On squares of irreducible characters

We study the finite groups G with a faithful irreducible character whose square is a linear combination of algebraically conjugate irreducible characters of G. In conclusion, we offer another proof of one theorem of Isaacs-Zisser

Pythagoras as a mathematician

AbstractIn this article, two questions are posed: Just how reliable is the evidence concerning Pythagoras's mathematical studies, and can we reconstruct his contribution to mathematics? All known fragments of evidence by fourth-century B.C. authors on Pythagoras's mathematical investigations are examined, and it is shown that all the discoveries they mentioned belong to the sixth century B.C. The opinion that the Pythagoreans ascribed their own discoveries to Pythagoras is refuted, and it is shown that we are able to establish logically his contribution to mathematics

Precise Control of Dynamic Object by Combining of the Advantages of Different Sensors

Precise control of dynamic objects with negative feedback loop is widely used in science and industry [1-3]. Control accuracy depends on properties of the regulator, as well as on the accuracy of the sensor of the output value. Often the choice of the best sensor is impossible, because the different sensors may have different, and none of them is the best over the whole frequency range. In this paper, the research work is carried out in the base of the mathematical simulation and some theory. The modeling proof of the method effectiveness is carried out on specific examples. The sensors together with the object give the task with single input and two outputs (SITO)

Characteristic Barriers to the Implementation of the Roadmap for Augmented Reality Technology Development Program

The paper discusses the characteristic barriers for the development of a detailed map of the Program for the Development of Virtual and Augmented Reality (VR/AR) Technologies. The team of authors took part in the development of an alternative version of such a roadmap, since the main executor was another consortium of experts. An alternative point of view is always useful, in particular also because so far, the specified roadmap has not gone beyond the stage of discussion, it is theoretically possible to make amendments and additions to it. At the same time, even in case of its approval, a five-year term has been released for its implementation. During this period of time, possible adjustments to plans, opening of unrecorded technological barriers with which to fight. Therefore, this paper may be useful for those who are planning the development of these technologies, and for those who will work on these plans. The article contains the results of an in-depth analysis of the situation and forecasts on this basis, made during the expert consultation process of the main developers of the roadmap (some of the authors were among the authors of the final roadmap to be submitted for approval by the Government of the Russian Federation)