global attractor in l 2 r n for each positive finite diffusion coefficient and we show that the family of attractors behaves upper semicontinuously with respect to positive finite diffusion parameters

continued fraction estimates for the psi function we present continued fraction estimates for the psi function as a consequence we educe inequality for the euler mascheroni constant which improves a result of detemple

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

parallel integer relation detection techniques and applications let x1 x2 xn be a vector of real numbers an integer relation algorithm is a computational scheme to find the n integers ak if they exist such that a1x1 a2x2 anxn 0 in the past few years integer relation algorithms have been utilized to discover new results in mathematics and physics existing programs for this purpose require very large amounts of computer time due in part to the requirement for multiprecision arithmetic yet are poorly suited for parallel processing this paper presents a new integer relation algorithm designed for parallel computer systems but as a bonus it also gives superior results on single processor systems single and multi level implementations of this algorithm are described together with performance results on a parallel computer system several applications of these programs are discussed including some new results in number theory quantum field theory and chaos theory

an extended multistep shanks transformation and convergence acceleration algorithm with their convergence and stability analysis the molecule solution of an extended discrete lotka volterra equation is constructed from which a new sequence transformation is proposed a convergence acceleration algorithm for implementing this sequence transformation is found it is shown that our new sequence transformation accelerates some kinds of linearly convergent sequences and factorially convergent sequences with good numerical stability some numerical examples are also presented

analysis of pslq an integer relation finding algorithm let k be either the real complex or quaternion number system and let o k be the corresponding integers let x x 1 x n be a vector in k n the vector x has an integer relation if there exists a vector m m 1 m n o k n m 0 such that m 1 x 1 m 2 x 2 m n x n 0 in this paper we define the parameterized integer relation construction algorithm pslq where the parameter can be freely chosen in a certain interval beginning with an arbitrary vector x x 1 x n k n iterations of pslq will produce lower bounds on the norm of any possible relation for x thus pslq can be used to prove that there are no relations for x of norm less than a given size let m x be the smallest norm of any relation for x for the real and complex case and each fixed parameter in a certain interval we prove that pslq constructs a relation in less than o n 3 n 2 logm x iterations

limits and inequalities associated with the euler mascheroni constant i we present several limits associated with the euler mascheroni constant ii let c 0 577215 be the euler mascheroni constant and let t n k 1 n1k lnn 12 124n and p n k 1 n22k 1 ln 4n we determine the best possible constants a b a and b such that the inequalities148 n a 3 c t n 148 n b 3and124 n a 2 1

numerical results on the transcendence of constants involving pi e and euler s constant the existence of simple polynomial equations integer relations for the constants e pi e pi log pi gamma euler s constant e exp gamma gamma e gamma pi and log gamma is investigated by means of numerical computations the recursive form of the ferguson fourcade algorithm ferguson and fourcade 1979 ferguson 1986 and 1987 is implemented on the cray 2 supercomputer at nasa ames applying multiprecision techniques similar to those described by bailey 1988 except that ffts are used instead of dual prime modulus transforms for multiplication it is shown that none of the constants has an integer relation of degree eight or less with coefficients of euclidean norm 10 to the 9th or less

advances in the theory of box integrals box integrals expectations or over the unit n cube or n box have over three decades been occasionally given closed forms for isolated n s by employing experimental mathematics together with a new global analytic strategy we prove that for n le 4 dimensions the box integrals are for any integer s hypergeometrically closed in a sense we clarify herein for n 5 dimensions we show that a single unresolved integral we call k sub 5 stands in the way of such hyperclosure proofs we supply a compendium of exemplary closed forms that naturally arise algorithmically from this theory

the asymptotic series of the generalized stirling formula the aim of this paper is to construct some asymptotic expansions which produce increasingly accurate approximations of the gamma function

new sequence converging towards the euler mascheroni constant we propose new sequences containing a modified logarithmic term which converge to the euler mascheroni constant faster than sequences known from the literature

best estimates of the generalized stirling formula the aim of this paper is to introduce an approximations family of the factorial function that contains stirling s formula burnside s formula and gosper s formula the parameters which provide the best approximations are indicated finally numerical computations are made to show the superiority of our formulas over other known formulas

optimal rate of convergence for sequences of a prescribed form abstract we provide a highly convergent version of the generalized euler sequence and we determine the element with the optimal rate of convergence in several classes of sequences of a prescribed form the new approach extends and unifies many previous efforts in this direction in addition we answer an open problem on the asymptotic expansion of the harmonic number sequence

polynomial time algorithms for finding integer relations among real numbers in this article we state and prove a corrected version of theorem 3 5 in siam j comput 18 1989 pp 859 881

disproof of the mertens conjecture the mertens conjecture states that m x 1 where m x n x n and n is the mo bius function this conjecture has attracted a substantial amount of interest in its almost 100 years of existence because its truth was known to imply the truth of the riemann hypothesis this paper disproves the mertens conjecture by showing that x lim sup m x x 2 1 06 the disproof relies on extensive computations with the zeros of the zeta function and does not provide an explicit counterexample disproof of the mertens conjecture a m odlyzko at t bell laboratories murray hill new jersey 07974 usa and h j j te riele centre for mathematics and computer science kruislaan 413 1098 sj amsterdam the netherlands

pde and ode limit problems for p x laplacian parabolic equations in this work we prove continuity of solutions with respect to initial conditions and parameters and we prove upper semicontinuity of a family of global attractors for problems of the form ut div d u p x 2 u b u in a bounded smooth domain in rn

on p laplacian differential inclusions global existence compactness properties and asymptotic behavior abstract in this work we consider coupled systems of p laplacian differential inclusions we obtain the global existence of solutions and good compactness properties in such way that the set of all possible solutions compose a generalized semiflow which has a global attractor for each pair of positive diffusion coefficients we also prove that the attractors are upper semicontinuous on positive finite diffusion parameters

some properties of the gamma and psi functions with applications in this paper some monotoneity and concavity properties of the gamma beta and psi functions are obtained from which several asymptotically sharp inequalities follow applying these properties the authors improve some well known results for the volume n of the unit ball b n r n the surface area n 1 of the unit sphere s n 1 and some related constants

complexity confusion and perceptual grouping part ii mapping complexity intermediate level vision is central to form perception and we outline an approach to intermediate level segmentation based on complexity analysis in this second of a pair of papers we continue the focus on edge element grouping and the motivating example of an edge element inferred from an unknown image is this local edge part of a long curve or part of a texture if the former which is the next element along the curve if the latter is the texture like a well combed hair pattern in which nearby elements are oriented similarly or more chaotic as in a spaghetti pattern in the previous paper we showed how these questions raise issues of complexity and dimensionality and how context in both position and orientation are important we now propose a measure based on tangential and normal complexities and illustrate its computation tangential complexity is related to extensions normal complexity to density taken together they define four canonical classes of tangent distributions those arising from curves from texture flows from turbulent textures and from isolated dust examples are included

parameter dependent quasi linear parabolic equations abstract in this work we are concerned with non linear reaction diffusion equations with principal part given by p laplacian and positive diffusion coefficient a l 0 a which has global attractors a we obtain some properties about the convergence of the solutions of these equations and show the upper semicontinuity of the attractors

the arithmetic geometric mean and fast computation of elementary functions we produce a self contained account of the relationship between the gaussian arithmetic geometric mean iteration and the fast computation of elementary functions a particularly pleasant algorithm for x is one of the by products

asymptotic properties in parabolic problems dominated by a p laplacian operator with localized large diffusion abstract this paper is concerned with upper semicontinuity of the family of attractors associated with nonlinear reaction diffusion equations with principal part governed by a degenerate p laplacian in which the diffusion d blows up in localized regions inside the domain

statistical mechanics of convex bodies the difficulties inherent in the construction of two dimensional pressure ensembles are discussed and are tackled by defining an energy cost depending on the convex hull of the set of particles an energy proportional to the area of the convex hull is not able to prevent evaporation of the system whereas an energy proportional to the area of the circumcircle of the convex hull ensures a thermodynamic behavior in the latter model which turns out to be exactly solvable various characterizations are given of the geometry of a typical state

best k digit rational approximation of irrational numbers pre computer versus computer era abstract the best k digit rational approximation for a given irrational number where the numerator has k digits is presented such an approximation allows better error free computation in the real world scenario than that permitted by the k digit decimal approximation of the irrational number it is pointed out that such a best k digit rational approximation though exponential has been made possible due to current high speed computation performed by a digital computer to appreciate the importance of such an approximation we have also focused on the rational approximation not always the best one of some of the famous irrational numbers such as the and the exponential function e by the ingenuity of super mathematicians in several parts of the world during the pre computer era spanning over centuries

the computation of π to 29 360 000 decimal digits using borweins quartically convergent algorithm in a recent work 6 borwein and borwein derived a class of algorithms based on the theory of elliptic integrals that yield very rapidly convergent approximations to elementary constants the author has implemented borweins quartically convergent algorithm for 1 using a prime modulus transform multi precision technique to compute over 29 360 000 digits of the decimal expansion of the result was checked by using a different algorithm also due to the borweins that converges quadratically to these computations were performed as a system test of the cray 2 operated by the numerical aerodynamical simulation nas program at nasa ames research center the calculations were made possible by the very large memory of the cray 2

large diffusivity and asymptotic behavior in parabolic systems abstract for systems of reaction diffusion equations with neumann boundary conditions it is shown that the solutions are asymptotic to the solutions of an ordinary differential equation if the diffusivity is large the methods apply also to reaction diffusion systems with time delays

error bounds on the estimation of fractal dimension the use of fractal dimension as an index of complexity is widely used in natural science studies related to the significance of the estimates obtained have rarely been presented in the past this paper is intended to present an error analysis in the estimation of the fractal dimension of a particular class of objects namely graphs of knopp functions the algorithm used to estimate the fractal dimension is the variation method various numerical approximations of the variation will be presented using functional properties of the chosen parametric family of sets we derive error bounds useful in the assessment of the accuracy that can be achieved in the numerical approximation of the dimension at a given scale and resolution

monotonicity theorems and inequalities for the complete elliptic integrals we prove monotonicity properties of certain combinations of complete elliptic integrals of the first and second kind k and e these results lead to sharp symmetrical bounds for k and e which improve recently discovered inequalities

fast and efficient parallel evaluation of the zeros of a polynomial having only real zeros abstract given a polynomial p x of degree n with integer coefficients between 2 m and 2 m it suffices to use o log 2 n log b parallel arithmetic steps and n 2 processors in order to compute all the zeros of p x with absolute errors at most 2 h provided that all the zeros are real and b m h the algorithm combines the recent techniques and results of 1 3 in order to improve the previous record processor bound of 1 at least on the factor of n preserving its upper bound on parallel time

existence for reaction diffusion systems a compactness method approach the authors study the existence of weak solutions for the following system ut u f u v vt v g u v in 0 t u v 0 on 0 t u 0 x u0 x v 0 x v0 x in the region rn with smooth boundary the functions r r are assumed to be continuous and nondecreasing with 0 0 0 u0 v0 l f g r2 2r with f an upper semicontinuous mapping u s c the following local existence results are shown 1 for the diffusive case i e when both and are strictly increasing with u s c g 2 for the semi diffusive case only one function is strictly increasing with g being either with separated variables i e having the form of the product or of the sum of two functions g u and h v or globally lipschitz with respect to its second variable i e g u v g u v l v v for each u b r v v r and some l l b additional conditions of linear form on the growth of f and g are indicated to guarantee global existence results

a solution to an open problem on the euler mascheroni constant the classical le verrier algorithm for the calculation of the characteristic polynomial of a matrix has led us to a solution of an open problem concerning the euler mascheroni constant c more exactly we prove that there exists uniquely a sequence of rational numbers n n 1 such that for any integer q 1 the sequence k 1n1k logn log1 1n qn q is an n q 1 order approximation of c

estimating the digamma and trigamma functions by completely monotonicity arguments abstract we establish new sharp bounds for the digamma and trigamma functions using the complete monotonicity of some class of functions

improved asymptotic formulas for the gamma function the aim of this paper is to improve the ramanujan formula for approximation the gamma function a fast asymptotic series is constructed

a noncontinuous generalization of the arithmetic geometric mean the notions of prickly set scalar and vectorial mean are defined a noncontinuous generalization of the arithmetic geometric mean is given by considering the recursion x n 1 f x n where f c c is a vectorial mean and c is a closed prickly subset of r m the convergence of this recursion is proved and it is shown that the limit is contained in the diagonal of c if f is continuous it is deduced that the limit of the recursion is a continuous function of the initial value x x 0 denoting the limit by f x it is proved that if f is monotone then f it is also monotone where the monotonicity is considered with respect to the closed cone r m

well posed p laplacian problems with large diffusion abstract in this work we study the asymptotic behavior of p laplacian parabolic problems of the form u t d p u u p 2 u b u in a bounded smooth domain in r n and under neumann boundary conditions when the diffusion coefficient d becomes large we prove under suitable assumptions that the family of attractors behaves lower and upper semicontinuously as the diffusion increases to infinity

inconstancy of finite and infinite sequences in order to study large variations or fluctuations of finite or infinite sequences time series we bring to light an 1868 paper of crofton and the cauchy crofton theorem after surveying occurrences of this result in the literature we introduce the inconstancy of a sequence and we show why it seems more pertinent than other criteria for measuring its variational complexity we also compute the inconstancy of classical binary sequences including some automatic sequences and sturmian sequences