As one can see, without several examples worked out with a pencil and paper, this formal definition is not very insightful. To understand where restricted patterns really originated from, we draw on visual imagery and replace “one-dimensional” permutations by “twodimensional” objects, matrices. In doing so, we shall violate the customary labeling of the top row as the “first” row of a matrix. I...

Diffusion mechanism models the movement of many individuals in an environment or media. The individuals can be very small such as basic particles in physics, bacteria, molecules, or cells, or very large objects such as animals, plants, or certain kind of events like epidemics, or rumors. The particles reside in a region, which we call Ω, and we assume that Ω is open subset of Rn (the n-th dimen...

This study proposes the use of an innovative array of accelerometers for inertial tracking that is enabled through the use of a non-Cartesian hyper-coordinate frame. Traditional inertial tracking technologies employ an array of accelerometers and gyroscopes oriented in the orthogonal axes of the Cartesian coordinate system. The gyroscope sensors are responsible for deducing the relative orienta...

Diffusion mechanism models the movement of many individuals in an environment or media. The individuals can be very small such as basic particles in physics, bacteria, molecules, or cells, or very large objects such as animals, plants, or certain kind of events like epidemics, or rumors. The particles reside in a region, which we call Ω, and we assume that Ω is open subset of Rn (the n-th dimen...

In this paper, an autonomous hovering control method of multicopter using only Web camera is proposed. Recently, various control method of an autonomous flight for multicopter are proposed. But, in the previous proposed methods, a motion capture system (i. e., OptiTrack) and laser range finder are often used to measure the position and posture of multicopter. To achieve an autonomous flight con...

The present analysis deals with the steady, incompressible flow of a viscous fluid over a stretching sheet having a layer of porous medium of uniform thickness. The two-dimensional flow equations are derived in a Cartesian coordinate system. The semi-infinite region filled with a viscous fluid is divided into two regions namely, a clear fluid region and a region having a uniform pores. Darcy's ...

The purpose of the research is to study aerodynamics and heat transfer in duct a high-temperature recuperation system. object flat with thickness-to-height ratio a:b = 1:10, length c 400·a one-sided input surface, complicated mixed air movement duct. objectives are determine: (a) average temperatures on surfaces; (b) temperature distribution along duct; (c) local integral values (d) flow densit...

Canonical quantization entails using Cartesian coordinates, and Cartesian coordinates exist only in flat spaces. This situation can either be questioned or accepted. In this paper we offer a brief and introductory overview of how a flat phase space metric can be incorporated into a covariant, coordinate-free quantization procedure involving a continuous-time (Wiener measure) regularization of t...

The automatic detection of bilateral symmetry is a challenging task in computer vision and pattern recognition. This paper presents an approach for the detection of bilateral symmetry in digital single object images. Our method relies on the extraction of Scale Invariant Feature Transform (SIFT) based feature points, which serves as the basis for the ascertainment of the centroid of the object;...

Many spatio-temporal phenomena (both natural and human) change in time cycles, e.g., seasonal change of weather and pattern of people’s daily activities, which required a cyclic view of time. However, most GIS systems and cartographic representation adopt Cartesian Coordinate Systems (CCSs), which force time to be perceived as a linear dimension. Therefore, the cyclic change cannot be effective...