Minimum Convex Partitions and Maximum Empty Polytopes

Let $S$ be a set of $n$ points in $\mathbb{R}^d$. A Steiner convex partition is a tiling of ${\rm conv}(S)$ with empty convex bodies. For every integer $d$, we show that $S$ admits a Steiner convex partition with at most $\lceil (n-1)/d\rceil$ tiles. This bound is the best possible for points in general position in the plane, and it is best possible apart from constant factors in every fixed dimension $d\geq 3$. We also give the first constant-factor approximation algorithm for computing a minimum Steiner convex partition of a planar point set in general position. Establishing a tight lower bound for the maximum volume of a tile in a Steiner convex partition of any $n$ points in the unit cube is equivalent to a famous problem of Danzer and Rogers. It is conjectured that the volume of the largest tile is $\omega(1/n)$. Here we give a $(1-\varepsilon)$-approximation algorithm for computing the maximum volume of an empty convex body amidst $n$ given points in the $d$-dimensional unit box $[0,1]^d$.Comment: 16 pages, 4 figures; revised write-up with some running times improve

Inscape April 1972

The April 1972 edition of the Inscape: Literary and Art Magazine.https://scholarworks.moreheadstate.edu/inscape_magazine_archive/1015/thumbnail.jp

Finding planar regions

Preiskovali smo problem iskanja ravnin na trianguliranem terenu. Za množico točk v prostoru zgradimo Delaunayjevo triangulacijo in z dvema različnima metodama poiščemo ravnino na terenu. V prvi metodi uporabimo algoritem za iskanje največjega konveksnega poligona. Algoritem se dobro obnese na manjši množici točk, na večji množici točk, pa zaradi svoje kvadratične časovne zahtevnosti ne pride v poštev. V drugi metodi uporabimo aproksimacijski algoritem. Ta se bolje obnese tudi na večji množici podatkov, kot tudi na realnih geografskih podatkih, ki jih lahko dobimo na spletnem portalu LIDAR. Implementiran vmesnik nam pomaga, da na enostaven način testiramo obe metodi in vizualiziramo rezultate.We studied the problem of finding planar regions in a triangulated terrain. For a set of points in 3-space, we construct the Delaunay triangulation. Then, with two different methods we look for a region which is flat. The first method uses an algorithm to find the largest convex polygon. The algorithm works well on smaller sets of points, but on larger sets of points it performs poorly due to its quadratic time complexity. In the second method, we use an approximation algorithm. It performs better on larger data sets, as well as on real geographical data, which can be obtained on the web portal LIDAR. The implemented interface helps us to test both methods in an easy way and visualize the results

Evaluation of Seal Integrity of Flexible Food Polytrays by Destructive and Non-Destructive Techniques

The companies which supply military ration packages (MRP) have been suffering significant loss due to high rejection rate (more than 20 %) by the military. The standards set by the military, as far as acceptance of packages is concerned, are very high and conservative. The means employed are also based mostly on visual observation. The aim of the project is to quantitatively device test which reduce the high rejections the companies are incurring. Thus the drive behind this project is to determine the extent to which certain defects affect the seal strength of food trays. Earlier work on this project was used as a guideline to decide the parameters for an optimized test. A package which develops a significant leak under a pressure of 20 psi is considered a defective package irrespective whether it has any visual defects. With the current laboratory set-up, leaks as low as 4-5 cc/minute were identified. The food packages with different defects namely; short seals, entrapped matter, blisters and air bubbles, tunneling, and wrinkles from Stegner and Wornick Co were tested destructively and non-destructively. A destructive burst test was used to test the burst pressures and the leak developed in trays. A computer interface was designed using National Instrument Labview® program which could automatically detect the leak through the seal and measure the pressure in the package while simultaneously increasing the pressure in step mode. Based on the results from the burst test, a systematic study of the burst pressures that different types of defective packages withstood and the correlation with the seal width was carried out. It was found that non-defective trays from both Stegner and Wornick performed equally well averaging 34.2 and 34.4 psi respectively. Blisters and entrapped matter seemed to drastically reduce the average burst pressure for Stegner trays, while Wornick trays with these defects did not show a substantial reduction in the burst pressure. Stegner trays with blisters in their seals sustained the average burst pressure of 23 psi, while those from Wornick performed better than their counterparts sustaining 35 psi. Short seal trays from Wornick were found to perform better than non-defective trays sustaining 37.7 psi, while those from Stegner sustained 28.3 psi. Although burst test gives the quantitative measure of seal strength, it cannot be implemented on the production line to test 100% of the production packages. The stress condition developed in the package as a result of burst test was simulated using a finite element analysis program Femlab®. Simulations were performed to better understand the visual presentation of stresses in the package; especially across the seal. Three-dimensional simulations although more effective; needed the coupling equations between the acrylic plate of a burst chamber and lid of a package. Two-dimensional simulations were performed with varying distances between acrylic plate and lid at constant boundary conditions gave exponential increase in the stress across the seal. Non-destructive techniques such as ultrasonic C-scan inspection and infrared thermography were examined as techniques which could be installed in-line to detect the defects in the seal and reduce the defective packages reaching the consumer. Pulse-echo technique was used for ultrasonic inspection. Only packages with tunneling defects were tested. The presence of tunneling could be seen on the images. But the presence of small diameter channels like 50.8 microns could not be seen at all. So after some experiments the technique was not found of high utility and lacked the reproducibility. The infrared thermography on the other hand showed promise as a useful utility. Polytrays with many kinds of defects were examined using infrared camera. A 100W lamp was used to heat the packages. Differential heat loss across the defect was recorded by the camera. The results from burst tests were complimented using characterization techniques such as scanning electron microscopy (SEM). The SEM data was also complimented by FTIR/ATR spectroscopy technique to analyze as to which layer was undergoing delamination during the burst. Delamination was seen to occur between PP/PET layers for the trays which burst. Crazing was seen as the failure mechanism for PP

Best Available Techniques (BAT) Reference Document for the Food, Drink and Milk Industries. Industrial Emissions Directive 2010/75/EU (Integrated Pollution Prevention and Control)

The Best Available Techniques (BAT) Reference Document (BREF) for the Food, Drink and Milk Industries is part of a series of documents presenting the results of an exchange of information between EU Member States, the industries concerned, non-governmental organisations promoting environmental protection, and the Commission, to draw up, review and – where necessary – update BAT reference documents as required by Article 13(1) of Directive 2010/78/EU on Industrial Emissions (the Directive). This document is published by the European Commission pursuant to Article 13(6) of the Directive. The BREF for the Food, Drink and Milk Industries covers the treatment and processing, other than exclusively packaging, of the animal and/or vegetable raw materials, whether previously processed or unprocessed, intended for the production of food or feed, as specified in Section 6.4 (b) of Annex I to Directive 2010/75/EU. Important issues for the implementation of Directive 2010/75/EU in the food, drink and milk (FDM) sector are emissions to water, energy and water consumption. Chapter 1 provides general information on the FDM sector and on the industrial processes and techniques used within this sector. Chapter 2 provides information on the common industrial processes, abatement systems and general techniques that are used across the FDM sector. General techniques to consider in the determination of BAT (i.e. those techniques to consider that are widely applied in the FDM sector) are reported in Chapter 2. Chapters 3 to 15 give the applied processes, current emission and consumption levels, techniques to consider in the determination of BAT and emerging techniques for the FDM sectors that are covered by these chapters. Chapter 16 provides thumbnail descriptions of additional FDM sectors, for which a data collection via questionnaires has not been carried out. Chapter 17 presents the BAT conclusions as defined in Article 3(12) of the Directive, both general and sector-specific. Concluding remarks and recommendations for future work are presented in Chapter 18.JRC.B.5-Circular Economy and Industrial Leadershi

The Knowledge Weapon: Ways of Knowing

This collection of poems explores the language of knowledge and instruction. While it can provide a sense of security, what we are given as ‘knowledge’ is frequently unreliable or even misleading, and used much like a weapon