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The data on the reactions K^+Xe --> K^0 ��X and K^+Xe --> K^+ ��X, obtained with the bubble chamber DIANA, have been analyzed for possible radiative decays of the ��^+(1540) baryon: ��^+ --> K^0 p ��and ��^+ --> K^+ n ��. No signals have been observed, and we derive the upper limits ��(��^+ --> K^0 p ��) / ��(��^+ --> K^0 p) < 0.032 and ��(��^+ --> K^+ n ��) / ��(��^+ --> K^+ n) < 0.041 which, using our previous measurement of ��(��^+ --> KN) = (0.39+-0.10) MeV, translate to ��(��^+ --> K^0 p ��) < 8 keV and ��(��^+ --> K^+ n ��) < 11 keV at 90% confidence level. We have also measured the cross sections of K^+ -induced reactions involving emission of a neutral pion: ��(K^+n --> K^0 p ��^0) = (68+-18) \mub and ��(K^+N --> K^+ N ��^0) = (30+-8) \mub for incident K^+ momentum of 640 MeV., 8 pages

The monotonicity and stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability and monotonicity of a non-linear scheme in terms of its corresponding scheme in variations. Such an approach leads to application of the stability theory for linear equation systems to establish stability of the corresponding non-linear scheme. The main methodological innovation is the theorems establishing the notion that a non-linear scheme is stable (and monotone) if the corresponding scheme in variations is stable (and, respectively, monotone). Criteria are developed for monotonicity and stability of difference schemes associated with the numerical analysis of systems of partial differential equations. The theorem of Friedrichs (1954) is generalized to be applicable to variational schemes with non-symmetric matrices. A new modification of the central Lax-Friedrichs (LxF) scheme is developed to be of the second order accuracy. A monotone piecewise cubic interpolation is used in the central schemes to give an accurate approximation for the model in question. The stability and monotonicity of the modified scheme are investigated. Some versions of the modified scheme are tested on several conservation laws, and the scheme is found to be accurate and robust. As applied to hyperbolic conservation laws with, in general, stiff source terms, it is constructed a second order scheme based on operator-splitting techniques., Comment: 48 pages, 6 figures. Found inexactitudes are corrected. A second order scheme based on operator-splitting techniques is constructed