Computer aided geometric design of form-rolls for NC manufacture

Conventional methods of form-roll design and manufacture for Cold Roll-Forming of thin-walled metal sections have been entirely manual, time consuming and prone to errors, resulting in inefficiency and high production costs. With the use of computers, lead time can be significantly improved, particularly for those aspects involving routine but tedious human decisions and actions. This thesis describes the development of computer aided tools for producing form-roll designs for NC manufacture in the CAD/CAM environment. The work was undertaken to modernise the existing activity of a company manufacturing thin-walled sections. The investigated areas of the activity, including the design and drafting of the finished section, the flower patterns, the 10 to 1 templates, and the rolls complete with pinch-difference surfaces, side-rolls and extension-contours, have been successfully computerised by software development . Data generated by the developed software can be further processed for roll manufacturing using NC lathes. The software has been specially designed for portability to facilitate its implementation on different computers. The Opening-Radii method of forming was introduced as a subsitute to the conventional method for better forming. Most of the essential aspects in roll design have been successfully incorporated in the software. With computerisation, extensive standardisation in existing roll design practices and the use of more reliable and scientifically-based methods have been achieved. Satisfactory and beneficial results have also been obtained by the company in using the software through a terminal linked to the University by a GPO line. Both lead time and productivity in roll design and manufacture have been significantly improved. It is therefore concluded that computerisation in the design of form-rolls for automation by software development is viable. The work also demonstrated the promising nature of the CAD/CAM approach.

The geometric correction and registration of airborne line-scanned imagery for temporal thermal studies

This thesis begins by providing a review of techniques for interpreting the thermal response at the earth's surface acquired using remote sensing technology. Historic limitations in the precision with which imagery acquired from airborne platforms can be geometrically corrected and co-registered has meant that relatively little work has been carried out examining the diurnal variation of surface temperature over wide regions. Although emerging remote sensing systems provide the potential to register temporal image data within satisfactory levels of accuracy, this technology is still not widely available and does not address the issue of historic data sets which cannot be rectified using conventional parametric approaches. In overcoming these problems, the second part of this thesis describes the development of an alternative approach for rectifying airborne line-scanned imagery. The underlying assumption that scan lines within the imagery are straight greatly reduces the number of ground control points required to describe the image geometry. Furthermore, the use of pattern matching procedures to identify geometric disparities between raw line-scanned imagery and corresponding aerial photography enables the correction procedure to be almost fully automated. By reconstructing the raw image data on a truly line-by-line basis, it is possible to register the airborne line-scanned imagery to the aerial photography with an average accuracy of better than one pixel. Providing corresponding aerial photography is available, this approach can be applied in the absence of platform altitude information allowing multi-temporal data sets to be corrected and registered.

Geometric spectral accuracy of airborne remote sensing

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Geometric Stable Laws Through Series Representations

Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study the asymptotic behavior of the partial sum process SN (t) = ⅀( i=1 ... [N t] ) Xi , and derive series representations of the limiting geometric stable process and the corresponding stochastic integral. We also obtain strong invariance principles for stable and geometric stable laws.

The Divisibility Modulo 4 of Kloosterman Sums over Finite Fields of Characteristic 3

Recently Garashuk and Lisonek evaluated Kloosterman sums K (a) modulo 4 over a finite field F3m in the case of even K (a). They posed it as an open problem to characterize elements a in F3m for which K (a) ≡ 1 (mod4) and K (a) ≡ 3 (mod4). In this paper, we will give an answer to this problem. The result allows us to count the number of elements a in F3m belonging to each of these two classes.

Construction of Optimal Linear Codes by Geometric Puncturing

Dedicated to the memory of S.M. Dodunekov (1945–2012)Abstract. Geometric puncturing is a method to construct new codes. ACM Computing Classification System (1998): E.4.

A Characterization of the Negative Binomial Distribution

Only a few characterizations have been obtained in literatute for the negative binomial distribution (see Johnson et al., Chap. 5, 1992). In this article a characterization of the negative binomial distribution related to random sums is obtained which is motivated by the geometric distribution characterization given by Khalil et al. (1991). An interpretation in terms of an unreliable system is given.

Controlled Multitype Branching Models: Geometric Growth

2000 Mathematics Subject Classi cation: 60J80, 60F25.

Extremes of Bivariate Geometric Variables with Application to Bisexual Branching Processes

2000 Mathematics Subject Classification: 60J80, 60G70.

Zeros of Sequences of Partial Sums and Overconvergence

2000 Mathematics Subject Classification: 30B40, 30B10, 30C15, 31A15.

A geometriai Brown-mozgás feltevésének elfogadhatósága a reálopciók értékelésében (The acceptability of the assumption of geometric brownian motion in the valuation of real options)

A reálopciók a döntési rugalmasság megtestesítőiként jelen vannak a vállalatvezetők mindennapjaiban, és cégtől függően jelentős értéket képviselhetnek. Értékelésük a hagyományos diszkontált pénzáramlás módszerekkel csak korlátozottan lehetséges, ezért alternatívaként felmerül a pénzügyi opcióárazás módszertana, amelynek hagyományos változatai az alaptermék alakulásáról geometriai Brown-mozgást feltételeznek. A cikk ezt a feltevést veszi górcső alá a reálopciókra történő alkalmazás szempontjából, és megmutatja, hogy habár önkényesnek tűnhet, valójában nem pusztán egy matematikai szempontból kényelmes megoldás, hanem pénzügyileg is elfogadható feltétel. _______ Real options represent the fl exibility of decision-making, and are thus part of the everyday work of corporate executives, often having great value. Valuing them with the use of traditional Discounted Cash Flow models has limited relevance, therefore arises the alternative methodology of fi nancial option pricing, the traditional versions of which assume that the price of the underlying asset follows Geometric Brownian Motion. The paper examines this assumption from the aspect of real option valuation and shows that although it might seem arbitrary, it is not only a mathematically convenient choice, but also a fi nancially acceptable one.

Thinking in three dimensions: Exploring students' geometric thinking and spatial ability with the Geometer's Sketchpad

Current reform initiatives recommend that geometry instruction include the study of three-dimensional geometric objects and provide students with opportunities to use spatial skills in problem-solving tasks. Geometer's Sketchpad (GSP) is a dynamic and interactive computer program that enables the user to investigate and explore geometric concepts and manipulate geometric structures. Research using GSP as an instructional tool has focused primarily on teaching and learning two-dimensional geometry. This study explored the effect of a GSP based instructional environment on students' geometric thinking and three-dimensional spatial ability as they used GSP to learn three-dimensional geometry. For 10 weeks, 18 tenth-grade students from an urban school district used GSP to construct and analyze dynamic, two-dimensional representations of three-dimensional objects in a classroom environment that encouraged exploration, discussion, conjecture, and verification. The data were collected primarily from participant observations and clinical interviews and analyzed using qualitative methods of analysis. In addition, pretest and posttest measures of three-dimensional spatial ability and van Hiele level of geometric thinking were obtained. Spatial ability measures were analyzed using standard t-test analysis. ^ The data from this study indicate that GSP is a viable tool to teach students about three-dimensional geometric objects. A comparison of students' pretest and posttest van Hiele levels showed an improvement in geometric thinking, especially for students on lower levels of the van Hiele theory. Evidence at the p < .05 level indicated that students' spatial ability improved significantly. Specifically, the GSP dynamic, visual environment supported students' visualization and reasoning processes as students attempted to solve challenging tasks about three-dimensional geometric objects. The GSP instructional activities also provided students with an experiential base and an intuitive understanding about three-dimensional objects from which more formal work in geometry could be pursued. This study demonstrates that by designing appropriate GSP based instructional environments, it is possible to help students improve their spatial skills, develop more coherent and accurate intuitions about three-dimensional geometric objects, and progress through the levels of geometric thinking proposed by van Hiele. ^

Effects of roadway geometric features on run-off road crashes on the Florida State Highway System

Run-off-road (ROR) crashes have increasingly become a serious concern for transportation officials in the State of Florida. These types of crashes have increased proportionally in recent years statewide and have been the focus of the Florida Department of Transportation. The goal of this research was to develop statistical models that can be used to investigate the possible causal relationships between roadway geometric features and ROR crashes on Florida's rural and urban principal arterials. ^ In this research, Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) Regression models were used to better model the excessive number of roadway segments with no ROR crashes. Since Florida covers a diverse area and since there are sixty-seven counties, it was divided into four geographical regions to minimize possible unobserved heterogeneity. Three years of crash data (2000–2002) encompassing those for principal arterials on the Florida State Highway System were used. Several statistical models based on the ZIP and ZINB regression methods were fitted to predict the expected number of ROR crashes on urban and rural roads for each region. Each region was further divided into urban and rural areas, resulting in a total of eight crash models. A best-fit predictive model was identified for each of these eight models in terms of AIC values. The ZINB regression was found to be appropriate for seven of the eight models and the ZIP regression was found to be more appropriate for the remaining model. To achieve model convergence, some explanatory variables that were not statistically significant were included. Therefore, strong conclusions cannot be derived from some of these models. ^ Given the complex nature of crashes, recommendations for additional research are made. The interaction of weather and human condition would be quite valuable in discerning additional causal relationships for these types of crashes. Additionally, roadside data should be considered and incorporated into future research of ROR crashes. ^

Engineering Analysis in Imprecise Geometric Models

Engineering analysis in geometric models has been the main if not the only credible/reasonable tool used by engineers and scientists to resolve physical boundaries problems. New high speed computers have facilitated the accuracy and validation of the expected results. In practice, an engineering analysis is composed of two parts; the design of the model and the analysis of the geometry with the boundary conditions and constraints imposed on it. Numerical methods are used to resolve a large number of physical boundary problems independent of the model geometry. The time expended due to the computational process are related to the imposed boundary conditions and the well conformed geometry. Any geometric model that contains gaps or open lines is considered an imperfect geometry model and major commercial solver packages are incapable of handling such inputs. Others packages apply different kinds of methods to resolve this problems like patching or zippering; but the final resolved geometry may be different from the original geometry, and the changes may be unacceptable. The study proposed in this dissertation is based on a new technique to process models with geometrical imperfection without the necessity to repair or change the original geometry. An algorithm is presented that is able to analyze the imperfect geometric model with the imposed boundary conditions using a meshfree method and a distance field approximation to the boundaries. Experiments are proposed to analyze the convergence of the algorithm in imperfect models geometries and will be compared with the same models but with perfect geometries. Plotting results will be presented for further analysis and conclusions of the algorithm convergence

Geometric inequalities for initial data with symmetries

We consider a class of initial data sets (Σ,h,K) for the Einstein constraint equations which we define to be generalized Brill (GB) data. This class of data is simply connected, U(1)²-invariant, maximal, and four-dimensional with two asymptotic ends. We study the properties of GB data and in particular the topology of Σ. The GB initial data sets have applications in geometric inequalities in general relativity. We construct a mass functional M for GB initial data sets and we show:(i) the mass of any GB data is greater than or equals M, (ii) it is a non-negative functional for a broad subclass of GB data, (iii) it evaluates to the ADM mass of reduced t − φi symmetric data set, (iv) its critical points are stationary U(1)²-invariant vacuum solutions to the Einstein equations. Then we use this mass functional and prove two geometric inequalities: (1) a positive mass theorem for subclass of GB initial data which includes Myers-Perry black holes, (2) a class of local mass-angular momenta inequalities for U(1)²-invariant black holes. Finally, we construct a one-parameter family of initial data sets which we show can be seen as small deformations of the extreme Myers- Perry black hole which preserve the horizon geometry and angular momenta but have strictly greater energy.