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Showing papers in "Journal of Mathematical Analysis and Applications in 1965"




Journal ArticleDOI
TL;DR: The series-parallel connection is a simple type of electric network termed a series parallel connection which occurs frequently in both theoretical and applied electrical engineering as mentioned in this paper, where the joint resistance is easily evaluated by the following two rules due to Ohm: 0 s.

554 citations



Journal ArticleDOI
TL;DR: Only certain formal properties of the loss function will be required, they will be kept to a minimum, and their significance will be discussed as they are introduced.

179 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that uniform convergence of u(x, t)/x to 0 is sufficient but not necessary; the proper condition is that of integrable convergence, which we shall now define.

137 citations




Journal ArticleDOI
J.B Rosen1
TL;DR: It is shown that the pattern separation problem can be formulated and solved as a conveX pro gramming problem, i.e., the minimization of a convex function subject to linear constraints.

74 citations


Journal ArticleDOI
TL;DR: In this article, the authors show that the methods of dynamic programming may be applied to problems involving partially ordered criterion functions; specifically, the existence of optimal policies and the principle of optimality are established for a category of problems in which the criterion space is a conditionally complete multiplicative lattice.

72 citations




Journal ArticleDOI
David McGarvey1
TL;DR: In this paper, the authors studied representation of operators used to employ perturbation techniques and conditions were given on the coefficients of these operators that ensure that they be completely reducible even though they have continuous spectrum.

Journal ArticleDOI
TL;DR: In this paper, a simple inequality involving expectations of convex functions and the notion of G-majorization is derived, which extends a similar inequality of Marshall and Proschan (1965), J. Math. Anal. Applic.


Journal ArticleDOI
TL;DR: In this article, the authors restrict themselves to the case where all ui and bi are positive, except in Section 3(e), where the equality sign holds only if the sets (u) and (b) are proportional (i.e., if there are two numbers h and p, both not zero, such that Au, = & for all i = 1,..... n).



Journal ArticleDOI
TL;DR: Operator theory of pseudo-inverse generalized to encompass linear bounded operators on Hilbert spaces was studied in this article, where the operator theory was generalized to a linear bounded operator on Hilbert space.

Journal ArticleDOI
TL;DR: In this paper, the B.G.K. model is used to solve the slip-flow problem for a wall with accomodation coefficient α and convergence series expansions are given, particularly useful for α near to the extreme values.

Journal ArticleDOI
TL;DR: In this paper, a necessary and sufficient condition for the existence of a saddle point of a function when certain assumptions are satisfied, and derived some duality relations from this result, is given.


Journal ArticleDOI
TL;DR: In this article, the authors continue the study of Hilbert spaces of analytic functions which are involved in the structural analysis of non-self-adjoint transformations in Hilbert space, and show that the characteristic operator function is applied to transformations which have no connection with differential equations.

Journal ArticleDOI
TL;DR: In this paper, a method for the computational treatment of differential-difference equations was extended to cover equations of the form given in (1) and can then be treated by means of successive approximations.



Journal ArticleDOI
TL;DR: In this article, different series expansions are constructed for the solution and are shown to be always convergent, however, the different expansions are such to ensure rapid convergence for different flow regimes, which is not the case in this paper.

Journal ArticleDOI
TL;DR: In this article, the authors analyzed the plane poiseuille flow with elementary solutions and showed that all the series expansions are always convergent, and the general results were applied to find the limiting behaviors for large and small Knudsen numbers, and to discuss the limits of application of continuum and slip-flow theories.

Journal ArticleDOI
TL;DR: In this paper, a generalization of Banach's principle of contraction mappings appears in a bood on fundamental analysis by Kolmogorov and Fomin, and it is shown that this generalization is a special case of an elementary fact.