关于一个素数和一个素数的k次方和问题

设k≥2,且Hk表示一个正整数n的集合,使得该集合中的元素满足a+bk≡n(modq)对任意的q,在模q的既约剩余系中有解,令Dk(N)表示所有的n≤N,且n∈Hk且不能表成p1+p2k=n形式的整数.那么在GRH下, Dk(N)相似文献   

关于一个素数和一个素数的k次方和问题

设k≥2,Hk表示一个正整数n的集合,使对任意的正整数q,同余方程a+b2三n(modq)在模q的既约剩余系中有解a,b.Dk(N)表示n≤N,n∈Hk,但不能表成p1+p22=n的数的个数,其中p1,p2表示素数.则在GRH下,Dk(N)<<N1-1/k(h(k)+1)+ε,这里k=2,3;h(2)=2,h(3)=8.     

一个素数和一个素数的平方和问题

H表示一个正整数N的集合,使对任意的正整数q,同余方程a+b~2≡N(mod q)在模q的既约剩余系中有解a;b.E(x)表示N≤x,N∈H,但不能表成p_1+p_2~2=N的数的个数,其中p_1,p_2个表示素数,则E(x)<相似文献   

关于非线性微分系统的无界性

研究一类非线性微分系统=h(y)-φ(x),=-h(y)f(x)-g(x)k(y)解的无界性问题.给出了判断该系统解的无界性的两个新的充分条件.     

图的光滑支架分解

设G是一个图,A为其边集的子集。G的一个支架分解是（G－A,A）,其中G－A是去掉A后的连通图,G的一个光滑支架分解是适合下列条件的支架分解：（1）G－A的每一叶具有连通余树;（2）G－B（G－A）割边集为A,其中B（G－A）为G－A的割边集。本文给出了求一个图的光辉支架分解的一个有效算法。     

Embedding a graph-like continuum in a surface

Graph-like continua provide a very natural setting for generalizing finite graphs to infinite, compact structures. For example, the Freudenthal compactification of a locally finite graph, exploited by Diestel and his students in their study of the cycle space of an infinite graph, is an example of a graph-like continuum. Generalizing earlier works in special cases, the authors, along with Christian, have proved MacLane’s and Whitney’s characterizations of planarity for graph-like continua (Electron. J. Combin. 17 (2010)). In this work, we consider embeddings of graph-like continua in compact surfaces and show that: (i) every edge is in an open disc that meets the graph-like continuum precisely in that edge; (ii) there are natural analogues of face boundary walks; (iii) there is a graph-like continuum triangulating the same surface and containing as a sub-graphlike continuum the original embedded graph-like continuum; (iv) the face boundaries generate a subspace of the cycle space; and (v) the quotient of the cycle space by the boundary cycles is the homology of the surface. These all generalize results known for embeddings of finite graphs.     

A multielement boundary-value problem with a piecewise-smooth shift on a piecewise-Lyapunov contour for a function analytic in a domain

In an L_p-formulation (1 < p="><>) there is constructed for a function (z) analytic in a multiconnected domain with a piecewise-Lyapunov boundary a Noether theory of the boundary-value problem

Deformation of a kinematic surface in a hyperbolic space

We give a representation of the variational problem on a time (space) like surface immersed in a hyperbolic space. The geometric properties of the deformed surfaces are given. The variational problem for the Klein images of 2-parametric continuous motion of a line (kinematic surface) are introduced. The theory of Klein images is applied to a time like and space like congruence. Finally, additional results are mentioned in the concluding remarks. The technique adapted here is based on Cartan's methods of moving frames, exterior differential forms and the group of motions [Result. Math. 39 (2001) 1; Tensor. N.S. 51 (3) (1992) 224; Tensor. N.S. 59 (1998) 36; Collect. Math. 45 (1994) 153].     

An integral equation and a representation for a Green's function

The final step in the mathematical solution of many problems in mathematical physics and engineering is the solution of a linear, two-point boundary-value problem such as $$\begin{gathered} \ddot u - q(t)u = - g(t), 0< t< x \hfill \\ (0) = 0, \dot u(x) = 0 \hfill \\ \end{gathered} $$ Such problems frequently arise in a variational context. In terms of the Green's functionG, the solution is $$u(t) = \int_0^x {G(t, y, x)g(y) dy} $$ It is shown that the Green's function may be represented in the form $$G(t,y,x) = m(t,y) - \int_y^x {q(s)m(t, s) m(y, s)} ds, 0< t< y< x$$ wherem satisfies the Fredholm integral equation $$m(t,x) = k(t,x) - \int_0^x k (t,y) q(y) m(y, x) dy, 0< t< x$$ and the kernelk is $$k(t, y) = min(t, y)$$      

On Rings Whose Elements are the Sum of a Unit and a Root of a Fixed Polynomial

A ring R with identity is called “clean” if for every element a ? R there exist an idempotent e and a unit u in R such that a = e + u. Let C(R) denote the center of a ring R and g(x) be a polynomial in the polynomial ring C(R)[x]. An element r ? R is called “g(x)-clean” if r = s + u where g(s) = 0 and u is a unit of R and R is g(x)-clean if every element is g(x)-clean. Clean rings are g(x)-clean where g(x) ? (x ? a)(x ? b)C(R)[x] with a, b ? C(R) and b ? a ? U(R); equivalent conditions for (x² ? 2x)-clean rings are obtained; and some properties of g(x)-clean rings are given.     

交换环上矩阵代数的局部化导子

Let R be a commutative ring with identity, Nn（R） the matrix algebra consisting of all n × n strictly upper triangular matrices over R. Several types of proper local derivations of Nn（R） （n ≤ 4） are constructed, based on which all local derivations of Nn（R） （n ≤ 4） are characterized when R is a domain.     

Combining a regression model with a multivariate Markov chain in a forecasting problem

This paper proposes a new concept: the usage of Multivariate Markov Chains (MMC) as covariates. Our approach is based on the observation that we can treat possible categorical (or discrete) regressors, whose values are unknown in the forecast period, as an MMC in order to improve the forecast error of a certain dependent variable. Hence, we take advantage of the information about the past state interactions between the MMC categories to forecast the categorical (or discrete) regressors and improve the forecast of the actual dependent variable.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix

Summary. Using a slightly different discretization scheme in time and adapting the approach in Nochetto et al. (1998) for analysing the time discretization error in the backward Euler method, we improve on the error bounds derived in (i) Barrett and Blowley (1998) and (ii) Barrett and Blowey (1999c) for a fully practical piecewise linear finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix and (i) a logarithmic free energy, and (ii) a non-smooth free energy (the deep quench limit); respectively. Moreover, the improved error bound in the deep quench limit is optimal. Numerical experiments with three components illustrating the above error bounds are also presented. Received June 28, 1999 / Revised version received December 3, 1999 / Published online November 8, 2000     

Application of a Heuristic Scheduling Rule for a Tyre Testing Department

This paper presents the development and application of a heuristic scheduling rule for the Testing Department of a tyre and rubber company. The company had set down five major objectives for this department: (1) minimize average flow-time; (2) maintain an average flow-time of less than two weeks; (3) maintain pre-set maximum individual test flow times; (4) assign a higher priority to important jobs; (5) maintain a balanced mix between truck and passenger tyres. A composite scheduling rule was designed to meet these objectives which contains the following four components: (a) slack-time per remaining operation; (b) shortest processing time; (c) an urgency factor to prioritize important jobs; (d) a balancing factor to enable a desired proportion between truck and passenger tyres. This composite rule is tested against the existing scheduling scheme used by the foreman and against the simple S.P.T. rule. The results are very encouraging.     

The motion in a perfect fluid of a body containing a moving point mass

The motion of a system (a rigid body, symmetrical about three mutually perpendicular planes, plus a point mass situated inside the body) in an unbounded volume of a perfect fluid, which executes vortex-free motion and is at rest at infinity, is considered. The motion of the body occurs due to displacement of the point mass with respect to the body. Two cases are investigated: (a) there are no external forces, and (b) the system moves in a uniform gravity field. An analytical investigation of the dynamic equations under conditions when the point performs a specified plane periodic motion inside the body showed that in case (a) the system can be displaced as far as desired from the initial position. In case (b) it is proved that, due to the permanent addition of energy of the corresponding relative motion of the point, the body may float upwards. On the other hand, if the velocity of relative motion of the point is limited, the body will sink. The results of numerical calculations, when the point mass performs random walks along the sides of a plane square grid rigidly connected with the body, are presented.     

Detecting a hyperbolic quadratic eigenvalue problem by using a subspace algorithm

Numerical Algorithms - We consider the quadratic eigenvalue problem (QEP) Q(λ)x := (λ2M + λD + K)x =?0. A Hermitian QEP is hyperbolic if M is positive definite and (xHDx)2...     

The motion of a point mass along a string

An equation for the trajectory of a point mass (a particle) when it moves (slides) in a plane by inertia along a weightless elastic thread (string), stretched between two fixed points is obtained. The time dependence of the trajectory parameter is established. An equation of the trajectory of the particle when it suddenly decelerates is obtained. Forced motion of the particle along a straight string (as a model of the swinging of a lift on an elastic tether in zero gravity) is considered.     

On a repeated game without a recursive structure

The solution is given here for the infinitely repeated two-person zero-sum games of incomplete information characterized by 2×2 games, with information matrices $\left( {{*{20}c} a & b \\ b & b \\ } \right)$\left( {\begin{array}{*{20}c} a & b \\ b & b \\ \end{array} } \right) for the first game and $\left( {{*{20}c} b & b \\ b & a \\ } \right)$\left( {\begin{array}{*{20}c} b & b \\ b & a \\ \end{array} } \right) for the second game.     

Similarity of a Triangular Operator to a Diagonal Operator

We give sufficient conditions under which the non-self-adjoint operator A = G + iV ^1/2 JV ^1/2 (with a well-defined imaginary part) is similar to a self-adjoint one. We also give sufficient conditions (these conditions become necessary in the dissipative case) under which the triangular operator is similar to a self-adjoint one. Bibliography: 34 titles.     

Eigenvectors for a random walk on a hyperplane arrangement

We find explicit eigenvectors for the transition matrix of the Bidigare–Hanlon–Rockmore random walk, from Bidigare et al. (1999) [1]. This is accomplished by using Brown and Diaconis? (1998) analysis in [3] of the stationary distribution, together with some combinatorics of functions on the face lattice of a hyperplane arrangement, due to Gel?fand and Varchenko (1987) [10].