Functional-differential geometry

Random fractional functional differential equations

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Geometry II - Discrete Differential Geometry

Differential Geometry

We discuss intrinsic aspects of Krupka's approach to nite{order variational sequences. We recover in an intrinsic way the second{order varia-tional calculus for aane Lagrangians by means of a natural generalisation of rst{ordertheories. Moreover, we nd an intrinsic expressionfor the Helmholtz morphism using a technique introduced by Koll a r that we have adapted to our context. Introduction The...

Differential Geometry

When studying curves, we studied how the curve twisted and turned in space. We now turn to surfaces, two-dimensional objects in three-dimensional space and examine how the concept of curvature translates to surfaces. In Calculus 3, you have encounter surfaces defined as graphs of real valued functions of two variables z = f(x, y). This function also can take the form x = f(y, z) or y = f(x, z)....

Differential Geometry

In recent years the graph of a foliation, an object which has been known for a long time, cf. 10], has known new interest. In fact there are two groupoids associated with a foliation, the homotopy groupoid and the holonomy groupoid, sometimes called the graph. It serves as a basis for the construction of the C-algebra associated to the foliation. Moreover, the homotopy groupoid of the character...