A necessary condition forB-stability

A necessary condition forB-stability is derived. Then it is shown that the Runge-Kutta methods of Lobatto type III _A and III _B and some other methods are notB-stable.     

A necessary condition for controlled approximation

A necessary condition is given on the Fourier transforms of a finite family of functions in R^sso that the finite family and their translates will approximate an arbitrary function within certain precision.     

拟圆的一个充分必要条件

利用拟双曲度量研究了平面拟共形映照中的拟圆，得到了拟圆的一个充分必要条件。     

A necessary condition forB-convergence of Runge-Kutta methods

Algebraic stability is a well-known property necessary forB-convergence of a Runge-Kutta method, provided its nodesc _i are such thatc _i – c _j wheneveri j. In this paper a slightly weaker property is established which becomes algebraic stability as soon asc _i – c _j , wheneveri j is excluded.Using this condition it is shown that the Lobatto IIIA methods with more than two stages cannot beB-convergent.This paper was written while the author was visiting the Rijksuniversiteit Leiden in the Netherlands, supported by the Netherlands Organization for Scientific Research (N.W.O.) and by an Erwin Schrödinger scholarship from the Fonds zur Förderung der wissenschaftlichen Forschung.     

0-对偶预同态的一个充要条件

我们对带零逆半群定义了0-对偶预同态的概念,给出并证明了0-对偶预同态的一个等价条件.     

A sufficient and necessary condition for global optimization

We consider a class of global optimization problems, in which the objective function is Lebesgue integrable. In this paper, we present a sufficient and necessary condition for computing the essential infimum. This optimality condition can be used to design algorithms for solving the global optimization problem.     

A necessary and sufficient condition for the nirenberg problem

We seek metrics conformal to the standard ones on Sⁿ having prescribed Gaussian curvature in case n = 2 (the Nirenberg Problem), or prescribed scalar curvature for n ≧ 3 (the Kazdan-Warner problem). There are well-known Kazdan-Warner and Bourguignon-Ezin necessary conditions for a function R(x) to be the scalar curvature of some conformally related metric. Are those necessary conditions also sufficient? This problem has been open for many years. In a previous paper, we answered the question negatively by providing a family of counter examples. In this paper, we obtain much stronger results. We show that, in all dimensions, if R(x) is rotationally symmetric and monotone in the region where it is positive, then the problem has no solution at all. It follows that, on S², for a non-degenerate, rotationally symmetric function R(θ), a necessary and sufficient condition for the problem to have a solution is that Rθ changes signs in the region where it is positive. This condition, however, is still not sufficient to guarantee the existence of a rotationally symmetric solution, as will be shown in this paper. We also consider similar necessary conditions for non-symmetric functions. ©1995 John Wiley & Sons, Inc.     

A necessary and sufficient condition for Hardy's operator in

The equivalent conditions are proved for the Hardy inequality to be fulfilled in the norms of a Lebesgue space with variable exponent . It is assumed that the function is monotone and positive on (0, 1).     

A necessary condition for the consistency of LAD estimate

If in the linear model (1) the random errorse ₁, e₂, satisfy assumption (B) (See Section 1), then a necessary condition for the consistency of the LAD estimate of ₀ is .Supported by the National Natural Sciences Foundation of China.     

A necessary condition for lower semicontinuity of line energies

We are interested in some energy functionals concentrated on the discontinuity lines of divergence-free 2D vector fields valued in the circle \(\mathbb {S}^1\). This kind of energy has been introduced first by Aviles and Giga (A mathematical problem related to the physical theory of liquid crystal configurations, 1987). They show in particular that, with the cubic cost function \(f(t)=t^3\), this energy is lower semicontinuous. In this paper, we construct a counter-example which excludes the lower semicontinuity of line energies for cost functions of the form \(t^p\) with \(0<p<1\). We also show that, in this case, the viscosity solution corresponding to a certain convex domain is not a minimizer.     

A necessary optimality condition for nondifferentiable constrained extremum problems

The purpose of this paper is to establish a necessary optimality condition for a certain class of nondifferentiable extremum problems. The analysis is developed via image-space approach and the result generalizes, in finite-dimensional spaces, the classical results concerning locally Lipschitz mathematical programming.     

A necessary condition of optimality for uncertain optimal control problem

This paper is concerned with optimal control problem whose state equation is an uncertain differential equation. A necessary condition of optimality for uncertain optimal control problem is presented by using classical variational method. Meanwhile, an existence theorem of solution to backward uncertain differential equation is proved.     

A necessary extremality condition for a set-valued stochastic control problem

For a controlled stochastic dynamic system with set-valued drift coefficient and a terminal cost functional we derive a necessary extremality condition in form of a minimum principle.     

A necessary and sufficient condition for lifting the hyperelliptic involution

Let denote a Riemann surface which possesses a fixed point free group of automorphisms with a hyperelliptic orbit space. A criterion is proved which determines whether the hyperelliptic involution lifts to an automorphism of Necessary and sufficient conditions are stated which determine when a lift of the hyperelliptic involution is fixed point free. A complete determination is made of the abelian groups which may arise as automorphism groups of surfaces which possess a fixed point free lift.