a method has been presented for finding the solution surface of the npde: u  c , bounded by a general space curve. the method is based on the geometric characteristics of the surface, and is called the “cone-slot method”. it has been shown that such a surface can be obtained by movement of a cone inside the slot formed by the boundary space curve. an algorithm has been suggested on the basis ...

We study integral points on the quadratic twists $\mathcal{E}_D:y^2=x^3-D^2x$ of congruent number curve. give upper bounds in each coset $2\mathcal{E}_D(\mathbb{Q})$ $\mathcal{E}_D(\mathbb{Q})$ and show that their total is $\ll (3.8)^{\mathrm{rank} \mathcal{E}_D(\mathbb{Q})}$. further average non-torsion this family bounded above by $2$. As an application we also deduce from our system simultan...

We propose a segmentation method for vector fields that employs geometrical curve attributes to classify the behavior of the integral curves. In particular, we assign to a given spatio-temporal position the attribute value associated with the integral curve initiated at that point. With this attribute information, our segmentation strategy first performs a region classification. Then, connected...

Proof: Jf there exists a closed integral curve, then both r* and C* are in the kernel of F*, so F*0. If there is no closed integral curve, let r' be a cycle without contact.3 Any integral curve of F meets r' infinitely often; let P be a point of accumulation of these intersections. We may then construct a C' closed curve C' which differs from the integral curve only in an arbitrarily small neig...

‎in this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎this problem consists of determining the temperature on the interior boundary curve from the cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎to this end‎, ‎the boundary integral equation method is used‎. ‎since the resulting system of linea...

v. dannon showed that spherical curves in e4 can be given by frenet-like equations, and he thengave an integral characterization for spherical curves in e4 . in this paper, lorentzian spherical timelike andspacelike curves in the space time 41 r are shown to be given by frenet-like equations of timelike andspacelike curves in the euclidean space e3 and the minkowski 3-space 31 r . thus, finding...

We introduce Integral Curve Coordinates, which identify each point in a bounded domain with a parameter along an integral curve of the gradient of a function f on that domain; suitable functions have exactly one critical point, a maximum, in the domain, and the gradient of the function on the boundary points inward. Because every integral curve intersects the boundary exactly once, Integral Cur...

We introduce Integral Curve Coordinates, which identify each point in a bounded domain with a parameter along an integral curve of the gradient of a function f on that domain; suitable functions have exactly one critical point, a maximum, in the domain, and the gradient of the function on the boundary points inward. Because every integral curve intersects the boundary exactly once, Integral Cur...