On the sequence n! mod pn! \bmod p

We prove, that the sequence $1!, 2!, 3!, \dots$ produces at least $(\sqrt{2} + o(1))\sqrt{p}$ distinct residues modulo prime $p$. Moreover, factorials on an interval $\mathcal{I} \subseteq \{0, 1, \dots, p - 1\}$ of length $N > p^{7/8 + \varepsilon}$ produce at least $(1 - o(1))\sqrt{p}$ distinct residues modulo $p$. As a consequence, we obtain a polynomial improvement in the problem of representing a given residue class as a product of seven small factorials.Comment: 9 page

Legal Regulation of Relations in the Sphere of Crowdfunding in the Republic of Belarus

Objective: to study the theoretical and legal bases of crowdfunding and to elaborate scientifically grounded proposals for improving the Republic of Belarus legislation in this sphere.Methods: the methodological basis of the research is a system of principles, methods and techniques of studying the general regularities of emergence, formation and development of social-legal phenomena. In the research, general and specific methods of scientific cognition were used: analysis, synthesis, comparative-legal, logical, systemic, formal-legal, dialectic and other methods.Results: the history of emergence and formation of crowdfunding was analyzed. The social-economic and technical-technological factors were revealed, which facilitate the popularization of crowdfunding among the Internet users. The origins of the “crowdfunding” notion were discussed, as well as its filling with a definite meaning. The types of crowdfunding were listed, depending on the goal of investment on the part of investors. The main subject composition of legal relations in crowdfunding was established, which consists of the following persons: funding seeker; funder; operator of online-funding service. The overall algorithm of legal relations between the main subjects of crowdfunding was described. The positive and negative aspects of crowdfunding were characterized. An overall analysis of foreign legislation in the crowdfunding legal regulation was performed. Based on the analysis, the general trends of legislation development were presented. The program and normative legal acts on developing crowdfunding in the Republic of Belarus were reviewed. The probable contract models of the parties’ legal relations registering were named. The technical and legal requirements to the functional of an online-funding service were determined. The minimal necessary set of measures was proposed, which may prevent risks and threats associated with procurement and extension of funds through onlinefunding services. Based on the operator functions, specific requirements to the rules of online-funding service were determined.Scientific novelty: the author comprehensively studied the notion, legal nature and features of legal regulation of crowdfunding. The factors were revealed, which influence the formation of the legal norms regulating the procurement and extension of funds through online-funding services. The author elaborated proposals for improving the Republic of Belarus legislation in the sphere of social relations under study.Practical significance: the research results are significant for developing the studies in the sphere of civil, economic, and informational law. The obtained results may be used in teaching a course in civil, economic, and informational law, as well as be applied by law subjects when elaborating and introducing the respective drafts of laws and be an object of further scientific research on the issue

Algebraic Model for scattering of three-s-cluster systems; 2, Resonances in the three-cluster continuum of 6He and 6Be

The resonance states embedded in the three-cluster continuum of 6He and 6Be are obtained in the Algebraic Version of the Resonating Group Method. The model accounts for a correct treatment of the Pauli principle. It also provides the correct three-cluster continuum boundary conditions by using a Hyperspherical Harmonics basis. The model reproduces the observed resonances well and achieves good agreement with other models. A better understanding for the process of formation and decay of the resonance states in six-nucleon systems is obtained

Generation of Terahertz Pulsed Radiation with Photoconductive Antennas Based of Low-Temperature-Grown Gallium Arsenide and Its Applications

The design and technological conditions for manufacturing photoconductive antennas based on low-temperature-grown gallium arsenide (LT-GaAs) have been developed. An optimized photoconductive THz antenna based on LT-GaAs with flag geometry of the contacts was fabricated. LT-GaAs samples were obtained by molecular-beamepitaxy at temperatures of 230 ∘C on GaAs (100) substrates. On an optical setup with a femtosecond titanium-sapphire laser, a volt (watt)-ampere characteristics and photocurrent efficiency of the photo-conductive antenna measured by the pyroelectric sensor. The optimum annealing temperature of LT-GaAs was determined for generation of intense THz radiation. PCA have been tested in the terahertz radiation generation. The substantial effect of water vapor in the air and the environment of transparent objects is THz. The useful terahertz bandwidth extends from 0.1 to 2.7 THz and the source of terahertz wave is the most commonly used nonlinear crystal ZnTe in the biomedicine applications. However, in comparison PCA on LT-GaAs with ZnTe have better results in the intensity and the power of the THz response. Therefore, it will be possible to detect a lower concentration of biological objects. Keywords: Photoconductive antennas; low-temperature grown gallium arsenide

Geostrophic balance preserving interpolation in mesh adaptive shallow-water ocean modelling

The accurate representation of geostrophic balance is an essential requirement for numerical modelling of geophysical flows. Significant effort is often put into the selection of accurate or optimal balance representation by the discretisation of the fundamental equations. The issue of accurate balance representation is particularly challenging when applying dynamic mesh adaptivity, where there is potential for additional imbalance injection when interpolating to new, optimised meshes. In the context of shallow-water modelling, we present a new method for preservation of geostrophic balance when applying dynamic mesh adaptivity. This approach is based upon interpolation of the Helmholtz decomposition of the Coriolis acceleration. We apply this in combination with a discretisation for which states in geostrophic balance are exactly steady solutions of the linearised equations on an f-plane; this method guarantees that a balanced and steady flow on a donor mesh remains balanced and steady after interpolation onto an arbitrary target mesh, to within machine precision. We further demonstrate the utility of this interpolant for states close to geostrophic balance, and show that it prevents pollution of the resulting solutions by imbalanced perturbations introduced by the interpolation

Double or binary: on the multiplicity of open star clusters

Observations indicate that the fraction of potential binary star clusters in the Magellanic Clouds is about 10%. In contrast, it is widely accepted that the binary cluster frequency in the Galaxy disk is much lower. Here we investigate the multiplicity of clusters in the Milky Way disk to either confirm or disprove this dearth of binaries. We quantify the open cluster multiplicity using complete, volume-limited samples from WEBDA and NCOVOCC. At the Solar Circle, at least 12% of all open clusters appear to be experiencing some type of interaction with another cluster; i.e., are possible binaries. As in the Magellanic Clouds, the pair separation histogram hints of a bimodal distribution. Nearly 40% of identified pairs are probably primordial. Most of the remaining pairs could be undergoing some type of close encounter, perhaps as a result of orbital resonances. Confirming early theoretical predictions, the characteristic time scale for destruction of bound pairs in the disk is 200 Myr or one galactic orbit. Our results show that the fraction of possible binary clusters in the Galactic disk is comparable to that in the Magellanic Clouds.Comment: 6 pages, 3 figures; accepted by Astronomy and Astrophysics Letter

Generating a checking sequence with a minimum number of reset transitions

Given a finite state machine M, a checking sequence is an input sequence that is guaranteed to lead to a failure if the implementation under test is faulty and has no more states than M. There has been much interest in the automated generation of a short checking sequence from a finite state machine. However, such sequences can contain reset transitions whose use can adversely affect both the cost of applying the checking sequence and the effectiveness of the checking sequence. Thus, we sometimes want a checking sequence with a minimum number of reset transitions rather than a shortest checking sequence. This paper describes a new algorithm for generating a checking sequence, based on a distinguishing sequence, that minimises the number of reset transitions used.This work was supported in part by Leverhulme Trust grant number F/00275/D, Testing State Based Systems, Natural Sciences and Engineering Research Council (NSERC) of Canada grant number RGPIN 976, and Engineering and Physical Sciences Research Council grant number GR/R43150, Formal Methods and Testing (FORTEST)

Development and Approbation of Cognitive Behavioral Coaching Methodology

В исследовании описываются процесс и результаты разработки и апробации методологии когнитивно-поведенческого коучинга. Уточняется понятие коучинга и определяются его границы с близкими видами профессиональной деятельности, анализируются основные ожидания от коучинга как вида профессиональной деятельности.The report describes process and results of development and approbation of cognitive behavioral coaching methodology. The concept of coaching is clarified and its boundaries with similar types of professional activities are defined, general expectations from coaching as a type of professional activity are analyzed