http://dspace.nbuv.gov.ua:80/handle/123456789/6274 2026-04-16T16:28:34Z http://dspace.nbuv.gov.ua:80/handle/123456789/6332 On the efficient method of solving ill-posed problems by adaptive discretization Solodky, S.G.; Volynets, E.A. To solve ill-posed problems Ax = f is used the Fakeev-Lardy regularization, using an adaptive discretization strategy. It is shown that for some classes of finitely smoothing operators proposed algorithm achieves the optimal order of accuracy and is more economical in the sense of amount of discrete information then standard methods 2009-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/6331 Morse-Bott functions on manifolds with semi-free circle action Sharko, V.V. Let W²ⁿ be a closed manifold of dimension ≥ 6 with semi-free circle having finitely many fixed points. We study S¹-invariant Morse-Bott functions on W²ⁿ. The aim of this paper is to obtain exact values of minimal numbers of singular circles of some indexes of S¹-invariant Morse-Bott functions on W²ⁿ. 2009-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/6330 On conjugate pseudo-harmonic functions Polulyakh, Ye. We prove the following theorem. Let U be a pseudo-harmonic function on a surface M². For a real valued continuous function V : M² → R to be a conjugate pseudo-harmonic function of U on M² it is necessary and sufficient that V is open on level sets of U. 2009-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/6329 High energy physics and algebraic geometry Malyuta, Yu.M.; Obikhod, T.V. Superstring theory is applied to construction of the Minimal Supersymmetric Standard Model. 2009-01-01T00:00:00Z