Theory of Polarization Attraction in Parametric Amplifiers Based on Telecommunication Fibers

We develop from first principles the coupled wave equations that describe polarization-sensitive parametric amplification based on four-wave mixing in standard (randomly birefringent) optical fibers. We show that in the small-signal case these equations can be solved analytically, and permit us to predict the gain experienced by the signal beam as well as its state of polarization (SOP) at the fiber output. We find that, independently of its initial value, the output SOP of a signal within the parametric gain bandwidth is solely determined by the pump SOP. We call this effect of pulling the polarization of the signal towards a reference SOP as polarization attraction, and such parametric amplifier as the FWM-polarizer. Our theory is valid beyond the zero polarization mode dispersion (PMD) limit, and it takes into account moderate deviations of the PMD from zero. In particular, our theory is capable of analytically predicting the rate of degradation of the efficiency of the parametric amplifier which is caused by the detrimental PMD effect

Методика експериментальної перевірки моделі системи розвитку інноваційної культури майбутнього керівника закладу загальної середньої освіти

The article is devoted to the description of individual parts of the experimental work, the general purpose of which was to determine the effectiveness of implementation of the developed structural and functional model of the system of the innovative culture development of the future manager of general secondary educational institution in the master training process. Defining the pedagogical experiment was the task of checking the effectiveness of pedagogical conditions for the mplementation of the specified structural and functional model, the ability to ensure the integrity of the process of development of the phenomenon under study.Стаття присвячена опису окремих частин експериментальної роботи, загальна мета якої передбачала визначення ефективності реалізації розробленої структурно-функціональної моделі системи розвитку інноваційної культури майбутнього керівника установи загальної середньої освіти в процесі магістерської підготовки. Визначальним у педагогічному експерименті стала задача по перевірці ефективності педагогічних умов реалізації зазначеної структурно-функціональної моделі, можливостей забезпечення цілісності процесу розвитку досліджуваного феномена

Hochshild cohomology of the associative conformal algebra Cend_{1,x}

It is established in this work that second Hochshild cohomology group of the associative conformal algebra Cend_{1,x} is zero. As a corollary, this algebra split off in each extension with a nilpotent kernel. Key words: associative conformal algebra, splitting off radical, Hochshild cohomology

Order complexes of noncomplemented lattices are nonevasive

We reprove and generalize in a combinatorial way the result of A. Bj\"orner [J.\ Comb.\ Th.\ A {\bf 30}, 1981, pp.~90--100, Theorem 3.3], that order complexes of noncomplemented lattices are contractible, namely by showing that these simplicial complexes are in fact nonevasive, in particular collapsible