Alternative sets of hyperspherical harmonics: Satisfying cusp conditions through frame transformations

By extending the concept of Euler-angle rotations to more than three dimensions, we develop the systematics under rotations in higher-dimensional space for a novel set of hyperspherical harmonics. Applying this formalism, we determine all pairwise Coulomb interactions in a few-body system without recourse to multipole expansions. Our approach combines the advantages of relative coordinates with those of the hyperspherical description. In the present method, each Coulomb matrix element reduces to the ``1/r'' form familiar from the two-body problem. Consequently, our calculation accounts for all the cusps in the wave function whenever an interparticle separation vanishes. Unlike a truncated multipole expansion, the calculation presented here is exact. Following the systematic development of the procedure for an arbitrary number of particles, we demonstrate it explicitly with the simplest nontrivial example, the three-body system.Comment: 19 pages, no figure

Extreme value statistics in Raman fiber lasers

We present the numerical study of the statistical properties of the partially coherent quasi-CW high-Q cavity Raman fiber laser. The statistical properties are different for the radiation generated at the spectrum center or spectral wings. It is found that rare extreme events are generated at the far spectral wings at one pass only. The mechanism of the extreme events generation is a turbulent-like four-wave mixing of numerous longitudinal generation modes. The similar mechanism of extreme waves appearance during the laser generation could be important in other types of fiber lasers

Fraunhofer diffraction description in the approximation of the light field theory

The wavelength is that natural scale that determines the applicability domains of the ray approximation and the wave approximation of light. If the change of the radiation power spatial density is significant at the wavelength scale, we deal with the light diffraction phenomenon, which is a subject to the wave optics. Let us consider the diffraction phenomenon at the diaphragm. It is possible to distinguish the near zone with significant wave inhomogeneities (i.e. the Fresnel zone) and the far Fraunhofer diffraction zone, in which the wave becomes close to homogeneous (the so-called quasi-homogeneous) and the ray approximation is possible. The problem is that there is no explicit relationship between the radiance of the rays before and after diaphragm. Method for determining the boundary conditions for the radiance in the Fraunhofer zone through the radiance of the incident radiation is proposed in the paper. This approach for computing the radiance field in the Fraunhofer zone can be generalized to other problems of optics, thereby providing the possibility of using computationally efficient ray-approximation-based methods to determine the light fields

APPLICATION OF FINANCIAL AND LEGAL INSTRUMENTS FOR THE DEVELOPMENT OF INNOVATION CLUSTERS

Purpose: The purpose of this article is to study the issues of legislative regulation of innovation clusters in the system of financial and tax law. Methods: The authors proceeded from an interdisciplinary approach since the problem of the legal status of innovation clusters inevitably affects the subject of regulation of various branches of law and has both constitutional and legal, financial and legal, civil, administrative, and other aspects. Results: The article notes the underdevelopment of the legislative and legal field of clustering of the economy and the negative impact of the legislative factor on its full development. Legislation in the field of innovation (clustering) is not systemic, it is dominated by numerous disparate subordinate regulatory legal acts, including at the regional level. Conclusion: The main directions of financial and legal regulation of investment clusters include the budget vector, implemented through the effectiveness of the state as an investor through budget allocations. The tax regulation of innovation clusters, characterized by incentive-stimulating and mobilization orientation. The practical experience of the application of legislation in the field under consideration, as well as the most effective methods of stimulating innovation clusters, have been investigated

Using HCO+^+ isotopologues as tracers of gas depletion in protoplanetary disk gaps

The widespread rings and gaps seen in the dust continuum in protoplanetary disks are sometimes accompanied by similar substructures seen in molecular line emission. One example is the outer gap at 100 au in AS 209, which shows that the H$_{13}$CO$^+$ and C$_{18}$O emission intensities decrease along with the continuum in the gap, while the DCO$^+$ emission increases inside the gap. We aim to study the behavior of DCO$^+$/H$_{13}$CO$^+$ and DCO$^+$/HCO$^+$ ratios in protoplanetary disk gaps assuming the two scenarios: the gas depletion follows the dust depletion and only the dust is depleted. We first modeled the physical disk structure using the thermo-chemical model ANDES. This 1+1D steady-state disk model calculates the thermal balance of gas and dust and includes the FUV, X-rays, cosmic rays, and other ionization sources together with the reduced chemical network for molecular coolants. Afterward, this physical structure was adopted for calculations of molecular abundances with the extended gas-grain chemical network with deuterium fractionation. Ideal synthetic spectra and 0th-moment maps were produced with LIME. We are able to qualitatively reproduce the increase in the DCO$^+$ intensity and the decrease in the H$_{13}$CO$^+$ and C$_{18}$O intensities inside the disk gap, which is qualitatively similar to what is observed in the outer AS 209 gap. The corresponding disk model assumes that both the gas and dust are depleted in the gap. The model with the gas-rich gap, where only the dust is depleted, produces emission that is too bright in all HCO$^+$ isotopologues and C$_{18}$O. The DCO$^+$/H$_{13}$CO$^+$ line ratio can be used to probe gas depletion in dust continuum gaps outside of the CO snow line. The DCO$^+$/C$_{18}$O line ratio shows a similar, albeit weaker, effect; however, these species can be observed simultaneously with a single ALMA or NOEMA setup.Comment: 12 pages, 7 figures, Accepted for publication in Astronomy and Astrophysic

Photolysis of Fluorinated Graphites with Embedded Acetonitrile Using a White-Beam Synchrotron Radiation

Fluorinated graphitic layers with good mechanical and chemical stability, polar C–F bonds, and tunable bandgap are attractive for a variety of applications. In this work, we investigated the photolysis of fluorinated graphites with interlayer embedded acetonitrile, which is the simplest representative of the acetonitrile-containing photosensitizing family. The samples were continuously illuminated in situ with high-brightness non-monochromatized synchrotron radiation. Changes in the compositions of the samples were monitored using X-ray photoelectron spectroscopy and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. The NEXAFS N K-edge spectra showed that acetonitrile dissociates to form HCN and N2 molecules after exposure to the white beam for 2 s, and the latter molecules completely disappear after exposure for 200 s. The original composition of fluorinated matrices CF0.3 and CF0.5 is changed to CF0.10 and GF0.17, respectively. The highly fluorinated layers lose fluorine atoms together with carbon neighbors, creating atomic vacancies. The edges of vacancies are terminated with the nitrogen atoms and form pyridinic and pyrrolic units. Our in situ studies show that the photolysis products of acetonitrile depend on the photon irradiation duration and composition of the initial CFx matrix. The obtained results evaluate the radiation damage of the acetonitrile-intercalated fluorinated graphites and the opportunities to synthesize nitrogen-doped graphene materials

X-ray, Near-Ultraviolet, and Optical Flares Produced By Colliding Magnetospheres in The Young High-Eccentricity Binary DQ Tau

DQ Tau is a unique young high-eccentricity binary system that exhibits regular magnetic reconnection flares and pulsed accretion near periastron. We conducted NuSTAR, Swift, and Chandra observations during the July 30, 2022 periastron to characterize X-ray, near-ultraviolet (NUV), and optical flaring emissions. Our findings confirm the presence of X-ray super-flares accompanied by substantial NUV and optical flares, consistent with previous discoveries of periastron flares in 2010 and 2021. These observations, supported by new evidence, strongly establish the magnetosphere collision mechanism as the primary driver of magnetic energy release during DQ Tau's periastron flares. The energetics of the observed X-ray super-flares remain consistent across the three periastrons, indicating recurring energy sources during each passage, surpassing the capabilities of single stars. The observed flaring across multiple bands supports the Adams et al. model for magnetosphere interaction in eccentric binaries. Evidence from modeling and past and current observations suggests that both the mm/X-ray periastron flares and tentatively, the magnetic reconnection-related components of the optical/NUV emissions, conform to the classical solar/stellar non-thermal thick-target model, except for the distinctive magnetic energy source. However, our NuSTAR observations suffered from high background levels, hindering the detection of anticipated non-thermal hard X-rays. Furthermore, we report serendipitous discovery of X-ray super-flares occurring away from periastron, potentially associated with interacting magnetospheres. The current study is part of a broader multi-wavelength campaign, which is planned to investigate the influence of DQ Tau's stellar radiation on gas-phase ion chemistry within its circumbinary disk.Comment: 27 pages, 9 figures, 3 tables. Accepted for publication in The Astrophysical Journal, October 18, 202

An approach for clone detection in documentation reuse

The paper focuses on the searching method for repetitions in DocBook/DRL or plain text documents. An algorithm has been designed based on software clone detection. The algorithm supports filtering results: clones are rejected if clone length in the group is less than 5 symbols, intersection of clone groups is eliminated, meaningfulness clones are removed, the groups containing clones consisting only of XML are eliminated. Remaining search is supported: found clones are extracted from the documentation, and clone search is repeated. One step is proved to be enough. Adaptive reuse technique of Paul Bassett – Stan Jarzabek has been implemented. A software tool has been developed on the basis of the algorithm. The tool supports setting parameters for repetitions detection and visualization of the obtained results. The tool is integrated into DocLine document development environment, and provides refactoring of documents using found clones. The Clone Miner clone detection utility is used for clones search. The method has been evaluated for Linux Kernel Documentation (29 documents, 25000 lines). Five semantic kinds of clones have been selected: terms (abbreviations, one word and two word terms), hyperlinks, license agreements, functionality description, and code examples. 451 meaningful clone groups have been found, average clone length is 4.43 tokens, and average number of clones in a group is 3.56