We study the complexity of two Inverse Shortest Paths (ISP) problems with integer arc lengths and the requirement for uniquely determined shortest paths. Given a collection of paths in a directed graph, the task is to find positive integer arc lengths such that the given paths are uniquely determined shortest paths between their respective terminals. The first problem seeks for arc lengths that...

Abstract—We present a trigonometric scheme to approximate a circular arc with its two end points and two end tangents/unit tangents. A rational cubic trigonometric Bézier curve is constructed whose end control points are defined by the end points of the circular arc. Weight functions and the remaining control points of the cubic trigonometric Bézier curve are estimated by variational approach t...

In this study, the geometrically nonlinear behaviour caused by large displacements and rotations in cross sections of thin-walled composite beams subjected to axial loading is investigated. Newton–Raphson scheme an arc length method are used solution equations finite element determine mechanical effect. The Carrera-Unified formulation (CUF) solve nonlinear, low or high order kinematic refined s...

Given the periodicity of our model problem, it suffices to consider a single period cell (the dotted square in Figure 1), which has side length d. The front of the evolving step in this cell can be described by a simple 1D curve in the plane. We first discretize this 1D curve in space with N grid points, (xi, yi), i = 1, 2, . . . , N , which are uniformly spaced with respect to the arc length, ...

In this paper, we propose a new framework for joint encryption encoding scheme based on polar codes, namely efficient and secure joint secret key encryption channel coding scheme. The issue of using new coding structure, i.e. polar codes in Rao-Nam (RN) like schemes is addressed. Cryptanalysis methods show that the proposed scheme has an acceptable level of security with a relatively smaller ke...

We demonstrate that the apparent length of a thin white arc on a black disk, rotating concentrically at 2.5 rps, varies with angular length and exposure duration. While short arcs (9-18 degrees ) gradually expand, long arcs (36-72 degrees ) first undergo a brief contraction, before they also expand. On average, perceived elongation asymptotes after 15 s equivalent to visual persistencies rangin...

A semi-analytical approach to the elastic nonlinear stability analysis of rectangular plates is developed. Arbitrary boundary conditions and general out-of-plane and in-plane loads are considered. The geometrically nonlinear formulation for the elastic rectangular plate is derived using the thin plate theory with the nonlinear von Kármán strains and the variational multi-term extended Kantorovi...

An element of arc length or an element of surface area can naturally be approximated using either an inscribed object or a tangential object. An approach often followed is to use inscribed objects for arc length and tangential objects for surface area. Why the difference? This paper explores the roads less traveled. Both inscribed and tangential approximations can be used in either situation ar...