Methods of optimization of Hausdorff distance between convex rotating figures

We studied the problem of optimizing the Hausdorff distance between two convex polygons. Its minimization is chosen as the criterion of optimality. It is believed that one of the polygons can make arbitrary movements on the plane, including parallel transfer and rotation with the center at any point. The other polygon is considered to be motionless. Iterative algorithms for the phased shift and rotation of the polygon are developed and implemented programmatically, providing a decrease in the Hausdorff distance between it and the fixed polygon. Theorems on the correctness of algorithms for a wide class of cases are proved. Moreover, the geometric properties of the Chebyshev center of a compact set and the differential properties of the Euclidean function of distance to a convex set are essentially used. When implementing the software package, it is possible to run multiple times in order to identify the best found polygon position. A number of examples are simulated.

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Iterative algorithms for minimizing the Hausdorff distance between convex polyhedrons

10.35634/2226-3594-2021-57-06 ◽

2021 ◽

Vol 57 ◽

pp. 142-155

Author(s):

P.D. Lebedev ◽

A.A. Uspenskii ◽

V.N. Ushakov

Keyword(s):

Euclidean Space ◽

Computational Geometry ◽

Hausdorff Distance ◽

Software Package ◽

Nonsmooth Analysis ◽

Three Dimensional ◽

Iterative Algorithms ◽

Optimal Location ◽

Dimensional Euclidean Space ◽

Moving Bodies

The problem of finding the optimal location of moving bodies in three-dimensional Euclidean space is considered. We study the problem of finding such a position for two given polytopes A and B at which the Hausdorff distance between them would be minimal. To solve it, the apparatus of convex and nonsmooth analysis is used, as well as methods of computational geometry. Iterative algorithms have been developed and justification has been made for the correctness of their work. A software package has been created, its work is illustrated with specific examples.

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GreenPM®

Sustainability Integration for Effective Project Management - Practice, Progress, and Proficiency in Sustainability ◽

10.4018/978-1-4666-4177-8.ch003 ◽

2013 ◽

pp. 39-57 ◽

Cited By ~ 2

Author(s):

Tom Mochal ◽

Andrea Krasnoff

Keyword(s):

Project Management ◽

Software Package ◽

Material Handling ◽

Resource Depletion ◽

Project Managers ◽

The Other ◽

Management Process ◽

The World ◽

The Impact ◽

Unlimited Amount

The world is going green and we are collectively realizing that we do not have an unlimited amount of natural resources to utilize as we have done in the past. Material Handling Industry of America (2007) notes, “Not only do we have climate problems but we are also dealing with a resource depletion issue.” However, the project management profession seems to be in its infancy in applying green standards. How can we apply these “green” concepts to our project management discipline? One obvious way is that we can manage green projects more efficiently. For example, if you are the project manager on a project that will result in using less packaging in your products, it would be good if your project completed on time. The sooner that project ends, the sooner the green benefits will be achieved. On the other hand, if you are dealing with projects such as installing a new software package or upgrading network infrastructure, how can these projects become more environmentally friendly? The answer is Green Project Management (GreenPM®). Green project management is a model that allows project managers to think green throughout a project and make decisions that take into account the impact on the environment—if any. It is a way to ingrain “greenthink” (or green thinking) into every project management process. Greenthink connects the environment with the decisions that are made, whether project-related, professional, or in our everyday lives.

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Rapid Variation of Shell Line Parameters in ζ Tau

International Astronomical Union Colloquium ◽

10.1017/s0252921100116112 ◽

1987 ◽

Vol 92 ◽

pp. 99-100

Author(s):

M. Bossi ◽

G. Guerrero ◽

M. Scardia

Keyword(s):

Binary System ◽

Time Scales ◽

The Other ◽

Compact Set ◽

Rapid Variation ◽

Inverse Dispersion ◽

Be Star ◽

Hα Emission ◽

Emission Strength

ζTau is a Be star which probably showed already in 1973 rapid variations in Hα emission strength with time scales of a few minutes (Bahng, 1976). It represents, moreover, the primary of a well-known binary system with a period of 132.91 days (e.g., Hynek and Struve, 1942), and its shell displays long term instabilities with time scales of some years (Delplace and Chambon, 1976). The basis of the present work is a compact set of 82 grating photographic spectrograms obtained at Merate by means of the 137 cm reflector with an inverse dispersion of about 35 Å/mm between Jan 17 and Jan 24, 1983. Forty four of these spectra cover the range between ˜ 4000 and ˜ 5000 Å, the other ones being centered on Hα.

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NORMAL-MAP BETWEEN NORMAL-COMPATIBLE MANIFOLDS

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195907002422 ◽

2007 ◽

Vol 17 (05) ◽

pp. 403-421 ◽

Cited By ~ 7

Author(s):

FREDERIC CHAZAL ◽

ANDRE LIEUTIER ◽

JAREK ROSSIGNAC

Keyword(s):

Hausdorff Distance ◽

Arbitrary Dimension ◽

The Other ◽

Fréchet Distance ◽

Feature Size ◽

Normal Map ◽

Frechet Distance ◽

Minimum Feature Size

Consider two (n−1)-dimensional manifolds, S and S′ in ℝn. We say that they are normal-compatible when the closest projection of each one onto the other is a homeomorphism. We give a tight condition under which S and S′ are normal-compatible. It involves the minimum feature size of S and of S′ and the Hausdorff distance between them. Furthermore, when S and S′ are normal-compatible, their Frechet distance is equal to their Hausdorff distance. Our results hold for arbitrary dimension n.

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A Methodology for Evaluating Application Software

Proceedings of the Human Factors Society Annual Meeting ◽

10.1177/154193128603000104 ◽

1986 ◽

Vol 30 (1) ◽

pp. 14-18 ◽

Cited By ~ 1

Author(s):

Andrew M. Cohill ◽

David M. Gilfoil ◽

John V. Pilitsis

Keyword(s):

Statistical Analysis ◽

Data Base ◽

Software Package ◽

Word Processing ◽

The Other ◽

Application Software ◽

Raw Data ◽

And Performance

A methodology for evaluating applications software is proposed, using five different categories of criteria. Three of the categories, functionality, usability, and performance, are tailored for each class of applications software. The other two categories, support and documentation, have generic criteria that can be applied to all types of application software. After a software package has been scored according to the criteria of a category, statistical analysis is used to convert the raw data to a numeric score that can be used to make between-product comparisons. The methodology has been successfully tested with UNIX-based* word processing and data base packages.

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Rates of convergence for random approximations of convex sets

Advances in Applied Probability ◽

10.1017/s0001867800048539 ◽

1996 ◽

Vol 28 (02) ◽

pp. 384-393 ◽

Cited By ~ 9

Author(s):

Lutz Dümbgen ◽

Günther Walther

Keyword(s):

Convex Subset ◽

Hausdorff Distance ◽

Convex Sets ◽

Convex Set ◽

Compact Convex ◽

Almost Sure Convergence ◽

Rates Of Convergence ◽

Random Sets ◽

Compact Convex Set

The Hausdorff distance between a compact convex set K ⊂ ℝd and random sets is studied. Basic inequalities are derived for the case of being a convex subset of K. If applied to special sequences of such random sets, these inequalities yield rates of almost sure convergence. With the help of duality considerations these results are extended to the case of being the intersection of a random family of halfspaces containing K.

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On Gaussian Correlation Inequalities for Rectangles and Symmetric Sets

Calcutta Statistical Association Bulletin ◽

10.1177/0008068320020307 ◽

2002 ◽

Vol 53 (3-4) ◽

pp. 245-248

Author(s):

Subir K. Bhandari ◽

Ayanendranath Basu

Keyword(s):

Development of Model Equations for Selecting Optimum Storage Parameters for Stored Cabbages

International Journal of Engineering Research in Africa ◽

10.4028/www.scientific.net/jera.12.95 ◽

2014 ◽

Vol 12 ◽

pp. 95-105

Author(s):

Musliu Olushola Sunmonu ◽

O. Chukwu ◽

Z.D. Osunde ◽

B.A. Alabadan

Keyword(s):

Vitamin E ◽

Vitamin A ◽

Software Package ◽

Evaporative Cooling ◽

Storage Conditions ◽

The Other ◽

Develop Model ◽

Jute Sack ◽

Model Equations ◽

Rate Of Evaporation

A study was carried to develop model equations for selecting optimum storage parameters for stored cabbages in passive evaporative cooling structures.Three sets of four different types of passive evaporative cooling structures made of two different materials; clay and aluminium were designed and constructed as part of the study. One set consists of four separate cooling chambers. Two cooling chambers were made with aluminium container (cylindrical and square shapes) and the other two were made of clay container (cylindrical and square). These four containers were separately inserted inside a bigger clay pot inter-spaced with clay soil of 5 cm (to form tin-in-pot, pot-in-pot, tin-in-wall and wall-in wall) with the outside structure wrapped with jute sack. The other two sets followed the same pattern with interspacing of 7 cm and 10 cm, respectively. The set with 7 cm clearance served as the control in which the interspace soil and the jute sacks were constantly wetted at intervals of between 2 to 4 hours depending on the rate of evaporation with water at room temperature. The other two sets (5 cm and 10 cm interspaced soil) were constantly wetted with salt solution (sodium chloride) at the same interval to keep the soil in moist condition. Freshly harvested matured cabbages were used for the experiments and the temperature and relative humidity were monitored daily. The vitamin A, vitamin E, bacterial and fungal counts of this produce were determined at intervals of three days for a period of 21 days. Mathematical models (using essential regression software package) were developed to predict the vitamin A and vitamin E contents of the stored produce at various conditions considered in the study. Further analysis by optimization process revealed optimum storage conditions for the stored produce using essential regression software package. Optimum values of 8.86IU and 4.03 mg/ml in storage were obtained for vitamin A and vitamin E contents, respectively for stored cabbages at various conditions.

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Invariance of green equilibrium measure on the domain

Filomat ◽

10.2298/fil1304593p ◽

2013 ◽

Vol 27 (4) ◽

pp. 593-600 ◽

Cited By ~ 1

Author(s):

Stamatis Pouliasis

Keyword(s):

Level Set ◽

Wide Class ◽

Equilibrium Measure ◽

The Other ◽

Equilibrium Potential ◽

Compact Set ◽

Compact Sets ◽

Equilibrium Measures ◽

The One

We prove that the Green equilibrium measure and the Green equilibrium energy of a compact set K relative to the domains D and ? are the same if and only if D is nearly equal to ?, for a wide class of compact sets K. Also, we prove that equality of Green equilibrium measures arises if and only if the one domain is related with a level set of the Green equilibrium potential of K relative to the other domain.

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Considerations on determining the explosion risk and the areas with explosion hazard in a natural gas compressor station

MATEC Web of Conferences ◽

10.1051/matecconf/201818403005 ◽

2018 ◽

Vol 184 ◽

pp. 03005 ◽

Cited By ~ 1

Author(s):

Alina Maria Gligor ◽

Valentin Petrescu

Keyword(s):

Natural Gas ◽

Research And Development ◽

Software Package ◽

Transportation Networks ◽

The Other ◽

Explosion Hazard ◽

Compressor Station ◽

Work Related ◽

The One ◽

Explosion Risk

Compressor stations are important components within natural gas transportation networks. The current paper analyses some of the safety aspects involved in the operation of such facilities – on the one hand related to the explosion risk for employees working in compressor stations and on the other hand related to determining to the areas with increased explosion hazard in such a station, in order to help reducing work-related accidents and the occurrence of professional illnesses. The explosion risk is determined based on a method devised by the National Institute for Research and Development for Environmental Protection Bucharest, while the explosion hazard areas are determined and displayed with the help of the software package AutoCAD Plant 3D.

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