We study the problem of secure transmission over a Gaussian two-user multi-input single-output (MISO) broadcast channel under the assumption that links connecting the transmitter to the two receivers may have unequal strength statistically. In addition to this, the state of the channel to each receiver is conveyed in a strictly causal manner to the transmitter. We focus on a two state topologic...

One of the main challenges of grid systems of large scale and data intensive is that of providing high availability and performance, in spite of the unreliability and delay occasioned by the size of Internet. Replication enables us to meet such a challenge with success. In the context of weak consistency, the fast consistency algorithm prioritizes replicas with high demand. Nevertheless, the fa...

It is well-known that if T is an everywhere defined bounded operator on a Banach space X to a Banach space Y and T* is its adjoint, then the range R(T*) of T* is closed in X* if and only if the range R(T) of T is closed in Y (cf. [2, pp. 487-489]). The object of this note is to establish this result for closed but possibly unbounded operators. This result, for the unbounded case, is of great ut...

We study the continuity of the correspondence of interim ε-rationalizable actions in incomplete information games. We introduce a topology on types, called uniformweak topology, under which two types of a player are close if they have similar firstorder beliefs, attach similar probabilities to other players having similar first-order beliefs, and so on, where the degree of similarity is uniform...

In functional analysis it is well known that every linear functional defined on the dual of a locally convex vector space which is continuous for the weak∗ topology is the evaluation at a uniquely determined point of the given vector space. M. Schröder and A. Simpson have obtained a similar result for lower semicontinuous linear functionals on the cone of all Scott-continuous valuations on a to...

‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...