Laser spark obtained by using a conical optics is much more appropriate to form conducting channels in atmosphere. Only two types of lasers are actively considered to be used in forming high-conductivity channels in atmosphere, controlled by laser spark: pulsed sub-microsecond gas and chemical lasers (CO₂, DF) and short pulse solid-state and UV lasers. 

Main advantage of short pulse lasers is their ability in forming of super long ionized channels with a characteristic diameter of ~100  µ  in atmosphere along the  beam propagation direction. At estimated electron densities below  10 ⋅ 16 cm^–3 in these filaments and laser wavelengths in the range of 0,5–1,0 mm, the plasma barely absorbs laser radiation.  In this case, the length of the track composed of many filaments is determined by the laser intensity and may reach many kilometers at a femtosecond pulse energy of ~100 mJ. However, these lasers could not be used to form high-conductivity long channels in atmosphere. The ohmic resistance of this type a conducting channels turned out to be very high, and the gas in the channels could not be strongly heated (< 1 J). An electric breakdown controlled by radiation of femtosecond solid-state laser was implemented in only at a length of 3 m with a voltage of 2 MV across the discharge gap (670 kV/m).

Not so long ago scientific group from P. N. Lebedev has improved that result, the discharge gap – 1 m had been broken under KrF laser irradiation when switching high-voltage (up to 390 kV/m) electric discharge by 100-ns UV pulses. Our previous result  –  16 m long conducting channel controlled by a  laser spark at the voltage  –  3 MV  – was obtained more than 20 years ago in Russia and Japan by using pulsed CO₂  laser with energy  –  0,5 kJ. An average electric field strength  was < 190 kV/m. It is still too much for efficient applications.

The paper offers a new method for approximate solution of one type of singular integral equations for elasticity theory which have been studied by other authors. The approximate solution is found in the form of asymptotic polynomial function of a low degree (first approximation) based on the Chebyshev second order polynomial. Other authors have obtained a solution (only in separate points) using a method of mechanical quadrature  and though they used also the Chebyshev polynomial of the second order they applied another system of junctures which were used for the creation of the required formulas.

The suggested method allows not only to find an approximate solution for the whole interval in the form of polynomial, but it also makes it possible to obtain a remainder term in the form of infinite expansion where coefficients are linear functional of the given integral equation and basis functions are the Chebyshev polynomial of the second order. Such presentation of the remainder term of the first approximation permits to find a summand of the infinite series, which will serve as a start for fulfilling the given solution accuracy. This number is a degree of the asymptotic polynomial (second approximation), which will give the approximation to the exact solution with the given accuracy. The examined polynomial functions tend asymptotically to the polynomial of the best uniform approximation in the space C, created for the given operator.

The paper demonstrates a convergence of the approximate solution to the exact one and provides an error estimation. The proposed algorithm for obtaining of the approximate solution and error estimation is easily realized with the help of computing technique and does not require considerable preliminary preparation during programming.

The paper investigates vibro-protection conditions for “operator-chair” system of a transport facility (“Belarus-tractorfamily). Experimental  research for the system vibroloading with due account of elastic shock-absorbing characteristics, operator’s comfortability. The paper has made it possible to determine a range of the system vibration frequency which is badlysustained by the operator because the last is located in the zone of natural frequency of human visceral organs vibrationsInfluence of physiological operator’s factors – heartbeat rate, variational height, mode amplitude, stress index has been investigated on the basis of a factor experiment and correlation dependences have been obtained in the paper. The developed methodology for investigation of algorithmic provision pertaining to better active vibroprotection of the “operator-chair” system presupposes an availability of mathematical model used for synthesis of control laws and selection of algorithms for formation of signals on physiological operator’s state. Structural algorithm scheme for vibroprotection of “driver – seat – road” system has been drawn in the paper.

Harmonic sinusoidal and poly-harmonic disturbances from the side of a power unit and discrete algorithms based on filtration of white noise with a linear filter and  prescribed correlation function have been accepted as a mathematical model for external environment disturbances. In case of harmonic excitation of “operator – chair” system  a force transferred to the system by a shock-absorber and also shock-absorber efficiency evaluation in the form of force transmission coefficient and vibration insulation value are estimated at decibels. Fourier’s series describes motion of the system in case of vibration forces initiated by the operation of the power unit. Piecewise-linear function describes a reaction on impact excitation of the system when final change in speed and motion quantity occurs. Quality evaluation of the vibro-protection system is determined as ratio of maximum effort transmitted by the system to maximum value of impact excitation. Decision support system, in otherwords a controlling system, consists of two  circuits: the first circuit organizes work with information forming correlations between great number of input and output signals and the second circuit consisting of blocks for state evaluation and decisionmaking organizes work with qualitative information.

 

By using potential effective interaction in the anharmonic correlated Einstein model on the basis of quantum statistical theory with phonon interaction procedure, the expressions describing asymmetric component (cumulants) and thermodynamic parameters including the anharmonic effects contributions and by new structural parameters of cubic crystals has been formulated. This new parameters describing the distribution of atoms. The expansion of cumulants and thermodynamic parameters through new structural parameters has been performed.

Analytical expressions describing dependence between basic parameters of potash ore crushing process have been constructed in the paper. While taking in account the generality of the Kirpichev formula some corrections have been made for direct applicability of the given hypothesis in calculation of energy which is required for crushing of potash ore specimen. Such approach makes it possible to consider not only general averaged size of specimens but percentage content of every concrete specimen of the specified dimensions. While investigating potash ore composition of the prescribed volume it has been established that every component contained in the specimen composition has its tensile strength and elastic modulus. In addition to this it has been demonstrated the percentage content of components in potash ore composition (sylvinite, halite and insoluble residue) is different.

It has been experimentally determined that the selected volume of the material (2 м³) supplied for benefication and the final product have normal distribution of ore pieces, it means that number of averaged size pieces is higher than pieces of minimum and maximum sizes. An expression has been obtained on the basis of the executed investigations and formula that corresponds to the Kirpichev hypothesis. The expression makes it possible to calculate energy required for crushing of the specified volume of potash ore. In this case chemical composition and percentage content of components included in the potash ore have been taken into account. The energy required for crushing of the potash ore volume consists of total sum of energy used for crushing of separate components included in chemical composition of potash ore and this sum is multiplied by percentage content of corresponding substance.

The paper considers a model of damage accumulation in parts of machines and structures which is based on a theory of fractals. Hidden process of destruction prior to the formation of macroscopic cracks is usually associated with the accumulation of micro-damages. Various models of damage accumulation and crack growth under the influence of power and thermal loads. However, models describing the accumulation process of micro-damages and their outgrowth into macro-crack are practically non-existent. Fractal structures with self-similarity are an adequate model of the fracture process. The MacDonald correlation function describing the medium structure allows to present the self-similarity of structures within a certain range of scales.

The paper reviews models of damage accumulation near an opening in a composite medium and at layer boundaries. The Cantor model in a forward algorithm and a backward algorithm have been used in order to describe the model of damage accumulation. As it is known, the Cantor fractal (Cantor dust) is obtained by using a recursive algorithm being applied to fracture mechanics can be regarded as a model of stepwise formation of dispersed micro-damages. The process of damage accumulation (latent destruction phase) and its transition in the formation process of macro-cracks and their unification in a through-thickness crack can be described, for example, by the Paris' law.

Method for calculation of the stressed state in a dynamic twin has been developed on the basis of a non-thin non-coherent micro-twin model with continuous distribution of twinning dislocations at twin boundaries. In this case there is no additional generation with the help of twinning dislocation source. The model takes into account that the twin has coherent and noncoherent boundary sections. The developed model has made it possible to take into consideration a form of non-coherent sections of twinning boundaries in calculations of stressed and deformed state at dynamic twins. It has been established that localized stresses are migrating together with non-coherent sections of the twin. Normal stresses σ_xx change their sign in relation to direction of the twin development. Shear stresses σ_xy are alternating in signs in relation to an axis which is perpendicular to the direction of the twin development and which is passing through a mid-point of non-coherent twin section. Distribution of stresses σ_yy и σ_yz has similar configuration. Stresses σ_zx in the second and fourth quarters of XOY plane are negative and the stresses in the first and third quarters are positive. Distribution of stresses σ_zz practically does not differ from distribution of stresses σ_yy according to configuration but numerical values of stress tensor component data are different.

The results have been obtained without thin twin model that permits to consider only elastic stage of the twinning process. The executed stress calculations at dynamic twin are important for forecasting at the accumulation stage of damage origination which is caused by twinning destruction and permit to improve forecasting accuracy of technical system resources on the basis of twinning materials such as alloys based on iron, copper, zinc, aluminium, titanium.

One of the problems facing chemists who are involved in obtaining disperse systems with micro- and nanoscale particles of the disperse phase is a size evaluation of the obtained particles. Formation of hydrated sol is one of the stages for obtaining nanopowders while using sol-gel-method. We have obtained titanium dioxide hydrosol while using titanium tetrachloride hydrolysis in the presence of organic solvent with the purpose to get titanium dioxide powder It has been necessary to evaluate size of titanium dioxide hydrosol particles because particle dimensions of disperse hydrosol phase are directly interrelated with the obtained powder dispersiveness.

Size calculation of titanium dioxide hydrosol particles of disperse phase has been executed in accordance with the Rayleigh equation and it has been shown that calculation results correspond to experimental data of atomic force microscopy and X-ray crystal analysis of the powder obtained from hydrosol.

In order to calculate particle size in the disperse system it is possible to use the Rayleigh equation if the particle size is not more than 1/10 of wave length of impinging light or the Heller equation for the system including particles with diameter less than wave length of the impinging light but which is more than 1/10 of its value. Titaniun dioxide hydrosol has been obtained and an index of the wave ration has been calculated in the Heller equation. The obtained value has testified about high dispersiveness of the system and possibility to use the Rayleigh equation for calculation of the particle size in the disperse phase. Calculation of disperse-phase particle size of titanium dioxide hydrosol has corresponded to experimental data of the atomic force microscopy and X-ray crystal analysis for the powder obtained from the system.

The paper considers a destruction criterion in a specific phenomenological model of elastic plastic medium which significantly differs from the known criteria. In case of vector interpretation of rank-2 symmetric tensors yield surface in the Cauchy stress space is formed by closed piecewise concave surfaces of its deviator sections with due account of experimental data. Section surface is determined by normal vector which is selected from two private vectors of criterial “deviator” operator. Such selection is not always possible in the case of anisotropy growth. It is expected that destruction can only start when a process point in the stress space is located in the current deviator section of the yield surface. It occurs when a critical point appears in the section, and a private value of an operator becomes N-fold in the point that determines the private vector corresponding to the normal vector. Unique and reasonable selection of the normal vector becomes impossible in the critical point and an yield criteria loses its significance in the point.

When the destruction initiation is determined there is a possibility of a special case due to the proposed conic form of the yield surface. The deviator section degenerates into the point at the yield surface peak. Criterion formulation at the surface peak lies in the fact that there is no physically correct solution while using a state equation in regard to elastic distortion measures with a fixed tensor of elastic turn. Such usage of the equation is always possible for the rest points of the yield surface and it is considered as an obligatory condition for determination of the deviator section. A critical point is generally absent at any deviator section of the yield surface for isotropic material. A limiting value of the mean stress has been calculated at uniform tension.

The paper considers a problem of the market relations development in the Belarusian housing area. It has been noted that the situation in transition to the market is characterized by vague notion of the State participation extent in solution of the housing problem. Thus the excessive rigidity is observed which is expressed in State intention to shift burden of responsibility for housing provision and exploitation to the forming class of housing owners. Low productivity of such actions is caused by discrepancy of basic provisions in housing reform to the national social and economic development level. The proposed housing policy strategy leans on an assessment of the State participation extent in the formation of separate market functions, i.e. reproduction (production), operation of real estate objects in the housing sphere and transfer of ownership. State participation extent is expressed in establishment of a rigid, partial regulation or assistance in formation of a market selfregulation.

Approaches of ordoliberal housing policy adapted for conditions of transition to the market are considered as basic ones for the investigation of the Belarusian housing policy. An idea about the maximum possible expansion necessity of the market housing relations under the rigid state control of activity in the market is realized in the proposed housing policy strategy. This approach has been justified by an intention to prevent possible speculations in housing, monopolization of the market from the side of large commercial structures that directly leads to aggravation of the housing problem. A special attention has been paid to a social subsystem of the market as a condition of social and economic stability of the State. The paper presents an effect calculation from introduction of the proposed housing policy strategy actions.

The paper considers a problem pertaining to reduction of the Armed Forces of the Republic of Belarus and necessity to carry out economically reasonable reforms optimizing strength of financial personnel with the purpose to decrease its number but without undermining financial and operational activities of the Armed Forces as a whole. It has been proposed to optimize strength of financial personnel in the Armed Forces while executing organizational staff transformations such as introduction of a centralized accounting system for service personnel by an example of the Ministry of Defense of the Russian Federation.

Normative for financial personnel strength of the supposed unified financial centre which is involved in accounting recordings on salary and other payments has been calculated on the basis of inter-branch standards. While taking as an example a conventional organization “B” with staff strength which is equal to the strength of the Armed Forces of the Republic of Belarus the possible efficiency in introduction of the centralized accounting system for service personnel has been determined in the paper. According to represented calculations reduction of financial personnel dealing with accounting recordings on salary and other payments in the whole organization “B” can constitute up to 60 persons with more than 200 branches which are carrying out independent payment accounting for personnel concerned.

Dependence of strength normative on number of financial bodies, percentage of personnel receiving payments through a unified financial centre and concentration of financial and economic document circulation has been determined in the paper. It has been pointed out that it is not sufficient to determine quantitative indices in order to ensure an objective reflection of the efficiency of possible introduction of the centralized accounting system for service personnel in the Armed Forces. In order to obtain complete information it is necessary to consider qualitative changes paying a special attention to problems and possible ways of their solution. The paper describes problems pertaining to labour norming and it is of interest for financial-economic and organizational and mobilization bodies of the Armed Forces.

Since admission of Poland to the European Union Polish enterprises can make use of the state support in various forms including support in investments, investigations and developments, consulting, higher qualification, financing of exhibition participation, salary additional payments for invalid workers, repayment of loan portions. The purpose of the given publication is to make an analysis of accounting method for state support which is granted for an organization within the frameworks of the accounting policy depending on the obtained grants.

Enterprises must select themselves a grant accounting form as in account books so while presenting financial reporting and these accounting and reporting forms must be reflected in the enterprise policy of accounting. The enterprise accounting policy indicates principles for creation of reserves and conditional obligations related with grants. Enterprises can use some simplifications and they can exclude creation of reserves and withhold conditional obligations concerning the grants if these measures are considered as insignificant.

In accordance with the enterprise accounting policy account books must contain recordings on grant provision when a grant is transferred to the bank account or when an enterprise receives a written notice confirming final decision about payments from a financing institution. The accounting policy must determine principles of bank operation break-up on grant accounts and security system of data and files including accounting documents, accounts and other documents related to the obtained grant and the required archivation term