Motivated by the topological theory of normal surface we give in this paper a complete study of the relations between geodesic curves and normal curves embedded in a triangulated Riemannian surface. Normal surface theory is a topological piecewise linear (p` for short) counterpart of the differential geometric theory of minimal surfaces. This theory studies the ways surfaces intersect with a gi...

several tables have been given due to a − minimal sets. our main aim in this paper is tocomplete these tables by employing several examples.

Argumentation Johannes P. Wallner, Georg Weissenbacher, and Stefan Woltran Institute of Information Systems, Vienna University of Technology, Favoritenstraße 9-11, A-1040 Vienna, Austria Abstract. In the area of propositional satisfiability (SAT), tremendous progress has been made in the last decade. Today’s SAT technology covers not only the standard SAT problem, but also extensions thereof, s...

In [Berarducci-Otero, 2004], the authors define an analogue of Lebesgue measure for bounded definable subsets of an o-minimal structure K , which expands a real closed field. Our aim is defining the area of a bounded definable d-dimensional subsets of Kn. Different possible definitions for such area are possible: we will prove that some of them are equivalent. On the reals, there are many diffe...

A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge-gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement e...

in this paper, to account for the effect of water stresses in the various growth stages under deficitirrigation, the multiplicative, seasonal and minimal approaches are integrated in the budgetmodel. to evaluate the model, the simulated yields for winter wheat (was grown in sharif abaddistrict) under various levels of water stress were compared with observed yields. the resultshowed, simulated ...

In this lecture we will see how to study a system of partial differential equations (henceforth denoted pde) from a geometric perspective. Example 1, the minimal surface equation. Given a surface in Euclidean 3-space, M 2 ⊂ E 3 , described locally as a graph z = z(x, y), at a point p = (x, y, z(x, y)), let H(p) = 1 2 (1 + z 2 y)z xx − 2z x z y z xy + (1 + z 2 x)z yy (1 + z 2 x + z 2 y) 3 2. H(p...