解三维抛物型方程的一个新的高精度显格式

本文构造了一个解三维抛物型方程的高精度三层显式差分格式,其稳定性条件为r=Δt/Δx2=Δt/Δy2=Δt/Δz2≤1/4,截断误差为O(Δt2+Δx4).     

四维抛物型方程的高精度分支稳定的显式差分格式

对四维抛物型方程构造了一个高精度显格式,格式的稳定性条件为r=Δt/Δx2=△t/Δy2=△t/△z2=Δt/Δw2<1/2,截断误差阶达到O(Δt2 Δx4),通过数值实验,表明本文理论分析的正确性和文中格式较同类格式的优越性.     

<Emphasis Type="Italic">H</Emphasis><Superscript>1</Superscript>-estimates of Littlewood-Paley and Lusin functions for Jacobi analysis

For α≥β≥ -1/2 let Δ(x) = (2shx)2α+1(2chx)2β+1 denote the weight function on R+ and L1(Δ) the space of integrable functions on R+ with respect to Δ(x)dx, equipped with a convolution structure. For a suitable φ∈ L1(Δ), we put φt(x) = t-1Δ(x)-1Δ(x/t)φ(x/t) for t > 0 and define the radial maximal operator Mφ as usual manner. We introduce a real Hardy space H1(Δ) as the set of all locally integrable functions f on R+ whose radial maximal function Mφ(f) belongs to L1(Δ). In this paper we obtain a relation between...     

多维抛物型方程的分支绝对稳定的显式格式

其中及R={0≤x_i≤1,j=1,2,…,p),(?)R只为区域只的边界。 对多维抛物型方程(1)的差分解法,古典显式格式的稳定性条件为r=Δt/(Δx)~2≤1/2p,十分苛刻;古典隐式格式虽是无条件稳定,却需解线性方程组。因此两者的计算量都很大,且它们的精度较低,其局部截断误差仅为O(Δt+(Δx)~2)。因此,对多维抛物型方程而言,构造显式计算、稳定性能良好且精度较高的差分格式便具有十分明显的理论意义和实用价值。本文针对上述古典显式与隐式格式所存在的问题,构造一类对任何p维空间变量的抛物型方程(1)都适用的。分支绝对稳定的显式差分格式,其局部截断误差阶为O((Δt)~2+(Δx)~2),从而避免了解线性代数方程组,大大地减少了计算工作量,且精度较高。 令Δx_k=h_k=Δx=h=1/M(k=1,2,…p)表示空间方向步长,Δt=τ=[T/N]表示时间方向步长,M、N均为正整数。 为简便计,引入下列记号     

读“sinx≤x≤tan x的简单运用“后的思考

武增明老师在文[1]中提到重要不等式:sinx≤x≤tanx,x∈0,2π,当且仅当x=0时等号成立.思考:x→0时,则sinx→x,tanx→x.在导数中,研究瞬时速度时会涉及这一知识的应用.例1、如图所示,质点P在半径为1的圆上逆时针作匀速圆周运动,且角速度为2rad/s,设A(1,0)为起始点,求t时刻时,点P在x轴上的射影M的速度.思路解析:设经过t时刻∠MOP=θradOM=OP·cosθ=cosθ,则影子的位移S=AM=-(1-cosθ)ΔSΔt=-[1-cos(θ ΔΔθt)] (1-cosθ)=cos(θ ΔΔθt)-cosθ=cosθ·cosΔθ-siΔntθ·sinΔθ-cosθ当Δθ→0时,cosΔθ→1,sinΔθ→Δθ∴ΔS=…     

解抛物型方程的一族高精度差分格式

1 引言 求解抛物型方程 u/t=u/x~2, 00, (1) 初边值问题的差分格式,精度高者当属[1]、[2]中的格式.本文对上述问题构造了一族三层(特殊情况下是两层)双参数、绝对稳定、高精度三对角线型的隐式格式,它不仅包含了[1]、[2]中所有的格式,而且还可以得到一个截断误差为O(Δt~3+Δx~4)的绝对稳定的差分格式,精度比[1]、[2]中的格式都高. 2 差分格式 设Δt为时间步长,Δx=L/M(M为正整数)为空间步长,网函数u(jΔx,nΔt )记为u_j~n,对     

具有跳扩散的美式期权二叉树计算格式的收敛速率

American put option with jump-diffusion can be modelled as a vari- ational inequality problem with an integral term.Under the stability condition (σ~2Δt)/(Δx~2)≤1,whereΔx=ln(S_n 1)/(S_n),the convergence rate O((Δx)~(2/3) (Δt)~(1/3))of the explicit finite scheme for this problem is obtained by using penalization technique. The binomial tree scheme of this model,which is equivalent to the explicit scheme, is convergent by the same rate.     

地下水污染中一离子反应数学模型的有限元方法

1　引　　言在地下水含水层中 ,污染物随地下水运移并常常发生各种化学反应 [1 ] .描述地下水含水层中一类阳离子交换反应 m M1 +r M2 k2k1 r M2 +m M1 的数学模型[2 ] 为 : s1 t- dΔs1 =f1 ,　　 x∈Ω ,t∈ J (1.1a) s2 t- dΔs2 =f2 ,　　 x∈Ω ,t∈ J (1.1b) c1 t+ρ s1 t- DΔc1 =0 ,　　 x∈Ω ,t∈ J (1.2 a) c2 t+ρ s2 t- DΔc2 =0 ,　　 x∈Ω ,t∈ J (1.2 b)其中 Ω R2为具有光滑边界的有界区域 ,J=(0 ,T].这里 D>d>0为扩散系数 ,ρ>0为固体颗粒密度 ,均为常数 .根据 [1,2 ]应有 :f1 =m[k1 Rm1 Rr2 cm1 sr2 -…     

OPERATOR-SPLITTING GALERKIN METHOD FOR ONE KIND OF OIN REACTION MODEL FOR THE POLLUTION IN GROUNDWATER

§ 1　 IntroductionIn the subsurface,the contaminations move with the groundwater where many kindsof chemical reactions take place[1 ] .The mathematical model to describe one kind of oin re-action in subsurface m M1 +r M2 k2k1r M2 +m M1 is given by[2 ]s1 t-dΔs1 =f1 ,x∈Ω ,t∈ J,( 1 .1 a)s2t-dΔs2 =f2 ,x∈Ω ,t∈ J,( 1 .1 b)c1 t+ρs1 t-DΔc1 =0 ,x∈Ω ,t∈ J,( 1 .2 a)c2t+ρs2t-DΔc2 =0 ,x∈Ω ,t∈ J,( 1 .2 b)whereΩ R2 is a bounded domain with smooth boundary.…     

一类n维非线性波动方程组的Cauchy问题

本文应用压缩映射原理和解的延拓定理证明下列n维非线性广义波动方程组utt-σΔu-Δutt=Δf(v),x∈Rn,t0,υtt-Δυtt=Δg(υ),x∈R,t0的Cauchy问题在空间C2([0,∞);Hs(Rn)×Hs(Rn))(sn/2)中存在唯一的整体广义解和在空间C2([0,∞);Hs(Rn)×H2(Rn))(s2+n/2)中存在唯一的整体古典解,此外给出解爆破的充分条件.     

Performance bounds on multiprocessor scheduling strategies for statically allocated programs

In multiprocessors with static allocation of processes to processors, scheduling can be done locally for each processor. The scheduling strategy may have dramatic effect on the execution time of a parallel program. It is an NP-hard problem to find an optimal schedule, and very little is known of how close the heuristic solutions get.The major result here is a theorem stating that if certain program parameters, which can be obtained from an execution of the program on a single-processor, are known, the execution time of the optimal schedule can be calculated within a factor equal to the largest number of border processes on one processor. Border processes are processes which communicate with other processors. The program parameters are obtained using a previously developed tool.Due to the generality of this theorem, the proof is rather complex because it has to cover a large range of situations. The theorem itself, however, is easy to apply, making it possible to compare the performance of different scheduling strategies with the optimal case. The proof also gives important hints on how to design efficient scheduling algorithms for statically allocated programs.     

On the design of reactive systems

The notion of joint actions provides a framework in which the granularity of atomic actions can be refined in the design of concurrent systems. An example of a telephone exchange is elaborated to demonstrate the feasibility of this approach for reactive systems and to illustrate transformations that are justifiable in such a process. Particular problems arise when a refinement would allow new interleavings of semantically relevant events. The meaning of a reactive computation is specified in a way that makes this possible.Dedicated to Peter Naur on the occasion of his 60th birthday     

Disk allocation methods for binary Cartesian product files

Since a file is usually stored on a disk, the response time to a query is dominated by the disk access time. In order to reduce the disk access time, a file can be stored on several independently accessible disks. In this paper, we discuss the problem of allocating buckets in a file among disks such that the maximum disk accessing concurrency can be achieved. We are particularly concerned with the disk allocation problem for binary Cartesian product files. A new allocation method is first proposed for the cases when the number (m) of available disks is a power of 2. Then it is extended to fit the cases wherem is not a power of 2. The proposed algorithm has a near strict optimal performance for a partial match query in which the number of unspecified attributes is greater than a small number (5 or 6).This work was supported in part by NSF Grant DCR-8405498.     

The paradox of trees in type theory

We show how to represent a paradox similar to Russell's paradox in Type Theory withW-types and a type of all types, and how to use this in order to represent a fixed-point operator in such a theory. It is still open whether such a construction is possible without theW-type.This research was partly supported by ESPIRIT Basic Research Action Logical Frameworks.     

Terminating general recursion

In Martin-Löf's type theory, general recursion is not available. The only iterating constructs are primitive recursion over natural numbers and other inductive sets. The paper describes a way to allow a general recursion operator in type theory (extended with propositions). A proof rule for the new operator is presented. The addition of the new operator will not destroy the property that all well-typed programs terminate. An advantage of the new program construct is that it is possible to separate the termination proof of the program from the proof of other properties.Dedicated to Peter Naur on the occasion of his 60:th birthday.     

The amortized complexity of Henriksen's algorithm

Henriksen's algorithm is a priority queue implementation that has been proposed for the event list found in discrete event simulations. It offers several practical advantages over heaps and tree structures.Although individual insertions ofO(n) complexity can easily be demonstrated to exist, the self-adjusting nature of the data structure seems to ensure that these will be rare. For this reason, a better measure of total running time is theamortized complexity: the worst case over a sequence of operations, rather than for a single operation.We show that Henriksen's algorithm has an amortized complexity of(n ^1/2) per insertion,O(1) per extract_min operation, andO(logn) for isolated deletions.     

On specifications,subset types and interpretation of proposition in type theory

In this paper we discuss some practical aspects of using type theory as a programming and specification language, where the viewpoint is to use it not only as a basis for program synthesis but also as a programming language with a programming logic allowing us to do ordinary verification.The subset type has been added to type theory in order to avoid irrelevant information in programs. We give an example of a proof which illustrates the problems that may occur if the subset type is used in specifications when we have the standard interpretation of propositions as types. Harrop-formulas and Squash are then discussed as solutions to these problems. It is argued that they are not acceptable from a practical point of view.An extension of the theory to include the two new judgment forms:A is a proposition, andA is true, is then given and explained in terms of the old theory. The logical constants are no longer identified with the corresponding type theoretical constants, but propositions are interpreted as Gödel formulas, which allow us to introduce and justify logical rules similar to rules for classical logic. The interpretation is extended to include predicates defined by using reflections of the ordinary definition of Gödel formulas in a type of small propositions.The programming example is then revisited and stronger elimination rules are discussed.     

An axiomatic semantics for nested concurrency

We give transformation rules for the concurrent parts of Hoare's language CSP, transforming concurrent CSP programs into nondeterministic, sequential programs.On the basis of these transformations we define an axiomatic semantics for CSP with nested concurrency.This axiomatic system includes a rule for binary, associative process composition, enabling modular verification dealing with parts of concurrent systems as well as full programs.The proof system is fully abstract, in the sense that the internal structure of processes is irrelevant in the specification inasmuch it is not externally observable.An outline of a verification of a recursive, concurrent sorter is given as an example.     

Uncle-attributed grammars

Evaluation of inherited attributes is a problem in conjunction with LR parsing, because the derivation tree is incomplete during parsing. An evaluation scheme for inherited attributes is presented based on a restricted grammar class, uncle-attributed grammars. A transformation to the uncle-attributed form is described for L-attributed grammars.     

Automatically replacing indices into parallel arrays with pointers to records

In older languages lists, trees and graphs are represented with sets of arrays where indices of elements correspond to pointers to the nodes of the data structure. We present an algorithm that replaces such arrays with objects allocated dynamically from the heap, and indices with true pointers. Generated pointers are strongly typed and elements of logically related arrays are combined into records. The algorithm is potentially useful, especially in automatic translation between high-level programming languages.