RELATIONS OF DERIVATIVE ALGEBRA AND RING OF DIFFERENTIAL OPERATORS IN CHARACTERISTIC p>0

Introduction　　 Let K be a field,K [X ]∶=K [x1,… ,xn]bethe polynomial ring in n variables.We know thatwhen K is a field with ch( K ) =0 ,then the Weylalgebra An( K) ,the ring of differential operatorsD( K[X]) ,and the derivative algebraΔ ( K [X])which is generated by{xi, i| i=1 ,… ,n}in End KK[X]are all isomorphic[1～ 3 ] .But if ch( K) =p>0 ,the three do not have that relation.In factΔ( K[X]) is only a quotientof An( K) [4] ;and Ref.[5 ]gives a comprehensive study to the rela…     

LINEAR SYSTEMS AND LINEAR INTERPOLATION I

Suppose V is a vector space over the real orcomplex field F.A linear transformation T on Vis a function T from V into itself such that T(αx βy) =αTx βTy holds for any vectors x,y∈ V,and any scalarsα,β∈ F.Linear transformationsare applied to represent linear systems.A systemis said to interpolate[1] a family Soflinear transfor-mations if for each input of the system the corre-sponding output can be obtained by the action ofsome member of S.Thatis,if foreach x∈V,Tx= Qxx,for some …     

Some Results on Unicity of Entire Functions Related to Normal Families

IntroductionLet D be a domain in C.Define for f mero-morphic on D and a,b∈C,we putE(a,f)={z∶f(z)-a=0}where a zero of multiplicity m is counted m times inthe set.And put-E(a,f)=f-1({a})∩D={z∈D∶f(z)=a}Then f and g share a IM(ignoring multiplicities),i.e.-E(a,f)=-E(a,g)If f-a and g-a have the same zeros with thesame multiplicities,then f and g share the value aCM(counting multiplicities),i.e.E(a,f)=E(a,g)A meromorphic function f on C is called anormal function if there exists a posit…     

M／M／1排队系统嵌入Markov链瞬态解的格路径算法

在定义了生灭过程状态转移的单格与升降格和降升格的基础上,证明了M／M／1排队系统{X（t）t≥0}的嵌入Markov链{X（n）,l≥0}的转移概率弱收敛于系统的瞬态解,并利用随机游动的格路径算法求出了该链的转移概率P（i,j,n）的显式算法表达式,从而达到确定M／M／1排队系统{x（t）f≥0}瞬态解的转移概率的目的．     

The Dimensions of Graphs and Constructions of Their Bases

IntroductionGraph G,considered in this paper,is finiteand simple with vertex set V ( G) and edge setE( G) .Let d( x,y) denote the distance between xand y in G and W={w1,w2 ,…,wk}denote the or-dered set of V( G) .For any given v∈V( G) ,therepresentation of v with respect to W is the k- vec-tor:r( v| W) ={d( v,w1) ,d( v,w2 ) ,…,d( v,wk) }.The ordered set W is called a resolving set of G ifr( u| W) =r( v| W) implies that u=v for all pairs{u,v}of vertices of G. A resolving set of G with…     

On Restricted Connectivity and Extra Connectivity of Hypercubes and Folded Hypercubes

Given a graph G and a non-negative integer h, the h-restricted connectivity k^h(G) of G is the minimum cardinality of a set of vertices of G, in which at least h neighbors of any vertex is not included, if any, whose deletion disconnects G and every remaining component has the minimum degree of vertex at least h; and the h-extra connectivity k^h(G) Of G is the minimum cardinality of a set of vertices of G, if any, whose deletion disconnects G and every remaining component has order more than h. This paper shows that for the hypercube Qn and the folded hypercube FQn, k1(Qn)=k^（1）(Qn)=2n-2 for n≥3, k2(Qn)=3n-5 for n≥4, k1(FQn)=k^(1)(FQn)=2n for n≥4 and k^(2)(FQn)=4n-4 for n≥8.     

Weak Isomorphism of Finite Group

On the basis of the quasi-isomorphism of finite groups, a new mapping, weak isomorphism, from a finite group to another finite group is defined. Let G and H be two finite groups and G be weak-isomorphic to H. Then G≌H if G satisfies one of the following conditions. 1） G is a finite Abelian group. 2） The order of G is p^3. 3 ） The order of G is p^n＋1 and G has a cyclic normal subgroup N = 〈a〉 of order p^n. 4） G is a nilpotent group and if p^││G│, then for any P ∈ Sylp （G）, P has a cyclic maximal subgroup, where p is a prime; 5） G is a maximal class group of order p4（p〉3）.     

A new black box analysis of hash functions based on block ciphers

For the 64 most basic ways to construct a hash function H:{0,1} → {0,1}n from a block cipher E:{0,1}n × {0,1}n → {0,1}n, Black et al.provided a formal and quantitative treatment of the 64 constructions, and proved that 20 schemes are collision resistant.This paper improves the upper and lower bounds and make contrast with a hash constructed from a random oracle.These 20 schemes have only one kind of collision resistance upper and lower bounds.In addition, we present new advantages for finding second preimages.     

Predicting the Dielectric Strength of c-C4F8 and SF6 Gas Mixtures by Monte Carlo Method

An improved Monte Carlo method was used to simulate the motion of electrons in c-C_4F_8 and SF_6 gas mixtures for pulsed townsend discharge. The electron swarm parameters such as effective ionization coefficient, [AKα-] and drift velocity over the E/N range from 280～700 Td(1Td=10-21 V·m2) were calculated by employing a set of cross sections available in literature. From the variation cure of [AKα-] with SF_6 partial pressure p, the limiting field (E/N)_lim of gas mixture at different gas content was determined. It is found that the limiting field of c-C_4F_8 and SF_6 gas mixture is higher than that of pure SF_6 at any SF_6 mixture ratio. Simulation results show excellent agreement with experiment data available in previous literature.     

关于不规则小波系统的框架研究

对于任意给定的g∈L2(Rn),考虑了具有这种形式{λn/2g(λjx-kb)}j∈,k∈xn(这里λj＞0,b＞0)的不规则的小波系统.对于这类小波,给出了它构成L2(Rn)空间中的框架的充分条件.同时,对于一类具有某种性质的函数g∈L2(Rn),证明了当对{λj}j∈x加一定的限制后,具有上述形式的不规则小波也能构成L2(Rn)空间中的框架.     

Splitting Extensions of Abelian by Hyper-（ cyclic or finite） Groups （Ⅱ ）

Let F be a locally defined formation consisting of locally solvable groups, G a hyper-（ cyclic or finite） locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The following conclusion is obtained： if G∈F, f（ ∞ ） include f（p）, f（p） ≠φ for each p∈π, and A has no nonzero F central ZG- images, then any extension E of A by G splits conjugately over A, and A has no nonzero F central ZG-factors.     

s-Conditionally Permutable Subgroups and p-Nilpotency of Finite Groups

A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G,there exists an element x∈G such that HTx=TxH.In this paper,we investigate further the influence of s-conditionally permutability of some 2-maximal subgroups of the Sylow subgroup of G,on the structure of finite groups.New criteria for a group G being p-nilpotent are obtained.     

TRAFFIC-BASED SCHEDULING MECHANISM IN AN IP/ATM ROUTER

Introduction　　 In recentyears,ATM has been installed com-prehensively,especially in the backbone of cam-puses and cities. On account of the differencesamong ATM,IP and other networks[1,2 ] ,how toeffectively integrate them is a very important andcritical issue to ATM and other networks.An IP/ATM router which can interconnect1 55M ATM,1 0 0 M Ethernet,2 M ATM,PPP,2 B D ISDN and X.2 5is under developing in ourlab.In prior work,we have designed its softwarearchitecture[3] .We als…     

Minimal Enclosing of an MPT (v,λ) in a TS (v+1,μ)

IntroductionA maximum packing of triples( or simply amaximum packing) of order v with indexλ,denot-ed by MPT( v,λ) ,is a pair( V,B) where V is a v-set and B is a collection of 3- subsets ( called blocksor triples) of V such that1 each2 - subset of V iscontained in atmostλ triples,2 if C is any collec-tion of 3- subsets satisfying 1 then | B|≥ | C| .Let ( V,B) be an MPT ( v,λ) ,the leave of ( V,B) ,denoted by L ( v,λ) ,is a multigraph( V,E)when an edge {x,y}∈ E with multiplicity…     

A Note on Shor’s Quantum Algorithm

Introduction Factoring integers is generally thought to behard on a classical computer. But it is now heldthat prime factorization can be accomplished inpolynomial time on a quantum computer. This re-markable work is due to Shor[1]. For a given num-ber n, he gave a quantum computer algorithm forfinding the order r of an element x (mod n) insteadof giving a quantum computer algorithm for factor-ing n directly. The indirect algorithm is feasiblebecause factorization can be reduced to finding th…     

PERSISTENT CURRENT IN A ONE-DIMENSIONAL MESOSCOPIC RING WITH ELECTRON-PHONON INTERACTION IN THE LATTICE MODEL

IntroductionSince the pioneering work of Büttiker etal[1,2 ] ,the problem of persistentcurrent in a meso-scopic ring has attracted much recent atten-tion[3～ 6] . In a normal- metal ring threaded by amagnetic flux,a persistent current exists as longas the phase coherence of electron is pre-served[1,2 ,4 ] . With the gauge transformation,thevector potential can be removed from Schrodingerequation with a modified boundary conditionψn(x L ) =exp(2πi/0 )ψn(x) ,where0 =h/e is theflux q…     

Segmentation of haustral folds and polyps on haustral folds in CT colonography using complementary geodesic distance transformation

Computer-aided detection （CAD） for CT colonography refers to a scheme that automatically detects polyps in CT images of colon. Current CAD schemes already have a relatively high sensitivity and a low false positive rate. However, misdiagnosis and missed diagnosis are still common to happen, mainly due to the existence of haustral folds （HFs）. An innovative idea of segmenting semilunar HFs from the smooth colonic wall and then using different methods to detect polyps on HFs and those on the smooth colonic wall is proposed in this paper to reduce the false positives and false negatives caused by HFs. For the polyps on HFs, a novel segmentation method is specially developed based on complementary geodesic distance transformation （CGDT）. The proposed method is tested on four different models and real CT data, The property of CGDT is proved and our method turns out to be effective for HF segmentation and polyp segmentation. The encouraging experimental results primarily show the feasibility of the proposed method and its potential to improve the detection performance of CAD schemes.     

NUMERICAL SIMULATION OF SINGLE-GROUP, STEADY STATE AND ISOTROPIC NEUTRON TRANSPORT EQUATION IN DIFFUSIVE REGIMES

The single-group,steadystate,isotropic for mofthe neutron transport equationis given by[1]Ω·+σtI-σsPψ(x,Ω)=q(x,Ω)(x,Ω)∈D×Sψ(x,Ω)=g(x,Ω)x∈Din={x∈D,γ(x)·Ω<0(1)whereσtis the total cross section,σSis the scatteringcross section,andψ(x,Ω)is the angular flux to bedeter mined for all pointsx∈D,D Rn(n=2,3)and all possible travel directionsΩ,ΩS(Sis a u-nit disk or a unit sphere),γ(x)denotes the out wardunit nor mal atx∈D,Idenotes the identity opera-tor,the operator…     

Active Contours and Mumford-Shah Segmentation Based on Level Sets

IntroductionThe basic idea in active contour models orsnakes is to evolve a curve,subject to constraintsfrom a given image,in order to detect objects inthat image.For instance,starting with a curvearound the object to be detected,the curve movestoward its interior normal and has to stop on theboundary of the object.LetΩ be a bounded open subset of R2 ,with Ω its boundary. Let u0 ∶Ω→ R be a given image,and C( s)∶ [0 ,1 ]→ R2 be a parameterized curve. Inthe classical snakes and active…     

关于图的负k-子确定数的上界

设G=(V,E)为一个n阶无向简单图,N(v)={u∈V|uv∈E},k为一个整数(1≤k≤n).若函数fV→{-1,1}满足条件:V中至少有k个顶点v,使得f(N(v))≤1成立,则称f为图G的一个负k-子确定函数.称βkD(G)=max{f(V)|f为图G的负k-子确定函数}为图G的负k-子确定数.文中主要给出了图...