ON THE ACCURACY OF THE LEAST SQUARES AND THE TOTAL LEAST SQUARES METHODS

Consider solving an overdetermined system of linear algebraic equations by both the least squares method (LS) and the total least squares method (TLS). Extensive published computational evidence shows that when the original system is consistent. one often obtains more accurate solutions by using the TLS method rather than the LS method. These numerical observations contrast with existing analytic perturbation theories for the LS and TLS methods which show that the upper bounds for the LS solution are always smaller than the corresponding upper bounds for the TLS solutions. In this paper we derive a new upper bound for the TLS solution and indicate when the TLS method can be more accurate than the LS method.Many applied problems in signal processing lead to overdetermined systems of linear equations where the matrix and right hand side are determined by the experimental observations (usually in the form of a lime series). It often happens that as the number of columns of the matrix becomes larger, the ra     

ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE NAVIER－STOKES EQUATIONS

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＯＦＴＨＥＳＯＬＵＴＩＯＮＴＯＴＨＥＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳＴａｎｇＸｉａｎｊｉａｎｇ（Ｄｅｐｔ．ｏｆＭａｔｈ．,Ｓｉｃｈｕａｎｕｎｉｖｅｒｓｉｔｙ,Ｃｈｅｎｇｄｕ６１００６４...     

ON THE ABSOLUTE STABILITY OF DIRECT CONTROL SYSTEMS

ＯＮＴＨＥＡＢＳＯＬＵＴＥＳＴＡＢＩＬＩＴＹＯＦＤＩＲＥＣＴＣＯＮＴＲＯＬＳＹＳＴＥＭＳＷａｎｇＪｉｚｈｏｎｇ(王继忠)（ＬｉｎｙｉＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ,临沂师专，邮编：２７６００５）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｉｎｖｅｓ?..     

NEW RESULTS ON THE EXISTENCE OF PERIODIC SOLUTIONS TO LINARD EQUATION

In this paper, a Liénard equation with a deviating argument has been studied by means of Mawhin's continuation theorem. A new result guaranteeing the existence of periodic solutions is obtained.     

ON THE ANISOTROPIC ACCURACY ANALYSIS OF ACM''''S NONCONFORMING FINITE ELEMENT

The main aim of this paper is to study the superconvergence accuracy analysis of thefamous ACM's nonconforming finite element for biharmonic equation under anisotropicmeshes. By using some novel approaches and techniques, the optimal anisotropic inter-polation error and consistency error estimates are obtained. The global error is of orderO(h~2). Lastly, some numerical tests are presented to verify the theoretical analysis.     

A NEW APPROACH TO THE LINEARITY OF TESTING PLANARITY OF GRAPHS

In testing planarity of graphs,there are many criteria.The earliest one as known is the Kuratowski's theorem,then Whitney's,Maclane's, and so forth.Since the early sixties,people have begun researches on algorithms.Up to 1974,Hopcroft and Tarjan found an algorithm with a computing time being a linear function of the order of a graph.This is the linearity concerned here.This paper presents a new approach to the linearity by means of transforming the problem of testing planarity of a graph G into that of finding a spanning tree on another graph H,called an auxiliary graph of G,with the order of H being a linear function of that of G.And moreover,we can also make the size of H be a linear function of that of G.The whole procedure is based on the building up of a theory of linear equations on GF(2)related to G.     

ON THE COMPLEXITY OF A PL HOMOTOPY ALGORITHM FOR ZEROS OF POLYNOMIALS

A PL homotopy algorithm is modified to yield a polynomial-time result on its computational complexity.We prove that the cost of locating all zeros of a polynomial of degree n to an accuracy of ε(measured by the number of evaluations of the polynomial)grows no faster than O(max{n~4,n~3log_2(n/ε)}).This work is in response to a question raised in a paper by S.Smale as to the efficiency of piecewise linear methods in solving equations.In comparison with a few results reported,the algorithm under discussion is the only one providing correct multiplicities and the only one employing vector labelling.     

ON THE EXISTENCE AND THE UNIQUENESS OF SOLUTIONS TO STOCHASTIC INTEGRAL EQUATIONS WITH TWODIMENSIONAL TIME PARAMETER

In this paper the following stochastic integral equation is considered where A is a continuous increasing process, M is a continuous martingale. Mappings φ, F, G map continuous adapted processes into continuous adapted processes. We will prove equation (*) has a unique continuous solution under some conditions.     

ON THE FINITE VOLUME ELEMENT VERSION OF RITZ-VOLTERRA PROJECTION AND APPLICATIONS TO RELATED EQUATIONS

In this paper, we present a general error analysis framework for the finite volume element (FVE) approximation to the Ritz-Volterra projection, the Sobolev equations and parabolic integro-differential equations. The main idea in our paper is to consider the FVE methods as perturbations of standard finite element methods which enables us to derive the optimal L2 and H1 norm error estimates, and the L∞ and W∞1 norm error estimates by means of the time dependent Green functions. Our disc ussions also include elliptic and parabolic problems as the special cases.     

ON THE DIFFERENTIAL AND DIFFERENCE INDEPENDENCE OF Γ AND ζ

In this paper, we study the algebraic differential and the difference independence between the Riemann zeta function and the Euler gamma function. It is proved that the Riemann zeta function and the Euler gamma function cannot satisfy a class of nontrivial algebraic differential equations and algebraic difference equations.     

ON THE CONSTRUCTION AND ENUMERATION OF HAMILTONIAN GRAPHS

In this paer we give a farmula for enumerating the equivalent classes of orderly labeled Hamiltonian graphs under group D.and two algorithms for constructing these equivalent classes and all nonisomorphic Hamiltonian graphs.Some computational results obtained by microcomputers are listed.     

ON THE CLASSIFICATION OF AF-ALGEBRAS AND THEIR DIMENSION GROUPS （Ⅱ）

ＯＮＴＨＥＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦＡＦ－ＡＬＧＥＢＲＡＳＡＮＤＴＨＥＩＲＤＩＭＥＮＳＩＯＮＧＲＯＵＰＳ（Ⅱ）￥ＨＵＡＮＧＺＨＡＯＢＯＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｉｓａｃｏｎｔｉｎｕａｔｉｏｎｏｆ［１］．Ｉｔｇｉｖｅｓｓｏｍｅａｐｐｌｉ...     

ON THE EXISTENCE AND UNIQUENESS OF CLASSICAL GLOBAL SOLUTION TO A TYPE OF B0USSINESQ EQUATIONS

The existence and uniqueness of classical global solutions to a type of Boussinesq equations withinitial and boundary values are studied in this paper. The existence of such solutions is proved bymeans of compactness theorem and Schauders fixed point theorem, and its uniqueness by the so calledenergy method.     

RATIONALITY OF THE OFFSETS TO ALGEBRAIC CURVES AND SURFACES

ＲＡＴＩＯＮＡＬＩＴＹＯＦＴＨＥＯＦＦＳＥＴＳＴＯＡＬＧＥＢＲＡＩＣＣＵＲＶＥＳＡＮＤＳＵＲＦＡＣＥＳ￥ＬＵＷＥＩ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｊｉａｎｇＵｎｉｖｅｒｓｉｔｙ，Ｈａｎｇｚｈｏｕ３１００２７）Ａｂ...     

ON THE ASYMPTOTIC ASSIGNMENT OF THE BOUNDS OF DECREASING RATE FOR A TIME-VARYING LINEAR CONTROL SYSTEM

In the paper the problem on the assignment of the bounds of decreasing rate for a time-varying linear control system is discussed. The sufficient and necessary condition for bounds of decreasing rate of a time-varying linear system to be assigned arbitrarily is presented. It is pointed out that for any given real number n, M, n相似文献   

ON THE FRACTAL NATURE OF INCREMENTS OF THE INFINITE SERIES OF OU PROCESSES RELATED TO THE CHUNG LIL

The author proves that the set of points where the Chung type LIL fails for the path of the infinite series of independent Ornstein-Uhlenbeck processes is a random fraetal, and evaluates its Hausdorff dimension.     

IMPACT OF OPERATING COSTS ON INVESTMENT STRATEGIES IN NEW TECHNOLOGY ADOPTION WITH A FURTHER NEW TECHNOLOGY ANTICIPATED

The adoption of new technologies often represents a crucial component of firms＇ investment decisions. This paper studies a dynamic duopoly model in which two firms compete in adoption of current technology with a further new technology anticipated. Here it is assumed that the operating costs are not zero which has more explanatory power of the real world. There exist three kinds of equilibria that may occur in adoption of current technology, which mainly depends on the level of operating costs and the first-move advantage. It shows that the faster technological substitution or innovation encourages the leader to invest earlier while induces the follower to invest later. Furthermore,like the investment costs,with the increase of operating costs the follower tends to invest later while the leader tends to invest earlier ,the investment thresholds are more sensitive to the change of operating costs than that of investment costs.     

ON EXISTENCE， UNIQUENESS AND REGULARITY OF STEADY STATE SOLUTIONS TO THE BASIC SEMICONDUCTOR EQUATIONS

ＯＮＥＸＩＳＴＥＮＣＥ,ＵＮＩＱＵＥＮＥＳＳＡＮＤＲＥＧＵＬＡＲＩＴＹＯＦＳＴＥＡＤＹＳＴＡＴＥＳＯＬＵＴＩＯＮＳＴＯＴＨＥＢＡＳＩＣＳＥＭＩＣＯＮＤＵＣＴＯＲＥＱＵＡＴＩＯＮＳＷａｎｇＹｕａｎｍｉｎｇ（王元明）ＦａｎＪｉｓｈａｎ（樊继山）（Ｄｅｐｔ...     

ON UNIQUENESS OF SOLUTION TO POINTWISE LANDAU PROBLEM ON THE FINITE INTERVAL

1. Introduction Let W_∞~((r)) (β) = {f| f∈W_∞~((r)) [-1,1], ||f||_(C[-1,1]) β, ||f~((r))||_∞ 1}.In this paper, we will consider the following Landau problem:λf~((k))(ξ) + μf~((k-1)) (ξ) →inf, f∈W_∞~((r)) (β), (1.1)where ξ∈[-1,1], 1(?)k(?)r-1, and λ, μ real and not all zero, (if k=1,suppose λ≠0 in addition ). A. Pinkus studied it first. To begin with, we introduce some fundamental definitions anddenotions. The perfect spline f, which satisfies || f~((r))||_∞ = 1 andhas n knots and n+r+1 points of equioscillation in [-1,1], isdenoted by x_(nr), which is refered as Tchebyshev perfect spline. And