Simon argued that the semi-classical theory of gravity, unless with some of its solutions excluded, is unacceptable for reasons of both self-consistency and experiment, and that it has to be replaced by a constrained semi-classical theory. We examined whether the evidence is conclusive. PACS Number: 04.20-q

We extend to semi-abelian categories the notion of characteristic subobject, which is widely used in group theory and in the theory of Lie algebras. Moreover, we show that many of the classical properties of characteristic subgroups of a group hold in the general semi-abelian context, or in stronger ones.

We devise a framework which leads to the formulation of a unified theory of normality (regularity), semi-normality (semi-regularity), s-normality (s-regularity), feeblynormality (feebly-regularity), pre-normality (pre-regularity), and others. Certain aspects of theory are given by unified proof.

Recently the distributive equations involving various classes of aggregation operators have aroused widespread attention because of their importance in the theoretic and applied communities of fuzzy set theory. 2-uninorms and semi-t-operators are two special classes of aggregation operators and have been proved to be useful in many areas such as fuzzy decision making, approximate reasoning and ...

In this paper, the well-known Egoroff’s theorem in classical measure theory is established on monotone non-additive measure spaces. Taylor’s theorem, which concerns almost everywhere convergence of measurable function sequence in classical measure theory, is also generalized. The converse problem of the theorems are discussed, and a necessary and sufficient condition for the Egoroff’s theorem i...

Model reduction of high order linear-in-parameters discrete-time systems is considered. The main novelty of the paper is that the coefficients of the original system model are assumed to be known only within given intervals, and the coefficients of the derived reduced order model are also obtained in intervals, such that the complex value sets of the uncertain original and reduced models will b...

We study the local Lipschitz–continuity of the value function v associated with a Bolza Problem in presence of a Lagrangian L(x, q), convex and uniformly superlinear in q, but only Borel–measurable in x. Under these assumptions, the associated integral functional is not lower semicontinuous with respect to the suitable topology which assures the existence of minimizers, so all results known in ...

Let PSel be the class of all P-selective sets. We show that DTIME(2nk+a) 6 Pnk T(PSel) for all k; a > 0. It implies EXP 6 Pnc T(PSel) for all c > 0. This greatly improves Toda's result that EXP 6 Ptt(PSel) since Ptt(PSel) is equal to PO(logn) T(PSel). We construct an oracle A such that DTIME(2nk)A PAnk+1+a-T(PSel). We also show that the symmetric di erence of a EPm-hard set and a P-selective se...