Showing papers in "Journal of Mathematical Analysis and Applications in 1973"

TL;DR: In this paper, an approximation scheme for a class of optimal control problems is presented, and an order of convergence estimate is developed for the error in the approximation of both the optimal control and the solution of the control equation.

TL;DR: In this paper, the authors discuss certain initial-boundary value problems for the nonlinear beam equation and present a solution to the first-order value problem for the beam equation.

TL;DR: In this article, the authors define cl∞-monoids, which are used to measure the degree of membership of points in sets, and define L- or "fuzzy" sets are defined, and suitable collections of these are called L-topological spaces.

TL;DR: In this paper, the authors studied more general iteration processes in certain Banach spaces with the purpose of extending this theorem and showed that sometimes their aim can indeed be (partially) achieved (see, for example, Theorem 2.10).

TL;DR: For each real number p, 1 < p < co, let L,(lR~; Cli) denote the usual Banach space of equivalence classes of C-valued functions on IR whose absolute values raised to the power p are Lebesgue integrable over IR as discussed by the authors.

TL;DR: In this article, the authors obtained conditions on T, D, and X which would guarantee the strong convergence and weak convergence of the iterates to a fixed point of T in D and X in X, respectively.

TL;DR: In this paper, it was shown that the linear differential equation, x = A(t) x, (1) x is a matrix function defined and continuous for all t on the real line R.

TL;DR: The author gives the proofs of several theorems on fuzzy functions introduced here, which are useful in classifying objects of which classes do not possess sharply defined boundaries.

TL;DR: In this article, the effect of a uniform magnetic field on the overstability of a viscoelastic fluid has been investigated and the dispersion relation has been analyzed in terms of the Prandtl number p 1, magnetic PrandTL number p 2, a parameter Q characterizing the strength of the magnetic field, and a parameter Γ which characterizes the elasticity of the fluid.

TL;DR: In this paper, the conditional distribution of the state of a Markov chain, given observations of a function of a state, is derived in matrix form and in differential equation form.

TL;DR: In this paper, the position of Z with respect to the light cone plays an important role in the determination of well posed problems for the equations (1), and it is assumed that Z is an n-dimensional manifold of class Cl.

TL;DR: In this paper, the spectrum of the generator of the group of motions of an inviscid fluid in a slowly rotating container was studied and it was shown that for all containers the spectrum is {ix ¦ x ϵ [− 2, 2]}.

TL;DR: In this article, the classical notion of stabilizing a controlled dynamical system to some specified equilibrium point is extended to include stabilization to a specified linear subspace, and necessary and sufficient conditions for existence of a solution are derived and an explicit solution recipe is given for one special case.

TL;DR: In this paper, the authors defined the conditional expectation of a normal convex integrand relative to a σ-algebra and proved its duality, and proved some properties of the subdifferential of the new functionals.

TL;DR: By means of the theory of complex variables, the solutions of z exp z = a, where a is in general complex, are established analytically, and thereby reduced to elementary quadratures as discussed by the authors.

TL;DR: In this article, it was shown that the Dirichlet problem for the equation &U + p(u) = f has a variational solution for each f E V * in the form a(v, v) + snp(v) v dx (v E C, Q)) is coercive.

TL;DR: In this article, necessary and sufficient conditions for the minimization of a differentiable function subject to differentiable equality and inequality constraints are given, and the connection with earlier work of Neustadt and Jacobson, Lele, and Speyer is given.

TL;DR: A new approach is taken to analyze stabilization of a general nonlinear system with a dither input and it is shown that if the relaxed system is stable, then the original system with dither control would be stable in the finite time.

TL;DR: The existence of infinite number of Pade approximants has been proved in this paper, and it has been shown that for any function f (z) there is a subsequence of f(z) which converges almost everywhere in ¦z¦ ⩽ ϱ to functions f ( z ) which are regular except for a finite number ( n ⩾ m of poles in the Riemann sphere.

TL;DR: In this article, error bounds for a wide class of linear and nonlinear boundary value problems are derived from the theory of dual extremum principles for heat transfer, which involve mixed boundary conditions.