Making use of the N = 2 Liouville theory and world-sheet techniques, we study the properties of D-branes wrapped around vanishing SUSY cycles of singular Calabi-Yau n-folds (n = 2, 3, 4). After constructing boundary states describing the wrapped branes, we evaluate the disc amplitudes corresponding to the periods of SUSY cycles. We use the old technique of KPZ scaling in Liouville theory and de...

We survey the current known relations between four classes of real numbers: Liouville numbers, computable reals, Borel absolutely normal numbers and Martin-Löf random reals. The expansions of the reals will play an important role. The paper refers to the original material and does not repeat the proofs; a characterisation of Liouville numbers in terms of their expansions will be proved. Finally...

Liouville theory seems to be a kind of universal building block for a variety of models for two-dimensional gravity and non-trivial backgrounds in string theory. Some aspects of it were important for understanding what the matrix models of 2D gravity actually describe (see e.g. [GM]), and it keeps popping up in sometimes unexpected circumstances such as the the physics of membranes in string th...

We present the extension of the successful Constant Perturbation Method (CPM) for Schrödinger problems to the more general class of Sturm-Liouville eigenvalue problems. Whereas the orginal CPM can only be applied to Sturm-Liouville problems after a Liouville transformation, the more general CPM presented here solves the Sturm-Liouville problem directly. This enlarges the range of applicability ...

We consider a recently discovered representation for the general solution of the Sturm-Liouville equation as a spectral parameter power series (SPPS). The coefficients of the power series are given in terms of a particular solution of the Sturm-Liouville equation with the zero spectral parameter. We show that, among other possible applications, this provides a new and efficient numerical method...

Solving an inverse Sturm-Liouville problem requires a mathematical process to determine unknown function in the Sturm-Liouville operator from given data in addition to the boundary values. In this paper, we identify a Sturm-Liouville potential function by using the data of one eigenfunction and its corresponding eigenvalue, and identify a spatial-dependent unknown function of a SturmLiouville d...

system (1.1) is completely integrable, which is well-known in integrable systems theory. The Liouville equation and the Toda system arise in many physical models. In Chern-Simons theories, the Liouville equation is closely related to Abelian models, while the Toda system is related to non-Abelian models. See for instance the books [10] and [24] and the references therein. Though the Liouville e...

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

in this paper, we investigate infinite product representation of the solution of a sturm-liouville equation with an indefinite weight function which has two zeros and/or singularitiesin a finite interval. first, by using of the asymptotic estimates provided in [w. eberhard, g.freiling, k. wilcken-stoeber, indefinite eigenvalue problems with several singular pointsand turning points, math. nachr...

In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. N...