We prove a lower semicontinuity result for polyconvex functionals of the Calculus of Variations along sequences of maps u : Ω ⊂ R → R in W , 2 ≤ m ≤ n, bounded in W 1,m−1 and convergent in L under mild technical conditions but without any extra coercivity assumption on the integrand.

In this paper, we give sufficient conditions for the upper semicontinuity property of the solution mapping of a parametric generalized vector quasiequilibrium problem with mixed relations and moving cones. The main result is proven under the assumption that moving cones have local openness/local closedness properties and set-valued maps are cone-semicontinuous in a sense weaker than the usual s...

Using the homotopy invariance property of the degree and a newly introduced concept of the interior-point-ε-exceptional family for continuous functions, we prove an alternative theorem concerning the existence of a certain interior-point of a continuous complementarity problem. Based on this result, we develop several sufficient conditions to assure some desirable properties (nonemptyness, boun...

The Banach space `∞/c0 is isomorphic to the linear space of continuous functions on N∗ with the supremum norm, C(N∗). Similarly, the canonical representation of the `∞ sum of `∞/c0 is the Banach space of continuous functions on the closure of any non-compact cozero subset of N∗. It is important to determine if there is a continuous linear lifting of this Banach space to a complemented subset of...

For Tychonoff X and α an infinite cardinal, let αdef X := the minimum number of α cozero-sets of the Čech-Stone compactification which intersect to X (generalizing R-defect), and let rtX := minα max(α, α def X). Give C(X) the compact-open topology. It is shown that τC(X) ≤ nχC(X) ≤ rtX = max(L(X), L(X) def X), where: τ is tightness; nχ is the network character; L(X) is the Lindelöf number. For ...

Map construction and task-oriented navigation constitute two important capabilities for mobile robots. Despite their value, progress to date in the development of stand-alone robots endowed with these capabilities has been limited. We describe an architecture for mobile robots based on the concept of semi-autonomy that employs communication with a human advisor in order to simplify the tasks of...

Conventional learning games have often limited flexibility to address individual needs of a learner. The concept gaming approach provides a frame for handling conceptual structures that are defined by a concept map. A single concept map can be used to create many alternative games and these can be chosen so that personal learning goals can be taken well into account. However, the workload of cr...