through a continuous-time function with bounded derivative satisfies a Volterra integral equation of the second kind whose kernel and right-hand term are ... LM Ricciardi,L Sacerdote,S Sato - 《Journal of Applied Probability》 被引量: 381发表: 1984年 The Problem of Edge Cracks in an Infinit...
of a function defined in space (or in a plane), the derivative in the direction of the normal to some surface (or to a curve lying in the plane). LetSbe a surface,Pa point onS, andfa function in some neighborhood ofP. Then the normal derivative offatPis equal to the limit of the...
Does the derivative of a P(V) eqn give the eqn for change in Pressure? I know the integral of a P(V) eqn gives an eqn for work. I was wondering if taking the derivative of a P(V) eqn gives an eqn for change in pressure?
A problem of boundary control of string vibrations with the fixed end with a bounded control resource is studied. The integral of the second derivative module of the boundary control is minimized. Estimates of upper and lower bounds are found for the extremum. In the vibration suppression problem...
ON RATIONAL APPROXIMATIONS OF FUNCTIONS WITH A CONVEX DERIVATIVE It is shown that if , and if the function has a convex th derivative for , then the least uniform deviation of from the rational functions of degree no higher than is bounded from above by the quantity where is a natural numbe...
Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students. With the exception of a few simple statements, all results are proven in the text. The presentation is elementary, where -...
Analytic functions of bounded mean oscillation and the Bloch space In this paper we show that the closure of the space BMOA of analytic functions of bounded mean oscillation in the Bloch spaceB is the image P(U) of space o... GD Zheng - 《Integral Equations & Operator Theory》 被引量:...
The last expression on the right is called the integral of f(x), and f(x) itself is called the integrand. This method of finding the limit of a sum can be used to determine the lengths of curves, the areas bounded by curves, and the volumes of solids bounded by curved surfaces, and...
whereis the Clarke’s generalized gradient ofat. We need the succeeding hypotheses: DomainGis subset from Domainδ. be continuous linear operator, such that (s.t.)∀in Domainand, whereis a constant. A compact semigroup of bounded operatorinis formed by Ξ and...
Eq. (3.77) gives the material derivative of a volume integral in which the velocity vj of the volume motion is the velocity of the material particle. For nonlinear fluid–structure interactions, we often investigate the problem in the ALE system, for which the material derivative of a volume ...