The geodesics for a sub-Riemannian metric on a threedimensional contact manifold M form a 1-parameter family of curves along each contact direction. However, a collection of such contact curves on M , locally equivalent to the solutions of a fourth-order ODE, are the geodesics of a sub-Riemannian metric only if a sequence of invariants vanish. The first of these, which was first identified by F...

This thesis presents a robust method for evaluating differential geometry properties of sculptured surfaces by using a validated ordinary differential equation (ODE) system solver based on interval arithmetic. Iso-contouring of curvature of a Bezier surface patch, computation of curvature lines of a Bezier surface patch and computation of geodesics of a Bezier surface patch are computed by the ...

This paper presents a brief instructions to nd geodesics equa-tions on two dimensional surfaces in R3. The resulting geodesic equations are solved numerically using Computer Program Matlab, the geodesics are dis-played through Figures.

Process integration in Software Engineering Environments (SEE) is very important to allow tool integration. In this paper, we present a knowledge-based approach to improve process integration in ODE, an ontology-based SEE.

The fundamental knowledge contained in the previous paper on “Cavity control system essential modeling for TESLA linear accelerator and free electron laser” is applied for Matlabs’ Simulink implementation of the basic models for the cavity resonator. Elementary simulations of the cavity behavior are carried out and some experimental results for signals and power considerations are presented.

Veech groups uniformize Teichmüller geodesics in Riemann moduli space. We gave examples of infinitely generated Veech groups; see Duke Math. J. 123 (2004), 49–69. Here we show that the associated Teichmüller geodesics can even have both infinitely many cusps and infinitely many infinite ends.

We consider the following singularly perturbed Neumann problem ε∆u− u+ u = 0 , u > 0 in Ω, ∂u ∂ν = 0 on ∂Ω, where p > 2 and Ω is a smooth and bounded domain in R2. We construct a new class of solutions which consist of large number of spikes concentrating on a segment of the boundary which contains a strict local minimum point of the mean curvature function and has the same mean curvature at th...

We carry out the programme of R. Liouville [18] to construct an explicit local obstruction to the existence of a Levi–Civita connection within a given projective structure [Γ] on a surface. The obstruction is of order 5 in the components of a connection in a projective class. It can be expressed as a point invariant for a second order ODE whose integral curves are the geodesics of [Γ] or as a w...

We consider the following singularly perturbed Neumann problem (Lin-Ni-Takagi problem) ε∆u− u+ u = 0 , u > 0 in Ω, ∂u ∂ν = 0 on ∂Ω, where p > 2 and Ω is a smooth and bounded domain in R2. We construct a new class of solutions which consist of large number of spikes concentrating on a segment of the boundary which contains a strict local minimum point of the mean curvature function and has the s...

subject to the constraint that q(0) and q(h) are constant. Standard ODE theory provides existence and uniqueness of the corresponding initial value problem because the derivatives q~(t) of the evolution curves q(t) are the integral curves of the corresponding Lagrangian vector field XE. Given two nearby ql, q2 6 Q, does there exist a unique evolution curve q(t) such that q(0) = q~ and q(h) = q2...