scholarly journals CONSEQUENCES OF THE FUNDAMENTAL CONJECTURE FOR THE MOTION ON THE SIEGEL–JACOBI DISK

2012 ◽  
Vol 10 (01) ◽  
pp. 1250076 ◽  
Author(s):  
STEFAN BERCEANU
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Three Dimensional ◽  
Quantum Evolution ◽  
Siegel Disk ◽  
Classical Motion ◽  
First Order ◽  
Jacobi Group ◽  
Upper Half Plane ◽  
The One

We find the homogeneous Kähler diffeomorphism FC which expresses the Kähler two-form on the Siegel–Jacobi domain [Formula: see text] as the sum of the Kähler two-form on ℂ and the one on the Siegel ball [Formula: see text]. The classical motion and quantum evolution on [Formula: see text] determined by a linear Hamiltonian in the generators of the Jacobi group [Formula: see text] is described by a Riccati equation on [Formula: see text] and a linear first-order differential equation in z ∈ ℂ, where H1 denotes the three-dimensional Heisenberg group. When the transformation FC is applied, the first-order differential equation for the variable z ∈ ℂ decouples of the motion on the Siegel disk. Similar considerations are presented for the Siegel–Jacobi space [Formula: see text], where [Formula: see text] denotes the Siegel upper half-plane.

scholarly journals A CONVENIENT COORDINATIZATION OF SIEGEL–JACOBI DOMAINS

2012 ◽  
Vol 24 (10) ◽  
pp. 1250024 ◽  
Author(s):  
STEFAN BERCEANU
Keyword(s):  
Differential Equation ◽  
Riccati Equation ◽  
Half Plane ◽  
Order Differential Equation ◽  
Quantum Evolution ◽  
Classical Motion ◽  
Matrix Riccati Equation ◽  
First Order ◽  
Upper Half Plane ◽  
Linear Differential

We determine the homogeneous Kähler diffeomorphism FC which expresses the Kähler two-form on the Siegel–Jacobi ball [Formula: see text] as the sum of the Kähler two-form on ℂn and the one on the Siegel ball [Formula: see text]. The classical motion and quantum evolution on [Formula: see text] determined by a hermitian linear Hamiltonian in the generators of the Jacobi group [Formula: see text] are described by a matrix Riccati equation on [Formula: see text] and a linear first-order differential equation in z ∈ ℂn, with coefficients depending also on [Formula: see text]. Hn denotes the (2n+1)-dimensional Heisenberg group. The system of linear differential equations attached to the matrix Riccati equation is a linear Hamiltonian system on [Formula: see text]. When the transform FC : (η, W) → (z, W) is applied, the first-order differential equation in the variable [Formula: see text] becomes decoupled from the motion on the Siegel ball. Similar considerations are presented for the Siegel–Jacobi upper half plane [Formula: see text], where [Formula: see text] denotes the Siegel upper half plane.

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

scholarly journals WORLD VOLUME SOLITONS OF THE D3-BRANE IN THE BACKGROUND OF (p, q) FIVE-BRANES

2000 ◽  
Vol 15 (28) ◽  
pp. 4477-4498 ◽  
Author(s):  
P. M. LLATAS ◽  
A. V. RAMALLO ◽  
J. M. SÁNCHEZ DE SANTOS
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Brane World ◽  
Invariant Solutions ◽  
First Order ◽  
World Volume ◽  
The World ◽  
Energy Bound

We analyze the world volume solitons of a D3-brane probe in the background of parallel (p, q) five-branes. The D3-brane is embedded along the directions transverse to the five-branes of the background. By using the S duality invariance of the D3-brane, we find a first-order differential equation whose solutions saturate an energy bound. The SO(3) invariant solutions of this equation are found analytically. They represent world volume solitons which can be interpreted as formed by parallel (-q, p) strings emanating from the D3-brane world volume. It is shown that these configurations are 1/4 supersymmetric and provide a world volume realization of the Hanany–Witten effect.

scholarly journals On the integration processes of A. Huťa

1963 ◽  
Vol 3 (2) ◽  
pp. 202-206 ◽  
Author(s):  
J. C. Butcher
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Sixth Order ◽  
Order Accuracy ◽  
First Order ◽  
Runge Kutta ◽  
Image Position

Huta [1], [2] has given two processes for solving a first order differential equation to sixth order accuracy. His methods are each eight stage Runge-Kutta processes and differ mainly in that the later process has simpler coefficients occurring in it.

Sign in / Sign up

Export Citation Format

Share Document