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41.
42.
Yu. V. Borovskikh 《Journal of Mathematical Sciences》1991,53(4):353-358
Estimates of a rate of convergence of orderO(n
–1) are obtained for integral functionals of an empirical process.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 10–16, 1987. 相似文献
43.
V. Yu. Korolev 《Journal of Mathematical Sciences》1991,57(4):3270-3277
Translated fromProblemy Ustoichivosti Stokhasticheskikh Modelei. Trudy Seminara, 1988, pp. 84–92. 相似文献
44.
V. O. Tarasov 《Journal of Mathematical Sciences》1991,54(3):958-967
A mixed boundary-value problem for the nonlinear Schrödinger equation and its generalization is studied by the method used for the inverse scattering problem. A connection is established between conservation laws and boundary conditions in integrable boundary-value problems for higher nonlinear Schrödinger equations. It is shown that the generalized boundary-value problem requires a joint consideration of regular and singular solutions for the nonlinear Schrödinger equation with repulsion.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 151–165, 1988. 相似文献
45.
V. L. Topunov 《Acta Appl Math》1989,16(2):191-206
In this paper, an application of the Riquer-Thomas-Janet theory is described for the problem of transforming a system of partial differential equations into a passive form, i.e., to a special form which contains explicitly both the equations of the initial system and all their nontrivial differential consequences. This special representation of a system markedly facilitates the subsequent integration of the corresponding differential equations. In this paper, the modern approach to the indicated problem is presented. This is the approach adopted in the Knuth-Bendix procedure [13] for critical-pair/completion and then Buchberger's algorithm for completion of polynomial ideal bases [13] (or, alternatively, for the construction of Groebner bases for ideals in a differential operator ring [14]). The algorithm of reduction to the passive form for linear system of partial differential equations and its implementation in the algorithmic language REFAL, as well as the capabilities of the corresponding program, are outlined. Examples illustrating the power and efficiency of the system are presented. 相似文献
46.
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49.
50.
M. Mirvaliev 《Journal of Mathematical Sciences》1987,38(6):2357-2363
One obtains a formula for the transformation of a vector with a given covariance matrix. The sum of the squares of the components of the transformed vector is equal to a chi-square type quadratic form, constructed with the aid of the initial vector. Taking into account this property, one finds the components of the Pearson statistic, Pearson-Fisher statistic, etc.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 337–350, 1986. 相似文献