http://dspace.nbuv.gov.ua:80/handle/123456789/146011 2026-04-06T01:52:37Z 2026-04-06T01:52:37Z Li, S. http://dspace.nbuv.gov.ua:80/handle/123456789/149191 2019-02-19T23:23:37Z 2012-01-01T00:00:00Z

Renormalization Method and Mirror Symmetry Li, S. This is a brief summary of our works [arXiv:1112.4063, arXiv:1201.4501] on constructing higher genus B-model from perturbative quantization of BCOV theory. We analyze Givental's symplectic loop space formalism in the context of B-model geometry on Calabi-Yau manifolds, and explain the Fock space construction via the renormalization techniques of gauge theory. We also give a physics interpretation of the Virasoro constraints as the symmetry of the classical BCOV action functional, and discuss the Virasoro constraints in the quantum theory.

2012-01-01T00:00:00Z Kalnins, E. Pogosyan, G.S. Yakhno, A. http://dspace.nbuv.gov.ua:80/handle/123456789/149190 2019-02-19T23:24:45Z 2012-01-01T00:00:00Z

Separation of Variables and Contractions on Two-Dimensional Hyperboloid Kalnins, E.; Pogosyan, G.S.; Yakhno, A. In this paper analytic contractions have been established in the R→∞ contraction limit for exactly solvable basis functions of the Helmholtz equation on the two-dimensional two-sheeted hyperboloid. As a consequence we present some new asymptotic formulae.

2012-01-01T00:00:00Z Muriel, C. Romero, J.L. http://dspace.nbuv.gov.ua:80/handle/123456789/149189 2019-02-19T23:24:35Z 2012-01-01T00:00:00Z

Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations Muriel, C.; Romero, J.L. This paper studies relationships between the order reductions of ordinary differential equations derived by the existence of λ-symmetries, telescopic vector fields and some nonlocal symmetries obtained by embedding the equation in an auxiliary system. The results let us connect such nonlocal symmetries with approaches that had been previously introduced: the exponential vector fields and the λ-coverings method. The λ-symmetry approach let us characterize the nonlocal symmetries that are useful to reduce the order and provides an alternative method of computation that involves less unknowns. The notion of equivalent λ-symmetries is used to decide whether or not reductions associated to two nonlocal symmetries are strictly different.

2012-01-01T00:00:00Z Roffelsen, P. http://dspace.nbuv.gov.ua:80/handle/123456789/149188 2019-02-19T23:24:42Z 2012-01-01T00:00:00Z

On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials Roffelsen, P. We study the real roots of the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlevé equation. It has been conjectured that the number of real roots of the nth Yablonskii-Vorob'ev polynomial equals [(n+1)/2]. We prove this conjecture using an interlacing property between the roots of the Yablonskii-Vorob'ev polynomials. Furthermore we determine precisely the number of negative and the number of positive real roots of the nth Yablonskii-Vorob'ev polynomial.

2012-01-01T00:00:00Z