The L-function and C-function of twisted T -adic exponential sums are defined. The Hodge bound for the T -adic Newton polygon of the C-function is established. As an application, the T -adic Newton polygons of the L-functions of twisted p-power order exponential sums associated to diagonal forms are explicitly given. 1. Preliminaries Let Fq be the field of characteristic p with q elements, and ...

Spatial knowledge representation (KR) schemes are important in many areas of computation, e.g., geographical information systems, natural language technology, image processing, battlefield management, etc. In this paper we have discussed a spatial KR technique for the purpose of expressing angular relations between points in Euclidean space. The scheme is a hybrid of what are known as quantitat...

A Numerically-Controlled (NC) machine typically consists of a worktable and a spindle (or cutter) with several axes of freedom for positioning the tool. In this paper, we restrict our attention to machines having only translational freedom. We focus on 2D milling, which can only cut out planar objects, and 2 1 2D milling where only two of the axes are continuous-path controlled and the third ax...

da Silva, I.P.F, On fillings of ZN-gons with rhombi, Discrete Mathematics 111 (1993) 137-144. In the first part of this paper we give a generalization of a result of Ringel [ll] on simple arrangements of pseudolines. In terms of fillings with rhombi of an N-zonogon, we obtain a way of generating every filling from a given one by successively performing the same local transformation. In the seco...

The purpose of this paper is the generalization of structure factor for rods by polygon section in two dimensional phononic crystals. If we use the plane wave expansion method (PWE) for the propagation of acoustic waves in 2D phononic crystals, structure factor will be an important quantity. In order to confirm the obtained relations, we have calculated the band structure for XY and Z vibration...

The electronic industries have been tried to develop the electronic packaging technology for high-density, light weight, and miniaturization of mobile personal information terminals such as notebook PC, personal digital assistant (PDA), or handheld PC as the performance and the portability of the system have been become important more and more. The generated heat from the CPU of the electronic ...

Triangulation is one of the most popular methods for decomposing a planar polygon into primitive cells. Often trapezoidation is performed as a first step in triangulation. That is, a polygon is decomposed into a set of trapezoids; a trapezoid being a four sided polygon with two parallel sides. Although much work has gone into fast triangulation methods, there has been little work on trapezoidat...

Given a small polygon S, a big simple polygon B and a positive integer k, it is shown to be NP-hard to determine whether k copies of the small polygon (allowing translation and rotation) can be placed in the big polygon without overlap. Previous NP-hardness results were only known in the case where the big polygon is allowed to be non-simple. A novel reduction from Planar-Circuit-SAT is present...