Cwikel’s bound is extended to an operator-valued setting. One application of this result is a semi-classical bound for the number of negative bound states for Schrödinger operators with operator-valued potentials. We recover Cwikel’s bound for the Lieb–Thirring constant L0,3 which is far worse than the best available by Lieb (for scalar potentials). However, it leads to a uniform bound (in the ...

Abstract. Long term optimal investment problems are studied in a factor model with matrix valued state variables. Explicit parameter restrictions are obtained under which, for an isoelastic investor, the finite horizon value function and optimal strategy converge to their long-run counterparts as the investment horizon approaches infinity. This convergence also yields portfolio turnpikes for ge...

Necessary optimality conditions for a nonsmooth semi-infinite interval-valued vec- tor programming problem are given in the paper by Jennane et al . ( RAIRO:OR (2020). DOI: 10.1051/ro/2020066 ). Having noticed inconsistencies their paper, Gadhi and Ichatouhane 10.1051/ro/2020107 ) made necessary corrections proposed what they considered more pertinent formulation of main Theorem. Recently, 10.1...

We consider the Cauchy problem for complex valued semi-linear heat equation $$\begin{aligned} \partial _t u - \Delta u^m =0, \ (0,x) = u_0(x), \end{aligned}$$ where $$m\ge 2$$ is an integer and initial data belong to super-critical spaces $$E^s_\sigma $$ which norms are defined by \Vert f\Vert _{E^s_\sigma } \langle \xi \rangle ^\sigma 2^{s|\xi |}\widehat{f}(\xi )\Vert _{L^2}, \sigma \in \mathb...

Logical systems with classical negation and means for sentential or propositional self-reference involve, in some way, paradoxical statements such as the liar. However, the paradox disappears if one replaces classical by an appropriate non-classical negation such as a paraconsistent one (no paradox arises if the liar is both true and false). We consider a non-Fregean logic which is a revised an...