transport diffusion models with nonlinear boundary conditions and solution by generalized collocation methods this paper deals with the derivation of a class of nonlinear transport and diffusion models implemented with nonlinear boundary conditions mathematical tools to treat the initial boundary value problems are developed based on generalized collocation methods focused on the treatment of nonlinear boundary conditions in one space dimension applications refer to a problem of interest in applied sciences

excursions of dual processes there has been considerable interest in the excursions of a markov process in recent years perhaps the most important general result is that of maisonneuve 13 in which the existence of an exit system is established this general result was applied to the study of specific excursions by getoor in 5 then maisonneuve recast and generalized these results in 14 where he showed how to discuss the excursion straddling a certain class of stopping times t these included the excursion straddling a fixed time and the first excursion whose length exceeds a given value which were discussed in 5 the purpose of this paper is to study excursions for processes which satisfy duality conditions a start in this direction was made in section 10 of 5 under assumptions that were much too strong it turns out that the appropriate duality hypotheses are stronger than those of classical duality as described in i we assume the existence of dual transition densities rather than the weaker assumption of dual potential kernel densities our precise assumptions are described in section 2 and especially in section 3 in particular it is shown in these sections that a systematic use of space time processes obviates the need for any regularity assumptions on the density over and above the chapman kolmogorov equation section 4 summarizes the special properties of additive functionals under our hypotheses that are needed in later sections in theorem 4 5 we show that if m is a closed homogeneous optional set then under duality assumptions there exists a borel set f c e e such that me3 0 and t 0 xt xt f are indistinguishable in section 5 we begin the discussion of excursions from a closed homogeneous optional set m with r i n f t 0 t c m if f e e corresponds to m as above r inf t xt art f almost surely especially important is 5 17 which gives the joint distribution of r x r and x r this is obtained by applying a reversal argument to the excursion

an assessment of the differential quadrature time integration scheme for nonlinear dynamic equations in 1996 xie an assessment of time integration schemes for non linear dynamic equations journal of sound and vibration 192 1 1996 321 331 presented an assessment on seven existing and commonly used time integration schemes for nonlinear dynamic equations in this work the differential quadrature dq time integration scheme proposed by fung in 2001 is assessed following the same procedures as xie s it is shown that accurate numerical results can be obtained by the dq method when using much larger time step over the commonly used time integration schemes based on the results reported herein some conclusions are drawn

coefficient ideals in and blowups of a commutative noetherian domain abstract the ratliff rush ideal associated to a nonzero ideal i in a commutative noetherian domain r with unity is n 1 in 1 rin is r s b i where b i r i a p a i 0 p spec r i a is the blowup of i we observe that certain ideals are minimal or even unique in the class of ideals having the same associated ratliff rush ideal if r m is local quasi unmixed and analytically unramified and if i is m primary then we show that the coefficient ideal i k of i i e the largest ideal containing i whose hilbert polynomial agrees with that of i in the highest k terms is also contracted from a blowup b i k which is obtained from b i by a process similar to s2 ification this allows us to generalise the notion of coefficient ideas we investigate these ideas in the specific context of a two dimentional regular local ring observing the interaction of these notions with the zariski theory of complete ideals

an enhanced exponential matrix approach aimed at the stability of piecewise beams on elastic foundation in this paper an enhanced exponential collocation method for the stability assessment of piecewise beams resting on elastic foundation and subjected to both non uniform distributed and concentrated loads is presented the exponential basis functions usually adopted in literature are enriched with trigonometric functions that make the eigenvalue analysis well posed without reducing the original simplicity of the method a measure of the error occurring from the proposed approach and its improvement are also proposed several examples aimed at estimating the buckling loads under typical end supports are discussed a comparison with exact and with other numerical results that are available in literature are carried out such a comparison shows the high accuracy and the fast convergence of the proposed approach

noetherian intersections of regular local rings of dimension two abstract let d be a 2 dimensional regular local ring and let q d denote the quadratic tree of 2 dimensional regular local overrings of d we describe the desingularization of projective models over d both algebraically in terms of the saturation of complete ideals and order theoretically in terms of the quadratic tree q d we prove that this describes all the noetherian rings that are intersections of rings in q d

blowing up finitely supported complete ideals in a regular local ring let i be a finitely supported complete m primary ideal of a regular local ring r m we consider singularities of the projective models projr it and projr it over spec r where r it denotes the integral closure of the rees algebra r it a theorem of lipman implies that the ideal i has a unique factorization as a product of special simple complete ideals with possibly negative exponents for some of the factors if projr it is regular we prove that projr it is the regular model obtained by blowing up the finite set of base points of i extending work of lipman and huneke sally in dimension 2 we prove that every local ring s on projr it that is a unique factorization domain is regular moreover if dim s 2 and s dominates r then s is an infinitely near point to r that is s is obtained from r by a finite sequence of local quadratic transforms

weak form quadrature element method for accurate free vibration analysis of thin skew plates in this paper a novel weak form quadrature element method qem is proposed for accurate free transverse vibration analysis of thin isotropic skew plates with general boundary conditions in the formulation of the stiffness matrix the first and second order derivatives of the shape functions at integration points are computed explicitly by using the differential quadrature rule this leads to a great simplicity in formulating an n n node quadrature plate element and a large reduction of programming effort different from the existing weak form quadrature element method or differential quadrature finite element method the element nodes can be either the same or different from the integration points convergence studies are performed free vibration of skew thin plates with various skew angles and different combinations of boundary conditions is analyzed it is shown that although the assumed displacement field does not explicitly consider the bending moment singularities at the obtuse angles the proposed qem can yield accurate frequencies even for the thin isotropic skew plate with large skew angles

a dqem for transverse vibration analysis of multiple cracked non uniform timoshenko beams with general boundary conditions in this paper a differential quadrature element method dqem for free transverse vibration analysis of multiple cracked non uniform timoshenko beams with general boundary conditions is proposed governing equations the compatibility conditions at the damaged cross sections and implementation of the external boundary conditions are derived and formulated by the differential quadrature analogue the accuracy convergence and versatility of the proposed method are confirmed by the exact solution of the uniform beam which has been presented by other authors and 2d finite element method fem numerical results for non uniform beam after the validation of the presented method the effect of quantity depth and location of the cracks on the frequency values of vibrations are investigated the achieved results show that the existence of the crack leads to a decrease in the frequencies of the vibrations through decrease in the stiffness of the beam meanwhile the compatibility conditions at the damaged section is considered as a discontinuity in slope and vertical displacement where the effect of the discontinuity in the slope is more considerable as many authors have neglected the discontinuity in the vertical displacement as it will be shown consideration of the discontinuity in the vertical displacement causes more decrease in the frequencies

elastoplastic buckling analysis of thick rectangular plates by using the differential quadrature method the paper investigates the elastoplastic buckling behavior of thick rectangular plates by using the differential quadrature dq method mindlin plate theory is adopted to take the transverse shear effect into considerations both incremental theory and deformation theory are employed due to the material non linearity iteration processes are involved for obtaining solutions detailed methodology and procedures are derived the elastoplastic buckling behavior of thick rectangular plates with ten combinations of boundary conditions and under various loadings is studied to verify the dq solution procedures dq results are compared with existing analytical solutions for plates with two boundaries simply supported and the others simply supported clamped or free then the dq method is used to obtain solutions of rectangular thick plates with other combinations of boundary conditions since no analytical solutions for such cases are available the buckling loads obtained by the dq method could serve as a reference the phenomenon reported in the literature namely the deformation theory generally gives consistently lower buckling loads than the incremental theory and large discrepancy in predictions between the two theories exists with increasing of plate thickness e s 0 and c in the ramberg osgood relations is also observed for the cases studied herein apart from the phenomenon reported earlier by durban that deformation theory predicted a progressively lower in plane shear modulus as the level of plasticity increased thus predicted lower buckling loads another reason is given herein to explain the large discrepancy in predictions for thicker plates with the deformation theory and incremental theory

differential quadrature element analysis using extended differential quadrature abstract the extended differential quadrature edq has been proposed a certain order derivative or partial derivative of the variable function with respect to the coordinate variables at an arbitrary discrete point is expressed as a weighted linear sum of the values of function and or its possible derivatives at all grid nodes the grid pattern can be fixed while the selection of discrete points for defining discrete fundamental relations is flexible this method can be used to the differential quadrature element and generalized differential quadrature element analyses

castelnuovo mumford regularity and ratliff rush closure abstract we establish strong relationships between the castelnuovo mumford regularity and the ratliff rush closure of an ideal our results have several interesting consequences on the computation of the ratliff rush closure the stability of the ratliff rush filtration the invariance of the reduction number and the computation of the castelnuovo mumford regularity of the rees algebra and the fiber ring in particular we prove that the castelnuovo mumford regularity of the rees algebra and of the fiber ring are equal for large classes of monomial ideals in two variables thereby verifying a conjecture of eisenbud and ulrich for these cases

on the numerical solutions of second order macroscopic models of pedestrian flows the main target of this paper is focused on the numerical simulation of macroscopic models two dimensional hyperbolic conservation law of pedestrian flows therefore finite volume methods can be used to discretize the equations actually the algorithms that have been used are particularly suited for solving hyperbolic problems moreover simulations using first order accurate numerical solvers and first godunov type schemes s k godunov a finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics mathematik sbornik 47 1959 271 290 have been developed this article is motivated by recent research activity focused on the problem of modelling systems of the living matter

brownian excursions from hyperplanes and smooth surfaces on obtient une decomposition en produit gauche de la loi d excursion brownienne a n dimensions n 2 a partir d un hyperplan

generalized collocation method for two dimensional reaction diffusion problems with homogeneous neumann boundary conditions nonlinear reaction diffusion problems are ubiquitous in science ranging from physics to engineering from economy to biology in particular in this paper two dimensional problems with generic dirichlet boundary conditions or homogeneous neumann boundary conditions are focused on to simulate this class of mathematical problems a quite simple generalized collocation method is proposed and developed moreover a test case and an application to the schnakenberg model are described in order to show the efficiency of the simulation method and the goodness of the numerical results

graded rings associated with contracted ideals the study of the ideals in a regular local ring r m of dimension 2 has a long and important tradition dating back to the fundamental work of zariski zs more recent contributions are due to several authors including cutkosky huneke lipman rees sally and teissier among others see c1 c2 h hs l lt r one of the main result in this setting is the unique factorization theorem for complete i e integrally closed ideals proved originally by zariski zs theorem 3 appendix 5 it asserts that any complete ideal can be factorized as a product of simple complete ideals in a unique way up to the order of the factors by definition an ideal is simple if it cannot be written as a product of two proper ideals another important property of a complete ideal i is that its reduction number is 1 which in turns implies that the associated graded ring gri r is cohen macaulay and its hilbert series is well understood this is due to lipman and teissier lt see also hs the class of contracted ideals plays an important role in the original work of zariski as well as in the work of huneke h an ideal i of r is contracted if i r ir m x for some x m m2 any complete ideal is contracted but not the other way round the associated graded ring gri r of a contracted ideal i need not be cohen macaulay and its hilbert series can be very complicated

on the structure of the fiber cone of ideals with analytic spread one for a given a local ring a m we study the fiber cone of ideals in a with analytic spread one in this case the fiber cone has a structure as a module over its noether normalization which is a polynomial ring in one variable over the residue field one may then apply the structure theorem for modules over a principal domain to get a complete description of the fiber cone as a module we analyze this structure in order to study and characterize in terms of the ideal itself the arithmetical properties and other numerical invariants of the fiber cone as multiplicity reduction number or castelnuovo mumford regularity

buckling and post buckling analysis of extensible beam columns by using the differential quadrature method buckling and post buckling analysis of extensible beam columns is performed numerically in this paper it was experienced earlier that in some cases the numerical integration would not produce the convergent post buckling solutions especially under high loads therefore a new differential quadrature dq based iterative numerical integration method is proposed to solve post buckling differential equations of extensible beam columns six cases including five classical euler buckling cases are analyzed critical loads and convergent post buckling solutions under different applied loads are obtained the results are compared with the existing multiple scales solutions it is found that under high applied loads the small rotation assumption in obtaining multiple scales solutions is no longer valid the proposed iterative dq based numerical integration method can yield reliable and accurate post buckling solutions even at high applied loads for the cases investigated

solution of nonlinear initial boundary value problems by sinc collocation interpolation methods abstract this paper deals with the solution of initial boundary value problems for nonlinear evolution equations in one and two space dimensions the solution technique is based on collocation interpolation methods which use sinc functions the application refers to some direct and inverse type problems

depth of fiber cones of ideals with almost minimal mixed multiplicity let r m be a cohen macaulay local ring of dimension d 0 i an m primary ideal with almost minimal mixed multiplicity such that depth g i d 1 we show that fm i has almost maximal depth i e depth fm i d 1

on brownian excursions in lipschitz domains part i local path properties a necessary and sufficient condition is given for a brownian excursion law in a lipschitz domain to share the local path properties with an excursion law in a halfspace this condition is satisfied for all boundary points of every c1 t domain ct 0 there exists a cl domain such that the condition is satisfied almost nowhere on the boundary a probabilistic interpretation and applications to minimal thinness and boundary behavior of green functions are given 0 introduction we will show that the local path properties of brownian excursions in cl domains a 0 are the same as the local path properties of brownian excursions in a half space theorem 3 1 this need not be the case if the domain is of class c proposition 3 1 the method of proof is based on the exit system theory of maisonneuve 12 we will study brownian excursion laws i e one of the ingredients of an exit system we will give a necessary and sufficient condition for an excursion law in a lipschitz domain to have the same local path properties as an excursion law in a half space theorems 2 1 and 2 2 this last result can be applied to obtain new criteria for minimal thinness theorem 4 1 and existence of a nondegenerate normal derivative for the green function theorem 4 2 local path properties of 1 dimensional brownian excursions have been known for some time they are the same as the local path properties of the 3 dimensional bessel process see 2 10 of ito and mckean 11 or ii 67 of williams 21 dvoretsky and erd6s 8 and shiga and watanabe 18 have given kolmogorov type tests for bessel processes local path properties of excursions of multidimensional brownian motion have been studied by shimura 19 excursions of 2 dimensional brownian motion from a line and burdzy 1 n dimensional case n 2 our theorem about minimal thinness generalizes results of essen and jackson 9 and burdzy 3 4 a new criterion for the existence of the nondegenerate normal derivative for the green function extends some results of widman 20 rippon 17 and burdzy 4 the present article mainly uses ideas from excursion theory see maisonneuve 12 williams 21 and burdzy 1 and potential theory see doob 7 received by the editors july 26 1985 1980 mathematics subject classification 1985 revision primary 60g17 60j50 60j65 secondary 31b25 60j45

the tree of quadratic transforms of a regular local ring of dimension two abstract let d be a 2 dimensional regular local ring and let q d denote the quadratic tree of 2 dimensional regular local overrings of d we explore the topology of the tree q d and the family r d of rings obtained as intersections of rings in q d if a is a finite intersection of rings in q d then a is noetherian and the structure of a is well understood however other rings in r d need not be noetherian the two main goals of this paper are to examine topological properties of the quadratic tree q d and to examine the structure of rings in the set r d

sinc collocation interpolation method for the simulation of nonlinear waves abstract numerical simulation is of great importance in the study of nonlinear waves where several delicate aspects must be dealt with the presence of spatial and time gradients of complex nonlinearities and high order derivatives in fact generates various complex problems this paper develops a collocation interpolation method based on interpolation by the sine functions after a description of the method several examples are shown these show the good results that can be obtained the efficency and stability of the method and the low computing time

quasi one fibered ideals in two dimensional muhly local domains abstract in this paper a two dimensional integrally closed noetherian local domain r m with algebraically closed residue field is said to be a muhly local domain if the associated graded ring is an integrally closed domain using the theory of degree functions developed by rees and sharp and the zariski lipman theory of complete ideals in two dimensional regular local rings we study m primary ideals of r having among their rees valuations exactly one valuation ord r we therefore call these ideals quasi one fibered some consequences are deduced

generalized hilbert coefficients and northcott s inequality abstract let r be a cohen macaulay local ring of dimension d with infinite residue field let i be an r ideal that has analytic spread l i d satisfies the g d condition and the weak artin nagata property a n d 2 we provide a formula relating the length i n 1 j i n to the difference p i n h i n where j is a general minimal reduction of i p i n and h i n are respectively the generalized hilbert samuel polynomial and the generalized hilbert samuel function we then use it to establish formulas to compute the generalized hilbert coefficients of i as an application we extend northcott s inequality to non m primary ideals furthermore when equality holds we prove that the ideal i enjoys nice properties indeed if this is the case then the reduction number of i is at most one and the associated graded ring of i is cohen macaulay we also recover results of g colome nin c polini b ulrich and y xie on the positivity of the generalized first hilbert coefficient j 1 i our work extends that of s huckaba c huneke and a ooishi to ideals that are not necessarily m primary

a martin boundary in the plane let e be an open connected subset of euclidean space with a green function and let a be harmonic measure on the martin boundary i of e we will show that except for a a x a null set of x y g i 2 x is an entrance point for brownian motion conditioned to leave e at y r s martin gave examples in dimension 3 or higher for which there exist minimal accessible martin boundary points x 7 y for which this condition fails we will give a similar example in dimension 2

integral degree of a ring reduction numbers and uniform artin rees numbers abstract the supremum of reduction numbers of ideals having principal reductions is expressed in terms of the integral degree a new invariant of the ring which is finite provided the ring has finite integral closure as a consequence one obtains bounds for the castelnuovo mumford regularity of the rees algebra and for the artin rees numbers

free vibration analysis of curvilinear quadrilateral plates by the differential quadrature method a methodology for applying the differential quadrature dq method to the free vibration analysis of arbitrary quadrilateral plates is developed in our approach the irregular physical domain is transformed into a rectangular domain in the computational space the governing equation and the boundary conditions are also transformed into relevant forms in the computational space then all the computations are based on the computational domain as compared to the approach proposed by c w bert and m malik int j mech sci 38 589 1996 the present approach requires much less computational effort and virtual storage in addition the present work uses a simple and convenient way to implement clamped and simply supported boundary conditions an exact mapping technique is used to perform the coordinate transformation in this study some numerical examples are provided to show the computational efficiency of the present scheme

a class of projectively full ideals in two dimensional muhly local domains abstract let r m be a regular local domain of dimension d 2 and let x 1 x d be a regular system of parameters then ciuperca heinzer ratliff jr and rush have proved that every ideal of the form i x 1 n x 2 x d r with n n is projectively full if r m is a two dimensional muhly local domain i e an integrally closed noetherian local domain with algebraically closed residue field and the associated graded ring an integrally closed domain then we are able to prove a similar result for every minimal ideal basis x 1 x d of m such that x 1 rad x 2 x d

two new approximate methods for analyzing free vibration of structural components two approximate methods which have not previously been used for structural dynamics problems are applied to the free vibration analysis of various structural components the first method is a new version of the complementary energy method it is shown to be considerably more accurate than the conventional rayleigh and rayleigh schmidt methods when applied to spatially one dimensional free vibration problems prismatic and tapered bars prismatic beams and axisymmetric motion of circular membranes the second method is the differential quadrature method introduced by bellman and his associates it is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates

brownian excursions and minimal thinness i on donne des criteres de type integral et un critere de type kolmogorov pour les excursions browniennes comme corollaire

three dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method this paper presents accurate three dimensional elasticity solutions for free vibrations of six types of plates having free lateral surfaces two opposite sides simply supported and two other sides having combinations of simply supported clamped and free boundary conditions the solution methodology adopted in the present work first reduces the spatial variables in the governing elasticity equations to two by using displacement functions in the forms which satisfy the boundary conditions of the assumed simply supported sides the eigenvalue equations are then formulated from the reduced governing equations and the boundary conditions via the differential quadrature method the numerical results include the first nine natural frequencies of the six plate configurations for combinations of three aspect ratios and two thickness ratios these results are supported by appropriate convergence studies and comparisons with the results of other authors

a new differential quadrature methodology for beam analysis and the associated differential quadrature element method this paper presents a computationally efficient and an accurate new methodology in differential quadrature analysis of beam elements the methodology would overcome the difficulties in boundary conditions implementations of fourth order differential equations encountered in such problems the methodology benefited from defining the second order derivatives along the boundaries as independent degrees of freedom would enable the differential quadrature method to exactly satisfy some types of boundary conditions where by most other conventional algorithms have to be satisfied approximately the weighting coefficients employed are not exclusive and any accurate and efficient method such as the generalized differential quadrature method may be used to produce the methods weighting coefficients by solving some typical stability deflection and frequency analysis beam problems and by comparing the results with those of exact solutions and or those of other methodologies accuracy convergency and efficiency of the methodology is asserted in order to generalize its application to large scale beam structures and to the cases with the discontinuity in loading conditions and geometry a new one dimensional differential quadrature element method formulation is presented and implemented

determination of critical buckling load for elastic columns of constant and variable cross sections using variational iteration method in this paper variational iteration method vim is applied to the problem of determination of critical buckling loads for euler columns with constant and variable cross sections vim is a powerful method for the solution of nonlinear ordinary and partial differential equations and integral equations hence it is a suitable approach for the analysis of engineering problems where an exact solution is difficult to obtain this study presents the application of vim to various buckling cases and results are produced for columns with different support conditions and with different variation of cross sections the results obtained are accurate which show that variational iteration method is a very efficient technique in the analysis of elastic stability problems

the diffusion limit of transport equations derived from velocity jump processes in this paper we study the diffusion approximation to a transport equation that describes the motion of individuals whose velocity changes are governed by a poisson process we show that under an appropriate scaling of space and time the asymptotic behavior of solutions of such equations can be approximated by the solution of a diffusion equation obtained via a regular perturbation expansion in general the resulting diffusion tensor is anisotropic and we give necessary and sufficient conditions under which it is isotropic we also give a method to construct approximations of arbitrary high order for large times in a second paper part ii we use this approach to systematically derive the limiting equation under a variety of external biases imposed on the motion depending on the strength of the bias it may lead to an anisotropic diffusion equation to a drift term in the flux or to both our analysis generalizes and simplifies previous derivations that lead to the classical patlak keller segel alt

analytical and numerical results for vibration analysis of multi stepped and multi damaged circular arches this paper investigates the in plane linear dynamic behaviour of multi stepped and multi damaged circular arches under different boundary conditions cracked cross sections are modelled as massless elastic rotational hinges in damaged configuration cracks can be located both at the interface between two adjacent portions as well as inside the portion itself for each arch portion bounded by two cracks the differential equations of motion have been established considering axial extension transverse shear effects and rotatory inertia the equilibrium equations of arch portions are combined in the coupled fundamental system in terms of radial displacement tangential displacement and rotation analytical and numerical solutions for multi stepped arches in undamaged as well as in damaged configurations are proposed the analytical solution is based on the euler characteristic exponent procedure involving the roots of characteristic polynomials while the numerical method is focused on the generalized differential quadrature gdq method and the generalized differential quadrature element gdqe technique numerical results are shown in terms of the first 10 analytical and numerical frequencies of multi stepped and multi damaged arches with different boundary conditions finally convergence and stability characteristics of the gdqe procedure are investigated the convergence rate of the natural frequencies is shown to be very fast and the stability of the numerical procedure is very good

sally modules of canonical ideals in dimension one and 2 agl rings abstract the notion of 2 agl ring in dimension one which is a natural generalization of almost gorenstein local ring is posed in terms of the rank of sally modules of canonical ideals the basic theory is developed investigating also the case where the rings considered are numerical semigroup rings over fields examples are explored

a generalized differential quadrature element method abstract the generalized differential quadrature element method gdqem has been proposed the element weighting coefficients are generated by a generic differential quadrature gdq with which the element weighting coefficients for elements having arbitrary configurations can be straightly generated by using this gdq technique the governing differential or partial differential equations defined on all elements the transition conditions on the inter element boundary of two adjacent elements and the boundary conditions can be discretized a global algebraic equation system can be obtained by assembling all of the discretized equations this method can convert a generic engineering or scientific problem having an arbitrary domain configuration into a computer algorithm without adopting the mapping technique

block marching in time with dq discretization an efficient method for time dependent problems abstract in this paper an efficient method is presented to solve time dependent problems the proposed method marches in the time direction block by block in each block there are several time levels and the numerical results at these time levels are obtained simultaneously the global method of differential quadrature is applied in each block to discretize both the spatial and temporal derivatives the proposed method is validated by a sample problem which has an exact solution for easy comparison it was found that as compared to the conventional 4 stage runge kutta method the present method could give much higher order of accuracy for numerical results and require much less computational effort

ratliff rush closures and coefficient modules let r m be ad dimensional noetherian local domain supposemis a finitely generated torsion freer module and supposefis a freer module containingm in analogy with a result of ratliff and rush indiana univ math j 27 1978 929 934 concerning ideals we define and prove existence and uniqueness of theratliff rushclosureofminf we also discuss properties of ratliff rush closure in addition to the preceding assumptions supposef mhas finite length as anr module then we define thebuchsbaum rimpolynomialofminf in analogy with the work of k shah trans amer math soc 327 1991 373 384 we definecoefficientmodulesofminf under the assumption thatris quasi unmixed we prove existence and uniqueness of coefficient modules ofminf

solving initial value problems by differential quadrature method part 1 first order equations in this paper the differential quadrature method is used to solve first order initial value problems the initial condition is given at the beginning of a time interval the time derivative at a sampling grid point within the time interval can be expressed as a weighted linear sum of the given initial condition and the function values at the sampling grid points within the time interval the order of accuracy and the stability property of the quadrature solutions depend on the locations of the sampling grid points it is shown that the order of accuracy of the quadrature solutions at the end of a time interval can be improved to 2n 1 or 2n if the n sampling grid points are chosen carefully in fact the approximate solutions are equivalent to the generalized pade approximations the resultant algorithms are therefore unconditionally stable with controllable numerical dissipation the corresponding sampling grid points are found to be given by the roots of the modified shifted legendre polynomials from the numerical examples the accuracy of the quadrature solutions obtained by using the proposed sampling grid points is found to be better than those obtained by the commonly used uniformly spaced or chebyshev gauss lobatto sampling grid points copyright 2001 john wiley sons ltd

finite volume and weno scheme in one dimensional vascular system modelling a finite volume and weno model is developed validated and applied to a one dimensional numerical investigation of the vascular system suitable balance laws are spatially integrated using a finite volume weno approach time integration is performed using a five steps fourth order accurate runge kutta strong stability preserving scheme a detailed investigation of different sets of reflecting and non reflecting boundary conditions is performed to achieve a correct representation of limited portions of the vascular system moreover special attention is devoted to the numerical discretisation of the source term finally as an application of the whole model the effect of an abdominal aorta aneurysm on the blood flow is evaluated

liftable derivations for generically separably algebraic morphisms of schemes we consider dominant generically algebraic e g generically fi nite and tamely ramified if the characteristic is positive morphisms n x s y s of s schemes where y 5 are ncetherian and integral and x is a krull scheme e g normal ncetherian and study the sheaf of tangent vector fields on y that lift to tangent vector fields on x we give an easily com putable description of these vector fields using valuations along the critical locus we apply this to answer the question when the liftable derivations can be defined by a tangency condition along the discriminant in particular if it is a blow up of a coherent ideal we show that tangent vector fields that preserve the ratliff rush ideal equals in 1 n for high n associated to are liftable and that all liftable tangent vector fields preserve the integral closure of we also generalise in positive characteristic seidenberg s theorem that all tangent vector fields can be lifted to the normalisation assuming tame ramification

bounds related to projective equivalence classes of ideals let z be a regular ideal in noetherian ring r and let i denote the integral closure of i a situation which is often of interest is when there is an integer b z 2 0 such that i b a e i for all n 2 1 for instance in an analytically unramified local ring such a b z exists for all i now recall that the ideal h is projectively equivalent to i if there are positive integers r and s with h i in section 1 we make the easy observation that the existence of b z as above is an invariant of the projective equivalence class of i that is if such a b z exists and if the ideal h is projectively equivalent to z then there is a b h with h bch n c h for all n 2 1 of course it may happen that b h b z the main purpose of section 1 is to study the stronger condition that there exist a fixed integer b 3 0 such that for all ideals h projectively equivalent to z h c h for all n 1 we make use of a key result namely that given z there exists an integer d such that for any ideal h projectively equivalent to z one can write hd p for some s let s 2 1 be an integer and let the ideal k be a reduction of i this means there is an integer e 20 depending on s and k with k z z in section 2 we discuss a situation in which e can in fact

from microscopic to macroscopic description of multicellular systems and biological growing tissues this paper presents an asymptotic theory for a large class of boltzmann type equations suitable to model the evolution of multicellular systems in biology the mathematical approach described herein shows how various types of diffusion phenomena linear and nonlinear can be obtained in suitable asymptotic limits time scaling related to cell movement and biological activity are shown to play a crucial role in determining the macroscopic equations corresponding to each case

bounds on the a invariant and reduction numbers of ideals abstract let r be a d dimensional standard graded ring over an artinian local ring let m be the unique maximal homogeneous ideal of r let hi r n denote the length of the nth graded component of the local cohomology module h i m r define the eisenbud goto invariant eg r of r to be the number q 0 d 1 d 1 q h q m r 1 q we prove that the a invariant a r of the top local cohomology module h m d r satisfies the inequality a r e r l r1 d 1 l r0 1 eg r this bound is used to get upper bounds for the reduction number of an m primary ideal i of a cohen macaulay local ring r m when the associated graded ring of i has depth at least d 1

a numerical comparison of seven grids for polynomial interpolation on the interval abstract seven types of chebyshev like grids in one dimension are compared according to four different criteria for accuracy the grid which minimizes the lebesgue constant is the best because it performs fairly well by all four criteria for the same reason minimizing the lebesgue constant seems to be the most useful measure of optimality because grids that are good according to this criterion are good when measured by other criteria too cfm optimality which is the property that all cardinal functions lagrange fundamental polynomials have maxima at the interpolation points seems to be the least discriminating criterion because all seven grids generate cardinal functions that have maxima at or very near the interpolation points the difference between these grids on all four criteria always less than a factor of two and usually much smaller are sufficiently modest so that the final choice between grids should probably not be made because of accuracy but rather based on other criteria such as ease of programming analytical simplicity conformality with other approximations and timestep in applications to partial differential equations to explore such nonaccuracy issues we also compared six of the grids on the basis of maximum allowed timestep when the grid is used to discretize the spatial coordinate and an explicit scheme is used for time marching the lebesgue optimal grid is also nearly optimal in the sense of allowing the longest timestep with a pseudospectral collocation algorithm the lebesgue grid allows a timestep three halves as long as that of the legendre lobatto spectral element method

differential quadrature method application to initial boundary value problems two non linear dynamical systems have been considered in both cases the governing equation of motion is reduced to two second order non linear non autonomous ordinary differential equations using the differential quadrature method with a careful distribution of sampling points to check the numerical results a comparison with those obtained using the galerkin approach is proposed

application of generalized differential quadrature method to structural problems summary this paper presents the first endeavour to exploit a generalized differential quadrature method as an accurate efficient and simple numerical technique for structural analysis firstly drawbacks existing in the method of differential quadrature dq are evaluated and discussed then an improved and simpler generalized differential quadrature method gdq is introduced to overcome the existing drawback and to simplify the procedure for determining the weighting coefficients subsequently the generalized differential quadrature is systematically employed to solve problems in structural analysis numerical examples have shown the superb accuracy efficiency convenience and the great potential of this method numerical approximation methods for solving partial differential equations have been widely used in various engineering fields classical techniques such as finite element and finite difference methods are well developed and well known these methods can provide very accurate results by using a large number of grid points however in a large number of cases reasonably approximate solutions are desired at only a few specific points in the physical domain in order to get results even at or around a point of interest with acceptable accuracy conventional finite element and finite difference methods still require the use of a large number of grid points consequently the requirement for computer capacity is often unnecessarily large in such cases in seeking an alternate numerical method using fewer grid points to find results with acceptable accuracy the method of differential quadrature dq was introduced by bellman et a the method of dq is a global approximate method this method is based on the ideas that the derivative of a function with respect to a co ordinate direction can be expressed as a weighted linear sum of all the function values at all mesh points along that direction and that a continuous function can be approximated by a higher order polynomial in the overall domain the dq method differs from the finite element method fem in two aspects firstly the fem uses lower order polynomials to approximate a function on a local element level while the dq method approximates a function on the global area using higher order polynomials secondly the dq method directly approximates the derivatives of a function at a point while the fem approximates a function over a local element and the derivatives can then be derived from the approximate function in this aspect the dq method is more similar to the finite difference method fdm however the fdm is also a local approximation method based on lower order polynomial approximation in fact it can be shown that the fdm is just a special case of the dq method where it is applied locally on the range xi xi l owing to the higher order

normal derivative for bounded domains with general boundary let d be a general bounded domain in the euclidean space rn a brownian motion which enters from and returns to the boundary symmetrically is used to define the normal derivative as a functional for f with f vf and a f all in l2 on d the corresponding neumann condition normal derivative 0 is an honest boundary condition for the l2 generator of reflected brownian notion on d a conditioning argument shows that for d and f sufficiently smooth this general definition of the normal derivative agrees with the usual one introduction bt t 0 is standard brownian motion on the euclidean space rn the case when the dimension n 1 is well understood and so we assume always that n 2 d is a bounded open connected subset of rn an important role will be played by a inf t 0 bt is not in d the hitting time for the complement rn d the absorbed process xt t 0 is xt bt for 0 a with a a dead point adjoined to d as an isolated point all functions are understood to vanish at 9 the absorbed transition operators po t 0 with action ptf x exf xt form a strongly continuous symmetric semigroup on l2 the hilbert space of real valued functions on d that are square integrable with respect to lebesgue measure dx the strong generator ao is selfadjoint and negative definite by the spectral theorem as formulated and proved in chapter ix of segal and kunze 1968 the operator a0 1 2 is a well defined positive definite selfadjoint operator the absorbed dirichlet space is the pair fo e where 0 1 f0 domain ao 2 e f g dx a 1 2f x a0 1 2g x f g in f received by the editors june 7 1987 1980 mathematics subject classification 1985 revision primary 60b85 secondary 35a85

numerical methods based on whittaker cardinal or sinc functions this paper summarizes the results known to date for using sine functions composed with other functions as bases for approximations in numerical analysis described in this paper are methods of interpolation and approximation of functions and their derivatives quadrature the approximate evaluation of transforms hilbert fourier laplace hankel and mellin and the approximate solution of differential and integral equations the methods have many advantages over classical methods which use polynomials as bases in addition all of the methods converge at an optimal rate if singularities on the boundary of approximation are ignored

multidimensional high field limit of the electrostatic vlasov poisson fokker planck system abstract in this paper the high field limit of the vlasov poisson fokker planck system for charged particles is rigorously derived the first result is obtained in any space dimension by using modulated energy techniques it requires the smoothness of the solutions of the limit problem in dimension 2 it is possible to handle more general data by using methods developed for a diagonal defect measures theory the convergence of the concentration of particles is obtained in the space of bounded measures in both cases the limit of the sequence of densities of distribution functions is shown to solve a nonlinear system of partial differential equations which is related to ohm s law

solution of nonlinear problems in applied sciences by generalized collocation methods and mathematica abstract this paper deals with the developments of mathematical methods for the discretization of continuous models and the solution of nonlinear problems of interest in applied sciences the contents refer to developments of the differential quadrature method which leads to the so called generalized collocation methods the method is developed and applied to the solution of initial boundary value problems the computational problems are technically solved with mathematica

a direct matrix method for computing analytical jacobians of discretized nonlinear integro differential equations in this article we present a simple direct matrix method for analytically computing the jacobian of nonlinear algebraic equations that arise from the discretization of nonlinear integro differential equations the method is based on a formulation of the discretized equations in vector form using only matrix vector products and component wise operations by applying simple matrix based differentiation rules the matrix form of the analytical jacobian can be calculated with little more difficulty than required to compute derivatives in single variable calculus after describing the direct matrix method we present numerical experiments demonstrating the computational performance of the method discuss its connection to the newton kantorovich method and apply it to illustrative 1d and 2d example problems from electrochemical transport

hilbert coefficients of hilbert filtrations adic filtrations see 7 11 18 21 wx in the first section of this paper we extend most of the techniques of 4 w5 to the case of hilbert filtrations and by doing so we are also able toxoffer alternative simple proofs of some results of 7 wxin the second section thanks to the setting just described if

extended gdq and related discrete element analysis methods for transient analyses of continuum mechanics problems abstract the extended gdq proposed by the author is used to develop solution algorithms for solving the discrete transient equation system of a continuum mechanics problem it is a direct integration approach two integration methods are developed they are time element by time element method and stages by stages method these two time integration algorithms can be used to solve a generic discrete transient equation system of an originally discrete system or a discrete system resulting from the discretization of a transient system of continuum mechanics problems by using a certain discretization technique such as the dqem fem fdm etc

lifetime of conditioned brownian motion in lipschitz domains if d d d 3 is bounded and has lipschitz boundary then the expected lifetime of any brownian h path process in d is finite

the development of irregular elements for differential quadrature element method steady state heat conduction analysis abstract a new numerical approach for solving steady state heat conduction problems by using the irregular elements of the differential quadrature element method dqem is proposed the mapping technique is used to transform the governing partial differential equation the natural transition condition of two adjacent elements and the newmann boundary condition defined on the irregular physical element into the parent space the differential quadrature technique is used to discretize the transformed relation equations defined on the regular element in the parent space various techniques for selecting and implementing the constraint conditions at element corners are proposed a global algebraic equation system can be obtained by assembling all of the discretized relation equations numerical procedures are summarized and the related computer code is developed numerical results are presented they demonstrate the developed dqem steady state heat conduction analysis model

geometric properties of 2 dimensional brownian paths let a be the set of all points of the plane visited by 2 dimensional brownian motion before time 1 with probability 1 all points of a are twist points except a set of harmonic measure zero twist points may be continuously approached in a only along a special spiral although negligible in the sense of harmonic measure various classes of cone points are dense in a with probability 1 cone points may be approached in a within suitable wedges

on the excursions of markov processes in classical duality on obtient des resultats comparables a ceux de getoor et sharpe 1982 sous des hypotheses de dualite classique

first coefficient ideals and the s2 ification of a rees algebra let a m k be a d dimensional d 1 quasi unmixed analytically unramified local domain with infinite residue field if i is an m primary ideal shah defined the first coefficient ideal of i to be the largest ideal i 1 containing i such that ei i ei i 1 for i 0 1 assume that a is s2 and let s n zintn be the s2 ification of the extended rees algebra s a it t 1 we prove that in in 1 for every n 1 one of the consequences is a procedure of computing first coefficient ideals