We first study some properties‎ ‎of $A$-module homomorphisms $theta:Xrightarrow Y$‎, ‎where $X$‎ ‎and $Y$ are Fréchet $A$-modules and $A$ is a unital‎ ‎Fréchet algebra‎. ‎Then we show that if there exists a‎ ‎continued bisection of the identity for $A$‎, ‎then $theta$ is‎ ‎automatically continuous under certain condition on $X$‎. ‎In‎ ‎particular‎, ‎every homomorphism from $A$ into certain‎ ‎Fr...

The present paper is a continuation of the work, carried out in [4] and [5] of investigating the relationship between a Gaussian process and its reproducing kernel Hilbert subspace. Our main result gives a characterization of the topological support of a Gaussian measure defined on a linear topological space of functions on an arbitrary set. As special cases we consider Gaussian processes on Ba...

We continue to study Lax (L-A, U-V) pairs (LP) joint covariance with respect to Darboux transformations (DT) as a classification principle. The scheme is based on a comparison of general expressions for the transformed coefficients of LP and its Frechet derivative. We use the compact expressions of the DT via some version of nonabelian Bell polynomials. It is shown that one more version of Bell...

This paper describes the formulation of optimization techniques based on control theory for aerodynamic shape design in viscous compressible flow, modelled by the Navier-Stokes equations. It extends previous work on optimization for inviscid flow. The theory is applied to a system defined by the partial differential equations of the flow, with the boundary shape acting as the control. The Frech...

In acoustic seismic-reeection experiments, because of the lack of low frequencies in the usual seismic sources, the reeection of the energy back to the surface is associated to the short wavelengths of the slowness (the reeectivityy parameters), while the long wavelengths of the slowness (the propagatorr parameters) are associated to the kinematics of the arrival times of this energy. Such a de...

In this paper, the largest and the smallest observations are considered, at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. We prove that sequences of the residual or past entropy of the current records characterizes F in the family of continuous distributions. The exponential and the ...

This paper investigates calculus rules for the limiting Fréchet-subdifferential of infimum value functions of locally Lipschitzian and non-Lipschitzian functions. It is not required that the infimum is attained.

Received (received date) Revised (revised date) Communicated by (Name) The article analyzes similarity of closed polygonal curves with respect to the Fréchet metric, which is stronger than the well-known Hausdorff metric and therefore is more appropriate in some applications. An algorithm is described that determines whether the Fréchet distance between two closed polygonal curves with m and n ...