23 citations · 54 across the 19 of their papers we have counts for
19 papers
On Merton's Optimal Portfolio Problem with Sporadic Bankruptcy for Isoelastic Utility
Yaacov Kopeliovich, Michael Pokojovy, Julia Bernatska
We consider a stock that follows a geometric Brownian motion (GBM) and a riskless asset continuously compounded at a constant rate. We assume that the stock can go bankrupt, i.e.,…
Igusa's map on modular forms vanishing on the hyperelliptic locus
J Bernatska, Y Kopeliovich
We extend Igusa's map to modular forms which vanish on the hyperelliptic locus of the Siegel upper half-plane. The lowest non-vanishing derivatives of such modular forms are co…
Solution of the Jacobi inversion problem on non-hyperelliptic curves
Julia Bernatska, Dmitry Leykin
In this paper we propose a method of solving the Jacobi inversion problem in terms of multiply periodic functions, also called Kleinian functions. This result is based…
Solution of Mumford's second problem
Julia Bernatska, Yaacov Kopeliovich
A complete solution of Mumford's second problem about representation of theta derivatives with rational characteristics in terms of theta constants with rational characteristics is…
New generalisation of Jacobi's derivative formula
Julia Bernatska
A stream of new theta relations is obtained. They follow from the general Thomae formula, which is a new result giving expressions for theta derivatives (the zero values of the low…
Addition via reduction algorithm on trigonal curves
Julia Bernatska, Yaacov Kopeliovich
In this paper we propose a direct and explicit realization of addition of divisors by means of an iterative reduction algorithm. Each iteration of the algorithm is the reduction of…
Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials
Julia Bernatska, Yaacov Kopeliovich
Two problems are addressed: reduction of an arbitrary degree non-special divisor to the equivalent divisor of the degree equal to genus of a curve, and addition of divisors of arbi…
General derivative Thomae formula for singular half-periods
Julia Bernatska
The paper develops the result of second Thomae theorem in hyperelliptic case. The main formula, called general Thomae formula, provides expressions for values at zero of the lowest…
Sato Grassmannian and Degenerate Sigma Function
Julia Bernatska, Victor Enolski, Atsushi Nakayashiki
The degeneration of the hyperelliptic sigma function is studied. We use the Sato Grassmannian for this purpose. A simple decomposition of a rational function gives a decomposition…
On Regularization of Second Kind Integrals
Julia Bernatska, Dmitry Leykin
We obtain expressions for second kind integrals on non-hyperelliptic -curves. Such a curve possesses a Weierstrass point at infinity which is a branch point where all sheets…
On degenerate sigma-functions of genus two
Julia Bernatska, Dmitry Leykin
We obtain explicit expressions for genus 2 degenerate sigma-function in terms of genus sigma-function and elementary functions as solutions of a system of linear PDEs satisfied…
Orbit Approach to Separation of Variables in sl(4)-Related Integrable Systems
Julia Bernatska
Separation of variables by means of the orbit method is implemented to integrable systems on coadjoint orbits in an loop algebra. This is a development and a kin…
SU(3) magnet: finite-gap integration on the lowest genus curve
Julia Bernatska, Petro Holod
We consider the integrable system of isotropic SU(3) Landau-Lifshits equation as a Hamiltonian system on a coadjoint orbit of the SU(3) loop group. We connect the mentioned equatio…
Orbit Approach to Separation of Variables in sl(3)-Related Integrable Systems
Julia Bernatska, Petro Holod
Using the orbit method we attempt to reveal geometric and algebraic meaning of separation of variables for the integrable systems on coadjoint orbits in an loop…
Harmonic analysis on Lagrangian manifolds of integrable Hamiltonian systems
Julia Bernatska, Petro Holod
For an integrable Hamiltonian system we construct a representation of the phase space symmetry algebra over the space of functions on a Lagrangian manifold. The representation is a…
On Separation of Variables for Integrable Equations of Soliton Type
Julia Bernatska, Petro Holod
We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra .…
Topological excitations in 2D spin system with high spin
Julia Bernatska, Petro Holod
We construct a class of topological excitations of a mean field in a two-dimensional spin system represented by a quantum Heisenberg model with high powers of exchange interaction.…
Ordered States and Nonlinear Large-Scale Excitations in a Plane Magnet with Spin s=1
Julia Bernatska, Petro Holod
We study ordered states and topological excitations in a quasi-two-dimensional magnet, modeled by a square lattice with spins at all sites, and the Hamiltonian with biqua…
A generalised Landau-Lifshitz equation for isotropic SU(3) magnet
Julia Bernatska, Petro Holod
In the paper we obtain equations for large-scale fluctuations of the mean field (the field of magnetization and quadrupole moments) in a magnetic system realized by a square (cubic…