On a Certain Congruence Associated with a Given Ruled Surface

Effective Divisor Classes on a Ruled Surface

The Neron-Severi group of divisor classes modulo algebraic equivalence on a smooth algebraic surface is often not difficult to calculate, and has classically been studied as one of the fundamental invariants of the surface. A more difficult problem is the determination of those divisor classes which can be represented by effective divisors; these divisor classes form a monoid contained in the N...

Some Results about Confluence on a Given Congruence Class

Nonpositivity of Certain Functions Associated with Analysis on Elliptic Surface

In this paper, we study some basic analytic properties of the boundary term of Fesenko’s two-dimensional zeta integrals. In the case of the rational number field, this term is the Laplace transform of certain infinite series consisting of KBessel functions. The positivity property of the fourth log derivative of such series is closely related to the Riemann hypothesis for the Hasse-Weil L-funct...

On the Design and Invariants of a Ruled Surface

This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical Bézierlike curve on the dual unit sphere (DUS) is obtained with respect the control points by a new method. So, with the aid of Study [1] transference principle, a dual unit spherical Bézier-like curve corresponds to a ruled sur...

A Study of Curved Surfaces by Means of Certain Associated Ruled Surfaces*

Introduction. In this paper a point correspondence is introduced which is proving to be very helpful in the study of a general non-ruled analytic surface in ordinary space. If on a surface S tangents to the curves of an asymptotic family are constructed at the points of two curves of 5 which are not members of the family and which intersect in a point y of S, two ruled surfaces are thereby form...