Charges in nonlinear higher-spin theory

Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS4 Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.Comment: 23 pages; V3: typos corrected; references and acknowledgement added; example of the topological contribution to spin-4 charge added; new Section 3.1 added establishing relation of our construction for asymptotic charges with the canonical one. Version published in JHE

Lorentz covariant form of extended higher-spin equations

The extension of nonlinear higher-spin equations in d=4 proposed in [arXiv:1504.07289] for the construction of invariant functional is shown to respect local Lorentz symmetry. The equations are rewritten in a manifestly Lorentz covariant form resulting from some Stueckelberg-like field transformation. We also show that the two field-independent central terms entering higher-spin equations which are not entirely fixed by the consistency alone get fixed unambiguously by the requirement of Lorentz symmetry. One of the important advantages of the proposed approach demonstrated in the paper is the remarkable simplification of the perturbative analysis.Comment: V2: 20 pages, typos corrected, references added. Version published in JHE

Financial management of small organizations based on a cognitive approach

In most cases small business organizations insufficiently justify economic calculations for the formation of financial resources, which adversely affects their sustainable development. Under the current circumstances, the need for sound financial management increases, which ensures a stable financial status of the organization and the prospects for increasing its value. The aim of this paper is to identify the conditions for the dynamic financial management of small organizations based on a cognitive approach. The proposed cognitive model allows establishing the mechanism of mutual influential factors of internal and external environment on the effective use of financial resources. Using the proposed model, it is possible to forecast changes in financial results.peer-reviewe

Classical double copy and higher-spin fields

Kerr-Schild double copy is shown to extend naturally to all free symmetric gauge fields propagating on $(A)dS$ in any dimensions. Similarly to the standard lower-spin case, the higher-spin multicopy comes along with the zeroth, single and double copies. The mass-like term of the Fronsdal spin $s$ field equations fixed by gauge symmetry and the mass of the zeroth copy both appear to be remarkably fine tuned to fit the multicopy pattern forming a spectrum organized by higher-spin symmetry. On the black hole side this curious observation fills up the list of miraculous properties of the Kerr solution.Comment: 14 page

Interferometry of hyper-Rayleigh scattering by inhomogeneous thin films

The use of specific symmetry properties of the optical second-harmonic generation (the s,s-exclusion rule) has allowed us to observe high-contrast hyper-Rayleigh interference patterns in a completely diffuse light - an effect having no analog in case of linear (Rayleigh) scattering.Comment: 8 pages, 3 figure

Professional education in tourism: problems of the regional level

The article reveals the main problems of professional education in the sphere of tourism at the regional leve

Agrobiological evaluation of Allium ampeloprasum L. variety samples in comparison with Allium sativum L. cultivars

ArticleThe purpose of investigation is to study the biological and morphological features, to establish the economic and valuable characteristics of the introduced and local forms of Allium ampeloprasum L. in comparison with Allium sativum L. and to study the effect of removal of the scape in the yield. The studies used field, statistical, settlement and analytical methods. The weight of the bulb without removing the inflorescence shoot of the cultivar Sofiivskyi was 28.4– 53.3 g smaller than the variety samples No. 2 and No. 3 respectively. With removing the scape the difference increased by 60.5–68.6 g. The yield of No. 2 variety sample Allium ampeloprasum L. without removing the scape was lower than the standard by 1.7 t ha-1 while the variety sample No. 3 exceeded the standard by 1.1 t ha-1 . With the removal of inflorescence shoot the yields of variety samples No. 2 and No. 3 exceeded the cultivar Sofiivskyi by 1.6 and 2.2 t ha-1 . It has been established according to the researches that introduced forms of Allium ampeloprasum L. have high indicators of economic and valuable characteristics, but they are limited in the first years of cultivation, by the period of adaptation to the new soil and climatic conditions