This paper deals with the existence of optimal transport maps for some optimal transport problems with a convex but non strictly convex cost. We give a decomposition strategy to address this issue. As part of our strategy, we have to treat some transport problems, of independent interest, with a convex constraint on the displacement. As an illustration of our strategy, we prove existence of opt...

We provide theorems extending both Kakutani and Browder fixed points theorems for multivalued maps on topological vector spaces, as well as some selection theorems. For this purpose we introduce convex structures more general than those of locally convex and non-locally convex topological vector spaces or generalized convexity structures due to Michael, van de Vel, and Horvath.

It is clear that a monotone map is pseudomonotone, while a pseudomonotone map is quasimonotone. The converse is not true. If T is pseudomonotone (quasimonotone) and w ∈ X*\{}, then T + w is not pseudomonotone (quasimonotone) in general. In the case of a single-valued linear map T defined on the whole space Rn, it is known that if T + w is quasimonotone, then T is monotone []. Many authors (se...

When the systems evolved from analog to digital, the performance was improved by the use of power control on the one hand and different modulations and coding schemes on the other. Condensing the available information we are able to propose a new concept of power control. The concept is applicable to real systems, since it uses the available measurements for estimating parameters necessary for ...

In this paper, optimal power allocation and relay selection strategies in energy harvesting cooperative wireless networks are studied. In particular, signal-to-noise ratio (SNR)-maximizing based power allocation and relay selection without and with energy cooperation—via wireless energy transfer—are considered. Moreover, total relay power minimization subject to target end-to-end SNR is investi...

The Schauder-Tychonoff theorem states that a continuous function from a compact convex subset of a locally convex topological vector space into itself must have a fixed point ([1, Chapter V, 10.5], or [2]). Using this theorem, we obtain here a stronger result, stating that a map from such a set into the surrounding vector space has a fixed point if the directions in which the points are moved s...

*Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Abstract In this paper, the existence of solutions for differential inclusions of fractional order q ∈ (1, 2] with nonlocal strip conditions is investigated. Our study includes two cases: (i) the multivalued map involved in the problem is not ...

The Kalina cycle is believed to be one of the most promising technologies for power generation from low temperature heat sources such as geothermal energy. So far, most Kalina cycle power plants are designed with a working fluid mixture having a fixed composition, and thus normally operate at a fixed condensing temperature. However, the ambient temperature (i.e., heat sink) varies over a large ...

Serratia marcescens wild-types ATCC 264 and Nima grew but did not synthesize prodigiosin in a glycerol-alanine medium containing 10 ng of Fe per ml. Wild-type 264 required the addition of 0.2 mug of Fe per ml for maximal growth and prodigiosin synthesis; Nima required 0.5 mug of Fe per ml. Three percent, but not 0.1%, sea salts inhibited prodigiosin synthesis in a complex medium containing up t...