Integral Semihereditary Orders, Extremality, and Henselization

Q-integral Equations of Fractional Orders

The aim of this paper is to study the existence of solutions for a class of q-integral equations of fractional orders. The techniques in this work are based on the measure of non-compactness argument and a generalized version of Darbo’s theorem. An example is presented to illustrate the obtained result.

Optimized Integral Controller Searching Prime Number Orders

The concept of integration is generally applicable to automatic control of processes. As shown in this paper, integral controller performs efficient searches in the extensive prime sets, too. An inspiration by the simple analytic rules for PID controller tuning results in integral controller that ensures predictable work regardless of the cardinality of primes. It gives an innovative applicatio...

Power Integral Bases in Orders of Composite Fields

Extremality of Gaussian quantum states.

We investigate Gaussian quantum states in view of their exceptional role within the space of all continuous variables states. A general method for deriving extremality results is provided and applied to entanglement measures, secret key distillation and the classical capacity of bosonic quantum channels. We prove that for every given covariance matrix the distillable secret key rate and the ent...

Extremality conditions for isolated and dynamical horizons

A maximally rotating Kerr black hole is said to be extremal. In this paper we introduce the corresponding restrictions for isolated and dynamical horizons. These reduce to the standard notions for Kerr but in general do not require the horizon to be either stationary or rotationally symmetric. We consider physical implications and applications of these results. In particular we introduce a para...