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The paper presents practical results of 60Co production in irradiation assemblies (IAs) in RBMK-1000 reactor during 1100 effective days of irradiation. Operational support of irradiation was performed by means of certified software system SAPFIR&RC-RBMK_RT. Integrity of IA in operating reactor was monitored by design system: no leaks in IAs were detected. Activity of 60Co contained in each capsule was measured in the hot cell by comparison, using reference dosimeter with absorbed gamma-dose rate measurement uncertainty not more than ±3% at confidence probability P=0.95. Total amount of 60Co produced was 2 MCi, average specific activity of 60Co—52±7 Ci/g. Achievable specific activity of 60Co in RBMK-reactor is 90±7 Ci/g and annual production capacity—about 8 MCi.

A mathematical model is proposed for longitudinal oscillations of a tackle used for salvaging sunken vessels to the sea surface. The numerical approximation of the obtained model along the tackle rope length is accomplished by means of the finite-difference method. To implement this method, the transformation of independent coordinates is introduced into the constant step mesh. The integration with respect to time is carried out by the Φ-Wilson method. To solve the nonlinear systems of algebraic equations, iteration methods are used. There are examples of calculations for the vessel separation from the seabed and salvage from 1655 m depth when using various methods of controlling the winch shaft moment. The area of winch moment and heaving motion amplitude values that provide vessel emergency-free separation from seabed are calculated. It is shown that, with accuracy sufficient for practical use, the rope system of the tackle can be replaced in some cases by a single equivalent rope. Moreover, the rope mass can be neglected if it is considerably less than the mass of the vessel being salvaged. It is emphasized that the selection of the control of the velocity of salvage depends to a large extent on winch operation peculiarities.

We first introduced a system of over 4000 thermoelectric modules (TEMs) to cool radioactive gases from +55 /spl deg/C to -20 /spl deg/C at the rate of 800 cubic meters per hour in the article Gas Cooling System with the Power 150 kW, the International Conference on Thermoelectrics, 1999. The gas cooling system (GCS) was mounted and launched at the Leningrad nuclear power plant facilities in September 2001. The present paper deals with the basic principles of the cooling system design and GCS performance data obtained over its operation period.

(1975). Experimental meramorphism of certain natural clays. International Geology Review: Vol. 17, No. 3, pp. 324-331.

The extraction of iron(III) with dithizone in the presence of different anions, was studied. The complex cation Fe(HDz) 2 + formed is extracted in the presence of sodium acetate and tetraphenylborate or capric acid as an ion associate, (Fe(HDz) 2 ) + X - , where X - is the anion of the indicated compounds. In the presence of perrhenate ion, rhenium is coextracted with iron in a 1:1 ratio; the ion associate (Fe(HDz) 2 ) + (ReO 4 ) - is apparently extracted. The isolation of iron from alkali metal chlorides and its atomic-absorption determination is described.

TABLES are given for the values of the nodes and weights of Gauss-Markov quadrature formulae for integration over the surface of a three-dimensional sphere, from 9-th up to and including the 17-th order, invariant under the octahedron group.

METHODS for obtaining Gauss type quadratures, invariant under the octahedron rotation group with inversion, are described and investigated, while Gauss-type quadratures for n = 19, 23, and Chebyshev quadratures for n = 11, 15 are quoted. Error estimates are given. A Monte Carlo method with small dispersion is outlined.

A system of quasi-linear partial differential equations describing the dynamic behavior of a flexible string in a rotational motion is obtained. To define frequency responses of a string the obtained system is linearized and then transformed to a two-point boundary-value problem. To solve the latter shooting methods are used. The paper develops an efficient original numerical algorithm based on the application of Taylor calculus and allowing for reduction of computational expenses, characteristic for traditional methods of a numerical solution of an initial-value problem, arising when the shooting methods are realized. The given example of the calculation of string frequency responses in a rotational motion illustrates the serviceability of the suggested procedure on the whole and its efficiency.

To accelerate the convergence of the iterations when finding the maximum eigenvalue and corresponding eigenfunction, a method is proposed which employs infinite sequences of Chebyshev parameters and guarantees stability of the computations. A generalization of Bernoulli's method is constructed.

GALERKIN'S method of solving multidimensional diffusion equations with piecewise-constant coefficients is explained, a method of constructing almost orthonormal systems of coordinate functions is proposed, a qualitative estimate of the ordering of the coordinate functions is given, and an analysis of the results of a calculation of two-group problems and of the coordinate functions obtained is presented.

A new method of qualitative and quantitative magnetic texture investigation is described. The description of the equipment used and results of measurements on three different samples are presented.

The theory of the infra-red absorption (IRA) and Raman scattering (RS) by anharmonic crystals with the point defects by Schottky is discussed. Expressions for the dependences of the dipole moment and of the optical polarizability on the normal modes of vibration are obtained by using second-order terms in the dipole moment expansion and shell model with the anharmonic terms. Using the method of temperature-dependent double-time Green' s function (GF) expressions for the dielectric susceptibility, the infra-red optical absorption and the Raman scattering intensity are investigated. It is shown, that the temperature dependence of the width of the fundamental absorption peaks and Raman spectra particular in the high temperature region may be explained taking into account the anharmonicity and the defects.

RECENTLY a number of papers has been published concerned with the investigation of iterative methods far the numerical solution of kinetic problems, which are related to finding solutions of the neutron transport equation; as an example we may mention [1–5]. It is obvious that we cannot investigate the convergence of these methods sufficiently fully, determine the region of their application, the value of each algorithm put forward [2, 4] and find inexpensive algorithms, without knowing sufficiently well the properties of the exact solutions for the transport equation. The mathematical basis of many standard one-group kinetic problems was first given in [6–8]. In [9] a complete system of general functions, which are solutions of a one-group homogeneous kinetic equation was found for a plane layer. Analytic solutions of various problems are given in [10]. To clarify the nature of the approximation of solutions of various problems to exact solutions, we find for a number of problems the solutions of the kinetic equation written in self-conjugate form [8]. In Section 2 we extend the results of [9] to the q -dimensional case and in Section 4 to difference equations. In Section 3 we find a fundamental solution for an re-group problem, and in Section 5 give a solution of an m-group periodic problem. In Section 6 one of the variants of the KP -method [2–5] is given for solving m -group problems. For a periodic problem we find the value of the KP -method and show that in practice the KP -method cannot be improved.

The sialitic layer is visualized as a gigantic weathered crust which has developed over the primordial basaltic crust of the planet, under the influence of climatic processes motivated by solar energy. – V.P. Sokoloff.

Quantitative data on neutron emission in the symmetrical fission region are obtained. The number of spurious events registered in this region has been reduced to 15–20%.

In recent times, in connection with the development of the theory of generalized functions and the theory of generalized solutions of boundary value problems for differential equations, the approach to the construction of difference operators, which approximate the differential problem, has essentially changed. First of all we have in mind the following: 1. (1) the rejection, because of results obtained, of the attempt to approximate (in more or less explicit form) a differential equation, with continuity conditions and boundary conditions, which must be done locally and independently of each other, by systems of finite difference equations; 2. (2) the development of numerical methods for a group of non-stationary problems, in which the form of the difference schemes is determined, not by the requirements of the best local approximation, but by conditions of stability and simplicity of calculation; 3. (3) the construction and basis of difference operators which possess the integral properties of differential operators of boundary value problems. We shall dwell only on the last group of methods. Difference equations for whose investigation integral characteristics were used, have been considered, for example, in works [1]–[13]. For the study of the properties of difference operators, which keep the integral properties of the differential problems, we can successfully use functional methods of investigation. It is well known with what success functional methods are applied to the study of problems of mathematical physics, in particular the method of orthogonal projections, which form a considerable part of the theory of generalized solutions (see [14]–[17]). A significant advance in the theory of difference equations has been marked by the fact that functional methods of directly investigating their inner properties (see [18]–[20]) have been applied to equations on a network. In the present work we put forward and systematically apply a method of orthogonal projections for network vector-functions. It permits us 1. (1)to investigate the structural properties of subspaces of a space of network functions, 2. (2) to compose difference equations for some problems of mathematical physics, 3. (3) to solve the question of difference analogues of boundary conditions by using the fact that the solution is a member of a definite subspace of functions, 4. (4) to investigate the properties of the solution of difference equations, 5. (5) to give optimal evaluations for the solutions of difference equations by means of projectional operators on the right-hand sides of these equations. The difference equations obtained for boundary value problems of types I, II and III, for self-conjugate elliptic equations of the second order, possess a regular closure of the computational algorithm; with symmetrization of these systems of equations they are converted into known systems of equations of a divergent type. We have called the difference equations obtained “difference analogues” of the problems considered, wishing thereby to stress the fact that in conclusions obtained from them we did not make use of the idea of local approximation of the differential operator by a difference operator, but obtained these equations by using functional (integral) methods. Local approximation was used only in replacing the first derivative of a function by a centrally divided difference. With the selected approach to the construction of difference operators we shall consider as a natural form of approximation an approximation, in the weak sense, which characterizes the nearness of two functionals, with which we may meet not only the case of local smallness of the discrepancy in the approximation of the differential operator by a difference, but also the case of its rapid oscillation. Both cases are equally well represented in the chosen method of evaluation of the errors of solutions. For clearness and simplicity of exposition we have limited ourselves to the case of three-dimensional space and have considered problems involving the Laplace operator.

A SOLUTION is offered for the problem of ordering the parameters in a cyclical iterative method used for solving the equation Au = f, in such a way as to eliminate computational instability.

The number of neutrons v emitted by fragments in the fission of U235 by thermal neutrons is measured with the aid of an ionization chamber and a neutron detector containing cadmium. The data thus obtained contradict the hypothesis of the universal dependence of v on the fragment mass. Calculations show that in the symmetric fission region the fragment excitation energy increases by ≈ 20 MeV.

THE solution of the problem of the circulation of a supersonic flow of radiating gas round a blunt body has been considered in [1]. Scheme II of the method of integral relations of [2] was used as the computational gas-dynamic scheme, and a problem was solved in the optically thin gas approximation (volume luminescence). In the present paper we develop an approximate computational scheme which imposes no constraints on the optical thickness of the gas and in which, by a differential approximation, a stricter calculation of radiation transfer is carried out, enabling us to consider not only radiation, but also absorption of energy by the gas. Because real gases as a rule radiate and absorb energy selectively, the dependence of the absorption coefficient of the gas not only on the pressure and temperature, but also on the frequency, is considered.

IN THIS paper we derive and investigate difference equations which arise in the solution of a single-speed kinetic equation using the method of characteristics. This method was first suggested for solving the kinetic equation by Vladimirov [1] and Neumann [2]. The description of some schemes of this method is given in [2], [3]. We maintain that tne method of cnaracteristics is in a sense more natural than the Sn-method, since the integration involved in it is carried out along the trajectories of neutrons in coordinate space, and tne principle of the construction of the difference equations is the same for all geometries. Some of the earlier published difference equations of tne method of characteristics possess one or even a few of the following drawbacks: (1) To carry out calculations using these equations repeated calculation of the values of some transcendental functions is required, which increases the time required to solve the problem; (2) Because the step ħ of integration along the characteristic for proolems with central symmetry can be a quantity of order O(Δr 1 2 ) , where Δr is the step along the radius, for some schemes the order of approximation of the differential operator by the difference operator becomes of order O(Δr); (3) The non-monotonicity of the scheme: in deriving the difference equations an upper limit on the step ħ is not shown to be necessary, and without observing this restriction the solution of the difference problem can go off into tae negative region with positive sources. In this paper difference equations are presented which are free from these drawbacks. The paper is divided into two parts according to the approach and the choice of questions for investigation. In the first part we are interested in questions concerning the derivation of the difference equations for the general case and also for the most difficult one-dimensional case — that of the infinite cylinder. Here we present, in as much detail as possible, difference equations which are satisfied in the solution of problems by the KP-method [4]. Considerable practical testing of the solution of variants confirms the possibility of solving by these difference schemes problems for a reactor and for a nucleus with complicated distribution of the media and the properties of these media [5, 6]. In the second part we investigate the convergence of the KP-method, evaluate the error and determine the value of the “inexpensive” algorithm of the KP-method for the case of a plane periodic problem. Here we proceed to the restrictions on the co-efficients of the equation for detecting singularities, watch are spherical for the problem considered, and obtaining effective quantitative evaluations for certain quantities. It appears to us that some of the detected singularities are present in the general case also. The paper also verifies the truth of some assumptions used by the author in [4].

AS is well known, to solve the equation Lu = f, (1) where u ϵ B, f ϵ B1, B, B1 are Banach spaces, and L a linear operator, the general principle for constructing the linear iterative processes, using information only about the preceding approximation and leaving the solution u as a stationary point, as a final result we construct a sequence of elements uk by the formulae uk = A(k)uk − 1 + Ψk, (2) where A(k) = I − H(k)L, Ψk = H(k)f, and H(k) is a sequence of operators which characterizes the type of iterative method [1, 2]. Various methods of accelerating the convergence of the iterations differ from one another either in the method of contructing the operators H(k) or in the computational scheme for the numberical realization of the operations A(k)uk − 1, H(k)f. The essence of each iterative method lies in the fact that in it, guided by some principle, the operators H(k) are chosen from some strictly defined class of operators R so that in this class Cy(A(k)) [3, 4] ∥ A(k) ∥ are fairly small. For convenience of notation we shall in future take the index (k) for the operators. It was shown in [2] that many known effective iterative methods can be realized by the scheme Cuk = Cuk − 1 − D(Luk − 1 − f), (3) where the class of operators H = C− 1D is defined by the fact that for each iterative method in a very wide circle of problems it is possible to form rather simply and constructively classes of operators C, D, for which the value of each iteration is low. The writing of (2) in the form (3) predetermines to some extent also the sequence of operations for the realization of each iteration. It must be noted that in [5] it has already been suggested that iterative processes be formed by scheme (3) with D = I, H = C− 1. Work has recently begun on questions connected with problems of evaluating the quality and complexity of numerical algorithms [6–10]. Using ideas of the value and entropy of the algorithm, which are connected with the time of computation and the storage capacity necessary to carry out the given algorithm, we put forward one of the methods of partial ordering as regards the effectiveness of numerical algorithms, in [3, 4] there is a refinement of the idea of the effectiveness of numerical algorithms for solving problem (1): the defining characteristics, with comparison between them, of various algorithms for the solution of problem (1), requiring storage of information of the same quantitative order, must be their value and not the “simplicity” (e.g. consecutive one-dimensionality) of the equations to be solved. But the effectiveness of the algorithm must also be evaluated by the amount to be stored and by the intermediate information to be used in solving the problem. If we omit to consider this fact we can seriously err in the real evaluation of the possibility of the algorithm. A convincing example of this is the paradox of “Maxwell's demon” [8] or some algorithms for solving problems of neutron transport, where on account of the large quantity of information to be stored we can put forward qualitatively new algorithms for the solution; thus, in [9] it was shown (see Lemma 1) that for some problems of neutron transport direct algorithms also exist for their solution, whose values with storage of the order of O(NM) numbers are of the order O(NM), where N is the number of space points xj of the network and M the number of angular directions at each point xj. Suppose that we are solving problem (1) by an iterative algorithm A , belonging to some set of algorithms M by the algorithm (A ϵ R) we may have in mind one of its realizations on an electronic computer with infinite homogeneous storage, conditionally divided into cells of the sam length; suppose that one and only one number is written in the cell. We shall assume that the assignment of R is defined by the indication of the set of permissible operators H and that each algorithm A ϵ R is defined by the form and fixed order of the logical and arithmetical operations carried out in it. We shall agree to consider that in the assignment of the algorithm A there is no fixed order of distribution and memory over the storage cells, which we shall denote by Mpr or of information about intermediate values, arising in the realization of the algorithm A and that the original data and results of computation, derived from the computer, are not related to the intermediate values. The partial ordering of the algorithms A ϵ R can be carried out as follows. Let A be some algorithm for the solution of problem (1), and its value [3], where O(A/L, B, e) is the number of arithmetic and logical operations, which are necessary for solving the algorithm A of problem L with accuracy ϵ, beginning with the initial approximation u0 = u − v. In the process of solving (1) we bear in mind and retain simultaneously in Mpr for further processing some block of N numbers. Let N = N(ϵ) be the number of cells in Mpr, with which it is possible to realize the algorithm A for the solution of (1) to within ϵ. We shall denote inf N(ϵ) by N0(ϵ), where the lower bound is taken over all possible methods of storing the information to be retained. We shall call the quantity En = En(ϵ) = En A, ϵ) = log2 N0(ϵ) the entropy of the algorithm A . Let W(ϕ(ϵ), Ψ(ϵ), ϵ) be a functional, defined on the vector functions (ϕ(ϵ), ψ(ϵ) belonging to some permissible set of functions D1. Let D = {(ϑ, ψ,e): (ϑ, ψ) ϵ D1}. As for A,A ϵ R we say that A1

The number of neutrons nu emitted by U/sup 234/ and Pu/sup 240/ is measured for different ratios of fragment masses. A sharp increase of nu is detected in the symmetrical fission region. The dependence of nu on the mass ratios correlates well with the total kinetic energy of the fragments. (auth)

The mean number v of neutrons emitted during the fission of Pu233 by thermal and epithermal (0·15 to 0·5 eV) neutrons has been measured, and found to be the same within 2% for both cases.

IT was shown in [1] for a kinetic equation written in selfconjugate form, that the method of estimating iteration deviations [2] may diverge when the method of simple iteration converges. However, the application of this method to the kinetic equations written in selfconjugate and non-selfconjugate form leads to different iteration schemes.

The number of neutrons λ emitted by U236 is measured for different ratios of the masses of fragments. A sharp increase of λ is detected in the symmetric fission region. The dependence of λ on the mass ratio well correlates with the total kinetic energy of the fragments.

This chapter discusses game theory and optimality of iterative methods. To estimate the effectiveness of iterative methods the criterion of optimum strategy from game theory is used. This chapter defines a game as a triple ( Σ , Ω , K ), where Σ , Ω are compact convex sets, and K = Κ ( σ , ω ) is a continuous function, defined on Σ × Ω (σ ∈ Σ, ω ∈ Ω), convex with respect to σ for fixed ω ∈ Ω, and concave with respect to ω for fixed σ ∈ Σ. It is assumed that Σ , Ω are strategy spaces for player I and player II, respectively. The chapter then states the main theorem of game theory. It also generalizes some results on the case of weighted distributed masses.

A 2 channel EKG transmitter system has been designed and tested on humans. Sports swimmers have had their EKG monitored during exercise in an open-air pool. Further application to medically supervised activites are being made with the biotelemeter.