Algorithmic and Combinatorial Results on Fence Patrolling, Polygon Cutting and Geometric Spanners

The purpose of this dissertation is to study problems that lie at the intersection of geometry and computer science. We have studied and obtained several results from three different areas, namely–geometric spanners, polygon cutting, and fence patrolling. Specifically, we have designed and analyzed algorithms along with various combinatorial results in these three areas. For geometric spanners, we have obtained combinatorial results regarding lower bounds on worst case dilation of plane spanners. We also have studied low degree plane lattice spanners, both square and hexagonal, of low dilation. Next, for polygon cutting, we have designed and analyzed algorithms for cutting out polygon collections drawn on a piece of planar material using the three geometric models of saw, namely, line, ray and segment cuts. For fence patrolling, we have designed several strategies for robots patrolling both open and closed fences

Investigation of the Formation Process of Hazardous and Harmful Production Factors When Cutting a Stone for Construction Works

Stone cutting for construction work is carried out by disk diamond wheels the rotation speed of which, and, consequently, the cutting speed is 35-50 m/s. In view of the high intensity of the cutting process and intensive microchip formation, the process of stone cutting is accompanied by considerable dust formation, which can be both harmful and dangerous in the work.The greatest danger is represented by dust particles, which dimensions are 5 μm or less. These particles have the greatest pathogenic effect on the respiratory system of the human body. In addition, the settling time of these particles is measured in hours. Thus, even after the termination of work, the risk of dust exposure to the human body remains. Insignificant time of inhalation of these particles can lead a person to disability and death. Insurance payments in case of disability and compensation in case of death of an employee for these reasons all over the world amount to multibillion sums, which, even for this reason, makes the issue of combating this phenomenon very urgent.In this paper, the process of generation of hazardous and harmful production factors arising as a result of dust formation during the stone cutting, the regularity of dust distribution by fractions, quantitative indicators of the process for improving equipment, as well as individual and collective means of personnel protection are determined. The shape and dimensions of the cutting grains of the cutting discs are studied in the paper, depending on the grain material and the grain size of the cutting disc. Thecurvature radii of the cutting grains depend on the grain material and the grain size of the cutting disc. The actual number of grains participating in cutting and, consequently, in dust formation is shown.The dimensions of the dust particles depend on the graininess of the cutting discs and the processing regimes. Using the law of normal particle size distribution, the percentage of dust particles is determined depending on processing conditions. The rate of particle settling depends on their size and mass. The formation of a dust-air mixture and its probable concentration and chemical composition of dust depend on the chemical composition of the cutting materials.Regularities are obtained, which can give an opportunity to improve the individual and collective protection of workers from this harmful production factor

Architecture, Building and Furniture Trades: Prospectus of Courses Session 1938-39

Courses and timetables for the College of Technology, Bolton Street, Dublin 1

Architecture, Building and Furniture Trades: Prospectus of Courses Session 1939-40

Courses and timetables for the College of Technology, Bolton Street, Dublin 1

Architecture, Building and Furniture Trades: Prospectus of Courses Session 1935-36

Courses and timetables for the College of Technology, Bolton Street, Dublin 1

Computation of the multi-chord distribution of convex and concave polygons

Analytical expressions for the distribution of the length of chords corresponding to the affine invariant measure on the set of chords are given for convex polygons. These analytical expressions are a computational improvement over other expressions published in 2011. The correlation function of convex polygons can be computed from the results obtained in this work, because it is determined by the distribution of chords. An analytical expression for the multi-chord distribution of the length of chords corresponding to the affine invariant measure on the set of chords is found for non convex polygons. In addition we give an algorithm to find this multi-chord distribution which, for many concave polygons, is computationally more efficient than the said analytical expression. The results also apply to non simply connected polygons.Comment: 22 figures, 40 pages, 43 reference

Architecture, Building and Furniture Trades: Time Table and Prospectus of Courses 1928-29

Courses and timetables for the College of Technology, Bolton Street, Dublin 1