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The method of noncommutative integration of linear differential equations is used to construct an exact solution of the Dirac equation, which does not presume complete separation of variables, in Stackel spaces. The Dirac equation in an external electromagnetic field is integrated by this method, using one example. The Stackel space under consideration does not enable one to solve this equation exactly within the framework of the theory of separation of variables.

Noncommuntative quadratic symmetry algebras of a certain class for the Schrodinger equation are classified. For each such algebra, the permissible potential is found. The application of noncommuntative integration of partial differential equations by means of quadratic algebras is demonstrated for a nontrivial example. The solution obtained forms the basis for the representation of quadratic algebras.

A method of noncommutative integration of linear partial differential equations that is analogous to noncommutative integration of finite-dimensional Hamiltonian systems is proposed. The method is based on the concept, introduced in the paper, of a λ representation of Lie algebras. The method can be applied to the integration of the Klein-Gordon equation in Riemannian spaces of non-Stackel type (i.e., in spaces that do not admit complete separation of the variables).

The present study is concerned with the application and investigation of a new method of exact integration of systems of linear differential equations, the method of noncommutative integration. The method is based on the use of noncommutative subalgebras of symmetry for finding an exact solution. The investigation of 5-dimensional subalgebras of symmetry of the d'Alembert equation lead to the claim that there exists a class of subalgebras which generate exact solutions in explicit form but which it is not possible to obtain in explicit form by means of complete separation of the variables.

This study continues an earlier investigation of applications of the method of noncommutative integration of linear partial differential equations [A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 1995; No. 5, 33 (1991)], which was a generalization of the analogous method for Hamiltonian systems. The method of noncommutative integration uses nonabelian algebra to characterize the symmetry of the equation, which makes it possible to construct exact solutions going beyond the framework of the method of separation of variables. The condition of noncommutative integrability is used to select the algebras of waveequation symmetry needed for the given method in Minkowski space R1,2. Nonequivalent noncommutative subalgebras of conformal algebra k1,2 are used to construct the basis of solutions of the three-dimensional wave equation.

The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented.

D'alambert's equation is used as an example to study the possibilities of a new method of exactly integrating systems of linear differential equations — the method of noncommutative integration (NI). The results confirm that use of the NI is equivalent to complete separation of the variables in the case of four-dimensional subalgebras of conformal algebra. However, the method does simplify determination of the exact solution in this instance.

A new cyclizing reagent is proposed for the synthesis of 5-unsubstituted 1,3,4-thiadiazoles. The latter are formed in good yields by the reactions of thiohydrazides with diethyl chlorophosphate in DMF.

The construction of a km 3 -scale neutrino telescope – the Gigaton Volume Detector (GVD) in Lake Baikal – is the central goal of the Baikal collaboration. During the R&D phase of the GVD project in 2008–2010 years the basic elements of GVD – new optical modules, FADC readout units, underwater communications and trigger systems – have been developed, produced and tested in situ by long-term operating prototype strings in Lake Baikal. The prototyping phase of the GVD project has been started in April 2011 with the installation of a three string array (prototype cluster) which comprises all basic elements and systems of the GVD-telescope in Lake Baikal. We describe configuration and technical design of the GVD, present selected results obtained during 2008–2010 with prototype strings, and describe configuration and design of the 2011 prototype cluster.

We report the present status and perspectives of the feasibility study to detect cosmic neutrinos acoustically in the Lake Baikal. The results of background studies are presented. It was shown that most of the detected neutrino-like pulses come from the lake surface. This fact has been used in the project of an acoustic prototype detector that consists of compact Acoustic Sensor Modules with 4-channel antennas each, arranged above the Baikal Neutrino Telescope at shallow depths and “listening” the deep-water layers of the lake.

It was established that martensitic-ferritic chrome-nickel steels type 03Kh13N4G5M2 are prone to embrittlement by solder based on copper at temperatures close to or somewhat exceeding the temperature of α-y transformation. It was discovered that embrittlement may be of catastrophic nature. The temperature range of embrittlement depends on the content of δ-ferrite in the alloys. With increasing content of δ-ferrite the temperature of the onset of embrittlement becomes higher at first, and then it decreases. The discovered effect of high-temperature (above 950‡C) embrittlement of steels by a liquid-metal melt has some equal and some different traits from ordinary liquid-metal embrittlement (LME).

The objective of the Baikal Project is the creation of a kilometer-scale high-energy neutrino observatory: the Gigaton Volume Detector (GVD) in Lake Baikal. Basic elements of the GVD – new optical modules, FADC readout units, and underwater communication systems – were investigated and tested in Lake Baikal with prototype strings in 2008–2010. We describe the results of prototype strings operation and review the preliminary design and expected sensitivity of the GVD telescope.

A project of the NT1000 deep-water neutrino telescope with an effective volume of ∼1 km3 is currently being developed by the BAIKAL collaboration. The telescope will be located in Lake Baikal in close vicinity of the NT200+ detector, which is currently in operation. The telescope will be composed of 12 clusters with 8 similar strings of optical modules in each (each string has two sections of the NT1000 optical modules). The section of the NT1000 optical modules has been developed using higher-efficiency photomultiplier tubes and state-of-the-art electronics. The field tests of the experimental string consisting of two sections with six optical modules in each have been performed. The results of these investigations are used in the project of the NT1000 neutrino telescope and in the hydrological study of Lake Baikal.

We review the status of the Lake Baikal Neutrino Experiment. Preparation towards a km3-scale Gigaton Volume Detector (GVD) in Lake Baikal is currently a central activity. As an important milestone, a km3-prototype string comprising of 12 optical modules and based on a completely new technology, has been installed and was put in operation together with NT200+ in April, 2009. We also present recent results from the long-term operation of NT200, including an improved limit on the diffuse astrophysical neutrino flux.

A new method is proposed for derivation of exactly integrable linear differential equations based on the theory of noncommutative integration. The equations are obtained by reduction from original equations which are integrable in the noncommutative sense, with a large number of independent variables. It is shown that the reduced equations cannot be solved by traditional methods, since they do not possess the required algebraic symmetry.

The method of noncommutative integration of linear differential equations [A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved. Fiz., No. 4, 116; No. 5, 100 (1991)] is used to integrate the Klein-Gordon equation in Riemannian spaces. The situation is investigated where the set of noncommuting symmetry operators of the Klein-Gordon equation consists of first-order operators and one second-order operator and forms a so-called F algebra, which generalizes the concept of a Lie algebra. The F algebra is a quadratic algebra in the given situation. A classification of four- and five-dimensional F algebras is given. The integration of the Klein-Gordon equation in a Riemannian space, which does not admit separation of variables, is demonstrated in a nontrivial example.

We review the status of the Lake Baikal Neutrino Experiment. Preparation towards a km3-scale Gigaton Volume Detector (GVD) in Lake Baikal is currently a central activity. As an important milestone, a km3-prototype string comprising 6 optical modules and based on a completely new technology, has been installed and was put into operation together with NT200+ in April, 2008. An upgraded version of the prototype string, which comprises 12 optical modules, was put into operation in April 2009. We also present new results from the long-term operation of NT200, including an improved limit on the diffuse astrophysical neutrino flux.

The quantum analogue is considered of the classical Euler equations on the Lie algebraso (4) for the integrable case. With the help of the method of non-commutative integration (A. V. Shapovalov, I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, p. 95; No. 5, p. 33 (1991)) and the method of separation of variables, the quantum equations are reduced to the solution of a system of ordinary differential equations.

The local symmetries of linear differential equations are investigated by means of proven theorems on the structure of the algebra of local symmetries of translationally and dilatationally invariant differential equations. For a nonparabolic second-order equation, the absence of nontrivial nonlinear local symmetries is proved. This means that the local symmetries reduce to the Lie algebra of linear differential symmetry operators. For the Laplace—Beltrami equation, all local symmetries reduce to the enveloping algebra of the algebra of the conformal group.

We study some properties of the nonlinear Poisson bracket and its analog for linear differential equations in partial derivatives (so-called F-algebras). We propose a method for noncommutative integration of linear differential equations for the case when the equation operator is embedded in an F-algebra. The method is based on the exact infinite irreducible representation of an F-algebra (λ-representation), which is introduced in the present paper.

Relativistic Poincare-invariant wave equations for zero-mass and heavy particles with an arbitrary spin are constructed on the basis of special infinite-dimensional representation of the Lorentz group. The equations form a compatible system of linear differential equations for an unknown scalar function and contain spin s as a parameter (arbitrary complex number). It is also shown that the equations obtained in this way include the well-known finite-component wave equations as a special case of half-integral or integral spin.

Studies have been made on how borosilicide coatings and individual chemical treatment stages affect the mechanical properties of the substrate metal (unalloyed vanadium and VTsU alloy). The redistribution of interstitial impurities between the liquid and solid metals reduces the plasticity of vanadium and VTsU. The working characteristics can be restored by heat treatment of the coated material, namely high-temperature ageing.

The mycolytic activity of 27 strains of antagonistic bacilli belonging to two taxonomic groups (18 strains of Bacillus subtilis and 9 strains of Paenibacillus ehimensis) capable of induced synthesis of chitinolytic enzymes was studied. Most of the B. subtilis strains neither displayed visible mycolytic effects on the phytopathogenic fungus Bipolaris sorokiniana in vitro, nor produced chitinases in the presence of an auto-claved mycelium. On the contrary, P. ehimensis strains grown under conditions favorable for induction of chitinases and other hydrolases exhibited a pronounced lytic effect on B. sorokiniana and actively grew by utilizing mycelium as the sole source of carbon and nitrogen. Comparison of the mycolytic activities of extracellular hydrolases in the studied strains demonstrated low correlation between chitinase production and the ability of the strains to degrade the cell walls of B. sorokiniana. Characterization of enzyme profiles in the studied strains revealed that beta-1,3-glucanase was a more significant factor than chitinase for determining the mycolytic potential of bacteria and their ability to utilize the mycelium of phytopathogenic fungi as a growth substrate.

Detectors on the “Universitetsky‐Tatiana” satellite measured a smoothly varying intensity of UV radiation from the night‐time atmosphere in the nadir direction and the intensity of the energetic electron flux at the orbit. At high latitudes the UV intensity in the auroral oval is interpreted as being due to electrons penetrating into the atmosphere. At middle latitudes the UV intensity is an order of magnitude less and more data are needed to reveal the origin of this radiation. Millisecond flashes of UV radiation were observed. The flashes’ energy, temporal profile and global distribution are similar to these parameters for Transient Luminous Events (TLEs). These studies will be continued aboard the next satellite “Tatiana‐2”.

We study identities in the enveloping algebra of the conformal group, which is the symmetry group of many wave equations: d'Alambert, Weyl, Maxwell, etc. We find all second-order identities for these equations and, in addition, the dimension of the space of nontrivial symmetry operators of any order for the d'Alambert equation.

Applying the method of noncommutative integration for linear differential equations, we build exact solutions for the Dirac equation in 4-dimensional Riemann spaces, which have a 5-parameter group of automorphisms and where the Klein-Gordon and the Dirac equations are nonintegrable using the technique of complete separation of variables.

Methods of generating exactly integrable potentials for the Schrodinger equation are consolidated within the framework of a simple construction. The Abraham-Moses method is generalized to the case of the nonstationary Schrodinger equation. An algorithm is proposed for solving the Schrodinger equation based on nonlocal symmetry operators.

By the method of non-coimmutative integration of linear differential equations proposed by the authors [Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 95 (1991)] the Klein-Gordon and Dirac equations are integrated in four-dimensional Riemannian spaces, not admitting separation of variables.

An algorithm is proposed for integrating linear partial differential equations with the help of a special set of noncommuting linear differential operators — an analogue of the method of noncommutative integration of finite-dimensional Hamiltonian systems. The algorithm allows one to construct a parametric family of solutions of an equation satisfying the requirement of completeness. The case is considered when the noncommutative set of operators form a Lie algebra. An essential element of the algorithm is the representation of this algebra by linear differential operators in the space of parameters. A connection is indicated of the given method with the method of separation of variables, and also with problems of the theory of representations of Lie algebras. Let us emphasize that on the whole the proposed algorithm differs from the method of separation of variables, in which sets of commuting symmetry operators are used.

For the wave equation in Minkowski space, a space is defined of nontrivial local second-order differential symmetry operators. The algebraic conditions, which, in accordance with the general theorems on the separation of variables, must be satisfied by the commutative subalgebras, including two first-order operators and second-order operator, are formulated in coordinate-free form. On the basis of these subalgebras, there are obtained all the complete sets of symmetry operators of types (2.0), (2.1). Sets are presented which do not have analogues in papers of other authors.

A 2 MeV proton tandem accelerator with vacuum insulation was developed and first experiments are carried out in the Budker Institute of Nuclear Physics (Novosibirsk). The accelerator is designed for neutron production via reaction (7)Li(p,n)(7)Be for the boron neutron-capture therapy of the brain tumors, and for explosive detection based on 9.1724 MeV resonance gamma, which are produced via reaction (13)C(p,gamma)(14)N, absorption in nitrogen.

We review the status of the Baikal neutrino telescope, which is operating in Lake Baikal since 1998 and has been upgraded to the 10 Mton detector NT 200 + in 2005. We present selected physics results on searches for upward going neutrinos, relativistic magnetic monopoles and for very high-energy neutrinos. We describe the strategy of creating a detector on the Gigaton ( km 3 ) scale at Lake Baikal. First steps of activities towards a km 3 Baikal neutrino telescope are discussed.

A prototype string for the future km3-scale Baikal neutrino telescope has been deployed in April, 2008 and is fully integrated into the NT200+ telescope. All basic string elements - optical modules (with 12"/13" hemispherical photomultipliers), 200MHz FADC readout and calibration system - have been redesigned following experience with NT200+. First results of in-situ operation of this prototype string are presented., Comment: 8 pages, 15 figures; presented at VLVNT08 (Very Large Volume Neutrino Telescope) Workshop, Toulon, France, April, 2008; to appear in NIM-A

The problem of complex separation of variables in the wave equation is considered in four-dimensional Minkowskii space-time. In contrast to the known series of researches by Kalnins and Miller (see Ref. Zh., Fiz., 2B9 (1978); 1B208 and 1B209 (1979), e.g.), underlying this research is a theorem on the necessary and sufficient conditions of total separation of variables in the non-parabolic V. N. Shapovalov equation (Differents. Uravn.,16, No. 10, 1864–1874 (1980)). Nonequivalent complete sets of three differential first-order symmetry operators are constructed, appropriate coordinate systems are found, and complete separation of variables is performed in the wave equation.

A similarity relationship is set up in the set of subalgebras with a nontrivial center of a conformal group algebra that separates it into classes of mutually similar subalgebras. In all 24 different classes of similar subalgebras are obtained and one representative is described in each class. All the nonequivalent two-dimensional commutative subalgebras of a conformal group algebra are obtained as an illustration of applying such a subalgebra system. The results of the research can be used to obtain the solutions of conformally invariant equations in the separated variables.

Copper tetra-4-(n-alkoxycarbonyl)phthalocyanines were synthesized, and their thermotropic and lyotropic mesomorphism at different lengths of lateral substituents was studied. Their possibility of forming both thermotropic and lyophilic mesophases (amphotropy) was found. The length of lateral substituents affects the type of supramolecular packing in the mesophase rather than the temperature of the crystal→mesophase phase transition. A rarecase of the mesogeneity of disk-like compounds of the same chemical nature possessing only four substituents is discussed.

Results of 178 operations with extended D3 lymphadenectomy (study group) performed at the patients with stomach cancer are analyzed. Control groups consisted of 175 patients undergone operations with D2 lymphadenectomy, and 266 patients undergone surgery of typical extension. Study and control groups were similar according to prognostic factors. Indications for extended lymphadenectomy are formulated. It was demonstrated that short-term results in both group were equal. Safety of extended D3 lymphadenectomies wasalso confirmed. Extended D3 lymphadenectomies permitted to increase the respectability on 6.7%.

In modern conditions of power consumption growing in Russia, apparently, it is difficult to find alternative to further development of nuclear power engineering. The negative party of nuclear power engineering is the spent fuel of nuclear reactors (radioactive waste). The gaseous and fluid radioactive waste furbished of highly active impurity, dumps in atmosphere or pools. The highly active fluid radioactive waste stores by the way of saline concentrates in special tanks in surface layers of ground, above the level of groundwaters. A firm radioactive waste bury in pods from a stainless steel in underground workings, salt deposits, at the bottom of oceans. However this problem can be esteemed in a positive direction, as irradiation is a hard radiation, which one can be used as a power source in nuclear - optical converters with further conversion of optical radiation into the electric power with the help of photoelectric converters. Thus waste at all do not demand special processing and exposure in temporary storehouses. And the electricity can be worked out in a constant mode within many years practically without gang of a stimulus source, if a level of a residual radioactivity and the half-lives of component are high enough. The nuclear-optical converter (NOC) esteem usually as a way of the ascent of energy from a nuclear reactor [1], a path of direct conversion of a nuclear energy into light.

We present the design of a device for detection of acoustic signals from high energy particle showers. The module will be stationary installed above the Baikal Neutrino Telescope NT-200+.

We review the status of the Baikal Neutrino Telescope, which has recently been upgraded to the 5 Mton detector NT200+. We present results on searches for upward going atmospheric neutrinos and relativistic magnetic monopoles, obtained from 1998-2002 with the predecessor detector NT200. A search for very high energy neutrinos yields an upper limit on the extraterrestrial diffuse neutrino flux for 20 TeV < E < 50 PeV. We describe the strategy of upgrading NT200 to NT200+ and creating a detector on the Gigaton (km3) scale at lake Baikal. R&D activities on that next stage detector have been started.