Gravitational waves from Sco X-1: A comparison of search methods and prospects for detection with advanced detectors

The low-mass X-ray binary Scorpius X-1 (Sco X-1) is potentially the most luminous source of continuous gravitational-wave radiation for interferometers such as LIGO and Virgo. For low-mass X-ray binaries this radiation would be sustained by active accretion of matter from its binary companion. With the Advanced Detector Era fast approaching, work is underway to develop an array of robust tools for maximizing the science and detection potential of Sco X-1. We describe the plans and progress of a project designed to compare the numerous independent search algorithms currently available. We employ a mock-data challenge in which the search pipelines are tested for their relative proficiencies in parameter estimation, computational efficiency, robust- ness, and most importantly, search sensitivity. The mock-data challenge data contains an ensemble of 50 Scorpius X-1 (Sco X-1) type signals, simulated within a frequency band of 50-1500 Hz. Simulated detector noise was generated assuming the expected best strain sensitivity of Advanced LIGO and Advanced VIRGO ($4 \times 10^{-24}$ Hz$^{-1/2}$). A distribution of signal amplitudes was then chosen so as to allow a useful comparison of search methodologies. A factor of 2 in strain separates the quietest detected signal, at $6.8 \times 10^{-26}$ strain, from the torque-balance limit at a spin frequency of 300 Hz, although this limit could range from $1.2 \times 10^{-25}$ (25 Hz) to $2.2 \times 10^{-26}$ (750 Hz) depending on the unknown frequency of Sco X-1. With future improvements to the search algorithms and using advanced detector data, our expectations for probing below the theoretical torque-balance strain limit are optimistic.Comment: 33 pages, 11 figure

Microwave absorption in the frustrated ferrimagnet Cu₂OSeO₃

The resonance properties of a new Cu₂OSeO₃ ferrimagnet have been investigated in a wide range of frequencies (17–142 GHz) at liquid helium temperature. The resonance data were used to plot the frequencyfield dependence of the ferrimagnetic spectrum described within the model of an anisotropic two-sublattice ferrimagnet. The effective magnetic anisotropy corresponding to the gap in the spin wave spectrum has been estimated (3 GHz). It is found that the spectrum has a multicomponent structure which is due to the diversity of the types of magnetization precession. As the amplitude of the high-frequency magnetic field increased, an additional absorption was observed in the external magnetic field lower than the field of the main resonance. The detected additional absorption corresponds to the nonuniform nonlinear parametric resonance, connected with nonuniformity of magnetic structure in the ferrimagnetic crystal Cu₂OSeO₃

The Principal Element of a Frobenius Lie Algebra

We introduce the notion of the \textit{principal element} of a Frobenius Lie algebra \f. The principal element corresponds to a choice of F\in \f^* such that $F[-,-]$ non-degenerate. In many natural instances, the principal element is shown to be semisimple, and when associated to \sl_n, its eigenvalues are integers and are independent of $F$. For certain ``small'' functionals $F$, a simple construction is given which readily yields the principal element. When applied to the first maximal parabolic subalgebra of \sl_n, the principal element coincides with semisimple element of the principal three-dimensional subalgebra. We also show that Frobenius algebras are stable under deformation.Comment: 10 page

Investigation of antiparkinsonian activity of new imidazole-4,5-dicarboxylic acid derivatives on the experimental model of catalepsy

To study the antiparkinsonian activity of new ligands of the glutamate NMDA receptor complex -1,2-substituted imidazole-4,5-dicarboxylic acids - on an experimental model of catalepsy caused by haloperidol intraabdominal injections in rat

Модели-полиады и их применение в обучении математике

Considered systems of models, called models-polyads. Components of the model-polyads are various models of a prototype object, describing the same its properties, and the exchange of information between the components of the modelpolyads occurring without distorting the information. The examples of modelspolyads, in particular, shows that in the form of models-polyads are the algebra of geometric vectors, algebra of complex numbers, etc. There are highlights the benefits of studying the objects in the form of models-polyads, and especially in the case of training, when the objects under study are presented in a models-polyads.Рассматриваются системы моделей, называемые моделями-полиадами. Компонентами модели-полиады (в частности, модели-диады, модели-триады) являются различные модели некоторого объекта- прототипа, описывающие одни и те же его особенности, причем обмен информацией между компонентами модели-полиады, происходящий без искажения этой информации. Приведены примеры моделей-полиад, в частности, показано, что в виде моделей-полиад представлены векторная алгебра, алгебра комплексных чисел и др. Выделены преимущества изучения объектов, представленных в виде моделей-полиад, и особенности обучения в случае, когда изучаемые объекты представлены в виде моделей-полиад