(Vanishing) Twist in the Saddle-Centre and Period-Doubling Bifurcation

The lowest order resonant bifurcations of a periodic orbit of a Hamiltonian system with two degrees of freedom have frequency ratio 1:1 (saddle-centre) and 1:2 (period-doubling). The twist, which is the derivative of the rotation number with respect to the action, is studied near these bifurcations. When the twist vanishes the nondegeneracy condition of the (isoenergetic) KAM theorem is not satisfied, with interesting consequences for the dynamics. We show that near the saddle-centre bifurcation the twist always vanishes. At this bifurcation a ``twistless'' torus is created, when the resonance is passed. The twistless torus replaces the colliding periodic orbits in phase space. We explicitly derive the position of the twistless torus depending on the resonance parameter, and show that the shape of this curve is universal. For the period doubling bifurcation the situation is different. Here we show that the twist does not vanish in a neighborhood of the bifurcation.Comment: 18 pages, 9 figure

Generating and sustaining long-lived spin states in 15N,15N′-azobenzene

Long-Lived spin States (LLSs) hold a great promise for sustaining non-thermal spin order and investigating various slow processes by Nuclear Magnetic Resonance (NMR) spectroscopy. Of special interest for such application are molecules containing nearly equivalent magnetic nuclei, which possess LLSs even at high magnetic fields. In this work, we report an LLS in trans-15N,15N′-azobenzene. The singlet state of the 15N spin pair exhibits a long-lived character. We solve the challenging problem of generating and detecting this LLS and further increase the LLS population by converting the much higher magnetization of protons into the 15N singlet spin order. As far as the longevity of this spin order is concerned, various schemes have been tested for sustaining the LLS. Lifetimes of 17 minutes have been achieved at 16.4 T, a value about 250 times longer than the longitudinal relaxation time of 15N in this magnetic field. We believe that such extended relaxation times, along with the photochromic properties of azobenzene, which changes conformation upon light irradiation and can be hyperpolarized by using parahydrogen, are promising for designing new experiments with photo-switchable long-lived hyperpolarization

Active and passive sensors for diagnostics quasi-zenith ionospheric HF communication channels

Background. There is a growing need for active sensory diagnostics of partial HF channels to provide frequency support to quasi-zenith HF radio links in varying signal propagation conditions. Enhancing the efficiency of active sensor algorithms, particularly by reducing emission time, is topical. To address this, a transition from sequential to parallel (simultaneous) diagnostics is proposed. Another significant challenge in HF communication is narrowband interference, and overcoming this issue involves the method of passive sensory diagnostics. This method assesses the availability of partial channels by analyzing the spectral density of interference power within them. Aim. The goal of this study is to develop algorithms and software tools that implement spectral monitoring and parallel sensing of partial channels for sensory diagnostics of ionospheric channels in quasi-zenith HF communication. Methods. The proposed approach involves integrating dynamic diagnostic methods into the development of intelligent sensors for ionospheric HF radio links, along with the creation of data analysis methods. Specialized computer software is employed to address the defined tasks. Experimental studies are conducted using the developed devices, which include intelligent active and passive radio sensors for HF radio links, to assess the load on HF communication channels. Results. A sensor for orthogonal quasi-zenith ionospheric radio channels has been created, incorporating algorithms for synthesizing a group pulse with orthogonal subcarriers while minimizing the peak factor. Additionally, algorithms for separating subcarriers and calculating the correlation function at the reception have been developed. The sensor employs the OFDM-BPSK signal modulation method, enabling operation in simultaneous-sequential sounding mode across the potential frequency range for communication. This led to an 8-fold reduction in the total signal emission time. Conclusion. The scientific results obtained have broad practical applications, particularly in enhancing the efficiency of wideband HF communication systems using spread spectrum signals

PROSECUTOR’S SUPERVISION OVER THE ACTIVITIES OF THE BODIES OF PRELIMINARY INVESTIGATION ON COMPENSATION FOR DAMAGE CAUSED BY A CRIME AT THE STAGE OF INITIATING A CRIMINAL CASE

Aim: The article is devoted to the consideration of the essence and main directions of prosecutorial supervision over the activities of officials of the preliminary investigation bodies for compensation for harm caused by a crime at the stage of initiating a criminal case. According to the deep conviction of the authors, one of the directions for ensuring the rights and legitimate interests of victims of crimes is to ensure compensation for property and physical damage, as well as compensation for moral damage and damage to business reputation. This area of activity of the preliminary investigation bodies is no less important than bringing the perpetrators to justice in order to assign them a fair punishment. Results: The author identified some reasons that negatively affect the implementation of prosecutorial supervision over the activities of these participants in criminal proceedings to ensure compensation for harm caused by a crime at the stage of pre-investigation verification. Conclusion: In conclusion, the authors substantiate the conclusion that at present, prosecutorial supervision over the activities of officials of the bodies of preliminary investigation is relevant and especially in demand to ensure the principle of competitiveness of the parties, the creation of legal guarantees for the realization by persons who have become victims of criminal acts, the right to full compensation for the harm caused. Prosecutorial supervision is proposed to be regarded as an important dominant of the procedural function of prosecutors, aimed at preventing violations in the activities of the preliminary investigation and inquiry bodies to compensate for harm caused by criminal acts, starting from the stage of initiating a criminal case

Role of exchange interaction in self-consistent calculations of endohedral fullerenes

Results of the self-consistent calculation of electronic structure of endohedral fullerene Ar@C$_{60}$ within the Hartree-Fock and the local density approximations are presented. Hartree-Fock approximation is used for the self-consistent description for the first time. It is shown that the accurate account of the exchange interaction between all electrons of the compound leads to the significant modification of the atomic valent shell which causes the noticeable charge redistribution inside the endohedral compound.Comment: 5 figures, Proceedings of the 5th Conference on Elementary Processes in Atomic Systems (CEPAS 2011), submitted to Nuclear Instruments and Methods in Physics Research Section

Manipulating spin hyper-polarization by means of adiabatic switching of a spin-locking RF-field

We propose a technique for transferring the multiplet spin polarization (CIDNP or PHIP, or one created by any other method), which is the mutual entanglement of spins, into net hyper-polarization with respect to the direction of a high magnetic field by slowly (adiabatically) switching-off a strong external RF- field with a specially selected frequency. The net hyper-polarized molecules can then be used in NMR spectroscopy or imaging for strong signal enhancement

Exploiting adiabatically switched RF-field for manipulating spin hyperpolarization induced by parahydrogen

A method for precise manipulation of non-thermal nuclear spin polarization by switching a RF-field is presented. The method harnesses adiabatic correlation of spin states in the rotating frame. A detailed theory behind the technique is outlined; examples of two-spin and three-spin systems prepared in a non- equilibrium state by Para-Hydrogen Induced Polarization (PHIP) are considered. We demonstrate that the method is suitable for converting the initial multiplet polarization of spins into net polarization: compensation of positive and negative lines in nuclear magnetic resonance spectra, which is detrimental when the spectral resolution is low, is avoided. Such a conversion is performed for real two-spin and three-spin systems polarized by means of PHIP. Potential applications of the presented technique are discussed for manipulating PHIP and its recent modification termed signal amplification by reversible exchange as well as for preparing and observing long-lived spin states

Human ribosomal protein S13 regulates expression of its own gene at the splicing step by a feedback mechanism

The expression of ribosomal protein (rp) genes is regulated at multiple levels. In yeast, two genes are autoregulated by feedback effects of the protein on pre-mRNA splicing. Here, we have investigated whether similar mechanisms occur in eukaryotes with more complicated and highly regulated splicing patterns. Comparisons of the sequences of ribosomal protein S13 gene (RPS13) among mammals and birds revealed that intron 1 is more conserved than the other introns. Transfection of HEK 293 cells with a minigene-expressing ribosomal protein S13 showed that the presence of intron 1 reduced expression by a factor of four. Ribosomal protein S13 was found to inhibit excision of intron 1 from rpS13 pre-mRNA fragment in vitro. This protein was shown to be able to specifically bind the fragment and to confer protection against ribonuclease cleavage at sequences near the 5′ and 3′ splice sites. The results suggest that overproduction of rpS13 in mammalian cells interferes with splicing of its own pre-mRNA by a feedback mechanism