Explicit computation of Drinfeld associator in the case of the fundamental representation of gl(N)

We solve the regularized Knizhnik-Zamolodchikov equation and find an explicit expression for the Drinfeld associator. We restrict to the case of the fundamental representation of $gl(N)$. Several tests of the results are presented. It can be explicitly seen that components of this solution for the associator coincide with certain components of WZW conformal block for primary fields. We introduce the symmetrized version of the Drinfeld associator by dropping the odd terms. The symmetrized associator gives the same knot invariants, but has a simpler structure and is fully characterized by one symmetric function which we call the Drinfeld prepotential.Comment: 14 pages, 2 figures; several flaws indicated by referees correcte

Non-perturbative results for the spectrum of surface-disordered waveguides

We calculated the spectrum of normal scalar waves in a planar waveguide with absolutely soft randomly rough boundaries beyond the perturbation theories in the roughness heights and slopes, basing on the exact boundary scattering potential. The spectrum is proved to be a nearly real non-analytic function of the dispersion $\zeta^2$ of the roughness heights (with square-root singularity) as $\zeta^2 \to 0$. The opposite case of large boundary defects is summarized.Comment: REVTEX 3, OSA style, 9 pages, no figures. Submitted to Optics Letter

CONCEPTIONS OF SELF-DEFENSE IN THE CRIMINAL LAW OF THE RUSSIA AND THE UNITED STATES

Purpose: This article is devoted to the analysis of the concepts of self-defense in the criminal law of Russia and the USA. The Russian Federation has developed a negative law enforcement practice in the field of implementation of the norms on necessary defense. Persons protecting themselves and their loved ones from criminals and causing harm to criminals who commit an attack are often prosecuted for violating the principle of proportionality of defense and attack, which under current law qualifies as exceeding the limits of necessary defense. Methodology: In the United States, criminal law provides citizens with ample opportunity to take defensive actions against criminal attacks. The basic doctrinal provisions of the institution of self-defense in the legal systems of Russia and the USA are considered. Under Russian criminal law, with the help of the institute of necessary defense, less specific rights are protected. Result: This leaves a wide scope for interpretation; law enforcement officials interpret the necessary defense in a limited way, not in the interests of the defenders. Implications/Applications: US criminal law proceeds from opposing assumptions, with the help of legitimate self-defense, not abstract rights are protected, but specific benefits: life, health, sexual integrity, the inviolability of the home; which allows for an unambiguous interpretation in the interests of defenders. Novelty/Originality: The article formulated proposals for the reception of the provisions of American criminal law into Russian law.as a result of which the criminal law should casually fix situations in which the necessity defense is possible and stipulates its limits

On stoichiometry and intermixing at the spinel/perovskite interface in CoFe2O4/BaTiO3 thin films

The performance of complex oxide heterostructures depends primarily on the interfacial coupling of the two component structures. This interface character inherently varies with the synthesis method and conditions used since even small composition variations can alter the electronic, ferroelectric, or magnetic functional properties of the system. The focus of this article is placed on the interface character of a pulsed laser deposited CoFe2O4/BaTiO3 thin film. Using a range of state-of-the-art transmission electron microscopy methodologies, the roles of substrate morphology, interface stoichiometry, and cation intermixing are determined on the atomic level. The results reveal a surprisingly uneven BaTiO3 substrate surface formed after the film deposition and Fe atom incorporation in the top few monolayers inside the unit cell of the BaTiO3 crystal. Towards the CoFe2O4 side, a disordered region extending several nanometers from the interface was revealed and both Ba and Ti from the substrate were found to diffuse into the spinel layer. The analysis also shows that within this somehow incompatible composite interface, a different phase is formed corresponding to the compound Ba2Fe3Ti5O15, which belongs to the ilmenite crystal structure of FeTiO3 type. The results suggest a chemical activity between these two oxides, which could lead to the synthesis of complex engineered interfaces

CRIMINAL RESPONSIBILITY OF MEDICAL WORKERS FOR ISPENSING NARCOTIC DRUGS TO REDUCE THE SUFFERING OF PATIENTS

Purposes: This article is devoted to the analysis of the problem that has been developed in the Russian Federation with the access of patients with severe pain to narcotic painkillers. Methodology: The legislation of the Russian Federation recognizes that patients have an unconditional right to pain relief, which is reflected in the Federal Law No. 323 dated November 21, 2011 “On the Basics of Protecting the Health of Citizens in the Russian Federation”. However, the procedural rules governing the receipt of narcotic painkillers by patients establish strict bureaucratic rules that impede the timely access of patients to the only effective narcotic drugs in their case.   Results: Deviation from these procedural rules threatens medical and pharmaceutical workers with criminal liability for illegal drug trafficking. As a result, Russian patients do not receive painkillers on a significant scale. The quality of life in the patient, who is forced to endure severe pain, is significantly reduced, which often leads to suicide. Various legislative solutions to this problem are proposed. Implications/Applications: Liberalization of the rules for dispensing narcotic painkillers are effective in the long term, but it has several problems. Slight liberalization is not able to fundamentally improve the situation of patients with severe pain. Novelty/Originality: Significant liberalization can create a negative narcotic situation due to market saturation with legal narcotic drugs. In the short term, an effective measure will be the exclusion of the criminal liability of medical and pharmaceutical workers for the prescription and dispensing narcotic painkillers to patients with severe pain syndrome in violation of the existing procedural rules, but for medical reasons

INFLUENCE OF PRESSURE OSCILLATIONS IN COMMON RAIL INJECTOR ON FUEL INJECTION RATE

Fuel injection causes considerable oscillations of fuel pressure at the injector inlet. One of the reasons is hydraulic impact when the needle valve closes. For multiple injections, the previous injections affect the following. As both the fuel pressure in rail pac and the injection rate grow, the oscillations increase. The pressure oscillation range at the common rail injector inlet at pac=1500 bar is up to 350 bar, and at the rail pressure pac=500 bar, the amplitude decreases to 80 bar. Physical properties of the fuel are also important. As the viscosity of the fuel increases, its hydraulic friction grows which results in a rapid damping of pressure oscillations. The data for an injector operating on sunflower oil is presented. As compared with diesel fuel, the oscillations range decreases from 400 to 250 bar at the same operating mode. The influence of the interval between the impulses of a double injection on the injection rate of the second fuel portion was investigated. Superposition of two waves during multiple injections may result in amplification and damping of the oscillations. Simulation was performed to estimate the influence of fuel type and time interval Δτ between control impulses of a double injection on the injection quantity of the second portion at pressures of 2000-3000 bar. When the rail pressure pac grows, the oscillations and their impact on the injection process increase. For diesel fuel at pressure of pac=2000 bar, the variation in injection rates of the second portion is 2.36-4.62 mg, and at pac=3000 bar – 1.58-6.63 mg