For multi-objective optimal reactive power dispatch (MORPD), a new approach is proposed where simultaneous minimization of the active power transmission loss, the bus voltage deviation and the voltage stability index of a power system are achieved. Optimal settings of continuous and discrete control variables (e.g. generator voltages, tap positions of tap changing transformers and the number of...

SUPPOSE D IS a bounded symmetric domain and I' c Aut (D) is a discrete group of arithmetic type. Then Borel and Baily [2] have shown that DIP can be canonically embedded as a Zariski-open subset in a projective variety Dir. However, Igusa [6] and others have found that the singularities of D/F are extraordinarily complicated and this presents a significant obstacle to using algebraic geometry o...

Phorbol myristate acetate (PMA), as a potent tumor promoter, may induce microglial senescence. The present study investigated the effect of PMA infection on microglial senescence. From 58 male Sprague‑Dawley rats, 10 were randomly selected and divided into a PMA injection group, containing five rats (0.5 µg/µl PMA) and a control group, containing five rats (commensurable 0.9% saline). Immunoflu...

A fundamental phenomenon of coherent control is investigated theoretically using the example neon photoionization by bichromatic field a free-electron laser. system exposed to fields with commensurable frequencies loses some symmetry, which manifests itself in angular distribution and spin polarization electron emission. We predict several such effects, for example, violation symmetry respect p...

For any self-similar measure $\mu$ in $\mathbb{R}$, we show that the distribution of is controlled by products non-negative matrices governed a finite or countable graph depending only on IFS. This generalizes net interval construction Feng from equicontractive type case. When satisfies weak separation condition, prove this directed has unique attractor. allows us to verify multifractal formali...

In 1939 Rademacher demonstrated how to express Klein’s modular invariant as a sum over elements of the modular group. In this article we generalize Rademacher’s approach so as to construct bases for the spaces of automorphic integrals of arbitrary even integer weight, for an arbitrary group commensurable with the modular group. Our methods provide explicit expressions for the Fourier expansions...

Introduction. The fundamental invariant of a Riemann surface is its genus. In this paper, using arithmetical means, we calculate the genus of certain Riemann surfaces defined by unit groups in quaternion algebras. First we recall a well-known general construction of Riemann surfaces. The group SL2(R) acts on the upper half-plane H by Möbius transformations. If G is a Fuchsian group, that is, a ...

We present a systematic investigation of two coinciding lattices and their spatial beating frequencies that lead to the formation of moiré patterns. A mathematical model was developed and applied for the case of a hexagonally arranged adsorbate on a hexagonal support lattice. In particular, it describes the moiré patterns observed for graphene grown on a hexagonally arranged transition metal su...