Subdivision Error Analysis and Compensation for Photoelectric Angle Encoder in a Telescope Control System

Directory of Open Access Journals (Sweden)

Yanrui Su

2015-01-01

Full Text Available As the position sensor, photoelectric angle encoder affects the accuracy and stability of telescope control system (TCS. A TCS-based subdivision error compensation method for encoder is proposed. Six types of subdivision error sources are extracted through mathematical expressions of subdivision signals first. Then the period length relationships between subdivision signals and subdivision errors are deduced. And the error compensation algorithm only utilizing the shaft position of TCS is put forward, along with two control models; Model I is that the algorithm applies only to the speed loop of TCS and Model II is applied to both speed loop and position loop. Combined with actual project, elevation jittering phenomenon of the telescope is discussed to decide the necessity of DC-type subdivision error compensation. Low-speed elevation performance before and after error compensation is compared to help decide that Model II is preferred. In contrast to original performance, the maximum position error of the elevation with DC subdivision error compensation is reduced by approximately 47.9% from 1.42″ to 0.74″. The elevation gets a huge decrease in jitters. This method can compensate the encoder subdivision errors effectively and improve the stability of TCS.

Electromyography Activation Levels of the 3 Gluteus Medius Subdivisions During Manual Strength Testing

DEFF Research Database (Denmark)

Otten, Roald; Tol, Johannes L; Holmich, Per

2015-01-01

deficits and guide specific rehabilitation programs. However, the optimal positions for assessing the strength and activation of these subdivisions are unknown. OBJECTIVE: The first aim was to establish which strength-testing positions produce the highest surface electromyography (sEMG) activation levels...... of the individual GM subdivisions. The second aim was to evaluate differences in sEMG activation levels between the tested and contralateral (stabilizing) leg. METHOD: Twenty healthy physically active male subjects participated in this study. Muscle activity using sEMG was recorded for the GM subdivisions in 8......STUDY DESIGN: Cross-sectional. CONTEXT: Gluteus medius (GM) muscle dysfunction is associated with overuse injury. The GM is functionally composed of 3 separate subdivisions: anterior, middle, and posterior. Clinical assessment of the GM subdivisions is relevant to detect strength and activation...

Architectonic subdivisions of the amygdalar complex of a primitive marsupial (Didelphis aurita).

Science.gov (United States)

Rocha-Rego, V; Canteras, N S; Anomal, R F; Volchan, E; Franca, J G

2008-05-15

The architecture of the amygdaloid complex of a marsupial, the opossum Didelphis aurita, was analyzed using classical stains like Nissl staining and myelin (Gallyas) staining, and enzyme histochemistry for acetylcholinesterase and NADPH-diaphorase. Most of the subdivisions of the amygdaloid complex described in eutherian mammals were identified in the opossum brain. NADPH-diaphorase revealed reactivity in the neuropil of nearly all amygdaloid subdivisions with different intensities, allowing the identification of the medial and lateral subdivisions of the cortical posterior nucleus and the lateral subdivision of the lateral nucleus. The lateral, central, basolateral and basomedial nuclei exhibited acetylcholinesterase positivity, which provided a useful chemoarchitectural criterion for the identification of the anterior basolateral nucleus. Myelin stain allowed the identification of the medial subdivision of the lateral nucleus, and resulted in intense staining of the medial subdivisions of the central nucleus. The medial, posterior, and cortical nuclei, as well as the amygdalopiriform area did not exhibit positivity for myelin staining. On the basis of cyto- and chemoarchitectural criteria, the present study highlights that the opossum amygdaloid complex shares similarities with that of other species, thus supporting the idea that the organization of the amygdala is part of a basic plan conserved through mammalian evolution.

Research on Remote Sensing Image Template Processing Based on Global Subdivision Theory

OpenAIRE

Xiong Delan; Du Genyuan

2013-01-01

Aiming at the questions of vast data, complex operation, and time consuming processing for remote sensing image, subdivision template was proposed based on global subdivision theory, which can set up high level of abstraction and generalization for remote sensing image. The paper emphatically discussed the model and structure of subdivision template, and put forward some new ideas for remote sensing image template processing, key technology and quickly applied demonstration. The research has ...

Testing block subdivision algorithms on block designs

Science.gov (United States)

Wiseman, Natalie; Patterson, Zachary

2016-01-01

Integrated land use-transportation models predict future transportation demand taking into account how households and firms arrange themselves partly as a function of the transportation system. Recent integrated models require parcels as inputs and produce household and employment predictions at the parcel scale. Block subdivision algorithms automatically generate parcel patterns within blocks. Evaluating block subdivision algorithms is done by way of generating parcels and comparing them to those in a parcel database. Three block subdivision algorithms are evaluated on how closely they reproduce parcels of different block types found in a parcel database from Montreal, Canada. While the authors who developed each of the algorithms have evaluated them, they have used their own metrics and block types to evaluate their own algorithms. This makes it difficult to compare their strengths and weaknesses. The contribution of this paper is in resolving this difficulty with the aim of finding a better algorithm suited to subdividing each block type. The proposed hypothesis is that given the different approaches that block subdivision algorithms take, it's likely that different algorithms are better adapted to subdividing different block types. To test this, a standardized block type classification is used that consists of mutually exclusive and comprehensive categories. A statistical method is used for finding a better algorithm and the probability it will perform well for a given block type. Results suggest the oriented bounding box algorithm performs better for warped non-uniform sites, as well as gridiron and fragmented uniform sites. It also produces more similar parcel areas and widths. The Generalized Parcel Divider 1 algorithm performs better for gridiron non-uniform sites. The Straight Skeleton algorithm performs better for loop and lollipop networks as well as fragmented non-uniform and warped uniform sites. It also produces more similar parcel shapes and patterns.

A Method of Vector Map Multi-scale Representation Considering User Interest on Subdivision Gird

Directory of Open Access Journals (Sweden)

YU Tong

2016-12-01

Full Text Available Compared with the traditional spatial data model and method, global subdivision grid show a great advantage in the organization and expression of massive spatial data. In view of this, a method of vector map multi-scale representation considering user interest on subdivision gird is proposed. First, the spatial interest field is built using a large number POI data to describe the spatial distribution of the user interest in geographic information. Second, spatial factor is classified and graded, and its representation scale range can be determined. Finally, different levels of subdivision surfaces are divided based on GeoSOT subdivision theory, and the corresponding relation of subdivision level and scale is established. According to the user interest of subdivision surfaces, the spatial feature can be expressed in different degree of detail. It can realize multi-scale representation of spatial data based on user interest. The experimental results show that this method can not only satisfy general-to-detail and important-to-secondary space cognitive demands of users, but also achieve better multi-scale representation effect.

Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs

Directory of Open Access Journals (Sweden)

Magda Dettlaff

2016-01-01

Full Text Available Given a graph \\(G=(V,E\\, the subdivision of an edge \\(e=uv\\in E(G\\ means the substitution of the edge \\(e\\ by a vertex \\(x\\ and the new edges \\(ux\\ and \\(xv\\. The domination subdivision number of a graph \\(G\\ is the minimum number of edges of \\(G\\ which must be subdivided (where each edge can be subdivided at most once in order to increase the domination number. Also, the domination multisubdivision number of \\(G\\ is the minimum number of subdivisions which must be done in one edge such that the domination number increases. Moreover, the concepts of paired domination and independent domination subdivision (respectively multisubdivision numbers are defined similarly. In this paper we study the domination, paired domination and independent domination (subdivision and multisubdivision numbers of the generalized corona graphs.

Electromyographic analysis of the three subdivisions of gluteus medius during weight-bearing exercises

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O'Sullivan Kieran

2010-07-01

Full Text Available Abstract Background Gluteus medius (GM dysfunction is associated with many musculoskeletal disorders. Rehabilitation exercises aimed at strengthening GM appear to improve lower limb kinematics and reduce pain. However, there is a lack of evidence to identify which exercises best activate GM. In particular, as GM consists of three distinct subdivisions, it is unclear if GM activation is consistent across these subdivisions during exercise. The aim of this study was to determine the activation of the anterior, middle and posterior subdivisions of GM during weight-bearing exercises. Methods A single session, repeated-measures design. The activity of each GM subdivision was measured in 15 pain-free subjects using surface electromyography (sEMG during three weight-bearing exercises; wall squat (WS, pelvic drop (PD and wall press (WP. Muscle activity was expressed relative to maximum voluntary isometric contraction (MVIC. Differences in muscle activation were determined using one-way repeated measures ANOVA with post-hoc Bonferroni analysis. Results The activation of each GM subdivision during the exercises was significantly different (interaction effect; p Discussion Posterior GM displayed higher activation across all three exercises than both anterior and middle GM. The WP produced the highest %MVIC activation for all GM subdivisions, and this was most pronounced for posterior GM. Clinicians may use these results to effectively progress strengthening exercises for GM in the rehabilitation of lower extremity injuries.

Effects of Worldwide Population Subdivision on ALDH2 Linkage Disequilibrium

OpenAIRE

Peterson, Raymond J.; Goldman, David; Long, Jeffrey C.

1999-01-01

The effect of human population subdivision on linkage disequilibrium has previously been studied for unlinked genes. However, no study has focused on closely linked polymorphisms or formally partitioned linkage disequilibrium within and among worldwide populations. With an emphasis on population subdivision, the goal of this paper is to investigate the causes of linkage disequilibrium in ALDH2, the gene that encodes aldehyde dehydrogenase 2. Haplotypes for 756 people from 17 populations acros...

Simplifying massive planar subdivisions

DEFF Research Database (Denmark)

Arge, Lars; Truelsen, Jakob; Yang, Jungwoo

2014-01-01

We present the first I/O- and practically-efficient algorithm for simplifying a planar subdivision, such that no point is moved more than a given distance εxy and such that neighbor relations between faces (homotopy) are preserved. Under some practically realistic assumptions, our algorithm uses ....... For example, for the contour map simplification problem it is significantly faster than the previous algorithm, while obtaining approximately the same simplification factor. Read More: http://epubs.siam.org/doi/abs/10.1137/1.9781611973198.3...

Planet map generation by tetrahedral subdivision

DEFF Research Database (Denmark)

Mogensen, Torben Ægidius

2010-01-01

We present a method for generating pseudo-random, zoomable planet maps for games and art.  The method is based on spatial subdivision using tetrahedrons.  This ensures planet maps without discontinuities caused by mapping a flat map onto a sphere. We compare the method to other map...

12 CFR 1.110 - Taxing powers of a State or political subdivision.

Science.gov (United States)

2010-01-01

... impact of any possible limitations regarding the State's or political subdivision's taxing powers, as... 12 Banks and Banking 1 2010-01-01 2010-01-01 false Taxing powers of a State or political subdivision. 1.110 Section 1.110 Banks and Banking COMPTROLLER OF THE CURRENCY, DEPARTMENT OF THE TREASURY...

Prospective relations between resting-state connectivity of parietal subdivisions and arithmetic competence.

Science.gov (United States)

Price, Gavin R; Yeo, Darren J; Wilkey, Eric D; Cutting, Laurie E

2018-04-01

The present study investigates the relation between resting-state functional connectivity (rsFC) of cytoarchitectonically defined subdivisions of the parietal cortex at the end of 1st grade and arithmetic performance at the end of 2nd grade. Results revealed a dissociable pattern of relations between rsFC and arithmetic competence among subdivisions of intraparietal sulcus (IPS) and angular gyrus (AG). rsFC between right hemisphere IPS subdivisions and contralateral IPS subdivisions positively correlated with arithmetic competence. In contrast, rsFC between the left hIP1 and the right medial temporal lobe, and rsFC between the left AG and left superior frontal gyrus, were negatively correlated with arithmetic competence. These results suggest that strong inter-hemispheric IPS connectivity is important for math development, reflecting either neurocognitive mechanisms specific to arithmetic processing, domain-general mechanisms that are particularly relevant to arithmetic competence, or structural 'cortical maturity'. Stronger connectivity between IPS, and AG, subdivisions and frontal and temporal cortices, however, appears to be negatively associated with math development, possibly reflecting the ability to disengage suboptimal problem-solving strategies during mathematical processing, or to flexibly reorient task-based networks. Importantly, the reported results pertain even when controlling for reading, spatial attention, and working memory, suggesting that the observed rsFC-behavior relations are specific to arithmetic competence. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

Divided Spheres Geodesics and the Orderly Subdivision of the Sphere

CERN Document Server

Popko, Edward S

2012-01-01

This well-illustrated book-in color throughout-presents a thorough introduction to the mathematics of Buckminster Fuller's invention of the geodesic dome, which paved the way for a flood of practical applications as diverse as weather forecasting and fish farms. The author explains the principles of spherical design and the three main categories of subdivision based on geometric solids (polyhedra). He illustrates how basic and advanced CAD techniques apply to spherical subdivision and covers modern applications in product design, engineering, science, games, and sports balls.

29 CFR 541.103 - Department or subdivision.

Science.gov (United States)

2010-07-01

... example, a large employer's human resources department might have subdivisions for labor relations, pensions and other benefits, equal employment opportunity, and personnel management, each of which has a... to time to a specific job or series of jobs and a unit with permanent status and function. A...

Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes

Institute of Scientific and Technical Information of China (English)

Ghulam MUSTAFA

2017-01-01

The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes (for any integer m,n ≥ 2).The proposed algorithm has been derived from uniform B-spline blending functions.In particular,we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data.Moreover,we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve.Furthermore,visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.

Study on the integration of layered water injection technology and subdivision adjustment

Science.gov (United States)

Zhang, Yancui

2018-06-01

With oil many infillings, thin and poor reservoir exploitation changes gradually to low permeability, thin and poor reservoir development characteristics of multiple layers thickness, low permeability, in the actual development process, the General Department of oil layers of encryption perforation long thin and poor mining, interlayer contradiction more prominent, by conventional layered water injection that can alleviate the contradiction between layers to a certain extent, by the injection interval and other factors can not fundamentally solve the problem, leading to the potential well area key strata or layers is difficult to determine, the layering test and slicing technology is difficult to adapt to the need of tap water control block. This paper through numerical simulation using the conceptual model and the actual block, it has a great influence on the low permeability reservoir of different stratified water permeability combination of permeability technology and application limits, profit and loss balance principle, low oil prices on the lower series of subdivision technical and economic limit, so the reservoir subdivision reorganization, narrow wells mining, reduce the interference between layers, from the maximum fundamental improvement of layered water injection efficiency. At the same time, in order to meet the needs of reservoir subdivision adjustment, subdividing distance with water, a small interlayer wells subdivision technology for further research in the pickup, solved using two ordinary bridge eccentric water regulator with injection of two layers, by throwing exercise distance limit card from the larger problem, the water distribution card size from 7.0m to 1.0m, and the testing efficiency is improved, and provide technical support for further subdivision water injection wells.

Long-term evaluation of Class II subdivision treatment with unilateral maxillary first molar extraction

NARCIS (Netherlands)

Livas, Christos; Pandis, Nikolaos; Booij, Johan Willem; Katsaros, Christos; Ren, Yijin

Objective: To evaluate the long-term effects of asymmetrical maxillary first molar (M1) extraction in Class II subdivision treatment. Materials and Methods: Records of 20 Class II subdivision whites (7 boys, 13 girls; mean age, 13.0 years; SD, 1.7 years) consecutively treated with the Begg technique

ACR BI-RADS Assessment Category 4 Subdivisions in Diagnostic Mammography: Utilization and Outcomes in the National Mammography Database.

Science.gov (United States)

Elezaby, Mai; Li, Geng; Bhargavan-Chatfield, Mythreyi; Burnside, Elizabeth S; DeMartini, Wendy B

2018-05-01

Purpose To determine the utilization and positive predictive value (PPV) of the American College of Radiology (ACR) Breast Imaging Data and Reporting System (BI-RADS) category 4 subdivisions in diagnostic mammography in the National Mammography Database (NMD). Materials and Methods This study involved retrospective review of diagnostic mammography data submitted to the NMD from January 1, 2008 to December 30, 2014. Utilization rates of BI-RADS category 4 subdivisions were compared by year, facility (type, location, census region), and examination (indication, finding type) characteristics. PPV3 (positive predictive value for biopsies performed) was calculated overall and according to category 4 subdivision. The χ 2 test was used to test for significant associations. Results Of 1 309 950 diagnostic mammograms, 125 447 (9.6%) were category 4, of which 33.3% (41 841 of 125 447) were subdivided. Subdivision utilization rates were higher (P use, subdivisions were utilized in the minority (33.3% [41 841 of 125 447]) of category 4 diagnostic mammograms, with variability based on facility and examination characteristics. When subdivisions were used, PPV3s were in BI-RADS-specified malignancy ranges. This analysis supports the use of subdivisions in broad practice and, given benefits for patient care, should motivate increased utilization. © RSNA, 2018 Online supplemental material is available for this article.

24 CFR 1710.115 - Subdivision characteristics and climate.

Science.gov (United States)

2010-04-01

... erosion, sedimentation or periodic flooding throughout the subdivision? (2) If there is a program... seeding in areas of heavy grading or cut and fill along with the construction of diversion channels, ditches, outlet channels, waterway stabilizers and sediment control basins.) (f) Nuisances. Are there any...

A Subdivision-Based Representation for Vector Image Editing.

Science.gov (United States)

Liao, Zicheng; Hoppe, Hugues; Forsyth, David; Yu, Yizhou

2012-11-01

Vector graphics has been employed in a wide variety of applications due to its scalability and editability. Editability is a high priority for artists and designers who wish to produce vector-based graphical content with user interaction. In this paper, we introduce a new vector image representation based on piecewise smooth subdivision surfaces, which is a simple, unified and flexible framework that supports a variety of operations, including shape editing, color editing, image stylization, and vector image processing. These operations effectively create novel vector graphics by reusing and altering existing image vectorization results. Because image vectorization yields an abstraction of the original raster image, controlling the level of detail of this abstraction is highly desirable. To this end, we design a feature-oriented vector image pyramid that offers multiple levels of abstraction simultaneously. Our new vector image representation can be rasterized efficiently using GPU-accelerated subdivision. Experiments indicate that our vector image representation achieves high visual quality and better supports editing operations than existing representations.

Performance improvement of haptic collision detection using subdivision surface and sphere clustering.

Directory of Open Access Journals (Sweden)

A Ram Choi

Full Text Available Haptics applications such as surgery simulations require collision detections that are more precise than others. An efficient collision detection method based on the clustering of bounding spheres was proposed in our prior study. This paper analyzes and compares the applied effects of the five most common subdivision surface methods on some 3D models for haptic collision detection. The five methods are Butterfly, Catmull-Clark, Mid-point, Loop, and LS3 (Least Squares Subdivision Surface. After performing a number of experiments, we have concluded that LS3 method is the most appropriate for haptic simulations. The more we applied surface subdivision, the more the collision detection results became precise. However, it is observed that the performance becomes better until a certain threshold and degrades afterward. In order to reduce the performance degradation, we adopted our prior work, which was the fast and precise collision detection method based on adaptive clustering. As a result, we obtained a notable improvement of the speed of collision detection.

Nanothermodynamics: a subdivision potential approach

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R. Moussavi

2005-12-01

Full Text Available  Classical thermodynamic laws and relations have been developed for macroscopic systems that satisfy the thermodynamic limit. These relations are challenged as the system size decreases to the scale of nano-systems, in which thermodynamic properties are overshadowed by system size, and the usual classical concepts of extensivity and intensivity are no longer valid. The challenges to the classical thermodynamics in relation to small systems are demonstrated, and via the approach introduced by Hill, the concept of sub-division potential is clarified in details. The fundamental thermodynamic relations are obtained using a rational-based method.

A Subdivision Method to Unify the Existing Latitude and Longitude Grids

Directory of Open Access Journals (Sweden)

Chengqi Cheng

2016-09-01

Full Text Available As research on large regions of earth progresses, many geographical subdivision grids have been established for various spatial applications by different industries and disciplines. However, there is no clear relationship between the different grids and no consistent spatial reference grid that allows for information exchange and comprehensive application. Sharing and exchange of data across departments and applications are still at a bottleneck. It would represent a significant step forward to build a new grid model that is inclusive of or compatible with most of the existing geodesic grids and that could support consolidation and exchange within existing data services. This study designs a new geographical coordinate global subdividing grid with one dimension integer coding on a 2n tree (GeoSOT that has 2n coordinate subdivision characteristics (global longitude and latitude subdivision and can form integer hierarchies at degree, minute, and second levels. This grid has the multi-dimensional quadtree hierarchical characteristics of a digital earth grid, but also provides good consistency with applied grids, such as those used in mapping, meteorology, oceanography and national geographical, and three-dimensional digital earth grids. No other existing grid codes possess these characteristics.

Stability of class II subdivision malocclusion treatment with 3 and 4 premolar extractions

OpenAIRE

Janson, Guilherme; Araki, Janine; Estelita, S?rgio; Camardella, Leonardo T

2014-01-01

Background The purpose of this study was to compare the occlusal stability of class II subdivision malocclusion treatment with 3 and 4 first premolar extractions. A sample of 156 dental casts from 52 patients with class II subdivision malocclusion was divided into two groups according to the extraction protocol. Group 1 comprised 24 patients treated with 3 premolar extractions and group 2 included 28 patients treated with 4 premolar extractions. Methods Peer assessment rating (PAR) indexes we...

Reclassification to the NCAA Division I Football Bowl Subdivision: A Case Study at Western Kentucky University

Science.gov (United States)

Upright, Paula A.

2009-01-01

The purpose of this study was to describe the reclassification process of Western Kentucky University's football program from the Football Championship Subdivision (FCS) to the Football Bowl Subdivision (FBS), the highest and most visible level of NCAA competition. Three research questions guided the study: (a) Why did Western Kentucky University…

Gender differences in functional connectivities between insular subdivisions and selective pain-related brain structures.

Science.gov (United States)

Dai, Yu-Jie; Zhang, Xin; Yang, Yang; Nan, Hai-Yan; Yu, Ying; Sun, Qian; Yan, Lin-Feng; Hu, Bo; Zhang, Jin; Qiu, Zi-Yu; Gao, Yi; Cui, Guang-Bin; Chen, Bi-Liang; Wang, Wen

2018-03-14

The incidence of pain disorders in women is higher than in men, making gender differences in pain a research focus. The human insular cortex is an important brain hub structure for pain processing and is divided into several subdivisions, serving different functions in pain perception. Here we aimed to examine the gender differences of the functional connectivities (FCs) between the twelve insular subdivisions and selected pain-related brain structures in healthy adults. Twenty-six healthy males and 11 age-matched healthy females were recruited in this cross-sectional study. FCs between the 12 insular subdivisions (as 12 regions of interest (ROIs)) and the whole brain (ROI-whole brain level) or 64 selected pain-related brain regions (64 ROIs, ROI-ROI level) were measured between the males and females. Significant gender differences in the FCs of the insular subdivisions were revealed: (1) The FCs between the dorsal dysgranular insula (dId) and other brain regions were significantly increased in males using two different techniques (ROI-whole brain and ROI-ROI analyses); (2) Based on the ROI-whole brain analysis, the FC increases in 4 FC-pairs were observed in males, including the left dId - the right median cingulate and paracingulate/ right posterior cingulate gyrus/ right precuneus, the left dId - the right median cingulate and paracingulate, the left dId - the left angular as well as the left dId - the left middle frontal gyrus; (3) According to the ROI-ROI analysis, increased FC between the left dId and the right rostral anterior cingulate cortex was investigated in males. In summary, the gender differences in the FCs of the insular subdivisions with pain-related brain regions were revealed in the current study, offering neuroimaging evidence for gender differences in pain processing. ClinicalTrials.gov, NCT02820974 . Registered 28 June 2016.

20 CFR 1002.39 - Are States (and their political subdivisions), the District of Columbia, the Commonwealth of...

Science.gov (United States)

2010-04-01

... 20 Employees' Benefits 3 2010-04-01 2010-04-01 false Are States (and their political subdivisions... REEMPLOYMENT RIGHTS ACT OF 1994 Eligibility For Reemployment Coverage of Employers and Positions § 1002.39 Are States (and their political subdivisions), the District of Columbia, the Commonwealth of Puerto Rico, and...

Afferent projections to the different medial amygdala subdivisions: a retrograde tracing study in the mouse.

Science.gov (United States)

Cádiz-Moretti, Bernardita; Otero-García, Marcos; Martínez-García, Fernando; Lanuza, Enrique

2016-03-01

The medial amygdaloid nucleus (Me) is a key node in the socio-sexual brain, composed of anterior (MeA), posteroventral (MePV) and posterodorsal (MePD) subdivisions. These subdivisions have been suggested to play a different role in reproductive and defensive behaviours. In the present work we analyse the afferents of the three Me subdivisions using restricted injections of fluorogold in female outbred CD1 mice. The results reveal that the MeA, MePV and MePD share a common pattern of afferents, with some differences in the density of retrograde labelling in several nuclei. Common afferents to Me subdivisions include: the accessory olfactory bulbs, piriform cortex and endopiriform nucleus, chemosensory amygdala (receiving direct inputs from the olfactory bulbs), posterior part of the medial bed nucleus of the stria terminalis (BSTM), CA1 in the ventral hippocampus and posterior intralaminar thalamus. Minor projections originate from the basolateral amygdala and amygdalo-hippocampal area, septum, ventral striatum, several allocortical and periallocortical areas, claustrum, several hypothalamic structures, raphe and parabrachial complex. MeA and MePV share minor inputs from the frontal cortex (medial orbital, prelimbic, infralimbic and dorsal peduncular cortices), but differ in the lack of main olfactory projections to the MePV. By contrast, the MePD receives preferential projections from the rostral accessory olfactory bulb, the posteromedial BSTM and the ventral premammillary nucleus. In summary, the common pattern of afferents to the Me subdivisions and their interconnections suggest that they play cooperative instead of differential roles in the various behaviours (e.g., sociosexual, defensive) in which the Me has been shown to be involved.

Rahvusooperi Estonia teatrihoone publikuruumide restaureerimistöödest / Liivi Künnapu

Index Scriptorium Estoniae

Künnapu, Liivi, 1953-

2006-01-01

Arhitektuuriajalooline ülevaade. 2005. a. restaureerimistöödest: garderoob-vestibüülist, peatrepist, ringfuajeedest, teatri- ja Valgest saalist, keldrikorruse ruumidest. Muinsuskaitse eritingimused, järelevalve: Liivi Künnapu. Projekteerijad: Peep Jänes, Indrek Suigussaar, AB Kolde Grupp. Sisekujundus: Juta Lember, Aulo Padar. Teostus: Koger ja Partnerid, projektijuht Indrek Võeras. Laemaali (E. Okas, E. Kits, R. Sagrits) restaureerimine, uuringud: KAR-Grupp. Akustik: Linda Madalik. Bibliogr. lk. 25. 8 vaadet

Totally odd K-4-subdivisions in 4-chromatic graphs

DEFF Research Database (Denmark)

Thomassen, Carsten

2001-01-01

We prove the conjecture made by Bjarne Toft in 1975 that every 4-chromatic graph contains a subdivision of K-4 in which each edge of K-4 corresponds to a path of odd length. As an auxiliary result we characterize completely the subspace of the cycle space generated by all cycles through two fixed...

75 FR 76038 - Zach System Corporation a Subdivision of Zambon Company, SPA Including On-Site Leased Workers of...

Science.gov (United States)

2010-12-07

... Subdivision of Zambon Company, SPA Including On-Site Leased Workers of Turner Industries and Go Johnson, La..., including on-site leased workers from Turner Industries and Go Johnson, La Porte, Texas. The Department's... investigation revealed that Zach System Corporation is a subdivision of Zambon Company, SPA, not Zach System SPA...

Influence of unilateral maxillary first molar extraction treatment on second and third molar inclination in Class II subdivision patients

NARCIS (Netherlands)

Livas, Christos; Pandis, Nikolaos; Booij, Johan Willem; Halazonetis, Demetrios J.; Katsaros, Christos; Ren, Yijin

Objective: To assess the maxillary second molar (M2) and third molar (M3) inclination following orthodontic treatment of Class II subdivision malocclusion with unilateral maxillary first molar (M1) extraction. Materials and Methods: Panoramic radiographs of 21 Class II subdivision adolescents (eight

Stability of class II subdivision malocclusion treatment with 3 and 4 premolar extractions.

Science.gov (United States)

Janson, Guilherme; Araki, Janine; Estelita, Sérgio; Camardella, Leonardo T

2014-12-30

The purpose of this study was to compare the occlusal stability of class II subdivision malocclusion treatment with 3 and 4 first premolar extractions. A sample of 156 dental casts from 52 patients with class II subdivision malocclusion was divided into two groups according to the extraction protocol. Group 1 comprised 24 patients treated with 3 premolar extractions and group 2 included 28 patients treated with 4 premolar extractions. Peer assessment rating (PAR) indexes were measured on the dental casts obtained before (T1) and after treatment (T2) and at a mean of 6.9 years after the end of treatment (T3). The groups were matching regarding sex distribution, pretreatment, posttreatment and long-term posttreatment ages, and treatment and long-term posttreatment times. They were also comparable concerning the initial malocclusion severity and the occlusal results at the end of treatment. Stability evaluation was calculated by subtracting the posttreatment from the long-term posttreatment index values (T3 - T2). T tests were used to compare the amount and percentage of long-term posttreatment changes. There were no intergroup differences regarding the amount and percentage of long-term posttreatment changes. Treatment of class II subdivision malocclusion with 3 and 4 premolar extractions have a similar long-term posttreatment occlusal stability.

45 CFR 303.52 - Pass-through of incentives to political subdivisions.

Science.gov (United States)

2010-10-01

... 45 Public Welfare 2 2010-10-01 2010-10-01 false Pass-through of incentives to political subdivisions. 303.52 Section 303.52 Public Welfare Regulations Relating to Public Welfare OFFICE OF CHILD SUPPORT ENFORCEMENT (CHILD SUPPORT ENFORCEMENT PROGRAM), ADMINISTRATION FOR CHILDREN AND FAMILIES...

Census County Subdivisions for the United States Virgin Islands (CENSUS.COUNTY_SUBDIV_USVI)

Data.gov (United States)

U.S. Environmental Protection Agency — County subdivisions are the primary divisions of counties and statistically equivalent entities for the reporting of decennial census data. They include census...

Land Subdivision in Peri-Urban Areas of Sub-Saharan African Cities ...

African Journals Online (AJOL)

USER

The review of literature on urban land subdivision provides us with useful ... The second section is the methodology detailing the literature review approach ... problem of shortages of urban land, and to increase access to land for the ..... gradual integration of the informal sector into political decision-making process and.

Analysis and Research on Several Global Subdivision Grids

Directory of Open Access Journals (Sweden)

SONG Shuhua

2016-12-01

Full Text Available In order to solve the problem that lacking of an unified organization frame about global remote sensing satellite image data, this paper introduces serval global subdivision grids as the unified organization frame for remote sensing image. Based on the characteristics of remote sensing image data, this paper analyzes and summarizes the design principles and difficulties of the organization frame. Based on analysis and comparison with these grids, GeoSOT is more suitable as the unified organization frame for remote sensing image. To provide a reference for the global remote sensing image organization.

Brainstem projections of neurons located in various subdivisions of the dorsolateral hypothalamic area—an anterograde tract-tracing study

OpenAIRE

Papp, Rege S.; Palkovits, Miklós

2014-01-01

The projections from the dorsolateral hypothalamic area (DLH) to the lower brainstem have been investigated by using biotinylated dextran amine (BDA), an anterograde tracer in rats. The DLH can be divided into 3 areas (dorsomedial hypothalamus, perifornical area, lateral hypothalamic area), and further subdivided into 8 subdivisions. After unilateral stereotaxic injections of BDA into individual DLH subdivisions, the correct sites of injections were controlled histologically, and the distribu...

TIGER/Line Shapefile, 2015, Series Information for the Current County Subdivision State-based Shapefiles

Data.gov (United States)

US Census Bureau, Department of Commerce — County subdivisions are the primary divisions of counties and their equivalent entities for the reporting of Census Bureau data. They include legally-recognized...

Spinning geometry = Twisted geometry

International Nuclear Information System (INIS)

Freidel, Laurent; Ziprick, Jonathan

2014-01-01

It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)

Brainstem projections of neurons located in various subdivisions of the dorsolateral hypothalamic area – an anterograde tract-tracing study

OpenAIRE

Rege Sugárka Papp; Rege Sugárka Papp; Miklos ePalkovits; Miklos ePalkovits

2014-01-01

The projections from the dorsolateral hypothalamic area (DLH) to the lower brainstem have been investigated by using biotinylated dextran amine (BDA), an anterograde tracer in rats. The DLH can be divided into 3 areas (dorsomedial hypothalamus, perifornical area, lateral hypothalamic area), and further subdivided into 8 subdivisions. After unilateral stereotaxic injections of BDA into individual DLH subdivisions, the correct sites of injections were controlled histologically, and the distribu...

Subdivisions of the adult zebrafish pallium based on molecular marker analysis [version 2; referees: 2 approved, 1 approved with reservations

Directory of Open Access Journals (Sweden)

Julia Ganz

2015-11-01

Full Text Available Background: The telencephalon shows a remarkable structural diversity among vertebrates. In particular, the everted telencephalon of ray-finned fishes has a markedly different morphology compared to the evaginated telencephalon of all other vertebrates. This difference in development has hampered the comparison between different areas of the pallium of ray-finned fishes and the pallial nuclei of all other vertebrates. Various models of homology between pallial subdivisions in ray-finned fishes and the pallial nuclei in tetrapods have been proposed based on connectional, neurochemical, gene expression and functional data. However, no consensus has been reached so far. In recent years, the analysis of conserved developmental marker genes has assisted the identification of homologies for different parts of the telencephalon among several tetrapod species. Results: We have investigated the gene expression pattern of conserved marker genes in the adult zebrafish (Danio rerio pallium to identify pallial subdivisions and their homology to pallial nuclei in tetrapods. Combinatorial expression analysis of ascl1a, eomesa, emx1, emx2, emx3, and Prox1 identifies four main divisions in the adult zebrafish pallium. Within these subdivisions, we propose that Dm is homologous to the pallial amygdala in tetrapods and that the dorsal subdivision of Dl is homologous to part of the hippocampal formation in mouse. We have complemented this analysis be examining the gene expression of emx1, emx2 and emx3 in the zebrafish larval brain. Conclusions: Based on our gene expression data, we propose a new model of subdivisions in the adult zebrafish pallium and their putative homologies to pallial nuclei in tetrapods. Pallial nuclei control sensory, motor, and cognitive functions, like memory, learning and emotion. The identification of pallial subdivisions in the adult zebrafish and their homologies to pallial nuclei in tetrapods will contribute to the use of the zebrafish

Subdivision, Sampling, and Initialization Strategies for Simplical Branch and Bound in Global Optimization

DEFF Research Database (Denmark)

Clausen, Jens; Zilinskas, A,

2002-01-01

We consider the problem of optimizing a Lipshitzian function. The branch and bound technique is a well-known solution method, and the key components for this are the subdivision scheme, the bound calculation scheme, and the initialization. For Lipschitzian optimization, the bound calculations are...

TIGER/Line Shapefile, 2014, Series Information File for the Current County Subdivision State-based Shapefile

Data.gov (United States)

US Census Bureau, Department of Commerce — County subdivisions are the primary divisions of counties and their equivalent entities for the reporting of Census Bureau data. They include legally-recognized...

Architectonic subdivisions of neocortex in the tree shrew (Tupaia belangeri)

OpenAIRE

Wong, Peiyan; Kaas, Jon H.

2009-01-01

Tree shrews are small mammals that bear some semblance to squirrels, but are actually close relatives of primates. Thus, they have been extensively studied as a model for the early stages of primate evolution. In the present study, subdivisions of cortex were reconstructed from brain sections cut in the coronal, sagittal or horizontal planes, and processed for parvalbumin (PV), SMI-32 immunopositive neurofilament protein epitopes, vesicle glutamate transporter 2 (VGluT2), free ionic zinc, mye...

Brainstem projections of neurons located in various subdivisions of the dorsolateral hypothalamic area – an anterograde tract-tracing study

Directory of Open Access Journals (Sweden)

Rege Sugárka Papp

2014-05-01

Full Text Available The projections from the dorsolateral hypothalamic area (DLH to the lower brainstem have been investigated by using biotinylated dextran amine (BDA, an anterograde tracer in rats. The DLH can be divided into 3 areas (dorsomedial hypothalamus, perifornical area, lateral hypothalamic area, and further subdivided into 8 subdivisions. After unilateral stereotaxic injections of BDA into individual DLH subdivisions, the correct sites of injections were controlled histologically, and the distribution patterns of BDA-positive fibers were mapped on serial sections between the hypothalamus and spinal cord in 22 rats. BDA-labeled fibers were observable over 100 different brainstem areas, nuclei or subdivisions. Injections into the 8 DLH subdivisions established distinct topographical patterns. In general, the density of labeled fibers was low in the lower brainstem. High density of fibers was seen only 4 of the 116 areas: in the lateral and ventrolateral parts of the periaqueductal gray, the Barrington’s and the pedunculopontine tegmental nuclei. All of the biogenic amine cell groups in the lower brainstem (9 noradrenaline, 3 adrenaline and 9 serotonin cell groups received labeled fibers, some of them from all, or at least 7 DLH subdivisions, mainly from perifornical and ventral lateral hypothalamic neurons. Some of the tegmental nuclei and nuclei of the reticular formation were widely innervated, although the density of the BDA-labeled fibers was generally low. No definitive descending BDA-positive pathway, but long-run solitaire BDA-labeled fibers were seen in the lower brainstem. These descending fibers joined some of the large tracts or fasciculi in the brainstem. The distribution pattern of BDA-positive fibers of DLH origin throughout the lower brainstem was comparable to patterns of previously published orexin- or melanin-concentrating hormone-immunoreactive fibers with somewhat differences.

A New Subdivision Of The Rat Midbrain Periaqueductal Gray Based On Its Myeloarchitecture.

NARCIS (Netherlands)

Holstege, G.; Gerrits, P.O.; Croon, D.H.

1993-01-01

A new subdivision of the periaqueductal gray (PAG) based on its myelin content is described. Using a methacrylate-resin embedding technique for high resolution light microscopy, a myeloarchitectonic map of the normal rat PAG was made. Six main columns were distinguished. Column I is the central thin

Investigating the mixture and subdivision of perceptual and conceptual processing in Japanese memory tests.

Science.gov (United States)

Gabeza, R

1995-03-01

The dual nature of the Japanese writing system was used to investigate two assumptions of the processing view of memory transfer: (1) that both perceptual and conceptual processing can contribute to the same memory test (mixture assumption) and (2) that both can be broken into more specific processes (subdivision assumption). Supporting the mixture assumption, a word fragment completion test based on ideographic kanji characters (kanji fragment completion test) was affected by both perceptual (hiragana/kanji script shift) and conceptual (levels-of-processing) study manipulations kanji fragments, because it did not occur with the use of meaningless hiragana fragments. The mixture assumption is also supported by an effect of study script on an implicit conceptual test (sentence completion), and the subdivision assumption is supported by a crossover dissociation between hiragana and kanji fragment completion as a function of study script.

Investigation of grain subdivision at very low plastic strains in a magnesium alloy

Energy Technology Data Exchange (ETDEWEB)

Hong, X. [Key Laboratory of Advanced Materials (MOE), School of Materials Science and Engineering, Tsinghua University, Beijing 100084 (China); Godfrey, A., E-mail: awgodfrey@mail.tsinghua.edu.cn [Key Laboratory of Advanced Materials (MOE), School of Materials Science and Engineering, Tsinghua University, Beijing 100084 (China); Zhang, C.L.; Liu, W. [Key Laboratory of Advanced Materials (MOE), School of Materials Science and Engineering, Tsinghua University, Beijing 100084 (China); Chapuis, A. [College of Materials Science and Engineering, Chongqing University, Chongqing 400044 (China)

2017-05-02

In-situ tensile loading combined with electron backscatter diffraction (EBSD) measurements has been used to investigate the plastic deformation of a magnesium alloy. A novel EBSD mapping is presented, based on construction of maps showing the rotation axis component in the sample coordinate frame of the misorientation from each pixel to the average grain orientation in the deformed sample. Using this mapping it is shown that the pattern of grain subdivision, even at very low plastic strains, can be revealed simultaneously in a large number of grains. In addition, it is demonstrated how maps of the rotation axis corresponding to the misorientation between each pixel and the initial grain orientation provide complimentary information directly useful for crystal plasticity analysis. A detailed slip system analysis shows that the grain subdivision can be accounted for according to the low energy dislocation structures (LEDS) model of work-hardening by differences in the slip amplitudes within different parts of each grain.

A global solution of the ICRH problem based on the combined use of a planar coupling model and hot-plasma ray-tracing in tokamak geometry

International Nuclear Information System (INIS)

Koch, R.; Bhatnagar, V.P.; Messiaen, A.M.; Eester, D. van

1986-01-01

The global solution of the theoretical problem of Ion Cyclotron Resonance Heating in tokamak plasmas is obtained by a subdivision of the problem into two simpler ones by virtue of the ''single pass absorption'' hypothesis. The coupling problem is solved in planar geometry, allowing computation of both the antenna electrical properties and the Radio-Frequency (RF) field distribution in the plasma facing the antenna. Starting from this field distribution, the initial conditions for ray-tracing are derived and the propagation and absorption of waves in the plasma bulk is solved in the geometric optics limit taking into account the full tokamak geometry and the kinetic wave description. In the minority heating, redistribution of the minority absorbed power to the other species is carred out using standard quasilinear theory. (orig.)

General Geometry and Geometry of Electromagnetism

OpenAIRE

Shahverdiyev, Shervgi S.

2002-01-01

It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...

[Genetic structure, subdivision, and population differentiation in Stankewiczii pine Pinus stankewiczii (Sukacz.) Fomin from Mountain Crimea].

Science.gov (United States)

Korshikov, I I; Gorlova, E M

2006-06-01

In order to analyze the genetic structure, subdivision and differentiation within and between two small isolated populations of the Crimea relict endemic, Pinus stankewiczii (Sukacz.) Fomin, electrophoretic analysis of the isozyme variation at nine enzymatic systems was carried out using 183 oldest trees. It was demonstrated that in populations of P. stankewiczii, 80% of the genes were in polymorphic state. Each tree was heterozygous at 19.1% loci, and at 21.6% loci in artificial 50-year-old plantation. The genetic structure of two populations was less differentiated (DN = 0.006), compared to their individual localities (DN = 0.008-0.009). Within-population subdivision of the diffusely dispersed populations was higher (FST-GST = 1.8-2.0%) than that of the populations themselves (0.8%).

Using subdivision surfaces and adaptive surface simplification algorithms for modeling chemical heterogeneities in geophysical flows

Science.gov (United States)

Schmalzl, JöRg; Loddoch, Alexander

2003-09-01

We present a new method for investigating the transport of an active chemical component in a convective flow. We apply a three-dimensional front tracking method using a triangular mesh. For the refinement of the mesh we use subdivision surfaces which have been developed over the last decade primarily in the field of computer graphics. We present two different subdivision schemes and discuss their applicability to problems related to fluid dynamics. For adaptive refinement we propose a weight function based on the length of triangle edge and the sum of the angles of the triangle formed with neighboring triangles. In order to remove excess triangles we apply an adaptive surface simplification method based on quadric error metrics. We test these schemes by advecting a blob of passive material in a steady state flow in which the total volume is well preserved over a long time. Since for time-dependent flows the number of triangles may increase exponentially in time we propose the use of a subdivision scheme with diffusive properties in order to remove the small scale features of the chemical field. By doing so we are able to follow the evolution of a heavy chemical component in a vigorously convecting field. This calculation is aimed at the fate of a heavy layer at the Earth's core-mantle boundary. Since the viscosity variation with temperature is of key importance we also present a calculation with a strongly temperature-dependent viscosity.

Manûtu ša Bābili = the Babylonian subdivision of the mina

NARCIS (Netherlands)

van der Spek, R.J.

A new interpretation of the term Manûtu ša Bābili is presented here. It is not the exchange rate between shekels and drachmas, as was generally assumed, but it is the Babylonian subdivision ("counting") of the mina as opposed to the Greek mina. A Babylonian mina counts 30 staters, a Greek mina 25

Theatre for Change: An Analysis of Two Performances by Women in Mundemba Sub-Division.

Science.gov (United States)

Tanyi-Tang, Anne

2001-01-01

Contends that theatre has the power to induce oppressors to change their attitudes permanently towards the groups they oppress. Describes theatrical performances by women in Mundemba Sub-Division, Cameroon, which created lasting changes in men's attitudes. Concludes that theatre calls for sociocultural and economic changes and it has the power to…

Augmenting Sand Simulation Environments through Subdivision and Particle Refinement

Science.gov (United States)

Clothier, M.; Bailey, M.

2012-12-01

Recent advances in computer graphics and parallel processing hardware have provided disciplines with new methods to evaluate and visualize data. These advances have proven useful for earth and planetary scientists as many researchers are using this hardware to process large amounts of data for analysis. As such, this has provided opportunities for collaboration between computer graphics and the earth sciences. Through collaboration with the Oregon Space Grant and IGERT Ecosystem Informatics programs, we are investigating techniques for simulating the behavior of sand. We are also collaborating with the Jet Propulsion Laboratory's (JPL) DARTS Lab to exchange ideas and gain feedback on our research. The DARTS Lab specializes in simulation of planetary vehicles, such as the Mars rovers. Their simulations utilize a virtual "sand box" to test how a planetary vehicle responds to different environments. Our research builds upon this idea to create a sand simulation framework so that planetary environments, such as the harsh, sandy regions on Mars, are more fully realized. More specifically, we are focusing our research on the interaction between a planetary vehicle, such as a rover, and the sand beneath it, providing further insight into its performance. Unfortunately, this can be a computationally complex problem, especially if trying to represent the enormous quantities of sand particles interacting with each other. However, through the use of high-performance computing, we have developed a technique to subdivide areas of actively participating sand regions across a large landscape. Similar to a Level of Detail (LOD) technique, we only subdivide regions of a landscape where sand particles are actively participating with another object. While the sand is within this subdivision window and moves closer to the surface of the interacting object, the sand region subdivides into smaller regions until individual sand particles are left at the surface. As an example, let's say

The extent of population genetic subdivision differs among four co-distributed shark species in the Indo-Australian archipelago

Directory of Open Access Journals (Sweden)

Giles Jenny

2009-02-01

Full Text Available Abstract Background The territorial fishing zones of Australia and Indonesia are contiguous to the north of Australia in the Timor and Arafura Seas and in the Indian Ocean to the north of Christmas Island. The area surrounding the shared boundary consists of a variety of bio-diverse marine habitats including shallow continental shelf waters, oceanic trenches and numerous offshore islands. Both countries exploit a variety of fisheries species, including whaler (Carcharhinus spp. and hammerhead sharks (Sphyrna spp.. Despite their differences in social and financial arrangements, the two countries are motivated to develop complementary co-management practices to achieve resource sustainability. An essential starting point is knowledge of the degree of population subdivision, and hence fisheries stock status, in exploited species. Results Populations of four commercially harvested shark species (Carcharhinus obscurus, Carcharhinus sorrah, Prionace glauca, Sphyrna lewini were sampled from northern Australia and central Indonesia. Neutral genetic markers (mitochondrial DNA control region sequence and allelic variation at co-dominant microsatellite loci revealed genetic subdivision between Australian and Indonesian populations of C. sorrah. Further research is needed to address the possibility of genetic subdivision among C. obscurus populations. There was no evidence of genetic subdivision for P. glauca and S. lewini populations, but the sampling represented a relatively small part of their distributional range. For these species, more detailed analyses of population genetic structure is recommended in the future. Conclusion Cooperative management between Australia and Indonesia is the best option at present for P. glauca and S. lewini, while C. sorrah and C. obscurus should be managed independently. On-going research on these and other exploited shark and ray species is strongly recommended. Biological and ecological similarity between species may

High performance ultrasonic field simulation on complex geometries

Science.gov (United States)

Chouh, H.; Rougeron, G.; Chatillon, S.; Iehl, J. C.; Farrugia, J. P.; Ostromoukhov, V.

2016-02-01

Ultrasonic field simulation is a key ingredient for the design of new testing methods as well as a crucial step for NDT inspection simulation. As presented in a previous paper [1], CEA-LIST has worked on the acceleration of these simulations focusing on simple geometries (planar interfaces, isotropic materials). In this context, significant accelerations were achieved on multicore processors and GPUs (Graphics Processing Units), bringing the execution time of realistic computations in the 0.1 s range. In this paper, we present recent works that aim at similar performances on a wider range of configurations. We adapted the physical model used by the CIVA platform to design and implement a new algorithm providing a fast ultrasonic field simulation that yields nearly interactive results for complex cases. The improvements over the CIVA pencil-tracing method include adaptive strategies for pencil subdivisions to achieve a good refinement of the sensor geometry while keeping a reasonable number of ray-tracing operations. Also, interpolation of the times of flight was used to avoid time consuming computations in the impulse response reconstruction stage. To achieve the best performance, our algorithm runs on multi-core superscalar CPUs and uses high performance specialized libraries such as Intel Embree for ray-tracing, Intel MKL for signal processing and Intel TBB for parallelization. We validated the simulation results by comparing them to the ones produced by CIVA on identical test configurations including mono-element and multiple-element transducers, homogeneous, meshed 3D CAD specimens, isotropic and anisotropic materials and wave paths that can involve several interactions with interfaces. We show performance results on complete simulations that achieve computation times in the 1s range.

Geometries

CERN Document Server

Sossinsky, A B

2012-01-01

The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...

Multiple approaches to valuation of conservation design and low-impact development features in residential subdivisions.

Science.gov (United States)

Bowman, Troy; Tyndall, John C; Thompson, Janette; Kliebenstein, James; Colletti, Joe P

2012-08-15

Residents, developers and civic officials are often faced with difficult decisions about appropriate land uses in and around metropolitan boundaries. Urban expansion brings with it the potential for negative environmental impacts, but there are alternatives, such as conservation subdivision design (CSD) or low-impact development (LID), which offer the possibility of mitigating some of these effects at the development site. Many urban planning jurisdictions across the Midwest do not currently have any examples of these designs and lack information to identify public support or barriers to use of these methods. This is a case study examining consumer value for conservation and low-impact design features in one housing market by using four different valuation techniques to estimate residents' willingness to pay for CSD and LID features in residential subdivisions. A contingent valuation survey of 1804 residents in Ames, IA assessed familiarity with and perceptions of subdivision development and used an ordered value approach to estimate willingness to pay for CSD and LID features. A majority of residents were not familiar with CSD or LID practices. Residents indicated a willingness to pay for most CSD and LID features with the exception of clustered housing. Gender, age, income, familiarity with LID practices, perceptions of attractiveness of features and the perceived effect of CSD and LID features on ease of future home sales were important factors influencing residents' willingness to pay. A hypothetical referendum measured willingness to pay for tax-funded conservation land purchases and estimated that a property tax of around $50 would be the maximum increase that would pass. Twenty-seven survey respondents participated in a subsequent series of experimental real estate negotiations that used an experimental auction mechanism to estimate willingness to pay for CSD and LID features. Participants indicated that clustered housing (with interspersed preserved forest

Does Becoming a Member of the Football Bowl Subdivision Increase Institutional Attractiveness to Potential Students

Science.gov (United States)

Jones, Willis A.

2014-01-01

In recent years, a number of colleges and universities have made the decision to pursue membership in the NCAA's Football Bowl Subdivision (FBS) with the idea that participating in higher profile intercollegiate football can help attract students to their institution. This belief, however, has not been empirically examined. Using…

Simulating Sand Behavior through Terrain Subdivision and Particle Refinement

Science.gov (United States)

Clothier, M.

2013-12-01

Advances in computer graphics, GPUs, and parallel processing hardware have provided researchers with new methods to visualize scientific data. In fact, these advances have spurred new research opportunities between computer graphics and other disciplines, such as Earth sciences. Through collaboration, Earth and planetary scientists have benefited by using these advances in hardware technology to process large amounts of data for visualization and analysis. At Oregon State University, we are collaborating with the Oregon Space Grant and IGERT Ecosystem Informatics programs to investigate techniques for simulating the behavior of sand. In addition, we have also been collaborating with the Jet Propulsion Laboratory's DARTS Lab to exchange ideas on our research. The DARTS Lab specializes in the simulation of planetary vehicles, such as the Mars rovers. One aspect of their work is testing these vehicles in a virtual "sand box" to test their performance in different environments. Our research builds upon this idea to create a sand simulation framework to allow for more complex and diverse environments. As a basis for our framework, we have focused on planetary environments, such as the harsh, sandy regions on Mars. To evaluate our framework, we have used simulated planetary vehicles, such as a rover, to gain insight into the performance and interaction between the surface sand and the vehicle. Unfortunately, simulating the vast number of individual sand particles and their interaction with each other has been a computationally complex problem in the past. However, through the use of high-performance computing, we have developed a technique to subdivide physically active terrain regions across a large landscape. To achieve this, we only subdivide terrain regions where sand particles are actively participating with another object or force, such as a rover wheel. This is similar to a Level of Detail (LOD) technique, except that the density of subdivisions are determined by

Geometry

CERN Document Server

Prasolov, V V

2015-01-01

This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

Guide for subdivision of spent fuel pool. Project UNESA MAAP5-SFP; Guia para subdivision de la piscina de combustible gastado. Proyecto UNESA MAAP5-SFP

Energy Technology Data Exchange (ETDEWEB)

Martinez Barrios, M.; Garcia Gonzalez, M.; Perez Martin, F. J.

2013-07-01

The main goal of the UNESA MAAP5-SFP project is to analyze the capabilities of MAAP5 code and, particularly, the Spent Fuel Pool (SFP) module in order to tackle its modeling and facilitate the development of specific SFP models of Spanish NPPs. Within the project, Empresarios Agrupados (EEAA) is the responsible for the development of the Guide for the subdivision of the Spent Fuel Pool (SFP). This Guide includes a theoretical description of the model that is used by the code and a sequence of practical cases with the aim to evaluate the influence of specific parameters.

75 FR 57327 - GNP Rly, Inc.-Acquisition and Operation Exemption-Redmond Spur and Woodinville Subdivision

Science.gov (United States)

2010-09-20

... subdivision of the State of Washington. The Port of Seattle (Port) owns the real estate associated with the... provisions of 49 U.S.C. 10902 to acquire and resume rail service over 2 segments of railbanked railroad right... acquire the ``residual common carrier rights and obligations,'' including the right to reinstate rail...

A filled duration illusion in music: Effects of metrical subdivision on the perception and production of beat tempo.

Science.gov (United States)

Repp, Bruno H; Bruttomesso, Meijin

2010-01-13

This study replicates and extends previous findings suggesting that metrical subdivision slows the perceived beat tempo (Repp, 2008). Here, musically trained participants produced the subdivisions themselves and were found to speed up, thus compensating for the perceived slowing. This was shown in a synchronization-continuation paradigm (Experiment 1) and in a reproduction task (Experiment 2a). Participants also judged the tempo of a subdivided sequence as being slower than that of a preceding simple beat sequence (Experiment 2b). Experiment 2 also included nonmusician participants, with similar results. Tempo measurements of famous pianists' recordings of two variation movements from Beethoven sonatas revealed a strong tendency to play the first variation (subdivided beats) faster than the theme (mostly simple beats). A similar tendency was found in musicians' laboratory performances of a simple theme and variations, despite instruc-tions to keep the tempo constant (Experiment 3a). When playing melodic sequences in which only one of three beats per measure was subdivided, musicians tended to play these beats faster and to perceive them as longer than adjacent beats, and they played the whole sequence faster than a sequence without any subdivisions (Experiments 3b and 3c). The results amply demonstrate a filled duration illusion in rhythm perception and music performance: Intervals containing events seem longer than empty intervals and thus must be shortened to be perceived as equal in duration.

RESEARCH OF APPROACHES TO INCREASE THE EFFICIENCY OF FUNCTIONING OF RAILWAY TRANSPORT SUBDIVISIONS FROM THE POINT OF VIEW OF SUSTAINABLE DEVELOPMENT

Directory of Open Access Journals (Sweden)

O. I. Kharchenko

2014-07-01

Full Text Available Purpose. Modern transport systems are not stable and can not stand up to the destabilizing factors. Global track record in the economic and commercial management systems is the use of the concept of sustainable development. It is necessary on the basis of analysis of literary sources to define the directions of efficiency increase of functioning of railway transport subdivisions from the point of view of sustainable development. Methodology. To achieve the purpose the features of the use of sustainable development conception and its realization were investigated at a management of the complex systems. The existent models were also analyzed in the field of efficiency increase of functioning of railway transport subdivisions. Findings. On the basis of literary sources analysis, keeping up the conceptual essence of the sustainable development, the main directions of efficiency increase of subdivisions functioning were selected. They take into account the basic requirements of steady development and should be considered as a complex. Originality. New directions to consider the efficiency increase issues from position of sustainable development were offered by the author. Three components of conceptions of sustainable development (economic, ecological and social should be examined in a balanced way. Thus, the above mentioned theoretical studies can promote the forming of new economy model corresponding to the purposes and principles of sustainable development. Practical value. The conducted analysis development confirms the necessity of researches on perspective directions of development of railway transport subdivisions, which are marked by the guidance of Ukrzaliznytsia. It enables to select basic directions for further research in the area of efficiency increase.

Functional Subdivision of Group-ICA Results of fMRI Data Collected during Cinema Viewing

Science.gov (United States)

Pamilo, Siina; Malinen, Sanna; Hlushchuk, Yevhen; Seppä, Mika; Tikka, Pia; Hari, Riitta

2012-01-01

Independent component analysis (ICA) can unravel functional brain networks from functional magnetic resonance imaging (fMRI) data. The number of the estimated components affects both the spatial pattern of the identified networks and their time-course estimates. Here group-ICA was applied at four dimensionalities (10, 20, 40, and 58 components) to fMRI data collected from 15 subjects who viewed a 15-min silent film (“At land” by Maya Deren). We focused on the dorsal attention network, the default-mode network, and the sensorimotor network. The lowest dimensionalities demonstrated most prominent activity within the dorsal attention network, combined with the visual areas, and in the default-mode network; the sensorimotor network only appeared with ICA comprising at least 20 components. The results suggest that even very low-dimensional ICA can unravel the most prominent functionally-connected brain networks. However, increasing the number of components gives a more detailed picture and functionally feasible subdivision of the major networks. These results improve our understanding of the hierarchical subdivision of brain networks during viewing of a movie that provides continuous stimulation embedded in an attention-directing narrative. PMID:22860044

Functional subdivision of group-ICA results of fMRI data collected during cinema viewing.

Directory of Open Access Journals (Sweden)

Siina Pamilo

Full Text Available Independent component analysis (ICA can unravel functional brain networks from functional magnetic resonance imaging (fMRI data. The number of the estimated components affects both the spatial pattern of the identified networks and their time-course estimates. Here group-ICA was applied at four dimensionalities (10, 20, 40, and 58 components to fMRI data collected from 15 subjects who viewed a 15-min silent film ("At land" by Maya Deren. We focused on the dorsal attention network, the default-mode network, and the sensorimotor network. The lowest dimensionalities demonstrated most prominent activity within the dorsal attention network, combined with the visual areas, and in the default-mode network; the sensorimotor network only appeared with ICA comprising at least 20 components. The results suggest that even very low-dimensional ICA can unravel the most prominent functionally-connected brain networks. However, increasing the number of components gives a more detailed picture and functionally feasible subdivision of the major networks. These results improve our understanding of the hierarchical subdivision of brain networks during viewing of a movie that provides continuous stimulation embedded in an attention-directing narrative.

Functional subdivision of group-ICA results of fMRI data collected during cinema viewing.

Science.gov (United States)

Pamilo, Siina; Malinen, Sanna; Hlushchuk, Yevhen; Seppä, Mika; Tikka, Pia; Hari, Riitta

2012-01-01

Independent component analysis (ICA) can unravel functional brain networks from functional magnetic resonance imaging (fMRI) data. The number of the estimated components affects both the spatial pattern of the identified networks and their time-course estimates. Here group-ICA was applied at four dimensionalities (10, 20, 40, and 58 components) to fMRI data collected from 15 subjects who viewed a 15-min silent film ("At land" by Maya Deren). We focused on the dorsal attention network, the default-mode network, and the sensorimotor network. The lowest dimensionalities demonstrated most prominent activity within the dorsal attention network, combined with the visual areas, and in the default-mode network; the sensorimotor network only appeared with ICA comprising at least 20 components. The results suggest that even very low-dimensional ICA can unravel the most prominent functionally-connected brain networks. However, increasing the number of components gives a more detailed picture and functionally feasible subdivision of the major networks. These results improve our understanding of the hierarchical subdivision of brain networks during viewing of a movie that provides continuous stimulation embedded in an attention-directing narrative.

Organization of development of plans of a production association and participation of enterprises and their subdivisions

Energy Technology Data Exchange (ETDEWEB)

Gubenko, I V

1982-01-01

Experimental development of plans with participation of enterprises and their subdivisions is presented. The method of determining the intensity of the plans of the drilling enterprises is revealed. Data are presented on the use of a computer to develop a technical-industrial financial plan of the enterprise and association.

Extension of the analytic nodal diffusion solver ANDES to triangular-Z geometry and coupling with COBRA-IIIc for hexagonal core analysis

International Nuclear Information System (INIS)

Lozano, Juan-Andres; Jimenez, Javier; Garcia-Herranz, Nuria; Aragones, Jose-Maria

2010-01-01

In this paper the extension of the multigroup nodal diffusion code ANDES, based on the Analytic Coarse Mesh Finite Difference (ACMFD) method, from Cartesian to hexagonal geometry is presented, as well as its coupling with the thermal-hydraulic (TH) code COBRA-IIIc for hexagonal core analysis. In extending the ACMFD method to hexagonal assemblies, triangular-Z nodes are used. In the radial plane, a direct transverse integration procedure is applied along the three directions that are orthogonal to the triangle interfaces. The triangular nodalization avoids the singularities, that appear when applying transverse integration to hexagonal nodes, and allows the advantage of the mesh subdivision capabilities implicit within that geometry. As for the thermal-hydraulics, the extension of the coupling scheme to hexagonal geometry has been performed with the capability to model the core using either assembly-wise channels (hexagonal mesh) or a higher refinement with six channels per fuel assembly (triangular mesh). Achieving this level of TH mesh refinement with COBRA-IIIc code provides a better estimation of the in-core 3D flow distribution, improving the TH core modelling. The neutronics and thermal-hydraulics coupled code, ANDES/COBRA-IIIc, previously verified in Cartesian geometry core analysis, can also be applied now to full three-dimensional VVER core problems, as well as to other thermal and fast hexagonal core designs. Verification results are provided, corresponding to the different cases of the OECD/NEA-NSC VVER-1000 Coolant Transient Benchmarks.

Both Isochronous and Non-Isochronous Metrical Subdivision Afford Precise and Stable Ensemble Entrainment: A Corpus Study of Malian Jembe Drumming.

Science.gov (United States)

Polak, Rainer; London, Justin; Jacoby, Nori

2016-01-01

Most approaches to musical rhythm, whether in music theory, music psychology, or musical neuroscience, presume that musical rhythms are based on isochronous (temporally equidistant) beats and/or beat subdivisions. However, rhythms that are based on non-isochronous, or unequal patterns of time are prominent in the music of Southeast Europe, the Near East and Southern Asia, and in the music of Africa and the African diaspora. The present study examines one such style found in contemporary Malian jembe percussion music. A corpus of 15 representative performances of three different pieces ("Manjanin," "Maraka," and "Woloso") containing ~43,000 data points was analyzed. Manjanin and Woloso are characterized by non-isochronous beat subdivisions (a short IOI followed by two longer IOIs), while Maraka subdivisions are quasi-isochronous. Analyses of onsets and asynchronies show no significant differences in timing precision and coordination between the isochronously timed Maraka vs. the non-isochronously timed Woloso performances, though both pieces were slightly less variable than non-isochronous Manjanin. Thus, the precision and stability of rhythm and entrainment in human music does not necessarily depend on metric isochrony, consistent with the hypothesis that isochrony is not a biologically-based constraint on human rhythmic behavior. Rather, it may represent a historically popular option within a variety of culturally contingent options for metric organization.

Modelling research on determining shape coefficients for subdivision interpretation in γ-ray spectral logging

International Nuclear Information System (INIS)

Yin Wangming; She Guanjun; Tang Bin

2011-01-01

This paper first describes the physical meaning of the shape coefficients in the subdivision interpretation of γ-ray logging; then discusses the theory, method to determine the practical shape coefficients with logging model and defines the formula to approximately calculate the coefficients. A great deal of experimental work has been preformed with a HPGe γ-ray spectrometer and reached satisfied result which has validated the effeciency of the modelling method. (authors)

Geologic and geotechnical investigation of the Windsor Park subdivision North Las Vegas, Nevada

International Nuclear Information System (INIS)

Linnert, L.M.; Werle, J.L.; Stilley, A.N.; Olsen, B.L.

1994-01-01

The Windsor Park subdivision in North Las Vegas, Nevada has received widespread attention for damage to the homes and infrastructure from fissures, land subsidence and adverse soil conditions. Between March and July, 1992, Converse Consultants Southwest, Inc. conducted a geologic and geotechnical investigation for the Windsor Park Revitalization Project. The purpose of the work was to investigate the probable factors contributing to the reported damage and distress in the area, evaluate the potential for future damage, and assess the feasibility of possible mitigation and repair. The site is constructed on the juncture of at least two subsidence-related fault scarps, and earth fissures have been extensively mapped in the Windsor Park and surrounding area. A total of twenty-one trenches and fifteen borings were located within the subdivision and around the perimeter to observe subsurface geologic features and to collect samples for laboratory testing. The primary causes of damage within the development were found to be (1) earth fissuring and (2) expansive clays. The risk of future damage to structures at the Windsor Park site was also evaluated. A high potential for fissuring was found at the site, and future structural distress in the area will likely be similar to past damage. Although engineering upgrades will reduce the risk posed by underlying expansive clays, they cannot totally eliminate the risk from fissuring. 10 refs., 8 figs., 1 tab

The Role of Quench-back in the Passive Quench Protection of Long Solenoids with Coil Sub-division

International Nuclear Information System (INIS)

Green, Michael A.; Guo, XingLong; Wang, Li; Pan, Heng; Wu, Hong

2009-01-01

This paper describes how a passive quench protection system can be applied to long superconducting solenoid magnets. When a solenoid coil is long compared to its thickness, the magnet quench process will be dominated by the time needed for uench propagation along the magnet length. Quench-back will permit a long magnet to quench more rapidly in a passive way. Quenchback from a conductive (low resistivity) mandrel is essential for spreading the quench along the length of a magnet. The andrel must be inductively coupled to the magnet circuit that is being quenched. Current induced in the mandrel by di/dt in the magnet produces heat in the mandrel, which in turn causes the superconducting coil wound on the mandrel to quench. Sub-divisions often employed to reduce the voltages to ground within the coil. This paper explores when it is possible for quench-back to be employed for passive quench protection. The role of sub-division of the coil is discussed for long magnets.

Optical geometry

International Nuclear Information System (INIS)

Robinson, I.; Trautman, A.

1988-01-01

The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem

The spatial scale of genetic subdivision in populations of Ifremeria nautilei, a hydrothermal-vent gastropod from the southwest Pacific

Directory of Open Access Journals (Sweden)

Thaler Andrew D

2011-12-01

Full Text Available Abstract Background Deep-sea hydrothermal vents provide patchy, ephemeral habitats for specialized communities of animals that depend on chemoautotrophic primary production. Unlike eastern Pacific hydrothermal vents, where population structure has been studied at large (thousands of kilometres and small (hundreds of meters spatial scales, population structure of western Pacific vents has received limited attention. This study addresses the scale at which genetic differentiation occurs among populations of a western Pacific vent-restricted gastropod, Ifremeria nautilei. Results We used mitochondrial and DNA microsatellite markers to infer patterns of gene flow and population subdivision. A nested sampling strategy was employed to compare genetic diversity in discrete patches of Ifremeria nautilei separated by a few meters within a single vent field to distances as great as several thousand kilometres between back-arc basins that encompass the known range of the species. No genetic subdivisions were detected among patches, mounds, or sites within Manus Basin. Although I. nautilei from Lau and North Fiji Basins (~1000 km apart also exhibited no evidence for genetic subdivision, these populations were genetically distinct from the Manus Basin population. Conclusions An unknown process that restricts contemporary gene flow isolates the Manus Basin population of Ifremeria nautilei from widespread populations that occupy the North Fiji and Lau Basins. A robust understanding of the genetic structure of hydrothermal vent populations at multiple spatial scales defines natural conservation units and can help minimize loss of genetic diversity in situations where human activities are proposed and managed.

Guide for subdivision of spent fuel pool. Project UNESA MAAP5-SFP

International Nuclear Information System (INIS)

Martinez Barrios, M.; Garcia Gonzalez, M.; Perez Martin, F. J.

2013-01-01

The main goal of the UNESA MAAP5-SFP project is to analyze the capabilities of MAAP5 code and, particularly, the Spent Fuel Pool (SFP) module in order to tackle its modeling and facilitate the development of specific SFP models of Spanish NPPs. Within the project, Empresarios Agrupados (EEAA) is the responsible for the development of the Guide for the subdivision of the Spent Fuel Pool (SFP). This Guide includes a theoretical description of the model that is used by the code and a sequence of practical cases with the aim to evaluate the influence of specific parameters

Introducing geometry concept based on history of Islamic geometry

Science.gov (United States)

Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.

2018-01-01

Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.

Subdivision of the Lochkovian Stage based on conodont faunas from the stratotype area (Prague Synform, Czech Republic)

Czech Academy of Sciences Publication Activity Database

Slavík, Ladislav; Carls, P.; Hladil, Jindřich; Koptíková, Leona

2012-01-01

Roč. 47, č. 6 (2012), s. 616-631 ISSN 0072-1050 R&D Projects: GA ČR GA205/09/0703 Institutional research plan: CEZ:AV0Z30130516 Keywords : Lochkovian subdivision * conodont biostratigraphy * Lower Devonian * stratigraphic correlation * Barrandian area * conodont zonation Subject RIV: DB - Geology ; Mineralogy Impact factor: 1.659, year: 2012

Geometry through history Euclidean, hyperbolic, and projective geometries

CERN Document Server

Dillon, Meighan I

2018-01-01

Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...

13,16-Dimethyl octacosanedioic acid (iso-diabolic acid), a common membrane-spanning lipid of Acidobacteria subdivisions 1 and 3

NARCIS (Netherlands)

Sinninghe Damsté, J.S.; Rijpstra, W.I.C.; Hopmans, E.C.; Weijers, J.W.H.; Foesel, B.U.; Overmann, J.; Dedysh, S.N.

2011-01-01

The distribution of membrane lipids of 17 different strains representing 13 species of subdivisions 1 and 3 of the phylum Acidobacteria, a highly diverse phylum of the Bacteria, were examined by hydrolysis and gas chromatography-mass spectrometry (MS) and by high-performance liquid

Architectural geometry

KAUST Repository

Pottmann, Helmut

2014-11-26

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

Architectural geometry

KAUST Repository

Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes

2014-01-01

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

Towards an improved lithostratigraphic subdivision of the chalk group in the Netherlands North Sea area - A seismic stratigraphic approach

NARCIS (Netherlands)

Molen, A.S. van der; Wong, Th.E.

2007-01-01

In the Netherlands North Sea area, the Chalk Group has thus far been subdivided into the Cenomanian Texel Formation, the Turonian to Maastrichtian Ommelanden Formation and the Danian Ekofisk Formation. This paper describes the attempt to arrive at a more detailed lithostratigraphic subdivision for

Two lectures on D-geometry and noncommutative geometry

International Nuclear Information System (INIS)

Douglas, M.R.

1999-01-01

This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)

Twistor geometry

NARCIS (Netherlands)

van den Broek, P.M.

1984-01-01

The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.

Geometry

Indian Academy of Sciences (India)

. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...

Availability, Sustainability, and Suitability of Ground Water, Rogers Mesa, Delta County, Colorado - Types of Analyses and Data for Use in Subdivision Water-Supply Reports

Science.gov (United States)

Watts, Kenneth R.

2008-01-01

The population of Delta County, Colorado, like that in much of the Western United States, is forecast to increase substantially in the next few decades. A substantial portion of the increased population likely will reside in rural subdivisions and use residential wells for domestic water supplies. In Colorado, a subdivision developer is required to submit a water-supply plan through the county for approval by the Colorado Division of Water Resources. If the water supply is to be provided by wells, the water-supply plan must include a water-supply report. The water-supply report demonstrates the availability, sustainability, and suitability of the water supply for the proposed subdivision. During 2006, the U.S. Geological Survey, in cooperation with Delta County, Colorado, began a study to develop criteria that the Delta County Land Use Department can use to evaluate water-supply reports for proposed subdivisions. A table was prepared that lists the types of analyses and data that may be needed in a water-supply report for a water-supply plan that proposes the use of ground water. A preliminary analysis of the availability, sustainability, and suitability of the ground-water resources of Rogers Mesa, Delta County, Colorado, was prepared for a hypothetical subdivision to demonstrate hydrologic analyses and data that may be needed for water-supply reports for proposed subdivisions. Rogers Mesa is a 12-square-mile upland mesa located along the north side of the North Fork Gunnison River about 15 miles east of Delta, Colorado. The principal land use on Rogers Mesa is irrigated agriculture, with about 5,651 acres of irrigated cropland, grass pasture, and orchards. The principal source of irrigation water is surface water diverted from the North Fork Gunnison River and Leroux Creek. The estimated area of platted subdivisions on or partially on Rogers Mesa in 2007 was about 4,792 acres of which about 2,756 acres was irrigated land in 2000. The principal aquifer on Rogers

Molecular geometry

CERN Document Server

Rodger, Alison

1995-01-01

Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans

About the Subdivision of Indoor Spaces in Indoorgml

Science.gov (United States)

Diakité, A. A.; Zlatanova, S.; Li, K.-J.

2017-10-01

Boosted by the dynamic urbanization of cities, indoor environments are getting more and more complex in order to be able to host people properly. While most of our time is spent inside buildings, the need of GIS tools to assist our daily activities that can become tedious, such as indoor navigation or facility management, became more and more urgent. In that perspective, the IndoorGML standard is aiming to address the gaps left by other standards regarding the spatial modelling for indoor navigation. It includes several concepts such as the organization of the spaces into cells along with their network representation and the possibility to represent multiple connected layers. However, being at its first stage, several concepts of the standard could be improved. One of these is the cell subspacing that is not enough discussed in the current version of the standard. In this paper, we explore all the aspects involved in the subdivision process, from the identification of the navigable and non-navigable space cells to the generation of a navigation graph. We propose several criteria on which the indoor sub-spacing can rely to be automatically performed and and illustrate them on a 3D indoor model.

Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology & Symplectic Geometry, Noncommutative Geometry and Physics

CERN Document Server

Eliashberg, Yakov; Maeda, Yoshiaki; Symplectic, Poisson, and Noncommutative geometry

2014-01-01

Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and ...

Application of information technology in the process analysis of structural subdivisions of light industry enterprises

Directory of Open Access Journals (Sweden)

Тарана Тахир кызы Мусаева

2016-02-01

Full Text Available The problems of application of information technologies in the process analysis of structural subdivisions of the enterprises of light industry enterprises are considered. For the functional cost analysis in the company it was prepared a computerized structure of the workplace and its principle of operation is described. The functionality of the computerized workplace is tested for textile enterprises. The results showed that the use of information technology has good prospects at the implementation of the quality management system at the textile enterprises

Treatment of Class II subdivision malocclusion with congenitally missing upper lateral incisors: A case report

Directory of Open Access Journals (Sweden)

Siddharth Mehta

2014-01-01

Full Text Available Orthodontic treatment for patients with unilateral or bilateral congenitally missing lateral incisor poses a challenge mainly with regard to treatment planning. The use of a diagnostic setup is one of the most important aids in the decision-making process. Two alternatives, orthodontic space closure or space opening for prosthetic replacement exist. The present case report shows use of the microimplant for unilateral upper molar distalization and space closure in a Class-II division 1 subdivision malocclusion case with bilateral congenitally missing upper lateral incisors.

Sexual risk behaviours of high school female learners in Mbonge subdivision of rural Cameroon.

Science.gov (United States)

Tarkang, Elvis Enowbeyang

2015-01-01

Since female learners in high schools in Cameroon fall within the age group hardest hit by HIV/AIDS, it is assumed that these learners might be exposed to sexual risk behaviours. However, little has been explored on the sexual risk behaviours of high school female learners in Cameroon. This study aimed at examining the sexual risk behaviours of high school female learners in Mbonge subdivision of rural Cameroon. A cross sectional design was adopted, using a self-administered questionnaire for data collection. Respondents were selected through disproportional stratified simple random sampling resulting in 210 female grade 10 to grade 12 learners from three participating high schools in Mbonge subdivision, Cameroon. Descriptive and inferential statistics were calculated using SPSS version 20 software program. Majority of the respondents, 54.0% reported being sexually active, of whom only 39.8% used condoms during first sex; 49.5% used condoms during last sex and 29.6% used condoms consistently. Up to 32% of the sexually active respondents had multiple sexual partners in the past one year before the study, while 9.3% had multiple sexual partners during the study period. The mean age of first sex was 15.6 years. Lack of parental control, religion, academic profile, poverty, place of residence and perception of risk of HIV infection were the main factors significantly associated with sexual risk behaviours. The findings indicate that sexual risk behaviours exist among high school female learners in Mbonge, Cameroon. There is need for campaigns and interventions to bring about sexual behaviour change.

Differential reward coding in the subdivisions of the primate caudate during an oculomotor task.

Science.gov (United States)

Nakamura, Kae; Santos, Gustavo S; Matsuzaki, Ryuichi; Nakahara, Hiroyuki

2012-11-07

The basal ganglia play a pivotal role in reward-oriented behavior. The striatum, an input channel of the basal ganglia, is composed of subdivisions that are topographically connected with different cortical and subcortical areas. To test whether reward information is differentially processed in the different parts of the striatum, we compared reward-related neuronal activity along the dorsolateral-ventromedial axis in the caudate nucleus of monkeys performing an asymmetrically rewarded oculomotor task. In a given block, a target in one position was associated with a large reward, whereas the other target was associated with a small reward. The target position-reward value contingency was switched between blocks. We found the following: (1) activity that reflected the block-wise reward contingency emerged before the appearance of a visual target, and it was more prevalent in the dorsal, rather than central and ventral, caudate; (2) activity that was positively related to the reward size of the current trial was evident, especially after reward delivery, and it was more prevalent in the ventral and central, rather than dorsal, caudate; and (3) activity that was modulated by the memory of the outcomes of the previous trials was evident in the dorsal and central caudate. This multiple reward information, together with the target-direction information, was represented primarily by individual caudate neurons, and the different reward information was represented in caudate subpopulations with distinct electrophysiological properties, e.g., baseline firing and spike width. These results suggest parallel processing of different reward information by the basal ganglia subdivisions defined by extrinsic connections and intrinsic properties.

Acidicapsa borealis gen. nov., sp. nov. and Acidicapsa ligni sp. nov., subdivision 1 Acidobacteria from Sphagnum peat and decaying wood

NARCIS (Netherlands)

Kulichevskaya, I.S.; Kostina, L.A.; Valášková, V.; Rijpstra, I.C.; Sinninghe Damsté, J.S.; De Boer, W.; Dedysh, S.N.

2012-01-01

Two strains of subdivision 1 Acidobacteria, namely the pink-pigmented bacterium KA1T and the colorless isolate WH120T, were obtained from acidic Sphagnum peat and wood under decay by the white-rot fungus Hyploma fasciculare, respectively. Cells of these isolates are Gram-negative, non-motile, short

Arithmetic noncommutative geometry

CERN Document Server

Marcolli, Matilde

2005-01-01

Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...

Radiation-induced grain subdivision and bubble formation in U3Si2 at LWR temperature

Science.gov (United States)

Yao, Tiankai; Gong, Bowen; He, Lingfeng; Harp, Jason; Tonks, Michael; Lian, Jie

2018-01-01

U3Si2, an advanced fuel form proposed for light water reactors (LWRs), has excellent thermal conductivity and a high fissile element density. However, limited understanding of the radiation performance and fission gas behavior of U3Si2 is available at LWR conditions. This study explores the irradiation behavior of U3Si2 by 300 keV Xe+ ion beam bombardment combining with in-situ transmission electron microscopy (TEM) observation. The crystal structure of U3Si2 is stable against radiation-induced amorphization at 350 °C even up to a very high dose of 64 displacements per atom (dpa). Grain subdivision of U3Si2 occurs at a relatively low dose of 0.8 dpa and continues to above 48 dpa, leading to the formation of high-density nanoparticles. Nano-sized Xe gas bubbles prevail at a dose of 24 dpa, and Xe bubble coalescence was identified with the increase of irradiation dose. The volumetric swelling resulting from Xe gas bubble formation and coalescence was estimated with respect to radiation dose, and a 2.2% volumetric swelling was observed for U3Si2 irradiated at 64 dpa. Due to extremely high susceptibility to oxidation, the nano-sized U3Si2 grains upon radiation-induced grain subdivision were oxidized to nanocrystalline UO2 in a high vacuum chamber for TEM observation, eventually leading to the formation of UO2 nanocrystallites stable up to 80 dpa.

A contribution to the subdivision of the precambrian in South America

International Nuclear Information System (INIS)

Brito Neves, B.B. de; Teixeira, W.; Tassinari, C.C.G.; Kawashita, K.

1990-01-01

On the shield areas of the South America continent (about 5,000,000 km 2 large) there are about 17,000 geochronological determinations available. More than 75% of this amount has been carried out in the Centro de Pesquisas Geocronologicas da Universidade de Sao Paulo, CPGeo-USP, in the last 25 years. The majority of these data were accomplished through Rb-Sr (ca.60%) and K-Ar (ca.40%) methods. The author tried to work this amount of data on a coherent way according to the progress observed in the geologic and geotectonic knowledge during the last two decades. One of the fundamental goals was to outline an up-to-date subdivision for the Precambrian of this continent, having in mind a contribution to the International Commission on Stratigraphy (ICS), Subcommission of Precambrian Stratigraphy (SPS) of the IUGS. (author)

Higher geometry an introduction to advanced methods in analytic geometry

CERN Document Server

Woods, Frederick S

2005-01-01

For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study

Non-Riemannian geometry

CERN Document Server

Eisenhart, Luther Pfahler

2005-01-01

This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.

The Geometry Conference

CERN Document Server

Bárány, Imre; Vilcu, Costin

2016-01-01

This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.

Hyperbolic geometry

CERN Document Server

Iversen, Birger

1992-01-01

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics

ABOUT THE SUBDIVISION OF INDOOR SPACES IN INDOORGML

Directory of Open Access Journals (Sweden)

A. A. Diakité

2017-10-01

Full Text Available Boosted by the dynamic urbanization of cities, indoor environments are getting more and more complex in order to be able to host people properly. While most of our time is spent inside buildings, the need of GIS tools to assist our daily activities that can become tedious, such as indoor navigation or facility management, became more and more urgent. In that perspective, the IndoorGML standard is aiming to address the gaps left by other standards regarding the spatial modelling for indoor navigation. It includes several concepts such as the organization of the spaces into cells along with their network representation and the possibility to represent multiple connected layers. However, being at its first stage, several concepts of the standard could be improved. One of these is the cell subspacing that is not enough discussed in the current version of the standard. In this paper, we explore all the aspects involved in the subdivision process, from the identification of the navigable and non-navigable space cells to the generation of a navigation graph. We propose several criteria on which the indoor sub-spacing can rely to be automatically performed and and illustrate them on a 3D indoor model.

Geometry of the Universe

International Nuclear Information System (INIS)

Gurevich, L.Eh.; Gliner, Eh.B.

1978-01-01

Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding

On organizing principles of discrete differential geometry. Geometry of spheres

International Nuclear Information System (INIS)

Bobenko, Alexander I; Suris, Yury B

2007-01-01

Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.

Staffing Levels at National Collegiate Athletic Association Football Bowl Subdivision-Level Institutions.

Science.gov (United States)

Ms, Suzie Aparicio; Welch Bacon, Cailee E; Parsons, John T; Bay, R Curtis; Cohen, Randy P; DeZeeuw, Terry; McLeod, Tamara C Valovich

2015-12-01

The "Appropriate Medical Coverage for Intercollegiate Athletics" (AMCIA) document was created to support assessment and calculation of athletic training personnel requirements. However, little is known regarding disparities between current and recommended staffing practices. To identify the staffing and employment characteristics of athletic health care services at Football Bowl Subdivision-level institutions. Cross-sectional study. Web-based survey. Head athletic trainers and athletic training staff members who were knowledgeable about budget and staff. The survey, Assessment of Staffing Levels at National Collegiate Athletic Association Football Bowl Subdivision-Level Institutions, was used to evaluate personal, university, and staff demographics; staffing and employment topics; and AMCIA variables and use. The survey was accessed and partially completed by 104 individuals (response rate = 84.6%). A total of 79 athletic trainers (response rate = 76%) completed the entire survey. One-third of the respondents (34.2%, n = 26) met the recommended number of full-time equivalents (FTEs) for football, two-thirds of the respondents (65.7%, n = 50) failed to meet the recommendation, and 26.2% (n = 27) were missing data needed for FTE calculation. Among those who did not meet the recommended FTEs (n = 50), 38.0% (n = 19) were within 1 FTE of being compliant, 26.0% (n = 13) were within 2 FTEs, and 24.0% (n = 12) were within 3 FTEs. About one-third of respondents (35.9%, n = 37) reported not using the AMCIA, citing lack of funding (29.7%, n = 11), lack of administrative support (21.6%, n = 8), and other reasons (37.8%, n = 14). The majority of institutions that used the AMCIA were able to provide justification for staffing. For most of the institutions that failed to meet their recommendation, adding 1-3 FTE athletic trainers for football would change their compliance status. A uniform definition of the term FTE within collegiate athletics is needed to allow for structured

'Combined reflectance stratigraphy' - subdivision of loess successions by diffuse reflectance spectrometry (DRS)

Science.gov (United States)

Szeberényi, Jozsef; Bradak-Hayashi, Balázs; Kiss, Klaudia; Kovács, József; Varga, György; Balázs, Réka; Szalai, Zoltán; Viczián, István

2016-04-01

The different varieties of loess (and intercalated paleosol layers) together constitute one of the most widespread terrestrial sediments, which was deposited, altered, and redeposited in the course of the changing climatic conditions of the Pleistocene. To reveal more information about Pleistocene climate cycles and/or environments the detailed lithostratigraphical subdivision and classification of the loess variations and paleosols are necessary. Beside the numerous method such as various field measurements, semi-quantitative tests and laboratory investigations, diffuse reflectance spectroscopy (DRS) is one of the well applied method on loess/paleosol sequences. Generally, DRS has been used to separate the detrital and pedogenic mineral component of the loess sections by the hematite/goethite ratio. DRS also has been applied as a joint method of various environmental magnetic investigations such as magnetic susceptibility- and isothermal remanent magnetization measurements. In our study the so-called "combined reflectance stratigraphy method" were developed. At First, complex mathematical method was applied to compare the results of the spectral reflectance measurements. One of the most preferred multivariate methods is cluster analysis. Its scope is to group and compare the loess variations and paleosol based on the similarity and common properties of their reflectance curves. In the Second, beside the basic subdivision of the profiles by the different reflectance curves of the layers, the most characteristic wavelength section of the reflectance curve was determined. This sections played the most important role during the classification of the different materials of the section. The reflectance value of individual samples, belonged to the characteristic wavelength were depicted in the function of depth and well correlated with other proxies like grain size distribution and magnetic susceptibility data. The results of the correlation showed the significance of

Staffing Levels at National Collegiate Athletic Association Football Bowl Subdivision-Level Institutions

Science.gov (United States)

MS, Suzie Aparicio; Welch Bacon, Cailee E.; Parsons, John T.; Bay, R. Curtis; Cohen, Randy P.; DeZeeuw, Terry; McLeod, Tamara C. Valovich

2015-01-01

Context The “Appropriate Medical Coverage for Intercollegiate Athletics” (AMCIA) document was created to support assessment and calculation of athletic training personnel requirements. However, little is known regarding disparities between current and recommended staffing practices. Objective To identify the staffing and employment characteristics of athletic health care services at Football Bowl Subdivision-level institutions. Design Cross-sectional study. Setting Web-based survey. Patients or Other Participants Head athletic trainers and athletic training staff members who were knowledgeable about budget and staff. Main Outcome Measure(s) The survey, Assessment of Staffing Levels at National Collegiate Athletic Association Football Bowl Subdivision-Level Institutions, was used to evaluate personal, university, and staff demographics; staffing and employment topics; and AMCIA variables and use. Results The survey was accessed and partially completed by 104 individuals (response rate = 84.6%). A total of 79 athletic trainers (response rate = 76%) completed the entire survey. One-third of the respondents (34.2%, n = 26) met the recommended number of full-time equivalents (FTEs) for football, two-thirds of the respondents (65.7%, n = 50) failed to meet the recommendation, and 26.2% (n = 27) were missing data needed for FTE calculation. Among those who did not meet the recommended FTEs (n = 50), 38.0% (n = 19) were within 1 FTE of being compliant, 26.0% (n = 13) were within 2 FTEs, and 24.0% (n = 12) were within 3 FTEs. About one-third of respondents (35.9%, n = 37) reported not using the AMCIA, citing lack of funding (29.7%, n = 11), lack of administrative support (21.6%, n = 8), and other reasons (37.8%, n = 14). Conclusions The majority of institutions that used the AMCIA were able to provide justification for staffing. For most of the institutions that failed to meet their recommendation, adding 1–3 FTE athletic trainers for football would change their

Geometry and its applications

CERN Document Server

Meyer, Walter J

2006-01-01

Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...

Exposure to high- and low-light conditions in an open-field test of anxiety increases c-Fos expression in specific subdivisions of the rat basolateral amygdaloid complex.

Science.gov (United States)

Hale, Matthew W; Bouwknecht, J Adriaan; Spiga, Francesca; Shekhar, Anantha; Lowry, Christopher A

2006-12-11

Anxiety states and anxiety-related behaviors appear to be regulated by a distributed and highly interconnected system of forebrain structures including the basolateral amygdaloid complex (basolateral amygdala). Despite a wealth of research examining the role of the basolateral amygdala in anxiety-related behaviors and anxiety states, the specific subdivisions of the basolateral amygdala that are involved in responses to anxiogenic stimuli have not been examined. In this study, we investigated the effects of exposure to a novel open-field environment, with either low- or high-levels of illumination, on expression of the protein product of the immediate-early gene c-Fos in subdivisions of the rat basolateral amygdala. The subdivisions studied included the lateral, ventrolateral and ventromedial parts of the lateral amygdaloid nucleus, the anterior, posterior and ventral parts of the basolateral amygdaloid nucleus and the anterior and posterior part of the basomedial amygdaloid nucleus. Small increases in the number of c-Fos-immunoreactive cells were observed in several, but not all, of the subdivisions of the basolateral amygdala studied following exposure of rats to either the high- or low-light conditions, compared to home cage or handled control groups. Open-field exposure in both the high- and low-light conditions resulted in a marked increase in c-Fos expression in the anterior part of the basolateral amygdaloid nucleus compared to either home cage or handled control groups. These findings point toward anatomical and functional heterogeneity within the basolateral amygdaloid complex and an important role of the anterior part of the basolateral amygdaloid nucleus in the neural mechanisms underlying physiological or behavioral responses to this anxiety-related stimulus.

Beautiful geometry

CERN Document Server

Maor, Eli

2014-01-01

If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur

Revolutions of Geometry

CERN Document Server

O'Leary, Michael

2010-01-01

Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull

Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry

Science.gov (United States)

Mammana, M. F.; Micale, B.; Pennisi, M.

2012-01-01

We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…

Information geometry

CERN Document Server

Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz

2017-01-01

The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...

Buffer zone monitoring plan for the Dos Rios subdivision, Gunnison, Colorado

International Nuclear Information System (INIS)

1996-02-01

This report presents a plan for water quality monitoring at the Dos Rios subdivision (Units 2, 3, and the Island Unit) that is intended to satisfy the informational needs of residents who live southwest (downgradient) of the former Gunnison processing site. Water quality monitoring activities described in this report are designed to protect the public from residual contamination that entered the ground water as a result of previous uranium milling operations. Requirements presented in this monitoring plan are also included in the water sampling and analysis plan (WSAP) for the Gunnison Uranium Mill Tailings Remedial Action (UMTRA) Project site. The Gunnison WSAP is a site-specific document prepared by the U.S. Department of Energy (DOE) that provides background, guidance, and justification for future ground water sampling and analysis activities for the UMTRA Project Gunnison processing and disposal sites. The WSAP will be updated annually, as additional water quality data are collected and interpreted, to provide ongoing protection for public health and the environment

Adaptive subdivision and the length and energy of Bézier curves

DEFF Research Database (Denmark)

Gravesen, Jens

1997-01-01

It is an often used fact that the control polygon of a Bézier curve approximates the curve and that the approximation gets better when the curve is subdivided. In particular, if a Bézier curve is subdivided into some number of pieces, then the arc-length of the original curve is greater than...... the sum of the chord-lengths of the pieces, and less than the sum of the polygon-lengths of the pieces. Under repeated subdivisions, the difference between this lower and upper bound gets arbitrarily small.If $L_c$ denotes the total chord-length of the pieces and $L_p$ denotes the total polygon...... combination, and it forms the basis for a fast adaptive algorithm, which determines the arc-length of a Bézier curve.The energy of a curve is half the square of the curvature integrated with respect to arc-length. Like in the case of the arc-length, it is possible to use the chord-length and polygon...

Geometry essentials for dummies

CERN Document Server

Ryan, Mark

2011-01-01

Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque

Novitates Gabonenses 83. Two new species of Cola (Sterculiaceae s.str.) from Gabon with an introductory note on the subdivision of the genus

NARCIS (Netherlands)

Breteler, F.J.

2014-01-01

Background and aims The existing subdivisions of the large genus Cola of the Sterculiaceae s.str. are briefly presented and their usefulness as regards the identification of newly acquired material is discussed. Material and methods Normal practices of herbarium taxonomy have been applied to study

Complex analysis and geometry

CERN Document Server

Silva, Alessandro

1993-01-01

The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.

Arsenic Removal from Drinking Water by Adsorptive Media - U.S. EPA Demonstration Project at Geneseo Hills Subdivision, in Geneseo, IL Final Performance Evaluation Report

Science.gov (United States)

This report documents the activities performed and the results obtained from the arsenic removal treatment technology demonstration project at the Geneseo Hills Subdivision in Geneseo, IL. The main objective of the project was to evaluate the effectiveness of AdEdge Technologies...

The Jurassic of Denmark and Greenland: The Upper Jurassic of Europe: its subdivision and correlation

Directory of Open Access Journals (Sweden)

Zeiss, Arnold

2003-10-01

Full Text Available In the last 40 years, the stratigraphy of the Upper Jurassic of Europe has received much attention and considerable revision; much of the impetus behind this endeavour has stemmed from the work of the International Subcommission on Jurassic Stratigraphy. The Upper Jurassic Series consists of three stages, the Oxfordian, Kimmeridgian and Tithonian which are further subdivided into substages, zones and subzones, primarily on the basis of ammonites. Regional variations between the Mediterranean, Submediterranean and Subboreal provinces are discussed and correlation possibilities indicated. The durations of the Oxfordian, Kimmeridgian and Tithonian Stages are reported to have been 5.3, 3.4 and 6.5 Ma, respectively. This review of the present status of Upper Jurassic stratigraphy aids identification of a number of problems of subdivision and definition of Upper Jurassic stages; in particular these include correlation of the base of the Kimmeridgian and the top of the Tithonian between Submediterranean and Subboreal Europe. Although still primarily based on ammonite stratigraphy, subdivision of the Upper Jurassic is increasingly being refined by the incorporation of other fossil groups; these include both megafossils, such as aptychi, belemnites, bivalves, gastropods, brachiopods, echinoderms, corals, sponges and vertebrates, and microfossils such as foraminifera, radiolaria, ciliata, ostracodes, dinoflagellates, calcareous nannofossils, charophyaceae, dasycladaceae, spores and pollen. Important future developments will depend on the detailed integration of these disparate biostratigraphic data and their precise combination with the abundant new data from sequence stratigraphy, utilising the high degree of stratigraphic resolution offered by certain groups of fossils. This article also contains some notes on the recent results of magnetostratigraphy and sequence chronostratigraphy.

Differential structural and resting state connectivity between insular subdivisions and other pain-related brain regions.

Science.gov (United States)

Wiech, K; Jbabdi, S; Lin, C S; Andersson, J; Tracey, I

2014-10-01

Functional neuroimaging studies suggest that the anterior, mid, and posterior division of the insula subserve different functions in the perception of pain. The anterior insula (AI) has predominantly been associated with cognitive-affective aspects of pain, while the mid and posterior divisions have been implicated in sensory-discriminative processing. We examined whether this functional segregation is paralleled by differences in (1) structural and (2) resting state connectivity and (3) in correlations with pain-relevant psychological traits. Analyses were restricted to the 3 insular subdivisions and other pain-related brain regions. Both type of analyses revealed largely overlapping results. The AI division was predominantly connected to the ventrolateral prefrontal cortex (structural and resting state connectivity) and orbitofrontal cortex (structural connectivity). In contrast, the posterior insula showed strong connections to the primary somatosensory cortex (SI; structural connectivity) and secondary somatosensory cortex (SII; structural and resting state connectivity). The mid insula displayed a hybrid connectivity pattern with strong connections with the ventrolateral prefrontal cortex, SII (structural and resting state connectivity) and SI (structural connectivity). Moreover, resting state connectivity revealed strong connectivity of all 3 subdivisions with the thalamus. On the behavioural level, AI structural connectivity was related to the individual degree of pain vigilance and awareness that showed a positive correlation with AI-amygdala connectivity and a negative correlation with AI-rostral anterior cingulate cortex connectivity. In sum, our findings show a differential structural and resting state connectivity for the anterior, mid, and posterior insula with other pain-relevant brain regions, which might at least partly explain their different functional profiles in pain processing. Copyright © 2014 The Authors. Published by Elsevier B.V. All

Geometry

CERN Document Server

Pedoe, Dan

1988-01-01

""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he

Complex algebraic geometry

CERN Document Server

Kollár, János

1997-01-01

This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

Hepatitis A outbreak in Ba subdivision, Fiji, October–December 2013

Directory of Open Access Journals (Sweden)

Aneley Getahun

2015-06-01

Full Text Available Objective: A cluster of suspected hepatitis A cases was notified to the Fiji Ministry of Health on 22 October 2013. An outbreak investigation team was mobilized to confirm the existence of an outbreak of hepatitis A and advise appropriate public health interventions. Methods: A case definition for the outbreak investigation was established, and standardized data collection tools were used to collect information on clinical presentation and risk factors. An environmental assessment was also conducted. Results: There were 160 clinical cases of hepatitis A of which 15 were laboratory-confirmed. The attack rate was 349 per 10 000 population in the Nukuloa nursing zone; there were no reported deaths. Residents of the Nukuloa settlement were 6.6 times more likely to present with symptomatic hepatitis A infection (95% confidence interval: 3.8–12.6 compared with residents of another village with a different water supply. Discussion: This is the first significant hepatitis A outbreak documented in Ba subdivision and possibly in Fiji. Enhanced surveillance of hepatitis A may reveal other clusters in the country. Improving the primary water source dramatically reduced the occurance of disease in the affected community and adjacent areas.

Hepatitis A outbreak in Ba subdivision, Fiji, October-December 2013.

Science.gov (United States)

Getahun, Aneley; Rafai, Eric; Tolosa, Maria Ximena; Dawainavesi, Akanisi; Tabua, Anaseini Maisema; Tabua, Josefa

2015-01-01

A cluster of suspected hepatitis A cases was notified to the Fiji Ministry of Health on 22 October 2013. An outbreak investigation team was mobilized to confirm the existence of an outbreak of hepatitis A and advise appropriate public health interventions. A case definition for the outbreak investigation was established, and standardized data collection tools were used to collect information on clinical presentation and risk factors. An environmental assessment was also conducted. There were 160 clinical cases of hepatitis A of which 15 were laboratory-confirmed. The attack rate was 349 per 10,000 population in the Nukuloa nursing zone; there were no reported deaths. Residents of the Nukuloa settlement were 6.6 times more likely to present with symptomatic hepatitis A infection (95% confidence interval: 3.8-12.6) compared with residents of another village with a different water supply. This is the first significant hepatitis A outbreak documented in Ba subdivision and possibly in Fiji. Enhanced surveillance of hepatitis A may reveal other clusters in the country. Improving the primary water source dramatically reduced the occurance of disease in the affected community and adjacent areas.

CMS geometry through 2020

International Nuclear Information System (INIS)

Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J

2014-01-01

CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.

Analisis Keterampilan Geometri Siswa Dalam Memecahkan Masalah Geometri Berdasarkan Tingkat Berpikir Van Hiele

OpenAIRE

Muhassanah, Nuraini; Sujadi, Imam; Riyadi, Riyadi

2014-01-01

The objective of this research was to describe the VIII grade students geometry skills atSMP N 16 Surakarta in the level 0 (visualization), level 1 (analysis), and level 2 (informaldeduction) van Hiele level of thinking in solving the geometry problem. This research was aqualitative research in the form of case study analyzing deeply the students geometry skill insolving the geometry problem based on van Hiele level of thingking. The subject of this researchwas nine students of VIII grade at ...

Differential Functional Connectivity Alterations of Two Subdivisions within the Right dlPFC in Parkinson's Disease

Directory of Open Access Journals (Sweden)

Julian Caspers

2017-05-01

Full Text Available Patients suffering from Parkinson's disease (PD often show impairments in executive function (EF like decision-making and action control. The right dorsolateral prefrontal cortex (dlPFC has been strongly implicated in EF in healthy subjects and has repeatedly been reported to show alterations related to EF impairment in PD. Recently, two key regions for cognitive action control have been identified within the right dlPFC by co-activation based parcellation. While the posterior region is engaged in rather basal EF like stimulus integration and working memory, the anterior region has a more abstract, supervisory function. To investigate whether these functionally distinct subdivisions of right dlPFC are differentially affected in PD, we analyzed resting-state functional connectivity (FC in 39 PD patients and 44 age- and gender-matched healthy controls. Patients were examined both after at least 12 h withdrawal of dopaminergic drugs (OFF and under their regular dopaminergic medication (ON. We found that only the posterior right dlPFC subdivision shows FC alterations in PD, while the anterior part remains unaffected. PD-related decreased FC with posterior right dlPFC was found in the bilateral medial posterior parietal cortex (mPPC and left dorsal premotor region (PMd in the OFF state. In the medical ON, FC with left PMd normalized, while decoupling with bilateral mPPC remained. Furthermore, we observed increased FC between posterior right dlPFC and the bilateral dorsomedial prefrontal cortex (dmPFC in PD in the ON state. Our findings point to differential disturbances of right dlPFC connectivity in PD, which relate to its hierarchical organization of EF processing by stronger affecting the functionally basal posterior aspect than the hierarchically higher anterior part.

Algorithms in Algebraic Geometry

CERN Document Server

Dickenstein, Alicia; Sommese, Andrew J

2008-01-01

In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

Non-Euclidean geometry

CERN Document Server

Kulczycki, Stefan

2008-01-01

This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff

Geometry on the space of geometries

International Nuclear Information System (INIS)

Christodoulakis, T.; Zanelli, J.

1988-06-01

We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs

A Lorentzian quantum geometry

Energy Technology Data Exchange (ETDEWEB)

Grotz, Andreas

2011-10-07

In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

A Lorentzian quantum geometry

International Nuclear Information System (INIS)

Grotz, Andreas

2011-01-01

In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

Intersection Group Dynamic Subdivision and Coordination at Intraregional Boundaries in Sudden Disaster

Directory of Open Access Journals (Sweden)

Ciyun Lin

2015-01-01

Full Text Available This paper aims at the traffic flow agglomeration effect characteristics and rapid evacuation requirement in sudden disaster; operation time of intraregional boundaries traffic signal coordination was presented firstly. Then intraregional boundaries intersection group dynamic subdivision and consolidation method based on relative similarity degree and similarity coefficient of adjacent intersections was put forward. As to make the traffic control strategy adapt to traffic condition of different intraregional boundaries intersection groups, this paper proposes an intraregional boundaries traffic signal coordination and optimization technology based on organic computing theory. Finally, this paper uses Delphi 7.0, MapX, and Oracle developing a software package, combined with Paramics V6 Simulator to validate the methods of this paper. The result shows that it can obviously improve disaster affected regional traffic signal control efficiency which reduces average traffic delay by 30–35%, decreases vehicle queue by more than 20% and reduces evacuation time more than 13.06%.

Geometry and Combinatorics

DEFF Research Database (Denmark)

Kokkendorff, Simon Lyngby

2002-01-01

The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...

Geometry and billiards

CERN Document Server

Tabachnikov, Serge

2005-01-01

Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...

Drawing Dynamic Geometry Figures Online with Natural Language for Junior High School Geometry

Science.gov (United States)

Wong, Wing-Kwong; Yin, Sheng-Kai; Yang, Chang-Zhe

2012-01-01

This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the…

Geographic information systems based demarcation of risk zones: the case of the Limbe Sub-Division – Cameroon

Directory of Open Access Journals (Sweden)

Buh Wung Gaston

2009-04-01

Full Text Available In the Limbe Subdivision of Cameroon, landslides and flooding are frequent threats. The worst recorded event occurred in June 2001, when floods and landslides took the lives of some 30 persons, left over 2000 people homeless, and destroyed property and social amenities including roads and telephone lines worth hundred of thousands of US Dollars. The objective of this project was to assist local administrative officers, other decision makers and planners to understand which areas to concentrate their efforts on in order to develop mitigation actions to protect the lives of the population in these zones that are affected by flooding and associated landslides. To meet this objective the project made extensive use of geospatial tools and existing digital spatial datasets. Series of field data collection exercises constituted an integral part of the project. The project focused on the Limbe subdivision in the south-western part of Cameroon. Areas with high (greater than 60% probability of sliding to occur, occupy 23% while areas with medium (greater than 40% and less than 60% probability of sliding to occur occupy 44% and areas with low (less than 40% probability of sliding occupy 33%. Settlements along the Atlantic coast all lie less than ~50m above sea level. These settlements (villages are susceptible to flooding. Again settlements in the town of Llimbe along the Djenguele river, i.e., Animal Farms, Cassava Farms, Lumpsum areas, Church Street, New Town and Down Beach, are more susceptible to inundation during raining periods and therefore have experienced persistent flooding over the years.

KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI

Directory of Open Access Journals (Sweden)

Irkham Ulil Albab

2014-10-01

Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews

Software Geometry in Simulations

Science.gov (United States)

Alion, Tyler; Viren, Brett; Junk, Tom

2015-04-01

The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).

Methods of information geometry

CERN Document Server

Amari, Shun-Ichi

2000-01-01

Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...

Developments in special geometry

International Nuclear Information System (INIS)

Mohaupt, Thomas; Vaughan, Owen

2012-01-01

We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.

Hydrologic, ecologic, and geomorphic responses of Brewery Creek to construction of a residential subdivision, Dane County, Wisconsin, 1999-2002

Science.gov (United States)

Selbig, William R.; Jopke, Peter L.; Marhshall, David W.; Sorge, Michael J.

2004-01-01

The U.S. Geological Survey (USGS), in cooperation with the Dane County Land Conservation Department (LCD) and the Wisconsin Department of Natural Resources (DNR), investigated the instream effects from construction of a residential subdivision on Brewery Creek in Dane County, Wisconsin. The purpose of the investigation was to determine whether a variety of storm-runoff and erosion-control best-management practices (BMPs) would effectively control the overall sediment load, as well as minimize any hydrologic, ecologic, and geomorphic stresses to Brewery Creek.

The design of geometry teaching: learning from the geometry textbooks of Godfrey and Siddons

OpenAIRE

Fujita, Taro; Jones, Keith

2002-01-01

Deciding how to teach geometry remains a demanding task with one of major arguments being about how to combine the intuitive and deductive aspects of geometry into an effective teaching design. In order to try to obtain an insight into tackling this issue, this paper reports an analysis of innovative geometry textbooks which were published in the early part of the 20th Century, a time when significant efforts were being made to improve the teaching and learning of geometry. The analysis sugge...

Crossover from normal (N) Ohmic subdivision to superconducting (S) equipartition of current in parallel conductors at the N-S transition: Theory

OpenAIRE

Kumar, N.

2007-01-01

The recently observed (1) equipartition of current in parallel at and below the Normal-Superconducting (N-S) transition can be understood in terms of a Landau-Ginzburg order-parameter phenomenology. This complements the explanation proposed earlier (1) based on the flux-flow resistance providing a nonlinear negative current feedback towards equipartition when the transition is approached from above. The present treatment also unifies the usual textbook inductive subdivision expected much belo...

Sources of hyperbolic geometry

CERN Document Server

Stillwell, John

1996-01-01

This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...

The geometry description markup language

International Nuclear Information System (INIS)

Chytracek, R.

2001-01-01

Currently, a lot of effort is being put on designing complex detectors. A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier. A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment. However, no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files, source code (C/C++/FORTRAN), to XML and database solutions. The XML (Extensible Markup Language) has proven to provide an interesting approach for describing detector geometries, with several different but incompatible XML-based solutions existing. Therefore, interoperability and geometry data exchange among different frameworks is not possible at present. The author introduces a markup language for geometry descriptions. Its aim is to define a common approach for sharing and exchanging of geometry description data. Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML

Complex analysis and CR geometry

CERN Document Server

Zampieri, Giuseppe

2008-01-01

Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...

Global aspects of complex geometry

CERN Document Server

Catanese, Fabrizio; Huckleberry, Alan T

2006-01-01

Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.

Analytic geometry

CERN Document Server

Burdette, A C

1971-01-01

Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st

Vector geometry

CERN Document Server

Robinson, Gilbert de B

2011-01-01

This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom

Physics- and engineering knowledge-based geometry repair system for robust parametric CAD geometries

OpenAIRE

Li, Dong

2012-01-01

In modern multi-objective design optimisation, an effective geometry engine is becoming an essential tool and its performance has a significant impact on the entire process. Building a parametric geometry requires difficult compromises between the conflicting goals of robustness and flexibility. The work presents a solution for improving the robustness of parametric geometry models by capturing and modelling relative engineering knowledge into a surrogate model, and deploying it automatically...

Noncommutative geometry

CERN Document Server

Connes, Alain

1994-01-01

This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat

Geometry Revealed

CERN Document Server

Berger, Marcel

2010-01-01

Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,

Discrete differential geometry. Consistency as integrability

OpenAIRE

Bobenko, Alexander I.; Suris, Yuri B.

2005-01-01

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

Performance Evaluation of Various STL File Mesh Refining Algorithms Applied for FDM-RP Process

Science.gov (United States)

Ledalla, Siva Rama Krishna; Tirupathi, Balaji; Sriram, Venkatesh

2018-06-01

Layered manufacturing machines use the stereolithography (STL) file to build parts. When a curved surface is converted from a computer aided design (CAD) file to STL, it results in a geometrical distortion and chordal error. Parts manufactured with this file, might not satisfy geometric dimensioning and tolerance requirements due to approximated geometry. Current algorithms built in CAD packages have export options to globally reduce this distortion, which leads to an increase in the file size and pre-processing time. In this work, different mesh subdivision algorithms are applied on STL file of a complex geometric features using MeshLab software. The mesh subdivision algorithms considered in this work are modified butterfly subdivision technique, loops sub division technique and general triangular midpoint sub division technique. A comparative study is made with respect to volume and the build time using the above techniques. It is found that triangular midpoint sub division algorithm is more suitable for the geometry under consideration. Only the wheel cap part is then manufactured on Stratasys MOJO FDM machine. The surface roughness of the part is measured on Talysurf surface roughness tester.

Spinorial Geometry and Branes

International Nuclear Information System (INIS)

Sloane, Peter

2007-01-01

We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

An introduction to incidence geometry

CERN Document Server

De Bruyn, Bart

2016-01-01

This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...

Spinorial Geometry and Branes

Energy Technology Data Exchange (ETDEWEB)

Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)

2007-09-15

We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

Introduction to non-Euclidean geometry

CERN Document Server

Wolfe, Harold E

2012-01-01

One of the first college-level texts for elementary courses in non-Euclidean geometry, this concise, readable volume is geared toward students familiar with calculus. A full treatment of the historical background explores the centuries-long efforts to prove Euclid's parallel postulate and their triumphant conclusion. Numerous original exercises form an integral part of the book.Topics include hyperbolic plane geometry and hyperbolic plane trigonometry, applications of calculus to the solutions of some problems in hyperbolic geometry, elliptic plane geometry and trigonometry, and the consistenc

Optical geometry across the horizon

International Nuclear Information System (INIS)

Jonsson, Rickard

2006-01-01

In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework

Convection in Slab and Spheroidal Geometries

Science.gov (United States)

Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.

2000-01-01

Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.

Complex and symplectic geometry

CERN Document Server

Medori, Costantino; Tomassini, Adriano

2017-01-01

This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

Initiation to global Finslerian geometry

CERN Document Server

Akbar-Zadeh, Hassan

2006-01-01

After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p

Algebraic geometry in India

Indian Academy of Sciences (India)

algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.

Generalizing optical geometry

International Nuclear Information System (INIS)

Jonsson, Rickard; Westman, Hans

2006-01-01

We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity

Introduction to combinatorial geometry

International Nuclear Information System (INIS)

Gabriel, T.A.; Emmett, M.B.

1985-01-01

The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity

Graded geometry and Poisson reduction

OpenAIRE

Cattaneo, A S; Zambon, M

2009-01-01

The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics

Geometry of multihadron production

Energy Technology Data Exchange (ETDEWEB)

Bjorken, J.D.

1994-10-01

This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.

Geometry of multihadron production

International Nuclear Information System (INIS)

Bjorken, J.D.

1994-10-01

This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions

Geometry of higher-dimensional black hole thermodynamics

International Nuclear Information System (INIS)

Aaman, Jan E.; Pidokrajt, Narit

2006-01-01

We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstroem (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four-dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for a d=5 Kerr black hole is curved and divergent in the extremal limit. For a d≥6 Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For the RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In d≥5 the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in d=5 with double angular momenta

Assessment of Water Pollution in Tipparthy Revenue Sub-Division, Nalgonda (District, Andhra Pradesh, India

Directory of Open Access Journals (Sweden)

Medikondu Kishore

2010-01-01

Full Text Available A systematic study has been carried out to explore the physicochemical characteristics of drinking water sources of Tipparthy revenue sub-division, Nalgonda (District, Andhra Pradesh, India. Totally 49 water samples were collected from the different locations (22 villages of the study area including bore well, open well and hand pump water and analyzed for pH, EC, TDS, turbidity, total hardness, fluoride, chloride, nitrate, nitrite, sulphate, phosphates, calcium, magnesium, sodium, potassium, Iron and dissolved oxygen. On an average, in almost all the samples, one or the other chemical constituent was beyond the permissible limits it was also concluded that water sources in the study area not fit for potability. Sodium absorption ratio (SAR and water quality (WQI studies indicate water available from all sources not fit for irrigation also. The study indicates the need for periodic monitoring of ground water in the study area.

Lectures on Symplectic Geometry

CERN Document Server

Silva, Ana Cannas

2001-01-01

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...

HEATMESH, Geometry Data Generator for Heat Transfer Calculation in Axisymmetric System

International Nuclear Information System (INIS)

Gabrielson, V.K.

1972-01-01

1 - Description of problem or function: HEATMESH is used to generate geometrical data required for studies of heat transfer in axisymmetric structures represented as surfaces of revolution. The program consists of two distinct phases. The first subdivides the given parts into a nodal network and evaluates the geometrical properties of the nodes. The second determines adjacent nodes and edits geometrical data for the thermal model. 2 - Method of solution: The structure to be studied, represented as a body of revolution, is divided into parts having common material properties and represented as bodies of revolution. Each part is then described as four surfaces of revolution subdivided into nodes which form a mesh. Data for each part are collected, i. e. volume, area, and part number of each node, and node surfaces on the part boundary and inside the part boundary. The distance between the center and the midpoint of each surface of the node is tabulated also. 3 - Restrictions on the complexity of the problem: Number of subdivisions between 1 and 50 for sides 1 and 3, Number of subdivisions between 1 and 12 for sides 2 and 4

Complex differential geometry

CERN Document Server

Zheng, Fangyang

2002-01-01

The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...

Computational synthetic geometry

CERN Document Server

Bokowski, Jürgen

1989-01-01

Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...

Designs and finite geometries

CERN Document Server

1996-01-01

Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.

d-geometries revisited

CERN Document Server

Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio

2013-01-01

We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.

Geometry success in 20 minutes a day

CERN Document Server

LLC, LearningExpress

2014-01-01

Whether you're new to geometry or just looking for a refresher, Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day: Covers all vital geometry skills, from the basic building blocks of geometry to ratio, proportion, and similarity to trigonometry and beyond Provides hundreds of practice exercises in test format Applies geometr

Medically Important Parasites Carried by Cockroaches in Melong Subdivision, Littoral, Cameroon

Directory of Open Access Journals (Sweden)

R. J. Atiokeng Tatang

2017-01-01

Full Text Available Cockroaches have been recognized as mechanical vectors of pathogens that can infest humans or animals. A total of 844 adult cockroaches (436 males and 408 females were caught. In the laboratory, cockroaches were first washed in saturated salt solution to remove ectoparasites and then rinsed with 70% alcohol, dried, and dissected for endoparasites. An overall transport rate of 47.39% was recorded. Six genera of parasites were identified. These were Ascaris (33.76%, Trichuris (11.97%, Capillaria (6.16%, Toxocara (4.86%, Hook Worm (4.86%, and Eimeria (2.73%. The parasites were more recorded on the external surface (54.27% of cockroaches than in the internal surface (GIT, 38.51%. The same tendency was obtained between sexes with female cockroaches having a higher transport rate (36.69%. Cockroaches caught in toilets carried more parasites (31.99% as compared to those from kitchens (22.63% and houses (11.14%. Almost all encountered parasites were recognized as responsible of zoonosis and they can be consequently released in nature by hosts and easily disseminated by cockroaches as mechanical vectors. Sanitary education, reenforcement of worms’ eradication programs, and the fight against these insects remain a necessity in the Mélong Subdivision.

Lectures on coarse geometry

CERN Document Server

Roe, John

2003-01-01

Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...

Introduction to tropical geometry

CERN Document Server

Maclagan, Diane

2015-01-01

Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...

Geometry Euclid and beyond

CERN Document Server

Hartshorne, Robin

2000-01-01

In recent years, I have been teaching a junior-senior-level course on the classi­ cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa­ rately. The remainder of the book is an exploration of questions that arise natu­ rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...

Basic algebraic geometry, v.2

CERN Document Server

Shafarevich, Igor Rostislavovich

1994-01-01

Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...

Canonical differential geometry of string backgrounds

International Nuclear Information System (INIS)

Schuller, Frederic P.; Wohlfarth, Mattias N.R.

2006-01-01

String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate differential geometric structure which is of relevance for the minimal surface equation in such a generalized geometry. In particular the notion of a derivative action of areas on areas emerges naturally. Area metric geometry provides new tools in differential geometry, which promise to play a role in the description of gravitational dynamics on D-branes

The Beauty of Geometry

Science.gov (United States)

Morris, Barbara H.

2004-01-01

This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…

Teaching Spatial Geometry in a Virtual World

DEFF Research Database (Denmark)

Förster, Klaus-Tycho

2017-01-01

Spatial geometry is one of the fundamental mathematical building blocks of any engineering education. However, it is overshadowed by planar geometry in the curriculum between playful early primary education and later analytical geometry, leaving a multi-year gap where spatial geometry is absent...

Trends and developments in computational geometry

NARCIS (Netherlands)

Berg, de M.

1997-01-01

This paper discusses some trends and achievements in computational geometry during the past five years, with emphasis on problems related to computer graphics. Furthermore, a direction of research in computational geometry is discussed that could help in bringing the fields of computational geometry

An approach for management of geometry data

Science.gov (United States)

Dube, R. P.; Herron, G. J.; Schweitzer, J. E.; Warkentine, E. R.

1980-01-01

The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.

"WGL," a Web Laboratory for Geometry

Science.gov (United States)

Quaresma, Pedro; Santos, Vanda; Maric, Milena

2018-01-01

The role of information and communication technologies (ICT) in education is nowadays well recognised. The "Web Geometry Laboratory," is an e-learning, collaborative and adaptive, Web environment for geometry, integrating a well known dynamic geometry system. In a collaborative session, teachers and students, engaged in solving…

Analytische Geometrie

Science.gov (United States)

Kemnitz, Arnfried

Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.

Connections between algebra, combinatorics, and geometry

CERN Document Server

Sather-Wagstaff, Sean

2014-01-01

Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resou...

Algebraic Geometry and Number Theory Summer School

CERN Document Server

Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk

2017-01-01

This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

Applications of Affine and Weyl geometry

CERN Document Server

García-Río, Eduardo; Nikcevic, Stana

2013-01-01

Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannia

The Idea of Order at Geometry Class.

Science.gov (United States)

Rishel, Thomas

The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…

Special geometry

International Nuclear Information System (INIS)

Strominger, A.

1990-01-01

A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)

Using Dynamic Geometry Software to Improve Eight Grade Students' Understanding of Transformation Geometry

Science.gov (United States)

Guven, Bulent

2012-01-01

This study examines the effect of dynamic geometry software (DGS) on students' learning of transformation geometry. A pre- and post-test quasi-experimental design was used. Participants in the study were 68 eighth grade students (36 in the experimental group and 32 in the control group). While the experimental group students were studying the…

Disformal transformation in Newton-Cartan geometry

Energy Technology Data Exchange (ETDEWEB)

Huang, Peng [Zhejiang Chinese Medical University, Department of Information, Hangzhou (China); Sun Yat-Sen University, School of Physics and Astronomy, Guangzhou (China); Yuan, Fang-Fang [Nankai University, School of Physics, Tianjin (China)

2016-08-15

Newton-Cartan geometry has played a central role in recent discussions of the non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can easily be rephrased in terms of Newton-Cartan geometry, we show that it requires a nontrivial procedure to arrive at the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained transformation, we use it to induce a geometric structure which may be seen as a particular non-relativistic version of the Weyl integrable geometry. (orig.)

Geometry and symmetry

CERN Document Server

Yale, Paul B

2012-01-01

This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi

Optimizing solar-cell grid geometry

Science.gov (United States)

Crossley, A. P.

1969-01-01

Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.

Geometry and Cloaking Devices

Science.gov (United States)

Ochiai, T.; Nacher, J. C.

2011-09-01

Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.

A first course in geometry

CERN Document Server

Walsh, Edward T

2014-01-01

This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl

Global affine differential geometry of hypersurfaces

CERN Document Server

Li, An-Min; Zhao, Guosong; Hu, Zejun

2015-01-01

This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.

Point Picking and Distributing on the Disc and Sphere

Science.gov (United States)

2015-07-01

interesting application of geodesic subdivision is the design of domes, buildings, and structures (e.g., Spaceship Earth14 at Epcot, Walt Disney World; the...Computational Geometry in C. Cambridge (United Kingdom): Cambridge University Press; 1993. 41 14. Spaceship Earth. Walt Disney World; [accessed 2014

Spectral dimension of quantum geometries

International Nuclear Information System (INIS)

Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

2014-01-01

The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)

Algebraic geometry

CERN Document Server

Lefschetz, Solomon

2005-01-01

An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

A geometry calibration method for rotation translation trajectory

International Nuclear Information System (INIS)

Zhang Jun; Yan Bin; Li Lei; Lu Lizhong; Zhang Feng

2013-01-01

In cone-beam CT imaging system, it is difficult to directly measure the geometry parameters. In this paper, a geometry calibration method for rotation translation trajectory is proposed. Intrinsic parameters are solved from the relationship built on geometry parameter of the system and projection trajectory of calibration object. Parameters of rotation axis are extrapolated from the unified intrinsic parameter, and geometry parameters of the idle trajectory are acquired too. The calibration geometry can be analytically determined using explicit formulae, it can avoid getting into local optimum in iterative way. Simulation experiments are carried out on misaligned geometry, experiment results indicate that geometry artifacts due to misaligned geometry are effectively depressed by the proposed method, and the image quality is enhanced. (authors)

Geometry modeling for SAM-CE Monte Carlo calculations

International Nuclear Information System (INIS)

Steinberg, H.A.; Troubetzkoy, E.S.

1980-01-01

Three geometry packages have been developed and incorporated into SAM-CE, for representing in three dimensions the transport medium. These are combinatorial geometry - a general (non-lattice) system, complex combinatorial geometry - a very general system with lattice capability, and special reactor geometry - a special purpose system for light water reactor geometries. Their different attributes are described

Molecular motion in restricted geometries

Indian Academy of Sciences (India)

Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...

Advances in discrete differential geometry

CERN Document Server

2016-01-01

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...

An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary Representation Geometry to Constructive Solid Geometry

Science.gov (United States)

2015-12-01

ARL-SR-0347 ● DEC 2015 US Army Research Laboratory An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary...US Army Research Laboratory An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary Representation Geometry to...from Non-Uniform Rational B-Spline Boundary Representation Geometry to Constructive Solid Geometry 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c

W-geometry

International Nuclear Information System (INIS)

Hull, C.M.

1993-01-01

The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)

Head First 2D Geometry

CERN Document Server

Fallow), Stray

2009-01-01

Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and

Numerically robust geometry engine for compound solid geometries

International Nuclear Information System (INIS)

Vlachoudis, V.; Sinuela-Pastor, D.

2013-01-01

Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)

Quantification of Porcine Vocal Fold Geometry.

Science.gov (United States)

Stevens, Kimberly A; Thomson, Scott L; Jetté, Marie E; Thibeault, Susan L

2016-07-01

The aim of this study was to quantify porcine vocal fold medial surface geometry and three-dimensional geometric distortion induced by freezing the larynx, especially in the region of the vocal folds. The medial surface geometries of five excised porcine larynges were quantified and reported. Five porcine larynges were imaged in a micro-CT scanner, frozen, and rescanned. Segmentations and three-dimensional reconstructions were used to quantify and characterize geometric features. Comparisons were made with geometry data previously obtained using canine and human vocal folds as well as geometries of selected synthetic vocal fold models. Freezing induced an overall expansion of approximately 5% in the transverse plane and comparable levels of nonuniform distortion in sagittal and coronal planes. The medial surface of the porcine vocal folds was found to compare reasonably well with other geometries, although the compared geometries exhibited a notable discrepancy with one set of published human female vocal fold geometry. Porcine vocal folds are qualitatively geometrically similar to data available for canine and human vocal folds, as well as commonly used models. Freezing of tissue in the larynx causes distortion of around 5%. The data can provide direction in estimating uncertainty due to bulk distortion of tissue caused by freezing, as well as quantitative geometric data that can be directly used in developing vocal fold models. Copyright © 2016 The Voice Foundation. Published by Elsevier Inc. All rights reserved.

Lectures on discrete geometry

CERN Document Server

2002-01-01

Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...

Discrete and computational geometry

CERN Document Server

Devadoss, Satyan L

2011-01-01

Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...

A prediction for bubbling geometries

OpenAIRE

Okuda, Takuya

2007-01-01

We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.

Geometry -----------~--------------RESONANCE

Indian Academy of Sciences (India)

Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.

Intermediate algebra & analytic geometry

CERN Document Server

Gondin, William R

1967-01-01

Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system

Prediction and error growth in the daily forecast of precipitation from the NCEP CFSv2 over the subdivisions of Indian subcontinent

Science.gov (United States)

Pandey, Dhruva Kumar; Rai, Shailendra; Sahai, A. K.; Abhilash, S.; Shahi, N. K.

2016-02-01

This study investigates the forecast skill and predictability of various indices of south Asian monsoon as well as the subdivisions of the Indian subcontinent during JJAS season for the time domain of 2001-2013 using NCEP CFSv2 output. It has been observed that the daily mean climatology of precipitation over the land points of India is underestimated in the model forecast as compared to observation. The monthly model bias of precipitation shows the dry bias over the land points of India and also over the Bay of Bengal, whereas the Himalayan and Arabian Sea regions show the wet bias. We have divided the Indian landmass into five subdivisions namely central India, southern India, Western Ghat, northeast and southern Bay of Bengal regions based on the spatial variation of observed mean precipitation in JJAS season. The underestimation over the land points of India during mature phase was originated from the central India, southern Bay of Bengal, southern India and Western Ghat regions. The error growth in June forecast is slower as compared to July forecast in all the regions. The predictability error also grows slowly in June forecast as compared to July forecast in most of the regions. The doubling time of predictability error was estimated to be in the range of 3-5 days for all the regions. Southern India and Western Ghats are more predictable in the July forecast as compared to June forecast, whereas IMR, northeast, central India and southern Bay of Bengal regions have the opposite nature.

Geometry The Language of Space and Form (Revised Edition)

CERN Document Server

Tabak, John

2011-01-01

Geometry, Revised Edition describes geometry in antiquity. Beginning with a brief description of some of the geometry that preceded the geometry of the Greeks, it takes up the story of geometry during the European Renaissance as well as the significant mathematical progress in other areas of the world. It also discusses the analytic geometry of Ren Descartes and Pierre Fermat, the alternative coordinate systems invented by Isaac Newton, and the solid geometry of Leonhard Euler. Also included is an overview of the geometry of one of the most successful mathematicians of the 19th century, Bernha

From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks

Science.gov (United States)

Jupri, Al

2017-04-01

In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems - considered as tasks inviting the use of problem solving and reasoning skills - theoretically in the light of the RME principles. Second, we tested two problems to 31 undergraduate students of mathematics education program and other two problems to 16 master students of primary mathematics education program. Finally, we analyzed student written work and compared these empirical to the theoretical results. We found that there are discrepancies between what we expected theoretically and what occurred empirically in terms of mathematization and of intertwinement of mathematical concepts from geometry to algebra and vice versa. We conclude that the RME principles provide a fruitful framework for analyzing geometry tasks that, for instance, are intended for assessing student problem solving and reasoning skills.

Differential geometry curves, surfaces, manifolds

CERN Document Server

Kohnel, Wolfgang

2002-01-01

This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.

Projective Geometry

Indian Academy of Sciences (India)

mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.

Second International workshop Geometry and Symbolic Computation

CERN Document Server

Walczak, Paweł; Geometry and its Applications

2014-01-01

This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups, and osculation; the articles in the applications portion concern some particular problems of the theory of dynamical systems, including mathematical problems of liquid flows and a study of cycles for non-dynamical systems. This Work is based on the second international workshop entitled "Geometry and Symbolic Computations," held on May 15-18, 2013 at the University of Haifa and is dedicated to modeling (using symbolic calculations) in differential geometry and its applications in fields such as computer science, tomography, and mechanics. It is intended to create a forum for students and researchers in pure and applied geometry to promote discussion of modern state-of-the-art in geometric modeling using symbolic programs such as Maple™ and Mathematica®, as well as presentation of new results. ...

Network geometry with flavor: From complexity to quantum geometry

Science.gov (United States)

Bianconi, Ginestra; Rahmede, Christoph

2016-03-01

Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but

The Persistification of the ATLAS Geometry

CERN Document Server

AUTHOR|(INSPIRE)INSPIRE-00068562; The ATLAS collaboration; Bianchi, Riccardo-Maria

2016-01-01

The complex geometry of the whole detector of the ATLAS experiment at LHC is currently stored only in custom online databases, from which it is built on-the- y on request. Accessing the online geometry guarantees accessing the latest version of the detector description, but requires the setup of the full ATLAS so ware framework “Athena”, which provides the online services and the tools to retrieve the data from the database. is operation is cumbersome and slows down the applications that need to access the geometry. Moreover, all applications that need to access the detector geom- etry need to be built and run on the same platform as the ATLAS framework, preventing the usage of the actual detector geometry in stand-alone applications. Here we propose a new mechanism to persistify and serve the geometry of HEP experiments. e new mechanism is composed by a new le format and a REST API. e new le format allows to store the whole detector description locally in a at le, and it is especially optimized to descri...

Implosions and hypertoric geometry

DEFF Research Database (Denmark)

Dancer, A.; Kirwan, F.; Swann, A.

2013-01-01

The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....

Granular flows in constrained geometries

Science.gov (United States)

Murthy, Tejas; Viswanathan, Koushik

Confined geometries are widespread in granular processing applications. The deformation and flow fields in such a geometry, with non-trivial boundary conditions, determine the resultant mechanical properties of the material (local porosity, density, residual stresses etc.). We present experimental studies of deformation and plastic flow of a prototypical granular medium in different nontrivial geometries- flat-punch compression, Couette-shear flow and a rigid body sliding past a granular half-space. These geometries represent simplified scaled-down versions of common industrial configurations such as compaction and dredging. The corresponding granular flows show a rich variety of flow features, representing the entire gamut of material types, from elastic solids (beam buckling) to fluids (vortex-formation, boundary layers) and even plastically deforming metals (dead material zone, pile-up). The effect of changing particle-level properties (e.g., shape, size, density) on the observed flows is also explicitly demonstrated. Non-smooth contact dynamics particle simulations are shown to reproduce some of the observed flow features quantitatively. These results showcase some central challenges facing continuum-scale constitutive theories for dynamic granular flows.

A vector space approach to geometry

CERN Document Server

Hausner, Melvin

2010-01-01

The effects of geometry and linear algebra on each other receive close attention in this examination of geometry's correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.

Integral geometry and valuations

CERN Document Server

Solanes, Gil

2014-01-01

Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...

CBM RICH geometry optimization

Energy Technology Data Exchange (ETDEWEB)

Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration

2016-07-01

The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.

Riemannian geometry

CERN Document Server

Petersen, Peter

2016-01-01

Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...

Kaehler geometry and SUSY mechanics

International Nuclear Information System (INIS)

Bellucci, Stefano; Nersessian, Armen

2001-01-01

We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed

GPS: Geometry, Probability, and Statistics

Science.gov (United States)

Field, Mike

2012-01-01

It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS

Energy Technology Data Exchange (ETDEWEB)

Singer, Isadore M.

2008-03-04

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.

Final Report: Geometry And Elementary Particle Physics

International Nuclear Information System (INIS)

Singer, Isadore M.

2008-01-01

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.

Discrete quantum geometries and their effective dimension

International Nuclear Information System (INIS)

Thuerigen, Johannes

2015-01-01

In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.

Introduction into integral geometry and stereology

DEFF Research Database (Denmark)

Kiderlen, Markus

Statistics and Random Fields and is a self-containing introduction into integral geometry and its applications in stereology. The most important integral geometric tools for stereological applications are kinematic formulas and results of Blaschke-Petkantschin type. Therefore, Crofton's formula......This text is the extended version of two talks held at the Summer Academy Stochastic Geometry, Spatial Statistics and Random Fields in the Soellerhaus, Germany, in September 2009. It forms (with slight modifications) a chapter of the Springer lecture notes Lectures on Stochastic Geometry, Spatial...

Surrogate Modeling for Geometry Optimization

DEFF Research Database (Denmark)

Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie

2009-01-01

A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....

Geometric control theory and sub-Riemannian geometry

CERN Document Server

Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario

2014-01-01

This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as  sub-Riemannian, Finslerian  geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods  has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group  of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.

Special metrics and group actions in geometry

CERN Document Server

Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi

2017-01-01

The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.

A Whirlwind Tour of Computational Geometry.

Science.gov (United States)

Graham, Ron; Yao, Frances

1990-01-01

Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)

Monte Carlo simulation of fully Markovian stochastic geometries

International Nuclear Information System (INIS)

Lepage, Thibaut; Delaby, Lucie; Malvagi, Fausto; Mazzolo, Alain

2010-01-01

The interest in resolving the equation of transport in stochastic media has continued to increase these last years. For binary stochastic media it is often assumed that the geometry is Markovian, which is never the case in usual environments. In the present paper, based on rigorous mathematical theorems, we construct fully two-dimensional Markovian stochastic geometries and we study their main properties. In particular, we determine a percolation threshold p c , equal to 0.586 ± 0.0015 for such geometries. Finally, Monte Carlo simulations are performed through these geometries and the results compared to homogeneous geometries. (author)

Tidal stresses and energy gaps in microstate geometries

Science.gov (United States)

Tyukov, Alexander; Walker, Robert; Warner, Nicholas P.

2018-02-01

We compute energy gaps and study infalling massive geodesic probes in the new families of scaling, microstate geometries that have been constructed recently and for which the holographic duals are known. We find that in the deepest geometries, which have the lowest energy gaps, the geodesic deviation shows that the stress reaches the Planck scale long before the probe reaches the cap of the geometry. Such probes must therefore undergo a stringy transition as they fall into microstate geometry. We discuss the scales associated with this transition and comment on the implications for scrambling in microstate geometries.

VIII International Meeting on Lorentzian Geometry

CERN Document Server

Flores, José; Palomo, Francisco; GeLoMa 2016; Lorentzian geometry and related topics

2017-01-01

This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathem...

Transformational plane geometry

CERN Document Server

Umble, Ronald N

2014-01-01

Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...

Multilevel geometry optimization

Science.gov (United States)

Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.

2000-02-01

Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.

Fractal geometry mathematical foundations and applications

CERN Document Server

Falconer, Kenneth

2013-01-01

The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals.  The book introduces and develops the general theory and applica

Planning for Evolution in a Production Environment: Migration from a Legacy Geometry Code to an Abstract Geometry Modeling Language in STAR

Science.gov (United States)

Webb, Jason C.; Lauret, Jerome; Perevoztchikov, Victor

2012-12-01

Increasingly detailed descriptions of complex detector geometries are required for the simulation and analysis of today's high-energy and nuclear physics experiments. As new tools for the representation of geometry models become available during the course of an experiment, a fundamental challenge arises: how best to migrate from legacy geometry codes developed over many runs to the new technologies, such as the ROOT/TGeo [1] framework, without losing touch with years of development, tuning and validation. One approach, which has been discussed within the community for a number of years, is to represent the geometry model in a higher-level language independent of the concrete implementation of the geometry. The STAR experiment has used this approach to successfully migrate its legacy GEANT 3-era geometry to an Abstract geometry Modelling Language (AgML), which allows us to create both native GEANT 3 and ROOT/TGeo implementations. The language is supported by parsers and a C++ class library which enables the automated conversion of the original source code to AgML, supports export back to the original AgSTAR[5] representation, and creates the concrete ROOT/TGeo geometry implementation used by our track reconstruction software. In this paper we present our approach, design and experience and will demonstrate physical consistency between the original AgSTAR and new AgML geometry representations.

MIFT: GIFT Combinatorial Geometry Input to VCS Code

Science.gov (United States)

1977-03-01

r-w w-^ H ^ß0318is CQ BRL °RCUMr REPORT NO. 1967 —-S: ... MIFT: GIFT COMBINATORIAL GEOMETRY INPUT TO VCS CODE Albert E...TITLE (and Subtitle) MIFT: GIFT Combinatorial Geometry Input to VCS Code S. TYPE OF REPORT & PERIOD COVERED FINAL 6. PERFORMING ORG. REPORT NUMBER...Vehicle Code System (VCS) called MORSE was modified to accept the GIFT combinatorial geometry package. GIFT , as opposed to the geometry package

Physical meaning of the optical reference geometry

International Nuclear Information System (INIS)

Abramowicz, M.A.

1990-09-01

I show that contrary to a popular misconception the optical reference geometry, introduced a few years ago as a formally possible metric of a 3-space corresponding to a static spacetime, is quite satisfactory also from the physical point of view. The optical reference geometry has a clear physical meaning, as it may be constructed experimentally by measuring light round travel time between static observers. Distances and directions in the optical reference geometry are more strongly connected to experiment than distances and directions in the widely used directly projected metric (discussed e.g. in Landau and Lifshitz textbook. In addition, the optical reference geometry is more natural and convenient than the directly projected one in application to dynamics. In the optical geometry dynamical behaviour of matter is described by concepts and formulae identical to those well known in Newtonian dynamics on a given two dimensional (curved) surface. (author). 22 refs

The Tools of Financial Policy in the Dairy Products Subdivision of the Agroindustrial Complex

Directory of Open Access Journals (Sweden)

Bielosviet Oleksandr. V.

2017-03-01

Full Text Available The article is aimed at definition and classification of tools of the State financial policy in the dairy products subdivision of the agroindustrial complex (DPS of AIC. The article considers the financial policy tools used in terms of targeted programs of the State support for the DPS of AIC: the State target program for development of Ukrainian villages, sectoral program for dairy breeding and the project of the conception of the State target program for development of dairy breeding in Ukraine for the period up to 2020. The existing tools are divided into direct and indirect action tools. As of 2016, the tasks that were relevant to the corresponding targeted programs have not been implemented on any item, except for the milk productivity of cows. Still the productivity indicator of 4500 kg/year of milk from a cow is low enough and does not correspond to the general world-wide tendencies. This suggests the need for further assessment of the existing list of tools with a view to adjusting them and defining priorities for the State support of the DPS of AIC.

Geometric Transformations in Engineering Geometry

Directory of Open Access Journals (Sweden)

I. F. Borovikov

2015-01-01

Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry

Transformasi Geometri Rotasi Berbantuan Software Geogebra

Directory of Open Access Journals (Sweden)

Muhamad Hanafi

2018-02-01

Full Text Available Penelitian  ini bertujuan untuk membantu visualisasi dan menemukan konsep pada Transformasi geometri Rotasi di titik Pusat  dengan menggunakan software GeoGebra. Penelitian ini mengulas tentang Koordinat Kartesius dan Polar, dan selanjutntya Transformasi geometri Rotasi di titik Pusat .

Algebra, Geometry and Mathematical Physics Conference

CERN Document Server

Paal, Eugen; Silvestrov, Sergei; Stolin, Alexander

2014-01-01

This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers a...

Homological mirror symmetry and tropical geometry

CERN Document Server

Catanese, Fabrizio; Kontsevich, Maxim; Pantev, Tony; Soibelman, Yan; Zharkov, Ilia

2014-01-01

The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory, and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Ge...

Use of information technologies in teaching course "Analytical geometry" in higher schools on example of software "ANALYTICAL GEOMETRY"

OpenAIRE

V. B. Grigorieva

2009-01-01

In article are considered the methodical questions of using of computer technologies, for example, the software "Analytical geometry", in process of teaching course of analytical geometry in the higher school.

Variable geometry Darrieus wind machine

Science.gov (United States)

Pytlinski, J. T.; Serrano, D.

1983-08-01

A variable geometry Darrieus wind machine is proposed. The lower attachment of the blades to the rotor can move freely up and down the axle allowing the blades of change shape during rotation. Experimental data for a 17 m. diameter Darrieus rotor and a theoretical model for multiple streamtube performance prediction were used to develop a computer simulation program for studying parameters that affect the machine's performance. This new variable geometry concept is described and interrelated with multiple streamtube theory through aerodynamic parameters. The computer simulation study shows that governor behavior of a Darrieus turbine can not be attained by a standard turbine operating within normally occurring rotational velocity limits. A second generation variable geometry Darrieus wind turbine which uses a telescopic blade is proposed as a potential improvement on the studied concept.

Flux compactifications and generalized geometries

International Nuclear Information System (INIS)

Grana, Mariana

2006-01-01

Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T 6 /(Z 3 x Z 3 ) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry

Flux compactifications and generalized geometries

Energy Technology Data Exchange (ETDEWEB)

Grana, Mariana [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France)

2006-11-07

Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T{sup 6} /(Z{sub 3} x Z{sub 3}) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.

Curvature tensor copies in affine geometry

International Nuclear Information System (INIS)

Srivastava, P.P.

1981-01-01

The sets of space-time and spin-connections which give rise to the same curvature tensor are constructed. The corresponding geometries are compared. Results are illustrated by an explicit calculation and comment on the copies in Einstein-Cartan and Weyl-Cartan geometries. (Author) [pt

Poisson geometry from a Dirac perspective

Science.gov (United States)

Meinrenken, Eckhard

2018-03-01

We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop Quantum Groups and Gravity at the University of Waterloo, April 2016.

Development of the geometry database for the CBM experiment

Science.gov (United States)

Akishina, E. P.; Alexandrov, E. I.; Alexandrov, I. N.; Filozova, I. A.; Friese, V.; Ivanov, V. V.

2018-01-01

The paper describes the current state of the Geometry Database (Geometry DB) for the CBM experiment. The main purpose of this database is to provide convenient tools for: (1) managing the geometry modules; (2) assembling various versions of the CBM setup as a combination of geometry modules and additional files. The CBM users of the Geometry DB may use both GUI (Graphical User Interface) and API (Application Programming Interface) tools for working with it.

SABRINA, Geometry Plot Program for MCNP

International Nuclear Information System (INIS)

SEIDL, Marcus

2003-01-01

1 - Description of program or function: SABRINA is an interactive, three-dimensional, geometry-modeling code system, primarily for use with CCC-200/MCNP. SABRINA's capabilities include creation, visualization, and verification of three-dimensional geometries specified by either surface- or body-base combinatorial geometry; display of particle tracks are calculated by MCNP; and volume fraction generation. 2 - Method of solution: Rendering is performed by ray tracing or an edge and intersection algorithm. Volume fraction calculations are made by ray tracing. 3 - Restrictions on the complexity of the problem: A graphics display with X Window capability is required

Differential geometry and topology of curves

CERN Document Server

Animov, Yu

2001-01-01

Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.

Geometry of surfaces a practical guide for mechanical engineers

CERN Document Server

Radzevich, Stephen P

2012-01-01

Presents an in-depth analysis of geometry of part surfaces and provides the tools for solving complex engineering problems Geometry of Surfaces: A Practical Guide for Mechanical Engineers is a comprehensive guide to applied geometry of surfaces with focus on practical applications in various areas of mechanical engineering. The book is divided into three parts on Part Surfaces, Geometry of Contact of Part Surfaces and Mapping of the Contacting Part Surfaces. Geometry of Surfaces: A Practical Guide for Mechanical Engineers combines differential geometry and gearing theory and presents new developments in the elementary theory of enveloping surfaces. Written by a leading expert of the field, this book also provides the reader with the tools for solving complex engineering problems in the field of mechanical engineering. Presents an in-depth analysis of geometry of part surfaces Provides tools for solving complex engineering problems in the field of mechanical engineering Combines differential geometry an...

Multilevel geometry optimization

Energy Technology Data Exchange (ETDEWEB)

Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)

2000-02-15

Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.

Machine learning spatial geometry from entanglement features

Science.gov (United States)

You, Yi-Zhuang; Yang, Zhao; Qi, Xiao-Liang

2018-02-01

Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on a 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS3 spatial geometry) as we tune the fermion system towards the gapless critical point (CFT2 point).

GEOMETRY – AN IMPORTANT MEANS OF EDUCATION IN THE CIVILISATION SCOPE

OpenAIRE

Liliana TOCARIU, PhD

2017-01-01

Geometry (from the Greek: γεωμετρία; geo = earth, metria = measure) is a genuine science, rooted in mathematics, which studies the plane and spatial forms of bodies from the objective or conceptual reality and the nature of the relationship that exists between them. Due to its complexity, geometry is divided into: Euclidian geometry, analytical geometry, descriptive geometry, projective geometry, kinematic geometry, surface and curve differential geometry, axiomatic geometry,...

Random geometry and Yang-Mills theory

International Nuclear Information System (INIS)

Froehlich, J.

1981-01-01

The author states various problems and discusses a very few preliminary rigorous results in a branch of mathematics and mathematical physics which one might call random (or stochastic) geometry. Furthermore, he points out why random geometry is important in the quantization of Yang-Mills theory. (Auth.)

Quantification of variability in bedform geometry

NARCIS (Netherlands)

van der Mark, C.F.; Blom, Astrid; Hulscher, Suzanne J.M.H.

2008-01-01

We analyze the variability in bedform geometry in laboratory and field studies. Even under controlled steady flow conditions in laboratory flumes, bedforms are irregular in size, shape, and spacing, also in case of well-sorted sediment. Our purpose is to quantify the variability in bedform geometry.

10th China-Japan Geometry Conference

CERN Document Server

Miyaoka, Reiko; Tang, Zizhou; Zhang, Weiping

2016-01-01

Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the Yau–Tian–Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger–Yau–Zaslow conjecture on mirror symmetry, the relative Yau–Tian–Donaldson conjecture in Kähler geometry, the Hopf conjecture, and the Yau conjecture on the first eigenvalue of an embedded minimal hypersurface of the sphere. For the younger generation to approach such problems and obtain the required techniques, it is of the utmost importance to provide them with up-to-date information from leading specialists. The geometry conference for the friendship of China and Japan has achieved this purpose during the past 10 years. Their talks deal with problems at the highest level, often accompanied with solutions and ideas, which extend across various fields in Riemannian geometry, sympl...

DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS

International Nuclear Information System (INIS)

BERG, J.S.; JOHNSTONE, C.; SUMMERS, D.

2001-01-01

Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective

Increasing insightful thinking in analytic geometry

NARCIS (Netherlands)

Timmer, Mark; Verhoef, Neeltje Cornelia

Elsewhere in this issue Ferdinand Verhulst described the discussion of the interaction of analysis and geometry in the 19th century. In modern times such discussions come up again and again. As of 2014, synthetic geometry will not be part of the Dutch 'vwo - mathematics B' programme anymore.

Development and application of CATIA-GDML geometry builder

International Nuclear Information System (INIS)

Belogurov, S; Chernogorov, A; Ovcharenko, E; Schetinin, V; Berchun, Yu; Malzacher, P

2014-01-01

Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. The paper presents an update on functionality and application practice of the CATIA-GDML geometry builder first introduced at CHEP2010. This set of CATIAv5 tools has been developed for building a MC optimized GEANT4/ROOT compatible geometry based on the existing CAD model. The model can be exported via Geometry Description Markup Language (GDML). The builder allows also import and visualization of GEANT4/ROOT geometries in CATIA. The structure of a GDML file, including replicated volumes, volume assemblies and variables, is mapped into a part specification tree. A dedicated file template, a wide range of primitives, tools for measurement and implicit calculation of parameters, different types of multiple volume instantiation, mirroring, positioning and quality check have been implemented. Several use cases are discussed.

Remarks on Hamiltonian structures in G2-geometry

International Nuclear Information System (INIS)

Cho, Hyunjoo; Salur, Sema; Todd, A. J.

2013-01-01

In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry

Classical geometry Euclidean, transformational, inversive, and projective

CERN Document Server

Leonard, I E; Liu, A C F; Tokarsky, G W

2014-01-01

Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which p

MOCUM: A two-dimensional method of characteristics code based on constructive solid geometry and unstructured meshing for general geometries

International Nuclear Information System (INIS)

Yang Xue; Satvat, Nader

2012-01-01

Highlight: ► A two-dimensional numerical code based on the method of characteristics is developed. ► The complex arbitrary geometries are represented by constructive solid geometry and decomposed by unstructured meshing. ► Excellent agreement between Monte Carlo and the developed code is observed. ► High efficiency is achieved by parallel computing. - Abstract: A transport theory code MOCUM based on the method of characteristics as the flux solver with an advanced general geometry processor has been developed for two-dimensional rectangular and hexagonal lattice and full core neutronics modeling. In the code, the core structure is represented by the constructive solid geometry that uses regularized Boolean operations to build complex geometries from simple polygons. Arbitrary-precision arithmetic is also used in the process of building geometry objects to eliminate the round-off error from the commonly used double precision numbers. Then, the constructed core frame will be decomposed and refined into a Conforming Delaunay Triangulation to ensure the quality of the meshes. The code is fully parallelized using OpenMP and is verified and validated by various benchmarks representing rectangular, hexagonal, plate type and CANDU reactor geometries. Compared with Monte Carlo and deterministic reference solution, MOCUM results are highly accurate. The mentioned characteristics of the MOCUM make it a perfect tool for high fidelity full core calculation for current and GenIV reactor core designs. The detailed representation of reactor physics parameters can enhance the safety margins with acceptable confidence levels, which lead to more economically optimized designs.

Electrodynamics and Spacetime Geometry: Foundations

Science.gov (United States)

Cabral, Francisco; Lobo, Francisco S. N.

2017-02-01

We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.

Dayside merging and cusp geometry

International Nuclear Information System (INIS)

Crooker, N.U.

1979-01-01

Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 0 provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle

Digital and discrete geometry theory and algorithms

CERN Document Server

Chen, Li

2014-01-01

This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData.The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and a

Attitudes of High School Students towards Geometry

Directory of Open Access Journals (Sweden)

Esat Avcı

2014-12-01

Full Text Available In this research, attitudes of high school students towards geometry were investigated in terms of gender, grade, types of the field and school. Population of research includes students who were studying at high school in five distincs of Mersin in 2013-2014 academical year. Sample of research includes 935 students from twelve high schools. Attitude scale which was developed by Su-Özenir (2008 was used for data collection. For data analysis, mean, standart deviation, t test and ANOVA were used. A meaningful difference between students’ attitudes towards geometry and variance of gender and grade level wasn’t observed, on the other hand a meaningful difference according to field and school type is observed.Key Words:    Attitudes towards geometry, high school geometry lesson, attitude scale

Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach

OpenAIRE

Bertram, Wolfgang

2013-01-01

By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via exercises using dynamical software (such as geogebra), hopefully accessible to a wide mathematical audience, from undergraduate students and high school teachers to researchers, proceeding in three steps: (1) experimental geometry, (2) algebra (linear algebr...

A Study of Geometry Content Knowledge of Elementary Preservice Teachers

Directory of Open Access Journals (Sweden)

Fatma ASLAN-TUTAK

2015-06-01

Full Text Available The purpose of this research is to examine preservice elementary school teachers’ geometry learning as investigated by both qualitative and quantitative methods. For the qualitative investigation, narrative analysis and thematic analysis methods were used. The findings of narrative analysis indicated two main kinds of stories: as a learner and as a beginning teacher. The thematic analysis findings yield to three themes: history of learning geometry, perceptions about geometry, effective geometry instructional practices. The findings informed the quantitative investigation on geometry content knowledge for the case of quadrilaterals. During the second phase of the study, 102 participants who enrolled in the methods course completed pre and post test of teachers’ geometry content knowledge. Treatment group participants (n=54 received series of activities (geometry activities and student work analysis focusing on quadrilaterals, and control group participants (n=48 received traditional instruction. Repeated measures ANOVA results showed a significant change in treatment group participants’ geometry content knowledge. The mixed ANOVA results indicated a significant main effect of knowledge but no significant interaction between geometry content knowledge and grouping. Even though treatment group participants’ geometry content knowledge growth was significant, the difference between treatment group and control group participants’ growth in geometry content knowledge was not significant. This study informs mathematics teacher education in three important areas; limited knowledge of preservice teachers’ geometry content knowledge, integrating mathematics content and the context of teaching into methods course, and use of student work with preservice teachers.

A study of geometry content knowledge of elementary preservice teachers

Directory of Open Access Journals (Sweden)

Fatma Aslan Tutak

2015-06-01

Full Text Available The purpose of this research is to examine preservice elementary school teachers’ geometry learning as investigated by both qualitative and quantitative methods. For the qualitative investigation, narrative analysis and thematic analysis methods were used. The findings of narrative analysis indicated two main kinds of stories: as a learner and as a beginning teacher. The thematic analysis findings yield to three themes: history of learning geometry, perceptions about geometry, effective geometry instructional practices. The findings informed the quantitative investigation on geometry content knowledge for the case of quadrilaterals. During the second phase of the study, 102 participants who enrolled in the methods course completed pre and post test of teachers’ geometry content knowledge. Treatment group participants (n=54 received series of activities (geometry activities and student work analysis focusing on quadrilaterals, and control group participants (n=48 received traditional instruction. Repeated measures ANOVA results showed a significant change in treatment group participants’ geometry content knowledge. The mixed ANOVA results indicated a significant main effect of knowledge but no significant interaction between geometry content knowledge and grouping. Even though treatment group participants’ geometry content knowledge growth was significant, the difference between treatment group and control group participants’ growth in geometry content knowledge was not significant. This study informs mathematics teacher education in three important areas; limited knowledge of preservice teachers’ geometry content knowledge, integrating mathematics content and the context of teaching into methods course, and use of student work with preservice teachers.

Combinatorial geometry in the plane

CERN Document Server

Hadwiger, Hugo; Klee, Victor

2014-01-01

Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa

Topology and geometry for physicists

CERN Document Server

Nash, Charles

1983-01-01

Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr

Fundamental concepts of geometry

CERN Document Server

Meserve, Bruce E

1983-01-01

Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

Non-commutative geometry inspired charged black holes

International Nuclear Information System (INIS)

Ansoldi, Stefano; Nicolini, Piero; Smailagic, Anais; Spallucci, Euro

2007-01-01

We find a new, non-commutative geometry inspired, solution of the coupled Einstein-Maxwell field equations describing a variety of charged, self-gravitating objects, including extremal and non-extremal black holes. The metric smoothly interpolates between de Sitter geometry, at short distance, and Reissner-Nordstrom geometry far away from the origin. Contrary to the ordinary Reissner-Nordstrom spacetime there is no curvature singularity in the origin neither 'naked' nor shielded by horizons. We investigate both Hawking process and pair creation in this new scenario

Euclidean geometry and its subgeometries

CERN Document Server

Specht, Edward John; Calkins, Keith G; Rhoads, Donald H

2015-01-01

In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...

Number theory III Diophantine geometry

CERN Document Server

1991-01-01

From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...

Riemannian geometry and geometric analysis

CERN Document Server

Jost, Jürgen

2017-01-01

This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research.  The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...

The Ganges basin geometry records a pre-15 Ma isostatic rebound of Himalaya

OpenAIRE

Mugnier , Jean-Louis; Huyghe , Pascale

2006-01-01

4 pages; The Tertiary continental strata of the Himalayan foreland basin are subdivided in two groups, but the meaning of this subdivision was previously unclear. From the analysis of drill-holes, seismic lines, dated sections, field outcrops and balanced cross-sections, we find that the southward migration rate of the deposition pinch-out of the younger group is 19 ± 5 mm/yr and equals the Himalayan shortening rate. This equality shows that the flexural foreland basin development is mainly c...

Comparison of different interpolation operators including nonlinear subdivision schemes in the simulation of particle trajectories

International Nuclear Information System (INIS)

Bensiali, Bouchra; Bodi, Kowsik; Ciraolo, Guido; Ghendrih, Philippe; Liandrat, Jacques

2013-01-01

In this work, we compare different interpolation operators in the context of particle tracking with an emphasis on situations involving velocity field with steep gradients. Since, in this case, most classical methods give rise to the Gibbs phenomenon (generation of oscillations near discontinuities), we present new methods for particle tracking based on subdivision schemes and especially on the Piecewise Parabolic Harmonic (PPH) scheme which has shown its advantage in image processing in presence of strong contrasts. First an analytic univariate case with a discontinuous velocity field is considered in order to highlight the effect of the Gibbs phenomenon on trajectory calculation. Theoretical results are provided. Then, we show, regardless of the interpolation method, the need to use a conservative approach when integrating a conservative problem with a velocity field deriving from a potential. Finally, the PPH scheme is applied in a more realistic case of a time-dependent potential encountered in the edge turbulence of magnetically confined plasmas, to compare the propagation of density structures (turbulence bursts) with the dynamics of test particles. This study highlights the difference between particle transport and density transport in turbulent fields

Graphical debugging of combinational geometry

International Nuclear Information System (INIS)

Burns, T.J.; Smith, M.S.

1992-01-01

A graphical debugger for combinatorial geometry being developed at Oak Ridge National Laboratory is described. The prototype debugger consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development

Introduction to topology and geometry

CERN Document Server

Stahl, Saul

2014-01-01

An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele

Description of SSG Geometry - phase 1

DEFF Research Database (Denmark)

Margheritini, Lucia; Kofoed, Jens Peter

The purpose of the study is to define the optimized geometry for the SSG in Svaheia, Norway and to provide the responsible for the turbines with useful information to their work.......The purpose of the study is to define the optimized geometry for the SSG in Svaheia, Norway and to provide the responsible for the turbines with useful information to their work....

Fractal geometry of high temperature superconductors

International Nuclear Information System (INIS)

Mosolov, A.B.

1989-01-01

Microstructural geometry of superconducting structural composites of Ag-Yba 2 Cu 3 O x system with a volumetric shave of silver from 0 to 60% is investigated by light and electron microscopy methods. It is ascertained that the structure of cermets investigated is characterized by fractal geometry which is sufficient for describing the electrical and mechanical properties of these materials

Morphing the feature-based multi-blocks of normative/healthy vertebral geometries to scoliosis vertebral geometries: development of personalized finite element models.

Science.gov (United States)

Hadagali, Prasannaah; Peters, James R; Balasubramanian, Sriram

2018-03-12

Personalized Finite Element (FE) models and hexahedral elements are preferred for biomechanical investigations. Feature-based multi-block methods are used to develop anatomically accurate personalized FE models with hexahedral mesh. It is tedious to manually construct multi-blocks for large number of geometries on an individual basis to develop personalized FE models. Mesh-morphing method mitigates the aforementioned tediousness in meshing personalized geometries every time, but leads to element warping and loss of geometrical data. Such issues increase in magnitude when normative spine FE model is morphed to scoliosis-affected spinal geometry. The only way to bypass the issue of hex-mesh distortion or loss of geometry as a result of morphing is to rely on manually constructing the multi-blocks for scoliosis-affected spine geometry of each individual, which is time intensive. A method to semi-automate the construction of multi-blocks on the geometry of scoliosis vertebrae from the existing multi-blocks of normative vertebrae is demonstrated in this paper. High-quality hexahedral elements were generated on the scoliosis vertebrae from the morphed multi-blocks of normative vertebrae. Time taken was 3 months to construct the multi-blocks for normative spine and less than a day for scoliosis. Efforts taken to construct multi-blocks on personalized scoliosis spinal geometries are significantly reduced by morphing existing multi-blocks.

Vectorising the detector geometry to optimize particle transport

CERN Document Server

Apostolakis, John; Carminati, Federico; Gheata, Andrei; Wenzel, Sandro

2014-01-01

Among the components contributing to particle transport, geometry navigation is an important consumer of CPU cycles. The tasks performed to get answers to "basic" queries such as locating a point within a geometry hierarchy or computing accurately the distance to the next boundary can become very computing intensive for complex detector setups. So far, the existing geometry algorithms employ mainly scalar optimisation strategies (voxelization, caching) to reduce their CPU consumption. In this paper, we would like to take a different approach and investigate how geometry navigation can benefit from the vector instruction set extensions that are one of the primary source of performance enhancements on current and future hardware. While on paper, this form of microparallelism promises increasing performance opportunities, applying this technology to the highly hierarchical and multiply branched geometry code is a difficult challenge. We refer to the current work done to vectorise an important part of the critica...

Students’ Errors in Geometry Viewed from Spatial Intelligence

Science.gov (United States)

Riastuti, N.; Mardiyana, M.; Pramudya, I.

2017-09-01

Geometry is one of the difficult materials because students must have ability to visualize, describe images, draw shapes, and know the kind of shapes. This study aim is to describe student error based on Newmans’ Error Analysis in solving geometry problems viewed from spatial intelligence. This research uses descriptive qualitative method by using purposive sampling technique. The datas in this research are the result of geometri material test and interview by the 8th graders of Junior High School in Indonesia. The results of this study show that in each category of spatial intelligence has a different type of error in solving the problem on the material geometry. Errors are mostly made by students with low spatial intelligence because they have deficiencies in visual abilities. Analysis of student error viewed from spatial intelligence is expected to help students do reflection in solving the problem of geometry.

Non-euclidean geometry

CERN Document Server

Coxeter, HSM

1965-01-01

This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.

Multiple-view, Multiple-selection Visualization of Simulation Geometry in CMS

International Nuclear Information System (INIS)

Bauerdick, L A T; Eulisse, G; Jones, C; McCauley, T; Osborne, I; Kovalskyi, D; Mrak Tadel, A; Tadel, M; Yagil, A

2012-01-01

Fireworks, the event-display program of CMS, was extended with an advanced geometry visualization package. ROOT's TGeo geometry is used as internal representation, shared among several geometry views. Each view is represented by a GUI list-tree widget, implemented as a flat vector to allow for fast searching, selection, and filtering by material type, node name, and shape type. Display of logical and physical volumes is supported. Color, transparency, and visibility flags can be modified for each node or for a selection of nodes. Further operations, like opening of a new view or changing of the root node, can be performed via a context menu. Node selection and graphical properties determined by the list-tree view can be visualized in any 3D graphics view of Fireworks. As each 3D view can display any number of geometry views, a user is free to combine different geometry-view selections within the same 3D view. Node-selection by proximity to a given point is possible. A visual clipping box can be set for each geometry view to limit geometry drawing into a specified region. Visualization of geometric overlaps, as detected by TGeo, is also supported. The geometry visualization package is used for detailed inspection and display of simulation geometry with or without the event data. It also serves as a tool for geometry debugging and inspection, facilitating development of geometries for CMS detector upgrades and for SLHC.

Geometry, topology, and string theory

Energy Technology Data Exchange (ETDEWEB)

Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)

2003-01-01

A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.

Stochastic geometry and its applications

CERN Document Server

Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph

2013-01-01

An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a

Spatial geometry and special relativity

DEFF Research Database (Denmark)

Kneubil, Fabiana Botelho

2016-01-01

In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame......-dependent and frame-independent entities. We depart from a subject well known by students, which is the three-dimensional geometric space in order to compare, afterwards, with the treatment of four-dimensional space in the special relativity. The differences and similarities between these two subjects are also...

Geometry, topology, and string theory

International Nuclear Information System (INIS)

Varadarajan, Uday

2003-01-01

A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated

Simultaneous calibration phantom commission and geometry calibration in cone beam CT

Science.gov (United States)

Xu, Yuan; Yang, Shuai; Ma, Jianhui; Li, Bin; Wu, Shuyu; Qi, Hongliang; Zhou, Linghong

2017-09-01

Geometry calibration is a vital step for describing the geometry of a cone beam computed tomography (CBCT) system and is a prerequisite for CBCT reconstruction. In current methods, calibration phantom commission and geometry calibration are divided into two independent tasks. Small errors in ball-bearing (BB) positioning in the phantom-making step will severely degrade the quality of phantom calibration. To solve this problem, we propose an integrated method to simultaneously realize geometry phantom commission and geometry calibration. Instead of assuming the accuracy of the geometry phantom, the integrated method considers BB centers in the phantom as an optimized parameter in the workflow. Specifically, an evaluation phantom and the corresponding evaluation contrast index are used to evaluate geometry artifacts for optimizing the BB coordinates in the geometry phantom. After utilizing particle swarm optimization, the CBCT geometry and BB coordinates in the geometry phantom are calibrated accurately and are then directly used for the next geometry calibration task in other CBCT systems. To evaluate the proposed method, both qualitative and quantitative studies were performed on simulated and realistic CBCT data. The spatial resolution of reconstructed images using dental CBCT can reach up to 15 line pair cm-1. The proposed method is also superior to the Wiesent method in experiments. This paper shows that the proposed method is attractive for simultaneous and accurate geometry phantom commission and geometry calibration.

Unification of Electromagnetism and Gravitation in the Framework of General Geometry

OpenAIRE

Shahverdiyev, Shervgi

2005-01-01

A new geometry, called General geometry, is constructed. It is proven that its the most simplest special case is geometry underlying Electromagnetism. Another special case is Riemannian geometry. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. It is shown that equation of motion for a particle interacting with electromagnetic field coincides exactly with equation for geodesics of geometry underlying Electromag...

Gravity is Geometry.

Science.gov (United States)

MacKeown, P. K.

1984-01-01

Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)

Considering Variable Road Geometry in Adaptive Vehicle Speed Control

Directory of Open Access Journals (Sweden)

Xinping Yan

2013-01-01

Full Text Available Adaptive vehicle speed control is critical for developing Advanced Driver Assistance Systems (ADAS. Vehicle speed control considering variable road geometry has become a hotspot in ADAS research. In this paper, first, an exploration of intrinsic relationship between vehicle operation and road geometry is made. Secondly, a collaborative vehicle coupling model, a road geometry model, and an AVSC, which can respond to variable road geometry in advance, are developed. Then, based on H∞ control method and the minimum energy principle, a performance index is specified by a cost function for the proposed AVSC, which can explicitly consider variable road geometry in its optimization process. The proposed AVSC is designed by the Hamilton-Jacobi Inequality (HJI. Finally, simulations are carried out by combining the vehicle model with the road geometry model, in an aim of minimizing the performance index of the AVSC. Analyses of the simulation results indicate that the proposed AVSC can automatically and effectively regulate speed according to variable road geometry. It is believed that the proposed AVSC can be used to improve the economy, comfort, and safety effects of current ADAS.

A Gyrovector Space Approach to Hyperbolic Geometry

CERN Document Server

Ungar, Abraham

2009-01-01

The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. T

Computational commutative and non-commutative algebraic geometry

CERN Document Server

Cojocaru, S; Ufnarovski, V

2005-01-01

This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The topic is looked at from different perspectives in over 20 lecture reports. It emphasizes the current trends in commutative and non-commutative algebraic geometry and algebra. The contributors to this publication present the most recent and state-of-the-art progresses which reflect the topic discussed in this publication. Both researchers and graduate students will find this book a good source of information on commutative and non-commutative algebraic geometry.

Supersymmetric geometries of IIA supergravity III

International Nuclear Information System (INIS)

Gran, Ulf; Papadopoulos, George; Schultz, Christian von

2016-01-01

We find that (massive) IIA backgrounds that admit a G 2 ⋉ℝ 8 invariant Killing spinor must exhibit a null Killing vector field which leaves the Killing spinor invariant and that the rotation of the Killing vector field satisfies a certain g 2 instanton condition. This result together with those in http://dx.doi.org/10.1007/JHEP05(2014)024 and http://dx.doi.org/10.1007/JHEP12(2015)113 complete the classification of geometries of all (massive) IIA backgrounds that preserve one supersymmetry. We also explore the geometry of a class of backgrounds which admit a G 2 ⋉ℝ 8 invariant Killing spinor and where in addition an appropriate 1-form bilinear vanishes. In all cases, we express the fluxes of the theory in terms of the geometry.

Guided discovery learning in geometry learning

Science.gov (United States)

Khasanah, V. N.; Usodo, B.; Subanti, S.

2018-03-01

Geometry is a part of the mathematics that must be learned in school. The purpose of this research was to determine the effect of Guided Discovery Learning (GDL) toward geometry learning achievement. This research had conducted at junior high school in Sukoharjo on academic years 2016/2017. Data collection was done based on student’s work test and documentation. Hypothesis testing used two ways analysis of variance (ANOVA) with unequal cells. The results of this research that GDL gave positive effect towards mathematics learning achievement. GDL gave better mathematics learning achievement than direct learning. There was no difference of mathematics learning achievement between male and female. There was no an interaction between sex differences and learning models toward student’s mathematics learning achievement. GDL can be used to improve students’ mathematics learning achievement in geometry.

Geometry of time-spaces non-commutative algebraic geometry, applied to quantum theory

CERN Document Server

Landau, Olav Arnfinn

2011-01-01

This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory o

Model of Random Polygon Particles for Concrete and Mesh Automatic Subdivision

Institute of Scientific and Technical Information of China (English)

无

2001-01-01

In order to study the constitutive behavior of concrete in mesoscopic level, a new method is proposed in this paper. This method uses random polygon particles to simulate full grading broken aggregates of concrete. Based on computational geometry, we carry out the automatic generation of the triangle finite element mesh for the model of random polygon particles of concrete. The finite element mesh generated in this paper is also applicable to many other numerical methods.

Computational geometry for reactor applications

International Nuclear Information System (INIS)

Brown, F.B.; Bischoff, F.G.

1988-01-01

Monte Carlo codes for simulating particle transport involve three basic computational sections: a geometry package for locating particles and computing distances to regional boundaries, a physics package for analyzing interactions between particles and problem materials, and an editing package for determining event statistics and overall results. This paper describes the computational geometry methods in RACER, a vectorized Monte Carlo code used for reactor physics analysis, so that comparisons may be made with techniques used in other codes. The principal applications for RACER are eigenvalue calculations and power distributions associated with reactor core physics analysis. Successive batches of neutrons are run until convergence and acceptable confidence intervals are obtained, with typical problems involving >10 6 histories. As such, the development of computational geometry methods has emphasized two basic needs: a flexible but compact geometric representation that permits accurate modeling of reactor core details and efficient geometric computation to permit very large numbers of histories to be run. The current geometric capabilities meet these needs effectively, supporting a variety of very large and demanding applications

Aspects of differential geometry II

CERN Document Server

Gilkey, Peter

2015-01-01

Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups an...

Geometry and Hamiltonian mechanics on discrete spaces

International Nuclear Information System (INIS)

Talasila, V; Clemente-Gallardo, J; Schaft, A J van der

2004-01-01

Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed

Methods of algebraic geometry in control theory

CERN Document Server

Falb, Peter

1999-01-01

"Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry). While this is qui...

Rudiments of algebraic geometry

CERN Document Server

Jenner, WE

2017-01-01

Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.

The Finsler spacetime framework. Backgrounds for physics beyond metric geometry

International Nuclear Information System (INIS)

Pfeifer, Christian

2013-11-01

The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the

The Finsler spacetime framework. Backgrounds for physics beyond metric geometry

Energy Technology Data Exchange (ETDEWEB)

Pfeifer, Christian

2013-11-15

The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the

Comparison theorems in Riemannian geometry

CERN Document Server

Cheeger, Jeff

2008-01-01

The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re

Lectures on Algebraic Geometry I

CERN Document Server

Harder, Gunter

2012-01-01

This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho

Modern differential geometry for physicists

CERN Document Server

Isham, C J

1989-01-01

These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields

Algebraic geometry and theta functions

CERN Document Server

Coble, Arthur B

1929-01-01

This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and

Quasi-crystalline geometry for architectural structures

DEFF Research Database (Denmark)

Weizierl, Barbara; Wester, Ture

2001-01-01

Artikel på CD-Rom 8 sider. The quasi-crystal (QC) type of material was discovered in 1983 by Dan Schechtman from Technion, Haifa. This new crystalline structure of material broke totally with the traditional conception of crystals and geometry introducing non-periodic close packing of cells...... with fivefold symmetry in 3D space. The quasi-crystal geometry can be constructed from two different cubic cells with identical rhombic facets, where the relation between the diagonals is the golden section. All cells have identical rhombic faces, identical edges and identical icosahedral/dedecahedral nodes....... The purpose of the paper is to investigate some possibilities for the application of Quasi-Crystal geometry for structures in architecture. The basis for the investigations is A: to use the Golden Cubes (the two different hexahedra consisting of rhombic facets where the length of the diagonals has the Golden...

Quantum symplectic geometry. 1. The matrix Hamiltonian formalism

International Nuclear Information System (INIS)

Djemai, A.E.F.

1994-07-01

The main purpose of this work is to describe the quantum analogue of the usual classical symplectic geometry and then to formulate the quantum mechanics as a (quantum) non-commutative symplectic geometry. In this first part, we define the quantum symplectic structure in the context of the matrix differential geometry by using the discrete Weyl-Schwinger realization of the Heisenberg group. We also discuss the continuous limit and give an expression of the quantum structure constants. (author). 42 refs

Information geometry near randomness and near independence

CERN Document Server

Arwini, Khadiga A

2008-01-01

This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate process. We use information geometry to provide a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings in protein chains, cryptology studies, clustering of communications and galaxies, cosmological voids, coupled spatial statistics in stochastic fibre networks and stochastic porous media, quantum chaology. Introduction sections are provided to mathematical statistics, differential geometry and the information geometry of spaces of probability density functions.

The Geometry of the Universe: Part 2

Science.gov (United States)

Francis, Stephanie

2009-01-01

Hyperbolic geometry occurs on hyperbolic planes--the most commonly cited one being a saddle shape. In this article, the author explores negative hyperbolic curvature, and provides a detailed description of how she constructed two hyperbolic paraboloids. Hyperbolic geometry occurs on surfaces that have negative curvature. (Contains 11 figures and 4…

Torsional Newton-Cartan Geometry and Lifshitz Holography

NARCIS (Netherlands)

Christensen, M.H.; Hartong, J.; Obers, N.A.; Rollier, B.

2014-01-01

We obtain the Lifshitz UV completion in a specific model for z=2 Lifshitz geometries. We use a vielbein formalism which enables identification of all the sources as leading components of well-chosen bulk fields. We show that the geometry induced from the bulk onto the boundary is a novel extension

Multivariate calculus and geometry

CERN Document Server

Dineen, Seán

2014-01-01

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.

Geometry of quantum computation with qutrits.

Science.gov (United States)

Li, Bin; Yu, Zu-Huan; Fei, Shao-Ming

2013-01-01

Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.

Geometry and quantization of moduli spaces

CERN Document Server

Andersen, Jørgen; Riera, Ignasi

2016-01-01

This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.

Emergent Geometry from Entropy and Causality

Science.gov (United States)

Engelhardt, Netta

In this thesis, we investigate the connections between the geometry of spacetime and aspects of quantum field theory such as entanglement entropy and causality. This work is motivated by the idea that spacetime geometry is an emergent phenomenon in quantum gravity, and that the physics responsible for this emergence is fundamental to quantum field theory. Part I of this thesis is focused on the interplay between spacetime and entropy, with a special emphasis on entropy due to entanglement. In general spacetimes, there exist locally-defined surfaces sensitive to the geometry that may act as local black hole boundaries or cosmological horizons; these surfaces, known as holographic screens, are argued to have a connection with the second law of thermodynamics. Holographic screens obey an area law, suggestive of an association with entropy; they are also distinguished surfaces from the perspective of the covariant entropy bound, a bound on the total entropy of a slice of the spacetime. This construction is shown to be quite general, and is formulated in both classical and perturbatively quantum theories of gravity. The remainder of Part I uses the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence to both expand and constrain the connection between entanglement entropy and geometry. The AdS/CFT correspondence posits an equivalence between string theory in the "bulk" with AdS boundary conditions and certain quantum field theories. In the limit where the string theory is simply classical General Relativity, the Ryu-Takayanagi and more generally, the Hubeny-Rangamani-Takayanagi (HRT) formulae provide a way of relating the geometry of surfaces to entanglement entropy. A first-order bulk quantum correction to HRT was derived by Faulkner, Lewkowycz and Maldacena. This formula is generalized to include perturbative quantum corrections in the bulk at any (finite) order. Hurdles to spacetime emergence from entanglement entropy as described by HRT and its quantum

Symposium on Differential Geometry and Differential Equations

CERN Document Server

Berger, Marcel; Bryant, Robert

1987-01-01

The DD6 Symposium was, like its predecessors DD1 to DD5 both a research symposium and a summer seminar and concentrated on differential geometry. This volume contains a selection of the invited papers and some additional contributions. They cover recent advances and principal trends in current research in differential geometry.

The Hitchin model, Poisson-quasi-Nijenhuis, geometry and symmetry reduction

International Nuclear Information System (INIS)

Zucchini, Roberto

2007-01-01

We revisit our earlier work on the AKSZ-like formulation of topological sigma model on generalized complex manifolds, or Hitchin model, [20]. We show that the target space geometry geometry implied by the BV master equations is Poisson-quasi-Nijenhuis geometry recently introduced and studied by Stienon and Xu (in the untwisted case) in [44]. Poisson-quasi-Nijenhuis geometry is more general than generalized complex geometry and comprises it as a particular case. Next, we show how gauging and reduction can be implemented in the Hitchin model. We find that the geometry resulting form the BV master equation is closely related to but more general than that recently described by Lin and Tolman in [40, 41], suggesting a natural framework for the study of reduction of Poisson-quasi-Nijenhuis manifolds

The geometry of geodesics

CERN Document Server

Busemann, Herbert

2005-01-01

A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.

MM99.81 Projection welding of complex geometries

DEFF Research Database (Denmark)

Kristensen, Lars

The objective of this work has been to establish a profound knowledge about design rules for projection welding geometries dependent of the actual material combination.Design rules and recommendations for geometries and projections in projection welding given in literature is summarised...... and these are catalogued into geometry-classes. A simulation software, SORPAS, based on the finite element method (FEM) is chosen as tool to investigate projection weld quality. SORPAS needs input of the material flow stress as function of strain, strain rate and temperature. Flow stress experiments are performed using...... been investigated.Two different welding geometries, disc with triangular ring projection welded to ring and hat welded to inside hole in ring, are both experimentally and numerically used to investigate the influence of different geometric parameters (thicknesses and angles) on weldability and weld...

Physics and geometry

International Nuclear Information System (INIS)

Konopleva, N.P.

2009-01-01

The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered

Geometry and dynamics of integrable systems

CERN Document Server

Matveev, Vladimir

2016-01-01

Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mir...

Resistor trimming geometry; past, present and future

International Nuclear Information System (INIS)

Alafogianni, M; Penlington, R; Birkett, M

2016-01-01

This paper explores the key developments in thin film resistive trimming geometry for use in the fabrication of discrete precision resistors. Firstly an introduction to the laser trimming process is given with respect to well established trim geometries such as the plunge, 'L' and serpentine cuts. The effect of these trim patterns on key electrical properties of resistance tolerance and temperature co-efficient of resistance (TCR) of the thin films is then discussed before the performance of more recent geometries such as the three-contact and random trim approaches are reviewed. In addition to the properties of the standard trim patterns, the concept of the heat affected zone (HAZ) and ablation energy and the effect of introducing a 'fine' trim in areas of low current density to improve device performance are also studied. It is shown how trimming geometry and laser parameters can be systematically controlled to produce thin film resistors of the required properties for varying applications such as high precision, long term stability and high power pulse performance

Pearson's Functions to Describe FSW Weld Geometry

International Nuclear Information System (INIS)

Lacombe, D.; Coupard, D.; Tcherniaeff, S.; Girot, F.; Gutierrez-Orrantia, M. E.

2011-01-01

Friction stir welding (FSW) is a relatively new joining technique particularly for aluminium alloys that are difficult to fusion weld. In this study, the geometry of the weld has been investigated and modelled using Pearson's functions. It has been demonstrated that the Pearson's parameters (mean, standard deviation, skewness, kurtosis and geometric constant) can be used to characterize the weld geometry and the tensile strength of the weld assembly. Pearson's parameters and process parameters are strongly correlated allowing to define a control process procedure for FSW assemblies which make radiographic or ultrasonic controls unnecessary. Finally, an optimisation using a Generalized Gradient Method allows to determine the geometry of the weld which maximises the assembly tensile strength.

Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry

International Nuclear Information System (INIS)

Hartong, Jelle; Obers, Niels A.

2015-01-01

Recently it has been established that torsional Newton-Cartan (TNC) geometry is the appropriate geometrical framework to which non-relativistic field theories couple. We show that when these geometries are made dynamical they give rise to Hořava-Lifshitz (HL) gravity. Projectable HL gravity corresponds to dynamical Newton-Cartan (NC) geometry without torsion and non-projectable HL gravity corresponds to dynamical NC geometry with twistless torsion (hypersurface orthogonal foliation). We build a precise dictionary relating all fields (including the scalar khronon), their transformations and other properties in both HL gravity and dynamical TNC geometry. We use TNC invariance to construct the effective action for dynamical twistless torsional Newton-Cartan geometries in 2+1 dimensions for dynamical exponent 1geometries. We argue that TNC geometry, which is manifestly diffeomorphism covariant, is a natural geometrical framework underlying HL gravity and discuss some of its implications.

Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry

Energy Technology Data Exchange (ETDEWEB)

Hartong, Jelle [Physique Théorique et Mathématique and International Solvay Institutes, Université Libre de Bruxelles,C.P. 231, 1050 Brussels (Belgium); Obers, Niels A. [The Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark)

2015-07-29

Recently it has been established that torsional Newton-Cartan (TNC) geometry is the appropriate geometrical framework to which non-relativistic field theories couple. We show that when these geometries are made dynamical they give rise to Hořava-Lifshitz (HL) gravity. Projectable HL gravity corresponds to dynamical Newton-Cartan (NC) geometry without torsion and non-projectable HL gravity corresponds to dynamical NC geometry with twistless torsion (hypersurface orthogonal foliation). We build a precise dictionary relating all fields (including the scalar khronon), their transformations and other properties in both HL gravity and dynamical TNC geometry. We use TNC invariance to construct the effective action for dynamical twistless torsional Newton-Cartan geometries in 2+1 dimensions for dynamical exponent 1geometries. We argue that TNC geometry, which is manifestly diffeomorphism covariant, is a natural geometrical framework underlying HL gravity and discuss some of its implications.

On 3d bulk geometry of Virasoro coadjoint orbits: orbit invariant charges and Virasoro hair on locally AdS{sub 3} geometries

Energy Technology Data Exchange (ETDEWEB)

Sheikh-Jabbari, M.M. [Institute for Research in Fundamental Sciences (IPM), School of Physics, Tehran (Iran, Islamic Republic of); Yavartanoo, H. [Institute of Theoretical Physics, Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Beijing (China)

2016-09-15

Expanding upon [arXiv:1404.4472, arXiv:1511.06079], we provide a further detailed analysis of Banados geometries, the most general solutions to the AdS{sub 3} Einstein gravity with Brown-Henneaux boundary conditions. We analyze in some detail the causal, horizon, and boundary structure, and the geodesic motion on these geometries, as well as the two classes of symplectic charges one can associate with these geometries: charges associated with the exact symmetries and the Virasoro charges. We elaborate on the one-to-one relation between the coadjoint orbits of two copies of the Virasoro group and Banados geometries. We discuss that the information as regards the Banados geometries falls into two categories: ''orbit invariant'' information and ''Virasoro hairs''. The former concerns geometric quantities, while the latter are specified by the non-local surface integrals. We elaborate on multi-BTZ geometries which have a number of disconnected pieces at the horizon bifurcation curve. We study multi-BTZ black hole thermodynamics and discuss that the thermodynamic quantities are orbit invariants. We also comment on the implications of our analysis for a 2d CFT dual which could possibly be dual to AdS{sub 3} Einstein gravity. (orig.)

The Van Hiele geometry thinking levels of mild mental retardation students

Science.gov (United States)

Shomad, Z. A.; Kusmayadi, T. A.; Riyadi

2017-12-01

This research is to investigate the level of mild mental retardation geometry students thinking. This research focuses on the geometry thinking level based on Van Hiele theory. This study uses qualitative methods with case study strategy. Data obtained from observation and tests result. The subjects are 12 mental retardation students. The result show that ability of mild mental retardation students with each other is different but have same level of level thinking geometry. The geometry thinking level of mental retardation students was identified in level 1 of the Van Hiele theory. Based on the level thinking geometry of mental retardation students simplify geometry thinking teachers in selecting appropriate learning methods, choose the materials in accordance with ability, and can modify the material following the geometry thinking level of mental retardation students.

Perspectives in Analysis, Geometry, and Topology

CERN Document Server

Itenberg, I V; Passare, Mikael

2012-01-01

The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.

Modular Theory, Non-Commutative Geometry and Quantum Gravity

Directory of Open Access Journals (Sweden)

Wicharn Lewkeeratiyutkul

2010-08-01

Full Text Available This paper contains the first written exposition of some ideas (announced in a previous survey on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal.

An introduction to algebraic geometry and algebraic groups

CERN Document Server

Geck, Meinolf

2003-01-01

An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles.Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type.The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups

Bosonization in a two-dimensional Riemann Cartan geometry

International Nuclear Information System (INIS)

Denardo, G.; Spallucci, E.

1987-01-01

We study the vacuum functional for a Dirac field in a two dimensional Riemann-Cartan geometry. Torsion is treated as a quantum variable while the metric is considered as a classical background field. Decoupling spinors from the non-Riemannian part of the geometry introduces a chiral Jacobian into the vacuum generating functional. We compute this functional Jacobian determinant by means of the Alvarez method. Finally, we show that the effective action for the background geometry is of the Liouville type and does not preserve any memory of the initial torsion field. (author)

Conference on Strings, Duality, and Geometry

CERN Document Server

Phong, Duong; Yau, Shing-Tung; Mirror Symmetry IV

2002-01-01

This book presents contributions of participants of a workshop held at the Centre de Recherches Mathématiques (CRM), University of Montréal. It can be viewed as a sequel to Mirror Symmetry I (1998), Mirror Symmetry II (1996), and Mirror Symmetry III (1999), copublished by the AMS and International Press. The volume presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s. Some of the topics emphasized include the following: Integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; and elliptic genera and automorphic forms. Several introductory articles present an overview of the geometric and physical aspects of mirror symmetry and of corresponding developments in symplectic geometry. The book provides an efficient way for a very broad audience of mathematicians and physicists to explore the frontiers of research into this rapi...

From groups to geometry and back

CERN Document Server

Climenhaga, Vaughn

2017-01-01

Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering space...

Intrinsic geometry of biological surface growth

CERN Document Server

Todd, Philip H

1986-01-01

1.1 General Introduction The work which comprises this essay formed part of a multidiscip­ linary project investigating the folding of the developing cerebral cortex in the ferret. The project as a whole combined a study, at the histological level, of the cytoarchitectural development concom­ itant with folding and a mathematical study of folding viewed from the perspective of differential geometry. We here concentrate on the differential geometry of brain folding. Histological results which have some significance to the geometry of the cortex are re­ ferred to, but are not discussed in any depth. As with any truly multidisciplinary work, this essay has objectives which lie in each of its constituent disciplines. From a neuroana­ tomical point of view, the work explores the use of the surface geo­ metry of the developing cortex as a parameter for the underlying growth process. Geometrical parameters of particular interest and theoretical importance are surface curvatures. Our experimental portion reports...

Intelligent Patching of Conceptual Geometry for CFD Analysis

Science.gov (United States)

Li, Wu

2010-01-01

The iPatch computer code for intelligently patching surface grids was developed to convert conceptual geometry to computational fluid dynamics (CFD) geometry (see figure). It automatically uses bicubic B-splines to extrapolate (if necessary) each surface in a conceptual geometry so that all the independently defined geometric components (such as wing and fuselage) can be intersected to form a watertight CFD geometry. The software also computes the intersection curves of surface patches at any resolution (up to 10.4 accuracy) specified by the user, and it writes the B-spline surface patches, and the corresponding boundary points, for the watertight CFD geometry in the format that can be directly used by the grid generation tool VGRID. iPatch requires that input geometry be in PLOT3D format where each component surface is defined by a rectangular grid {(x(i,j), y(i,j), z(i,j)):1less than or equal to i less than or equal to m, 1 less than or equal to j less than or equal to n} that represents a smooth B-spline surface. All surfaces in the PLOT3D file conceptually represent a watertight geometry of components of an aircraft on the half-space y greater than or equal to 0. Overlapping surfaces are not allowed, but could be fixed by a utility code "fixp3d". The fixp3d utility code first finds the two grid lines on the two surface grids that are closest to each other in Hausdorff distance (a metric to measure the discrepancies of two sets); then uses one of the grid lines as the transition line, extending grid lines on one grid to the other grid to form a merged grid. Any two connecting surfaces shall have a "visually" common boundary curve, or can be described by an intersection relationship defined in a geometry specification file. The intersection of two surfaces can be at a conceptual level. However, the intersection is directional (along either i or j index direction), and each intersecting grid line (or its spine extrapolation) on the first surface should intersect

The Common Evolution of Geometry and Architecture from a Geodetic Point of View

Science.gov (United States)

Bellone, T.; Fiermonte, F.; Mussio, L.

2017-05-01

Throughout history the link between geometry and architecture has been strong and while architects have used mathematics to construct their buildings, geometry has always been the essential tool allowing them to choose spatial shapes which are aesthetically appropriate. Sometimes it is geometry which drives architectural choices, but at other times it is architectural innovation which facilitates the emergence of new ideas in geometry. Among the best known types of geometry (Euclidean, projective, analytical, Topology, descriptive, fractal,…) those most frequently employed in architectural design are: - Euclidean Geometry - Projective Geometry - The non-Euclidean geometries. Entire architectural periods are linked to specific types of geometry. Euclidean geometry, for example, was the basis for architectural styles from Antiquity through to the Romanesque period. Perspective and Projective geometry, for their part, were important from the Gothic period through the Renaissance and into the Baroque and Neo-classical eras, while non-Euclidean geometries characterize modern architecture.

Physical properties corresponding to vortical flow geometry

Energy Technology Data Exchange (ETDEWEB)

Nakayama, K, E-mail: nakayama@aitech.ac.jp [Department of Mechanical Engineering, Aichi Institute of Technology, Toyota, Aichi 470-0392 (Japan)

2014-10-01

We examine a vortical flow geometry specified by the velocity gradient tensor ∇v, and derive properties representing the symmetry (axisymmetry or skewness) of the vortical flow in the swirl plane and a property specifying inflowing (outflowing) motion in all directions around the point. We focus on the radial and azimuthal velocities in a plane nonparallel to the eigenvector corresponding to the real eigenvalue of ∇v and show that these components are expressed as specific quadratic forms. The real and imaginary parts of the complex eigenvalues of ∇v represent averages of these eigenvalues of the quadratic forms, and are inadequate to specify the detailed flow geometry uniquely. The new properties complement specifying the precise flow geometry of the vortical flow.

College geometry an introduction to the modern geometry of the triangle and the circle

CERN Document Server

Altshiller-Court, Nathan

2007-01-01

The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.

Vehicle response-based track geometry assessment using multi-body simulation

Science.gov (United States)

Kraft, Sönke; Causse, Julien; Coudert, Frédéric

2018-02-01

The assessment of the geometry of railway tracks is an indispensable requirement for safe rail traffic. Defects which represent a risk for the safety of the train have to be identified and the necessary measures taken. According to current standards, amplitude thresholds are applied to the track geometry parameters measured by recording cars. This geometry-based assessment has proved its value but suffers from the low correlation between the geometry parameters and the vehicle reactions. Experience shows that some defects leading to critical vehicle reactions are underestimated by this approach. The use of vehicle responses in the track geometry assessment process allows identifying critical defects and improving the maintenance operations. This work presents a vehicle response-based assessment method using multi-body simulation. The choice of the relevant operation conditions and the estimation of the simulation uncertainty are outlined. The defects are identified from exceedances of track geometry and vehicle response parameters. They are then classified using clustering methods and the correlation with vehicle response is analysed. The use of vehicle responses allows the detection of critical defects which are not identified from geometry parameters.

Quasi-crystalline geometry for architectural structures

DEFF Research Database (Denmark)

Wester, Ture; Weinzieri, Barbara

The quasi-crystal (QC) type of material was discovered in 1983 by Dan Schechtman from Technion, Haifa. This new crystalline structure of material broke totally with the traditional conception of crystals and geometry introducing non-periodic close packing of cells with fivefold symmetry in 3D space....... The quasi-crystal geometry can be constructed from two different cubic cells with identical rhombic facets, where the relation between the diagonals is the golden section. All cells have identical rhombic faces, identical edges and identical icosahedral/dodecahedral nodes....

The interplay between differential geometry and differential equations

CERN Document Server

Lychagin, V V

1995-01-01

This work applies symplectic methods and discusses quantization problems to emphasize the advantage of an algebraic geometry approach to nonlinear differential equations. One common feature in most of the presentations in this book is the systematic use of the geometry of jet spaces.

5000 years of geometry mathematics in history and culture

CERN Document Server

Scriba, Christoph J

2015-01-01

The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science, and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultur...

A SPECT reconstruction method for extending parallel to non-parallel geometries

International Nuclear Information System (INIS)

Wen Junhai; Liang Zhengrong

2010-01-01

Due to its simplicity, parallel-beam geometry is usually assumed for the development of image reconstruction algorithms. The established reconstruction methodologies are then extended to fan-beam, cone-beam and other non-parallel geometries for practical application. This situation occurs for quantitative SPECT (single photon emission computed tomography) imaging in inverting the attenuated Radon transform. Novikov reported an explicit parallel-beam formula for the inversion of the attenuated Radon transform in 2000. Thereafter, a formula for fan-beam geometry was reported by Bukhgeim and Kazantsev (2002 Preprint N. 99 Sobolev Institute of Mathematics). At the same time, we presented a formula for varying focal-length fan-beam geometry. Sometimes, the reconstruction formula is so implicit that we cannot obtain the explicit reconstruction formula in the non-parallel geometries. In this work, we propose a unified reconstruction framework for extending parallel-beam geometry to any non-parallel geometry using ray-driven techniques. Studies by computer simulations demonstrated the accuracy of the presented unified reconstruction framework for extending parallel-beam to non-parallel geometries in inverting the attenuated Radon transform.

Parcels and Land Ownership, Contains parcels, subdivisions, CSMs, Condominiums, Rights of Way and supporting annotation. Data within the City of West Bend are maintained by the City. Some areas are mapped at 1:1200, Published in 2013, 1:2400 (1in=200ft) scale, Washington County Government.

Data.gov (United States)

NSGIC Local Govt | GIS Inventory — Parcels and Land Ownership dataset current as of 2013. Contains parcels, subdivisions, CSMs, Condominiums, Rights of Way and supporting annotation. Data within the...

Numerical optimization of laboratory combustor geometry for NO suppression

International Nuclear Information System (INIS)

Mazaheri, Karim; Shakeri, Alireza

2016-01-01

Highlights: • A five-step kinetics for NO and CO prediction is extracted from GRI-3.0 mechanism. • Accuracy and applicability of this kinetics for numerical optimization were shown. • Optimized geometry for a combustor was determined using the combined process. • NO emission from optimized geometry is found 10.3% lower than the basis geometry. - Abstract: In this article, geometry optimization of a jet stirred reactor (JSR) combustor has been carried out for minimum NO emissions in methane oxidation using a combined numerical algorithm based on computational fluid dynamics (CFD) and differential evolution (DE) optimization. The optimization algorithm is also used to find a fairly accurate reduced mechanism. The combustion kinetics is based on a five-step mechanism with 17 unknowns which is obtained using an optimization DE algorithm for a PSR–PFR reactor based on GRI-3.0 full mechanism. The optimization design variables are the unknowns of the five-step mechanism and the cost function is the concentration difference of pollutants obtained from the 5-step mechanism and the full mechanism. To validate the flow solver and the chemical kinetics, the computed NO at the outlet of the JSR is compared with experiments. To optimize the geometry of a combustor, the JSR combustor geometry is modeled using three parameters (i.e., design variables). An integrated approach using a flow solver and the DE optimization algorithm produces the lowest NO concentrations. Results show that the exhaust NO emission for the optimized geometry is 10.3% lower than the original geometry, while the inlet temperature of the working fluid and the concentration of O_2 are operating constraints. In addition, the concentration of CO pollutant is also much less than the original chamber.

THE COMMON EVOLUTION OF GEOMETRY AND ARCHITECTURE FROM A GEODETIC POINT OF VIEW

Directory of Open Access Journals (Sweden)

T. Bellone

2017-05-01

Full Text Available Throughout history the link between geometry and architecture has been strong and while architects have used mathematics to construct their buildings, geometry has always been the essential tool allowing them to choose spatial shapes which are aesthetically appropriate. Sometimes it is geometry which drives architectural choices, but at other times it is architectural innovation which facilitates the emergence of new ideas in geometry. Among the best known types of geometry (Euclidean, projective, analytical, Topology, descriptive, fractal,… those most frequently employed in architectural design are: – Euclidean Geometry – Projective Geometry – The non-Euclidean geometries. Entire architectural periods are linked to specific types of geometry. Euclidean geometry, for example, was the basis for architectural styles from Antiquity through to the Romanesque period. Perspective and Projective geometry, for their part, were important from the Gothic period through the Renaissance and into the Baroque and Neo-classical eras, while non-Euclidean geometries characterize modern architecture.

Classification of radar echoes using fractal geometry

International Nuclear Information System (INIS)

Azzaz, Nafissa; Haddad, Boualem

2017-01-01

Highlights: • Implementation of two concepts of fractal geometry to classify two types of meteorological radar echoes. • A new approach, called a multi-scale fractal dimension is used for classification between fixed echoes and rain echoes. • An Automatic identification system of meteorological radar echoes was proposed using fractal geometry. - Abstract: This paper deals with the discrimination between the precipitation echoes and the ground echoes in meteorological radar images using fractal geometry. This study aims to improve the measurement of precipitations by weather radars. For this, we considered three radar sites: Bordeaux (France), Dakar (Senegal) and Me lbourne (USA). We showed that the fractal dimension based on contourlet and the fractal lacunarity are pertinent to discriminate between ground and precipitation echoes. We also demonstrated that the ground echoes have a multifractal structure but the precipitations are more homogeneous than ground echoes whatever the prevailing climate. Thereby, we developed an automatic classification system of radar using a graphic interface. This interface, based on the fractal geometry makes possible the identification of radar echoes type in real time. This system can be inserted in weather radar for the improvement of precipitation estimations.

Computational geometry lectures at the morningside center of mathematics

CERN Document Server

Wang, Ren-Hong

2003-01-01

Computational geometry is a borderline subject related to pure and applied mathematics, computer science, and engineering. The book contains articles on various topics in computational geometry, which are based on invited lectures and some contributed papers presented by researchers working during the program on Computational Geometry at the Morningside Center of Mathematics of the Chinese Academy of Science. The opening article by R.-H. Wang gives a nice survey of various aspects of computational geometry, many of which are discussed in more detail in other papers in the volume. The topics include problems of optimal triangulation, splines, data interpolation, problems of curve and surface design, problems of shape control, quantum teleportation, and others.

Parameterized combinatorial geometry modeling in Moritz

International Nuclear Information System (INIS)

Van Riper, K.A.

2005-01-01

We describe the use of named variables as surface and solid body coefficients in the Moritz geometry editing program. Variables can also be used as material numbers, cell densities, and transformation values. A variable is defined as a constant or an arithmetic combination of constants and other variables. A variable reference, such as in a surface coefficient, can be a single variable or an expression containing variables and constants. Moritz can read and write geometry models in MCNP and ITS ACCEPT format; support for other codes will be added. The geometry can be saved with either the variables in place, for modifying the models in Moritz, or with the variables evaluated for use in the transport codes. A program window shows a list of variables and provides fields for editing them. Surface coefficients and other values that use a variable reference are shown in a distinctive style on object property dialogs; associated buttons show fields for editing the reference. We discuss our use of variables in defining geometry models for shielding studies in PET clinics. When a model is parameterized through the use of variables, changes such as room dimensions, shielding layer widths, and cell compositions can be quickly achieved by changing a few numbers without requiring knowledge of the input syntax for the transport code or the tedious and error prone work of recalculating many surface or solid body coefficients. (author)

Analysis on geometry-aware received signal strength based ...

African Journals Online (AJOL)

These handle different scenarios such as environment, adaptation, hybridization and the choice of context is dependent on user requirements. This paper present geometry-aware received signal strength (RSS) based positioning techniques where the influences of the geometries of the BSs (where location estimation ...

A Geometry in which all Triangles are Isosceles

Indian Academy of Sciences (India)

The real number line has a geometry which is Euclidean. Imagine a small pygmy tortoise trying to travel along a very long path; assume that its destination is at a very ..... are: geometry of space-time at small distances; classi- cal and quantum ...

Differential geometry

CERN Document Server

Ciarlet, Philippe G

2007-01-01

This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and

Vanishing theorems and effective results in algebraic geometry

International Nuclear Information System (INIS)

Demailly, J.P.; Goettsche, L.; Lazarsfeld, R.

2001-01-01

The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks

Nonmonotonic Thermal Casimir Force from Geometry-Temperature Interplay

International Nuclear Information System (INIS)

Weber, Alexej; Gies, Holger

2010-01-01

The geometry dependence of Casimir forces is significantly more pronounced in the presence of thermal fluctuations due to a generic geometry-temperature interplay. We show that the thermal force for standard sphere-plate or cylinder-plate geometries develops a nonmonotonic behavior already in the simple case of a fluctuating Dirichlet scalar. In particular, the attractive thermal force can increase for increasing distances below a critical temperature. This anomalous behavior is triggered by a reweighting of relevant fluctuations on the scale of the thermal wavelength. The essence of the phenomenon becomes transparent within the worldline picture of the Casimir effect.

Vanishing theorems and effective results in algebraic geometry

Energy Technology Data Exchange (ETDEWEB)

Demailly, J P [Universite de Grenoble (France); Goettsche, L [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Lazarsfeld, R [University of Michigan (United States)

2001-12-15

The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks.

Micro-tomography based Geometry Modeling of Three-Dimensional Braided Composites

Science.gov (United States)

Fang, Guodong; Chen, Chenghua; Yuan, Shenggang; Meng, Songhe; Liang, Jun

2018-06-01

A tracking and recognizing algorithm is proposed to automatically generate irregular cross-sections and central path of braid yarn within the 3D braided composites by using sets of high resolution tomography images. Only the initial cross-sections of braid yarns in a tomography image after treatment are required to be calibrated manually as searching cross-section template. The virtual geometry of 3D braided composites including some detailed geometry information, such as the braid yarn squeezing deformation, braid yarn distortion and braid yarn path deviation etc., can be reconstructed. The reconstructed geometry model can reflect the change of braid configurations during solidification process. The geometry configurations and mechanical properties of the braided composites are analyzed by using the reconstructed geometry model.

Determination of Fracture System Geometry from Well Testing

International Nuclear Information System (INIS)

Doe, T.W.

1994-01-01

In this paper, the research and development for the description of the hydraulic geometry of fracture networks are discussed. The studies on fracture networks have developed on the premise that the structural geological information on fracture geometries could be used to develop the realistic models of flow. It has been widely recognized that a relatively small portion of natural fracture networks controls a major portion of groundwater flow. The key to efficient network modeling is to identify that portion of networks. It is the main purpose of this paper to discuss the methods for characterizing the hydraulic geometry of fracture flow systems. The methods described in this paper cover three approaches for defining the hydraulic geometry of fracture networks, that is, the determination of conductive fracture frequency in boreholes, the use of transient pressure and flow responses in single holes, and the use of cross hole test to assess connectivity. The information which can be obtained by each test is shown. Flow logging, well test distribution and conductive fracture frequency are discussed. The transient analysis of single hole well test and the cross hole analysis of well test for fracture network geometry are reported. The data taken by various methods together can provide network characterization. (K.I.)

Large-R jets in Atlas Tile Calorimeter current and upgraded geometry

CERN Document Server

Cecchini, Vincent Egidio

2017-01-01

This report describes a comparative study of two different geometries of the Atlas Tile Calorimeter to assess the performance of an increased granularity upgrade. The current geometry is compared to the upgraded one, needed because of the luminosity increase in the High-Luminosity LHC. Those geometries had been simulated in Geant4 to provide Monte-Carlo events simulations allowing us to compare the behaviour of the upgraded geometry with the current one. Data analysis is made from this simulation to compare the behaviour of the reconstructed jets substructure in the two different geometries.

Towards a Nano Geometry?

DEFF Research Database (Denmark)

Booss-Bavnbek, Bernhelm

2011-01-01

This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...

Diophantine geometry an introduction

CERN Document Server

Hindry, Marc

2000-01-01

This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

A Statistical Model for Synthesis of Detailed Facial Geometry

OpenAIRE

Golovinskiy, Aleksey; Matusik, Wojciech; Pfister, Hanspeter; Rusinkiewicz, Szymon; Funkhouser, Thomas

2006-01-01

Detailed surface geometry contributes greatly to the visual realism of 3D face models. However, acquiring high-resolution face geometry is often tedious and expensive. Consequently, most face models used in games, virtual reality, or computer vision look unrealistically smooth. In this paper, we introduce a new statistical technique for the analysis and synthesis of small three-dimensional facial features, such as wrinkles and pores. We acquire high-resolution face geometry for people across ...

Remarks on the foundations of geometry and immersion theory

Energy Technology Data Exchange (ETDEWEB)

Odon, P I [Harvard University, Extension School, Boston, MA (United States); Capistrano, A J S [Universidade Federal do Tocantins, Porto Nacional, TO, 77500-000 (Brazil)], E-mail: podon@fas.harvard.edu, E-mail: capistranoaj@mail.uft.edu.br

2010-04-15

In this paper, we deal with the evolution of physics and maths, and how one is intrinsically connected to the other. Euclid and his book Elements, and the importance of the fifth postulate for geometry led to the discovery of non-Euclidean geometries. We point out how these geometries play an essential role in immersion theory and Nash's theorem, and its importance for physics when applied to the brane-world theory.

Freudenthal duality and generalized special geometry

Energy Technology Data Exchange (ETDEWEB)

Ferrara, Sergio, E-mail: sergio.ferrara@cern.ch [Physics Department, Theory Unit, CERN, CH-1211, Geneva 23 (Switzerland); INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy); Marrani, Alessio, E-mail: Alessio.Marrani@cern.ch [Physics Department, Theory Unit, CERN, CH-1211, Geneva 23 (Switzerland); Yeranyan, Armen, E-mail: ayeran@lnf.infn.it [INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy); Department of Physics, Yerevan State University, Alex Manoogian St. 1, Yerevan, 0025 (Armenia)

2011-07-27

Freudenthal duality, introduced in Borsten et al. (2009) and defined as an anti-involution on the dyonic charge vector in d=4 space-time dimensions for those dualities admitting a quartic invariant, is proved to be a symmetry not only of the classical Bekenstein-Hawking entropy but also of the critical points of the black hole potential. Furthermore, Freudenthal duality is extended to any generalized special geometry, thus encompassing all N>2 supergravities, as well as N=2 generic special geometry, not necessarily having a coset space structure.

The geometry of classical Regge calculus

International Nuclear Information System (INIS)

Barrett, J.W.

1987-01-01

Standard notions of Riemannian geometry are applied to the case of piecewise-flat manifolds. Particular care is taken to explain how one may define some particular vectors and tensors in an invariant way at points of a conical singularity. The geometry surrounding the equations of motion and the energy-momentum of the piecewise-flat manifold is developed in detail. The resolution theorem is presented, which states that on certain resolution hypersurfaces there is a clear connection between the energy-momentum of the piecewise-flat manifold and the Regge equations of motion. (author)

The VSEPR model of molecular geometry

CERN Document Server

Gillespie, Ronald J

2012-01-01

Valence Shell Electron Pair Repulsion (VSEPR) theory is a simple technique for predicting the geometry of atomic centers in small molecules and molecular ions. This authoritative reference was written by Istvan Hartiggai and the developer of VSEPR theory, Ronald J. Gillespie. In addition to its value as a text for courses in molecular geometry and chemistry, it constitutes a classic reference for professionals.Starting with coverage of the broader aspects of VSEPR, this volume narrows its focus to a succinct survey of the methods of structural determination. Additional topics include the appli

Tensorial spacetime geometries and background-independent quantum field theory

International Nuclear Information System (INIS)

Raetzel, Dennis

2012-01-01

Famously, Einstein read off the geometry of spacetime from Maxwell's equations. Today, we take this geometry that serious that our fundamental theory of matter, the standard model of particle physics, is based on it. However, it seems that there is a gap in our understanding if it comes to the physics outside of the solar system. Independent surveys show that we need concepts like dark matter and dark energy to make our models fit with the observations. But these concepts do not fit in the standard model of particle physics. To overcome this problem, at least, we have to be open to matter fields with kinematics and dynamics beyond the standard model. But these matter fields might then very well correspond to different spacetime geometries. This is the basis of this thesis: it studies the underlying spacetime geometries and ventures into the quantization of those matter fields independently of any background geometry. In the first part of this thesis, conditions are identified that a general tensorial geometry must fulfill to serve as a viable spacetime structure. Kinematics of massless and massive point particles on such geometries are introduced and the physical implications are investigated. Additionally, field equations for massive matter fields are constructed like for example a modified Dirac equation. In the second part, a background independent formulation of quantum field theory, the general boundary formulation, is reviewed. The general boundary formulation is then applied to the Unruh effect as a testing ground and first attempts are made to quantize massive matter fields on tensorial spacetimes.

Geometric Monte Carlo and black Janus geometries

Energy Technology Data Exchange (ETDEWEB)

Bak, Dongsu, E-mail: dsbak@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); B.W. Lee Center for Fields, Gravity & Strings, Institute for Basic Sciences, Daejeon 34047 (Korea, Republic of); Kim, Chanju, E-mail: cjkim@ewha.ac.kr [Department of Physics, Ewha Womans University, Seoul 03760 (Korea, Republic of); Kim, Kyung Kiu, E-mail: kimkyungkiu@gmail.com [Department of Physics, Sejong University, Seoul 05006 (Korea, Republic of); Department of Physics, College of Science, Yonsei University, Seoul 03722 (Korea, Republic of); Min, Hyunsoo, E-mail: hsmin@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); Song, Jeong-Pil, E-mail: jeong_pil_song@brown.edu [Department of Chemistry, Brown University, Providence, RI 02912 (United States)

2017-04-10

We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.

Unit cell geometry of 3-D braided structures

Science.gov (United States)

Du, Guang-Wu; Ko, Frank K.

1993-01-01

The traditional approach used in modeling of composites reinforced by three-dimensional (3-D) braids is to assume a simple unit cell geometry of a 3-D braided structure with known fiber volume fraction and orientation. In this article, we first examine 3-D braiding methods in the light of braid structures, followed by the development of geometric models for 3-D braids using a unit cell approach. The unit cell geometry of 3-D braids is identified and the relationship of structural parameters such as yarn orientation angle and fiber volume fraction with the key processing parameters established. The limiting geometry has been computed by establishing the point at which yarns jam against each other. Using this factor makes it possible to identify the complete range of allowable geometric arrangements for 3-D braided preforms. This identified unit cell geometry can be translated to mechanical models which relate the geometrical properties of fabric preforms to the mechanical responses of composite systems.

Creating Dynamic Learning Environment to Enhance Students’ Engagement in Learning Geometry

Science.gov (United States)

Sariyasa

2017-04-01

Learning geometry gives many benefits to students. It strengthens the development of deductive thinking and reasoning; it also provides an opportunity to improve visualisation and spatial ability. Some studies, however, have pointed out the difficulties that students encountered when learning geometry. A preliminary study by the author in Bali revealed that one of the main problems was teachers’ difficulties in delivering geometry instruction. It was partly due to the lack of appropriate instructional media. Coupling with dynamic geometry software, dynamic learning environments is a promising solution to this problem. Employing GeoGebra software supported by the well-designed instructional process may result in more meaningful learning, and consequently, students are motivated to engage in the learning process more deeply and actively. In this paper, we provide some examples of GeoGebra-aided learning activities that allow students to interactively explore and investigate geometry concepts and the properties of geometry objects. Thus, it is expected that such learning environment will enhance students’ internalisation process of geometry concepts.

Hands On Activity Pada Pembelajaran Geometri Sekolah Sebagai Asesmen Kinerja Siswa

Directory of Open Access Journals (Sweden)

Kartono Kartono

2010-06-01

Full Text Available Geometri merupakan cabang matematika yang diajarkan mulai dari pendidikan dasar sampai pendidikan tinggi, namun berdasarkan suatu penelitian hasil belajar geometri kurang memuaskan khususnya hasil belajar geometri sekolah. Hasil belajar geometri sekolah terkait langsung dengan kegiatan pembelajarannya. Pembelajaran geometri akan efektif apabila kegiatan yang dilakukan sesuai dengan struktur kemampuan berpikir siswa. Menurut Teori Van Hiele tentang pembelajaran geometri, bahwa tingkat kemampuan berpikir siswa dalam belajar geometri meliputi lima tingkat , yaitu visualisasi, analisis, deduksi informal, deduksi, dan rigor.Tingkatan berpikir tersebut akan dilalui siswa secara berurutan, kecepatan berpindah dari tingkat ke tingkat berikutnya banyak bergantung pada isi dan metode pembelajarannya.Perlu disediakan aktivitas-aktivitas dalam pembelajaran yang sesuai dengan tingkat berpikir siswa dalam bentuk hands on activity. Melalui hands on activity akan terbentuk suatu penghayatan dan pengalaman untuk  menetapkan suatu pengertian, karena mampu membelajarkan secara bersama-sama kemampuan kognitif, afektif, dan psikomotorik serta dapat memberikan penghayatan secara mendalam terhadap apa yang dipelajari, sehingga apa yang diperoleh oleh siswa tidak mudah dilupakan. Hands on activity selain sebagai komponen kegiatan pembelajaran, dapat dimanfaatkan sebagai intrumen asesmen, khususnya asesmen kinerja siswa. Gunakanlah hands on activity pada pembelajaran geometri sekolah dan manfaatkan kegiatan tersebut sebagai bentuk asesmen kinerja siswa. 

Let??s teach geometry

OpenAIRE

Ca??adas, Mar??a C.; Molina, Marta; Gallardo, Sandra; Mart??nez-Santaolalla, Manuel J.; Pe??as, Mar??a

2010-01-01

In this work we present an activity for High School students in which various mathematical concepts of plane and spatial geometry are involved. The final objective of the proposed tasks is constructing a particular polyhedron, the cube, by using a modality of origami called modular origami.

Multiplicity in difference geometry

OpenAIRE

Tomasic, Ivan

2011-01-01

We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.

Topics in Riemannian geometry

International Nuclear Information System (INIS)

Ezin, J.P.

1988-08-01

The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs

Geometrical intuition and the learning and teaching of geometry

OpenAIRE

Fujita, Taro; Jones, Keith; Yamamoto, Shinya

2004-01-01

Intuition is often regarded as essential in the learning of geometry, but how such skills might be effectively developed in students remains an open question. This paper reviews the role and importance of geometrical intuition and suggests it involves the skills to create and manipulate geometrical figures in the mind, to see geometrical properties, to relate images to concepts and theorems in geometry, and decide where and how to start when solving problems in geometry. Based on these theore...

Effect of duct geometry on Wells turbine performance

International Nuclear Information System (INIS)

Shaaban, S.; Abdel Hafiz, A.

2012-01-01

Highlights: ► A Wells turbine duct design in the form of venturi duct is proposed and investigated. ► Optimum duct geometry is identified. ► Up to 14% increase of the turbine power can be achieved using the optimized duct geometry. ► Up to 9% improve of the turbine efficiency is attained by optimizing the turbine duct geometry. ► The optimized duct geometry results in tangible delay of the turbine stalling point. - Abstract: Wells turbines can represent important source of renewable energy for many countries. An essential disadvantage of Wells turbines is their low aerodynamic efficiency and consequently low power produced. In order to enhance the Wells turbine performance, the present research work proposes the use of a symmetrical duct in the form of a venturi tube with turbine rotor located at throat. The effects of duct area ratio and duct angle are investigated in order to optimize Wells turbine performance. The turbine performance is numerically investigated by solving the steady 3D incompressible Reynolds Averaged Navier–Stocks equation (RANS). A substantial improve of the turbine performance is achieved by optimizing the duct geometry. Increasing both the duct area ratio and duct angle increase the acceleration and deceleration upstream and downstream the rotor respectively. The accelerating flow with thinner boundary layer thickness upstream the rotor reduces the flow separation on the rotor suction side. The downstream diffuser reduces the interaction between tip leakage flow and blade suction side. Up to 14% increase in turbine power and 9% increase in turbine efficiency are achieved by optimizing the duct geometry. On other hand, a tangible delay of the turbine stall point is also detected.

Holographic free energy and thermodynamic geometry

Science.gov (United States)

Ghorai, Debabrata; Gangopadhyay, Sunandan

2016-12-01

We obtain the free energy and thermodynamic geometry of holographic superconductors in 2+1 dimensions. The gravitational theory in the bulk dual to this 2+1-dimensional strongly coupled theory lives in the 3+1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method.

Holographic free energy and thermodynamic geometry

International Nuclear Information System (INIS)

Ghorai, Debabrata; Gangopadhyay, Sunandan

2016-01-01

We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)

Holographic free energy and thermodynamic geometry

Energy Technology Data Exchange (ETDEWEB)

Ghorai, Debabrata [S.N. Bose National Centre for Basic Sciences, Kolkata (India); Gangopadhyay, Sunandan [Indian Institute of Science Education and Research, Kolkata, Nadia (India); West Bengal State University, Department of Physics, Barasat (India); Inter University Centre for Astronomy and Astrophysics, Pune (India)

2016-12-15

We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)

Finsler geometry, relativity and gauge theories

International Nuclear Information System (INIS)

Asanov, G.S.

1985-01-01

This book provides a self-contained account of the Finslerian techniques which aim to synthesize the ideas of Finslerian metrical generalization of Riemannian geometry to merge with the primary physical concepts of general relativity and gauge field theories. The geometrization of internal symmetries in terms of Finslerian geometry, as well as the formulation of Finslerian generalization of gravitational field equations and equations of motion of matter, are two key points used to expound the techniques. The Clebsch representation of the canonical momentum field is used to formulate the Hamilton-Jacobi theory for homogeneous Lagrangians of classical mechanics. As an auxillary mathematical apparatus, the author uses invariance identities which systematically reflect the covariant properties of geometrical objects. The results of recent studies of special Finsler spaces are also applied. The book adds substantially to the mathematical monographs by Rund (1959) and Rund and Bear (1972), all basic results of the latter being reflected. It is the author's hope that thorough exploration of the materrial presented will tempt the reader to revise the habitual physical concepts supported conventionally by Riemannian geometry. (Auth.)

c-Extremization from toric geometry

Science.gov (United States)

Amariti, Antonio; Cassia, Luca; Penati, Silvia

2018-04-01

We derive a geometric formulation of the 2d central charge cr from infinite families of 4d N = 1 superconformal field theories topologically twisted on constant curvature Riemann surfaces. They correspond to toric quiver gauge theories and are associated to D3 branes probing five dimensional Sasaki-Einstein geometries in the AdS/CFT correspondence. We show that cr can be expressed in terms of the areas of the toric diagram describing the moduli space of the 4d theory, both for toric geometries with smooth and singular horizons. We also study the relation between a-maximization in 4d and c-extremization in 2d, giving further evidences of the mixing of the baryonic symmetries with the exact R-current in two dimensions.

Formalization and Implementation of Algebraic Methods in Geometry

Directory of Open Access Journals (Sweden)

Filip Marić

2012-02-01

Full Text Available We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method, their implementation and integration in educational tools. The project includes formal verification of the algebraic methods within Isabelle/HOL proof assistant and development of a new, open-source Java implementation of the algebraic methods. The project should fill-in some gaps still existing in this area (e.g., the lack of formal links between algebraic methods and synthetic geometry and the lack of self-contained implementations of algebraic methods suitable for integration with dynamic geometry tools and should enable new applications of theorem proving in education.

Differential and complex geometry origins, abstractions and embeddings

CERN Document Server

Wells, Jr , Raymond O

2017-01-01

Differential and complex geometry are two central areas of mathematics with a long and intertwined history. This book, the first to provide a unified historical perspective of both subjects, explores their origins and developments from the sixteenth to the twentieth century. Providing a detailed examination of the seminal contributions to differential and complex geometry up to the twentieth century embedding theorems, this monograph includes valuable excerpts from the original documents, including works of Descartes, Fermat, Newton, Euler, Huygens, Gauss, Riemann, Abel, and Nash. Suitable for beginning graduate students interested in differential, algebraic or complex geometry, this book will also appeal to more experienced readers.

Electroweak vacuum geometry

International Nuclear Information System (INIS)

Lepora, N.; Kibble, T.

1999-01-01

We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory. (author)

Hybridization and molecular geometry: A number game | Ojha ...

African Journals Online (AJOL)

Present article emphasize the new pedagogy to learn the hybridization and molecular geometry. It is always a challenge for the students to remember the hybridization and geometry of the molecule correctly. This topic has several importance in subjective and objective type questions and answers since in most of the ...

Computational modeling of geometry dependent phonon transport in silicon nanostructures

Science.gov (United States)

Cheney, Drew A.

Recent experiments have demonstrated that thermal properties of semiconductor nanostructures depend on nanostructure boundary geometry. Phonons are quantized mechanical vibrations that are the dominant carrier of heat in semiconductor materials and their aggregate behavior determine a nanostructure's thermal performance. Phonon-geometry scattering processes as well as waveguiding effects which result from coherent phonon interference are responsible for the shape dependence of thermal transport in these systems. Nanoscale phonon-geometry interactions provide a mechanism by which nanostructure geometry may be used to create materials with targeted thermal properties. However, the ability to manipulate material thermal properties via controlling nanostructure geometry is contingent upon first obtaining increased theoretical understanding of fundamental geometry induced phonon scattering processes and having robust analytical and computational models capable of exploring the nanostructure design space, simulating the phonon scattering events, and linking the behavior of individual phonon modes to overall thermal behavior. The overall goal of this research is to predict and analyze the effect of nanostructure geometry on thermal transport. To this end, a harmonic lattice-dynamics based atomistic computational modeling tool was created to calculate phonon spectra and modal phonon transmission coefficients in geometrically irregular nanostructures. The computational tool is used to evaluate the accuracy and regimes of applicability of alternative computational techniques based upon continuum elastic wave theory. The model is also used to investigate phonon transmission and thermal conductance in diameter modulated silicon nanowires. Motivated by the complexity of the transmission results, a simplified model based upon long wavelength beam theory was derived and helps explain geometry induced phonon scattering of low frequency nanowire phonon modes.

History of analytic geometry

CERN Document Server

Boyer, Carl B

2012-01-01

Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.

Pengembangan Perangkat Pembelajaran Geometri Ruang dengan Model Proving Theorem

Directory of Open Access Journals (Sweden)

Bambang Eko Susilo

2016-03-01

Full Text Available Kemampuan berpikir kritis dan kreatif mahasiswa masih lemah. Hal ini ditemukan pada mahasiswa yang mengambil mata kuliah Geometri Ruang yaitu dalam membuktikan soal-soal pembuktian (problem to proof. Mahasiswa masih menyelesaikan secara algoritmik atau prosedural sehingga diperlukan pengembangan perangkat pembelajaran Geometri Ruang berbasis kompetensi dan konservasi dengan model Proving Theorem. Dalam penelitian ini perangkat perkuliahan yang dikembangkan yaitu Silabus, Satuan Acara Perkuliahan (SAP, Kontrak Perkuliahan, Media Pembelajaran, Bahan Ajar, Tes UTS dan UAS serta Angket Karakter Konservasi telah dilaksanakan dengan baik dengan kriteria (1 validasi perangkat pembelajaran mata kuliah Geometri ruang berbasis kompetensi dan konservasi dengan model proving theorem berkategori baik dan layak digunakan dan (2 keterlaksanaan RPP pada pembelajaran yang dikembangkan secara keseluruhan berkategori baik.Critical and creative thinking abilities of students still weak. It is found in students who take Space Geometry subjects that is in solving problems to to prove. Students still finish in algorithmic or procedural so that the required the development of Space Geometry learning tools based on competency and conservation with Proving Theorem models. This is a research development which refers to the 4-D models that have been modified for the Space Geometry learning tools, second semester academic year 2014/2015. Instruments used include validation sheet, learning tools and character assessment questionnaire. In this research, the learning tools are developed, namely Syllabus, Lesson Plan, Lecture Contract, Learning Media, Teaching Material, Tests, and Character Conservation Questionnaire had been properly implemented with the criteria (1 validation of Space Geometry learning tools based on competency and conservation with Proving Theorem models categorized good and feasible to use, and (2 the implementation of Lesson Plan on learning categorized

Almost-commutative geometries beyond the standard model

International Nuclear Information System (INIS)

Stephan, Christoph A

2006-01-01

In Iochum et al (2004 J. Math. Phys. 45 5003), Jureit and Stephan (2005 J. Math. Phys. 46 043512), Schuecker T (2005 Preprint hep-th/0501181) and Jureit et al (2005 J. Math. Phys. 46 072303), a conjecture is presented that almost-commutative geometries, with respect to sensible physical constraints, allow only the standard model of particle physics and electro-strong models as Yang-Mills-Higgs theories. In this paper, a counter-example will be given. The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs model which consists of the standard model of particle physics and two new fermions of opposite electro-magnetic charge. This is the second Yang-Mills-Higgs model within noncommutative geometry, after the standard model, which could be compatible with experiments. Combined to a hydrogen-like composite particle, these new particles provide a novel dark matter candidate

Tests of compressed geometry NEC acceleration tubes

International Nuclear Information System (INIS)

Raatz, J.E.; Rathmell, R.D.; Stelson, P.H.; Ziegler, N.F.

1985-01-01

Tests have been performed in the 3 MV Pelletron test machine at NEC on a compressed geometry tube which increases the insulating length of the tube by eliminating the heated electrode assemblies (approx.2.5 cm thick) at the end of each tube section. Some insert electrodes are changed to provide some trapping of secondary ions. The geometry tested provided an 18% increase in live ceramic in the tube. The compressed geometry tube allowed a terminal voltage of 3.55 MV on the 3 MV column at normal gradients of 30.3 kv/tube gap. The tube was also conditioned to more than 4 MV and remained stable in voltage with few sparks and with low x-ray levels for days at about 4 MV. This same performance could be achieved with or without arc discharge cleaning. 4 refs., 4 figs

Capillary condensation in a square geometry with surface fields.

Science.gov (United States)

Zubaszewska, M; Gendiar, A; Drzewiński, A

2012-12-01

We study the influence of wetting on capillary condensation for a simple fluid in a square geometry with surface fields, where the reference system is an infinitely long slit. The corner transfer matrix renormalization group method has been extended to study a two-dimensional Ising model confined in an L × L geometry with equal surface fields. Our results have confirmed that in both geometries the coexistence line shift is governed by the same scaling powers, but their prefactors are different.

Classical An-W-geometry

International Nuclear Information System (INIS)

Gervais, J.L.

1993-01-01

By analyzing the extrinsic geometry of two dimensional surfaces chirally embedded in C P n (the C P n W-surface), we give exact treatments in various aspects of the classical W-geometry in the conformal gauge: First, the basis of tangent and normal vectors are defined at regular points of the surface, such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the (conformal) A n -Toda Lax pair. Since the latter is known to be intrinsically related with the W symmetries, this gives the geometrical meaning of the A n W-Algebra. Second, W-surfaces are put in one-to-one correspondence with solutions of the conformally-reduced WZNW model, which is such that the Toda fields give the Cartan part in the Gauss decomposition of its solutions. Third, the additional variables of the Toda hierarchy are used as coordinates of C P n . This allows us to show that W-transformations may be extended as particular diffeomorphisms of this target-space. Higher-dimensional generalizations of the WZNW equations are derived and related with the Zakharov-Shabat equations of the Toda hierarchy. Fourth, singular points are studied from a global viewpoint, using our earlier observation that W-surfaces may be regarded as instantons. The global indices of the W-geometry, which are written in terms of the Toda fields, are shown to be the instanton numbers for associated mappings of W-surfaces into the Grassmannians. The relation with the singularities of W-surface is derived by combining the Toda equations with the Gauss-Bonnet theorem. (orig.)

Functional integration over geometries

International Nuclear Information System (INIS)

Mottola, E.

1995-01-01

The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted

Hyperbolic Metamaterials with Complex Geometry

DEFF Research Database (Denmark)

Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei

2016-01-01

We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...

Low Complexity Connectivity Driven Dynamic Geometry Compression for 3D Tele-Immersion

NARCIS (Netherlands)

R.N. Mekuria (Rufael); D.C.A. Bulterman (Dick); P.S. Cesar Garcia (Pablo Santiago)

2014-01-01

htmlabstractGeometry based 3D Tele-Immersion is a novel emerging media application that involves on the fly reconstructed 3D mesh geometry. To enable real-time communication of such live reconstructed mesh geometry over a bandwidth limited link, fast dynamic geometry compression is needed. However,

ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY

OpenAIRE

Enrique Gonzalo Reyes Garcia

2004-01-01

ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY Equations in partial derivatives appeared in the 18th century as essential tools for the analytic study of physical models and, later, they proved to be fundamental for the progress of mathematics. For example, fundamental results of modern differential geometry are based on deep theorems on differential equations. Reciprocally, it is possible to study differential equations through geometrical means just like it was done by o...

Geometry and topology of wild translation surfaces

OpenAIRE

Randecker, Anja

2016-01-01

A translation surface is a two-dimensional manifold, equipped with a translation structure. It can be obtained by considering Euclidean polygons and identifying their edges via translations. The vertices of the polygons form singularities if the translation structure can not be extended to them. We study translation surfaces with wild singularities, regarding the topology (genus and space of ends), the geometry (behavior of the singularities), and how the topology and the geometry are related.

Quantum algebras and Poisson geometry in mathematical physics

CERN Document Server

Karasev, M V

2005-01-01

This collection presents new and interesting applications of Poisson geometry to some fundamental well-known problems in mathematical physics. The methods used by the authors include, in addition to advanced Poisson geometry, unexpected algebras with non-Lie commutation relations, nontrivial (quantum) Kählerian structures of hypergeometric type, dynamical systems theory, semiclassical asymptotics, etc.

Exploring Concepts of Geometry not Euclidean

Directory of Open Access Journals (Sweden)

Luiz Ambrozi

2016-02-01

Full Text Available With this article we intend to propose different situations of teaching and learning, how they can be applied in schools, mediated by the use of concrete materials and Geogebra software, emphasizing the use of technology in the classroom, that this proposal has the role of assisting in the conceptualization and identification of elements of non-Euclidean geometry. In addition, this short course is designed to be a time of current and continuing education for teachers, with activities to be developed with dynamic geometry and based on the theory of Conceptual Fields of Vergnaud.

Geometry-Dependent Electrostatics near Contact Lines

International Nuclear Information System (INIS)

Chou, Tom

2001-01-01

Long-ranged electrostatic interactions in electrolytes modify contact angles on charged substrates in a scale and geometry-dependent manner. For angles measured at scales smaller than the typical Debye screening length, the wetting geometry near the contact line must be explicitly considered. Using variational and asymptotic methods, we derive new transcendental equations for the contact angle as functions of the electrostatic potential only at the three phase contact line. Analytic expressions are found in certain limits and compared with predictions for contact angles measured with lower resolution. An estimate for electrostatic contributions to line tension is also given

Noncommutative Geometry, Quantum Fields and Motives

CERN Document Server

Connes, Alain

2007-01-01

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book dea

Third sound in a restricted geometry

International Nuclear Information System (INIS)

Brouwer, P.W.; Draisma, W.A.; Pinkse, P.W.H.; Beelen, H. van; Jochemsen, R.; Frossati, G.

1992-01-01

Bergman's general treatment of third sound waves has been extended to a (restricted) parallel plate geometry. In a parallel plate geometry two independent third sound modes can propagate: a symmetric and an antisymmetric one. Calculations show that at temperatures below 1 K the antisymmetric mode carries the most important part of the temperature amplitude. Because of the relatively strong substrate influence the temperature amplitude of the symmetric mode is suppressed. The ΔT/Δh versus T measurements by Laheurte et al. and of the ΔT/Δh versus ω measurements by Ellis et al. are explained. 7 refs., 2 figs

Riemannian geometry in an orthogonal frame

CERN Document Server

Cartan, Elie Joseph

2001-01-01

Foreword by S S Chern. In 1926-27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of these Cartan's lectures and published them as a book entitled Riemannian Geometry in an Orthogonal Frame. This book has many innovations, such as the n

Noncommutative geometry and twisted conformal symmetry

International Nuclear Information System (INIS)

Matlock, Peter

2005-01-01

The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted coproduct. This allows for the definition of conformal symmetry in a noncommutative background geometry. The twisted coproduct is reviewed for the Poincare algebra and the construction is then extended to the full conformal algebra. The case of Moyal-type noncommutativity of the coordinates is considered. It is demonstrated that conformal invariance need not be viewed as incompatible with noncommutative geometry; the noncommutativity of the coordinates appears as a consequence of the twisting, as has been shown in the literature in the case of the twisted Poincare algebra

Donaldson invariants in algebraic geometry

International Nuclear Information System (INIS)

Goettsche, L.

2000-01-01

In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)

On the Generalized Geometry Origin of Noncommutative Gauge Theory

CERN Document Server

Jurco, Branislav; Vysoky, Jan

2013-01-01

We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of D-branes.

Symplectic geometry and Fourier analysis

CERN Document Server

Wallach, Nolan R

2018-01-01

Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.

Towards relativistic quantum geometry

Energy Technology Data Exchange (ETDEWEB)

Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)

2015-12-17

We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.

Dynamic geometry as a context for exploring conjectures

Science.gov (United States)

Wares, Arsalan

2018-01-01

The purpose of this paper is to provide examples of 'non-traditional' proof-related activities that can explored in a dynamic geometry environment by university and high school students of mathematics. These propositions were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these propositions.

Geometry of Quantum States

International Nuclear Information System (INIS)

Hook, D W

2008-01-01

A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric framework, and

``Stacked reservoirs`` in the Zechstein 2 carbonate (Ca2): inversion tectonics in the pre-Zechstein subdivision-saline base of the Lower Saxony basin (Germany); ``Stacked Reservoirs`` im Zechstein 2 Karbonat (Ca2): Inversionstektonik im prae-Zechstein-salinaren Sockel des Niedersaechsischen Beckens (NW-Deutschland)

Energy Technology Data Exchange (ETDEWEB)

Rockenbauch, K.; Brauckmann, F.; Schaefer, H.G.; Utermoehlen, S. [BEB Erdgas und Erdoel GmbH, Hannover (Germany)

1998-12-31

This article looks at areas in the Lower Saxony basis of North-West Germany where the carbonate of the 2nd Zechstein subdivision cycle (Ca2) was tectonically removed from its stratigraphic compound and is found in several stacks elsewhere. Modern 3D seismology and deep drillings were evaluated and tectonic models were developed which could be compared with examples from other saline provinces. This revealed new aspects of exploration for sour natural gas in the Zechstein subdivision (orig.). [Deutsch] Der Artikel behandelt Bereiche innerhalb des Niedersaechsischen Beckens von Nordwestdeutschland, wo das Karbonat des 2. Zechstein-Zyklus (Ca2) tektonisch aus seinem stratigraphischen Verband geloest wurde und an anderer Stelle mehrfach uebereinander gestapelt anzutreffen ist. Hierzu wurden moderne 3D Seismik sowie Tiefbohrungen ausgewertet und tektonische Modelle entwickelt, die mit Beispielen aus anderen Salinarprovinzen verglichen wurden. Hinsichtlich der Exploration auf Sauergas im Zechstein ergeben sich daraus neue Aspekte und Moeglichkeiten. (orig.)

Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries

International Nuclear Information System (INIS)

Bombelli, L.; Corichi, A.; Winkler, O.

2005-01-01

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at ''quantum scales'' and continuum, classical geometries at large scales. Such a correspondence can be meaningfully established when one has a ''semiclassical'' state in the underlying quantum gravity theory, and the uncertainties in the correspondence arise both from quantum fluctuations in this state and from the kinematical procedure of matching a smooth geometry to a discrete one. We focus on the latter type of uncertainty, and suggest the use of statistical geometry as a way to quantify it. With a cell complex as an example of discrete structure, we discuss how to construct quantities that define a smooth geometry, and how to estimate the associated uncertainties. We also comment briefly on how to combine our results with uncertainties in the underlying quantum state, and on their use when considering phenomenological aspects of quantum gravity. (Abstract Copyright [2005], Wiley Periodicals, Inc.)

An introduction to differential geometry

CERN Document Server

Willmore, T J

2012-01-01

This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

Geometry and Destiny

OpenAIRE

Krauss, Lawrence M.; Turner, Michael S.

1999-01-01

The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.

Interactions between Digital Geometry and Combinatorics on Words

Directory of Open Access Journals (Sweden)

Srečko Brlek

2011-08-01

Full Text Available We review some recent results in digital geometry obtained by using a combinatorics on words approach to discrete geometry. Motivated on the one hand by the well-known theory of Sturmian words which model conveniently discrete lines in the plane, and on the other hand by the development of digital geometry, this study reveals strong links between the two fields. Discrete figures are identified with polyominoes encoded by words. The combinatorial tools lead to elegant descriptions of geometrical features and efficient algorithms. Among these, radix-trees are useful for efficiently detecting path intersection, Lyndon and Christoffel words appear as the main tools for describing digital convexity; equations on words allow to better understand tilings by translations.

CIME-CIRM course Rationality Problems in Algebraic Geometry

CERN Document Server

Pirola, Gian

2016-01-01

Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel–Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.

The geometry of celestial mechanics

CERN Document Server

Geiges, Hansjörg

2016-01-01

Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.

Sex, subdivision, and domestic dispersal of Trypanosoma cruzi lineage I in southern Ecuador.

Science.gov (United States)

Ocaña-Mayorga, Sofía; Llewellyn, Martin S; Costales, Jaime A; Miles, Michael A; Grijalva, Mario J

2010-12-14

Molecular epidemiology at the community level has an important guiding role in zoonotic disease control programmes where genetic markers are suitably variable to unravel the dynamics of local transmission. We evaluated the molecular diversity of Trypanosoma cruzi, the etiological agent of Chagas disease, in southern Ecuador (Loja Province). This kinetoplastid parasite has traditionally been a paradigm for clonal population structure in pathogenic organisms. However, the presence of naturally occurring hybrids, mitochondrial introgression, and evidence of genetic exchange in the laboratory question this dogma. Eighty-one parasite isolates from domiciliary, peridomiciliary, and sylvatic triatomines and mammals were genotyped across 10 variable microsatellite loci. Two discrete parasite populations were defined: one predominantly composed of isolates from domestic and peridomestic foci, and another predominantly composed of isolates from sylvatic foci. Spatial genetic variation was absent from the former, suggesting rapid parasite dispersal across our study area. Furthermore, linkage equilibrium between loci, Hardy-Weinberg allele frequencies at individual loci, and a lack of repeated genotypes are indicative of frequent genetic exchange among individuals in the domestic/peridomestic population. These data represent novel population-level evidence of an extant capacity for sex among natural cycles of T. cruzi transmission. As such they have dramatic implications for our understanding of the fundamental genetics of this parasite. Our data also elucidate local disease transmission, whereby passive anthropogenic domestic mammal and triatomine dispersal across our study area is likely to account for the rapid domestic/peridomestic spread of the parasite. Finally we discuss how this, and the observed subdivision between sympatric sylvatic and domestic/peridomestic foci, can inform efforts at Chagas disease control in Ecuador.

Sex, subdivision, and domestic dispersal of Trypanosoma cruzi lineage I in southern Ecuador.

Directory of Open Access Journals (Sweden)

Sofía Ocaña-Mayorga

2010-12-01

Full Text Available Molecular epidemiology at the community level has an important guiding role in zoonotic disease control programmes where genetic markers are suitably variable to unravel the dynamics of local transmission. We evaluated the molecular diversity of Trypanosoma cruzi, the etiological agent of Chagas disease, in southern Ecuador (Loja Province. This kinetoplastid parasite has traditionally been a paradigm for clonal population structure in pathogenic organisms. However, the presence of naturally occurring hybrids, mitochondrial introgression, and evidence of genetic exchange in the laboratory question this dogma.Eighty-one parasite isolates from domiciliary, peridomiciliary, and sylvatic triatomines and mammals were genotyped across 10 variable microsatellite loci. Two discrete parasite populations were defined: one predominantly composed of isolates from domestic and peridomestic foci, and another predominantly composed of isolates from sylvatic foci. Spatial genetic variation was absent from the former, suggesting rapid parasite dispersal across our study area. Furthermore, linkage equilibrium between loci, Hardy-Weinberg allele frequencies at individual loci, and a lack of repeated genotypes are indicative of frequent genetic exchange among individuals in the domestic/peridomestic population.These data represent novel population-level evidence of an extant capacity for sex among natural cycles of T. cruzi transmission. As such they have dramatic implications for our understanding of the fundamental genetics of this parasite. Our data also elucidate local disease transmission, whereby passive anthropogenic domestic mammal and triatomine dispersal across our study area is likely to account for the rapid domestic/peridomestic spread of the parasite. Finally we discuss how this, and the observed subdivision between sympatric sylvatic and domestic/peridomestic foci, can inform efforts at Chagas disease control in Ecuador.

Construction and decoding of a class of algebraic geometry codes

DEFF Research Database (Denmark)

Justesen, Jørn; Larsen, Knud J.; Jensen, Helge Elbrønd

1989-01-01

A class of codes derived from algebraic plane curves is constructed. The concepts and results from algebraic geometry that were used are explained in detail; no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result is a decod...... is a decoding algorithm which turns out to be a generalization of the Peterson algorithm for decoding BCH decoder codes......A class of codes derived from algebraic plane curves is constructed. The concepts and results from algebraic geometry that were used are explained in detail; no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result...

Index theory for locally compact noncommutative geometries

CERN Document Server

Carey, A L; Rennie, A; Sukochev, F A

2014-01-01

Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.

Application of Tessellation in Architectural Geometry Design

Science.gov (United States)

Chang, Wei

2018-06-01

Tessellation plays a significant role in architectural geometry design, which is widely used both through history of architecture and in modern architectural design with the help of computer technology. Tessellation has been found since the birth of civilization. In terms of dimensions, there are two- dimensional tessellations and three-dimensional tessellations; in terms of symmetry, there are periodic tessellations and aperiodic tessellations. Besides, some special types of tessellations such as Voronoi Tessellation and Delaunay Triangles are also included. Both Geometry and Crystallography, the latter of which is the basic theory of three-dimensional tessellations, need to be studied. In history, tessellation was applied into skins or decorations in architecture. The development of Computer technology enables tessellation to be more powerful, as seen in surface control, surface display and structure design, etc. Therefore, research on the application of tessellation in architectural geometry design is of great necessity in architecture studies.

The estimation of collision probabilities in complicated geometries

International Nuclear Information System (INIS)

Roth, M.J.

1969-04-01

This paper demonstrates how collision probabilities in complicated geometries may be estimated. It is assumed that the reactor core may be divided into a number of cells each with simple geometry so that a collision probability matrix can be calculated for each cell by standard methods. It is then shown how these may be joined together. (author)

Transient potentials in dendritic systems of arbitrary geometry.

Science.gov (United States)

Butz, E G; Cowan, J D

1974-09-01

A simple graphical calculus is developed that generates analytic solutions for membrane potential transforms at any point on the dendritic tree of neurons with arbitrary dendritic geometries, in response to synaptic "current" inputs. Such solutions permit the computation of transients in neurons with arbitrary geometry and may facilitate analysis of the role of dendrites in such cells.

Conceptual design study of geothermal district heating of a thirty-house subdivision in Elko, Nevada, using existing water-distribution systems, Phase III. Final technical report, October 1, 1979-September 30, 1980

Energy Technology Data Exchange (ETDEWEB)

Pitts, D.R.

1980-09-30

A conceptual design study for district heating of a 30-home subdivision located near the southeast extremity of the city of Elko, Nevada is presented. While a specific residential community was used in the study, the overall approach and methodologies are believed to be generally applicable for a large number of communities where low temperature geothermal fluid is available. The proposed district heating system utilizes moderate temperature, clean domestic water and existing community culinary water supply lines. The culinary water supply is heated by a moderate temperature geothermal source using a single heat exchanger at entry to the subdivision. The heated culinary water is then pumped to the houses in the community where energy is extracted by means of a water supplied heat pump. The use of heat pumps at the individual houses allows economic heating to result from supply of relatively cool water to the community, and this precludes the necessity of supplying objectionably hot water for normal household consumption use. Each heat pump unit is isolated from the consumptive water flow such that contamination of the water supply is avoided. The community water delivery system is modified to allow recirculation within the community, and very little rework of existing water lines is required. The entire system coefficient of performance (COP) for a typical year of heating is 3.36, exclusive of well pumping energy.

More on microstate geometries of 4d black holes

International Nuclear Information System (INIS)

Bianchi, M.; Morales, J.F.; Pieri, L.; Zinnato, N.

2017-01-01

We construct explicit examples of microstate geometries of four-dimensional black holes that lift to smooth horizon-free geometries in five dimensions. Solutions consist of half-BPS D-brane atoms distributed in ℝ 3 . Charges and positions of the D-brane centers are constrained by the bubble equations and boundary conditions ensuring the regularity of the metric and the match with the black hole geometry. In the case of three centers, we find that the moduli spaces of solutions includes disjoint one-dimensional components of (generically) finite volume.

Evolutionary algorithm for optimization of nonimaging Fresnel lens geometry.

Science.gov (United States)

Yamada, N; Nishikawa, T

2010-06-21

In this study, an evolutionary algorithm (EA), which consists of genetic and immune algorithms, is introduced to design the optical geometry of a nonimaging Fresnel lens; this lens generates the uniform flux concentration required for a photovoltaic cell. Herein, a design procedure that incorporates a ray-tracing technique in the EA is described, and the validity of the design is demonstrated. The results show that the EA automatically generated a unique geometry of the Fresnel lens; the use of this geometry resulted in better uniform flux concentration with high optical efficiency.

More on microstate geometries of 4d black holes

Energy Technology Data Exchange (ETDEWEB)

Bianchi, M. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy); Morales, J.F. [I.N.F.N. - Sezione di Roma 2 and Università di Roma Tor Vergata, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Roma (Italy); Pieri, L. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy); Center for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London, Mile End Road, London, E1 4NS (United Kingdom); Zinnato, N. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy)

2017-05-29

We construct explicit examples of microstate geometries of four-dimensional black holes that lift to smooth horizon-free geometries in five dimensions. Solutions consist of half-BPS D-brane atoms distributed in ℝ{sup 3}. Charges and positions of the D-brane centers are constrained by the bubble equations and boundary conditions ensuring the regularity of the metric and the match with the black hole geometry. In the case of three centers, we find that the moduli spaces of solutions includes disjoint one-dimensional components of (generically) finite volume.

On spinor geometry: A genesis of extended supersymmetry

International Nuclear Information System (INIS)

Budini, P.

1980-08-01

It is conjectured that euclidean geometry should be derived from spinor geometry through the equivalence of simple semispinor with isotropic semi n-vectors. The only tensors of complex 2n dimensional Euclidean space Esub(c)sup(2n) should then be: isotropic n - vectors and their intersections. Esub(c) 4 spinor geometry generates two isotropic semi bivectors equivalent to the semispinors of Esub(c) 4 (their geometrical properties are those of light propagating in vacuum), and their intersection: an isotropic vector (possibly representing momenta of massless particle and/or light rays); but no scalar, pseudoscalar or pseudovector is generated. In order to generate vectors outside the light cone in Msup(3.1) one needs not less than Esub(c) 6 spinor geometry which also generates Lorentz pseudoscalars and non isotropic pseudovectors and tensors. Besides, Dirac spinor should then always appear in doublets in Msup(3.1). Furthermore the mere geometrical structure of Esub(c) 6 spinor geometry seems to suggest formally, both Poincare (extended) and conformal supersymmetry. The suggested spinor-geometrical approach privileges the elementary role of semispinors. Its relevance for the real world should be manifested by the privileged role of semispinors in elementary interactions as in fact seems to be the case with Lorentz semispinors in weak interactions (and could perhaps also be the case for strong ones where conformal semispinors (or twistors) could be the interacting spinor fields). (author)

Control of nonholonomic systems from sub-Riemannian geometry to motion planning

CERN Document Server

Jean, Frédéric

2014-01-01

Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems. In particular the usual notions of approximations at the first order, that are essential for control purposes, have to be defined in terms of this geometry. The aim of these notes is to present these notions of approximation and their application to the motion planning problem for nonholonomic systems.

RGG: Reactor geometry (and mesh) generator

International Nuclear Information System (INIS)

Jain, R.; Tautges, T.

2012-01-01

The reactor geometry (and mesh) generator RGG takes advantage of information about repeated structures in both assembly and core lattices to simplify the creation of geometry and mesh. It is released as open source software as a part of the MeshKit mesh generation library. The methodology operates in three stages. First, assembly geometry models of various types are generated by a tool called AssyGen. Next, the assembly model or models are meshed by using MeshKit tools or the CUBIT mesh generation tool-kit, optionally based on a journal file output by AssyGen. After one or more assembly model meshes have been constructed, a tool called CoreGen uses a copy/move/merge process to arrange the model meshes into a core model. In this paper, we present the current state of tools and new features in RGG. We also discuss the parallel-enabled CoreGen, which in several cases achieves super-linear speedups since the problems fit in available RAM at higher processor counts. Several RGG applications - 1/6 VHTR model, 1/4 PWR reactor core, and a full-core model for Monju - are reported. (authors)

Product forms in Gabor analysis for a quincunx-type sampling geometry

NARCIS (Netherlands)

Bastiaans, M.J.; Leest, van A.J.; Veen, J.P.

1998-01-01

Recently a new sampling lattice - the quincunx lattice - has been introduced [1] as a sampling geometry in the Gabor scheme, which geometry is different from the traditional rectangular sampling geometry. In this paper we will show how results that hold for rectangular sampling (see, for instance,

Architectural Geometry and Fabrication-Aware Design

KAUST Repository

Pottmann, Helmut

2013-04-27

Freeform shapes and structures with a high geometric complexity play an increasingly important role in contemporary architecture. While digital models are easily created, the actual fabrication and construction remains a challenge. This is the source of numerous research problems many of which fall into the area of Geometric Computing and form part of a recently emerging research area, called "Architectural Geometry". The present paper provides a short survey of research in Architectural Geometry and shows how this field moves towards a new direction in Geometric Modeling which aims at combining shape design with important aspects of function and fabrication. © 2013 Kim Williams Books, Turin.

Non-Euclidean geometry and curvature two-dimensional spaces, volume 3

CERN Document Server

Cannon, James W

2017-01-01

This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. Einstein showed how to interpret gravity as the dynamic response to the curvature of space-time. Bill Thurston showed us that non-Euclidean geometries and curvature are essential to the understanding of low-dimensional spaces. This third and final volume aims to give the reader a firm intuitive understanding of these concepts in dimension 2. The volume first demonstrates a number of the most important properties of non-Euclidean geometry by means of simple infinite graphs that approximate that geometry. This is followed by a long chapter taken from lectures the author gave at MSRI, wh...

Intrinsic and extrinsic geometries of a tidally deformed black hole

International Nuclear Information System (INIS)

Vega, Ian; Poisson, Eric; Massey, Ryan

2011-01-01

A description of the event horizon of a perturbed Schwarzschild black hole is provided in terms of the intrinsic and extrinsic geometries of the null hypersurface. This description relies on a Gauss-Codazzi theory of null hypersurfaces embedded in spacetime, which extends the standard theory of spacelike and timelike hypersurfaces involving the first and second fundamental forms. We show that the intrinsic geometry of the event horizon is invariant under a reparameterization of the null generators, and that the extrinsic geometry depends on the parameterization. Stated differently, we show that while the extrinsic geometry depends on the choice of gauge, the intrinsic geometry is gauge invariant. We apply the formalism to solutions to the vacuum field equations that describe a tidally deformed black hole. In a first instance, we consider a slowly varying, quadrupolar tidal field imposed on the black hole, and in a second instance, we examine the tide raised during a close parabolic encounter between the black hole and a small orbiting body.

Evaluation of a cone beam computed tomography geometry for image guided small animal irradiation

International Nuclear Information System (INIS)

Yang, Yidong; Armour, Michael; Wang, Ken Kang-Hsin; Gandhi, Nishant; Wong, John; Iordachita, Iulian; Siewerdsen, Jeffrey

2015-01-01

The conventional imaging geometry for small animal cone beam computed tomography (CBCT) is that a detector panel rotates around the head-to-tail axis of an imaged animal (‘tubular’ geometry). Another unusual but possible imaging geometry is that the detector panel rotates around the anterior-to-posterior axis of the animal (‘pancake’ geometry). The small animal radiation research platform developed at Johns Hopkins University employs the pancake geometry where a prone-positioned animal is rotated horizontally between an x-ray source and detector panel. This study is to assess the CBCT image quality in the pancake geometry and investigate potential methods for improvement. We compared CBCT images acquired in the pancake geometry with those acquired in the tubular geometry when the phantom/animal was placed upright simulating the conventional CBCT geometry. Results showed signal-to-noise and contrast-to-noise ratios in the pancake geometry were reduced in comparison to the tubular geometry at the same dose level. But the overall spatial resolution within the transverse plane of the imaged cylinder/animal was better in the pancake geometry. A modest exposure increase to two folds in the pancake geometry can improve image quality to a level close to the tubular geometry. Image quality can also be improved by inclining the animal, which reduces streak artifacts caused by bony structures. The major factor resulting in the inferior image quality in the pancake geometry is the elevated beam attenuation along the long axis of the phantom/animal and consequently increased scatter-to-primary ratio in that orientation. Not withstanding, the image quality in the pancake-geometry CBCT is adequate to support image guided animal positioning, while providing unique advantages of non-coplanar and multiple mice irradiation. This study also provides useful knowledge about the image quality in the two very different imaging geometries, i.e. pancake and tubular geometry

Evaluation of a cone beam computed tomography geometry for image guided small animal irradiation.

Science.gov (United States)

Yang, Yidong; Armour, Michael; Wang, Ken Kang-Hsin; Gandhi, Nishant; Iordachita, Iulian; Siewerdsen, Jeffrey; Wong, John

2015-07-07

The conventional imaging geometry for small animal cone beam computed tomography (CBCT) is that a detector panel rotates around the head-to-tail axis of an imaged animal ('tubular' geometry). Another unusual but possible imaging geometry is that the detector panel rotates around the anterior-to-posterior axis of the animal ('pancake' geometry). The small animal radiation research platform developed at Johns Hopkins University employs the pancake geometry where a prone-positioned animal is rotated horizontally between an x-ray source and detector panel. This study is to assess the CBCT image quality in the pancake geometry and investigate potential methods for improvement. We compared CBCT images acquired in the pancake geometry with those acquired in the tubular geometry when the phantom/animal was placed upright simulating the conventional CBCT geometry. Results showed signal-to-noise and contrast-to-noise ratios in the pancake geometry were reduced in comparison to the tubular geometry at the same dose level. But the overall spatial resolution within the transverse plane of the imaged cylinder/animal was better in the pancake geometry. A modest exposure increase to two folds in the pancake geometry can improve image quality to a level close to the tubular geometry. Image quality can also be improved by inclining the animal, which reduces streak artifacts caused by bony structures. The major factor resulting in the inferior image quality in the pancake geometry is the elevated beam attenuation along the long axis of the phantom/animal and consequently increased scatter-to-primary ratio in that orientation. Not withstanding, the image quality in the pancake-geometry CBCT is adequate to support image guided animal positioning, while providing unique advantages of non-coplanar and multiple mice irradiation. This study also provides useful knowledge about the image quality in the two very different imaging geometries, i.e. pancake and tubular geometry, respectively.

Thermal geometry from CFT at finite temperature

Directory of Open Access Journals (Sweden)

Wen-Cong Gan

2016-09-01

Full Text Available We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

Thermal geometry from CFT at finite temperature

Energy Technology Data Exchange (ETDEWEB)

Gan, Wen-Cong, E-mail: ganwencong@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Shu, Fu-Wen, E-mail: shufuwen@ncu.edu.cn [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Wu, Meng-He, E-mail: menghewu.physik@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China)

2016-09-10

We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

Geometry and experience: Einstein's 1921 paper and Hilbert's axiomatic system

International Nuclear Information System (INIS)

De Gandt, Francois

2006-01-01

In his 1921 paper Geometrie und Erfahrung, Einstein decribes the new epistemological status of geometry, divorced from any intuitive or a priori content. He calls that 'axiomatics', following Hilbert's theoretical developments on axiomatic systems, which started with the stimulus given by a talk by Hermann Wiener in 1891 and progressed until the Foundations of geometry in 1899. Difficult questions arise: how is a theoretical system related to an intuitive empirical content?

Cloaking of 2D particle geometries in a surface medium

Energy Technology Data Exchange (ETDEWEB)

Alexopoulos, A., E-mail: Aris.Alexopoulos@dsto.defence.gov.au [Electronic Warfare and Radar Division, Defence Science and Technology Organisation (DSTO), PO Box 1500, Edinburgh 5111 (Australia); Yau, K.S.B. [Electronic Warfare and Radar Division, Defence Science and Technology Organisation (DSTO), PO Box 1500, Edinburgh 5111 (Australia)

2013-06-17

We theoretically examine the cloaking condition for two-dimensional particles with varying geometry embedded inside a surface medium. General solutions are obtained for multi-layer particle configurations with either all positive or partially negative constitutive parameters respectively. Cloaking of particle geometries that are large relative to the incident wavelength is demonstrated. Theoretical predictions are compared to full-wave numerical simulations for arrays of particles consisting of different geometries.

Loading pattern optimization in hexagonal geometry using PANTHER

International Nuclear Information System (INIS)

Parks, G.T.; Knight, M.P.

1996-01-01

The extension of the loading pattern optimization capability of Nuclear Electric's reactor physics code PANTHER to hexagonal geometry cores is described. The variety of search methods available and the code's performance are illustrated by an example in which three search different methods are used in turn in order to find an optimal reload design for a sample hexagonal geometry problem. (author)

Conformal, Riemannian and Lagrangian geometry the 2000 Barrett lectures

CERN Document Server

Chang, Sun-Yung A; Grove, Karsten; Yang, Paul C; Freire, Alexandre

2002-01-01

Recent developments in topology and analysis have led to the creation of new lines of investigation in differential geometry. The 2000 Barrett Lectures present the background, context and main techniques of three such lines by means of surveys by leading researchers. The first chapter (by Alice Chang and Paul Yang) introduces new classes of conformal geometric invariants, and then applies powerful techniques in nonlinear differential equations to derive results on compactifications of manifolds and on Yamabe-type variational problems for these invariants. This is followed by Karsten Grove's lectures, which focus on the use of isometric group actions and metric geometry techniques to understand new examples and classification results in Riemannian geometry, especially in connection with positive curvature. The chapter written by Jon Wolfson introduces the emerging field of Lagrangian variational problems, which blends in novel ways the structures of symplectic geometry and the techniques of the modern calculus...

International conference on Algebraic and Complex Geometry

CERN Document Server

Kloosterman, Remke; Schütt, Matthias

2014-01-01

Several important aspects of moduli spaces and irreducible holomorphic symplectic manifolds were highlighted at the conference “Algebraic and Complex Geometry” held September 2012 in Hannover, Germany. These two subjects of recent ongoing progress belong to the most spectacular developments in Algebraic and Complex Geometry. Irreducible symplectic manifolds are of interest to algebraic and differential geometers alike, behaving similar to K3 surfaces and abelian varieties in certain ways, but being by far less well-understood. Moduli spaces, on the other hand, have been a rich source of open questions and discoveries for decades and still continue to be a hot topic in itself as well as with its interplay with neighbouring fields such as arithmetic geometry and string theory. Beyond the above focal topics this volume reflects the broad diversity of lectures at the conference and comprises 11 papers on current research from different areas of algebraic and complex geometry sorted in alphabetic order by the ...

Geometry of curves and surfaces with Maple

CERN Document Server

Rovenski, Vladimir

2000-01-01

This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource...

Nozzle geometry variations on the discharge coefficient

Directory of Open Access Journals (Sweden)

M.M.A. Alam

2016-03-01

Full Text Available Numerical works have been conducted to investigate the effect of nozzle geometries on the discharge coefficient. Several contoured converging nozzles with finite radius of curvatures, conically converging nozzles and conical divergent orifices have been employed in this investigation. Each nozzle and orifice has a nominal exit diameter of 12.7×10−3 m. A 3rd order MUSCL finite volume method of ANSYS Fluent 13.0 was used to solve the Reynolds-averaged Navier–Stokes equations in simulating turbulent flows through various nozzle inlet geometries. The numerical model was validated through comparison between the numerical results and experimental data. The results obtained show that the nozzle geometry has pronounced effect on the sonic lines and discharge coefficients. The coefficient of discharge was found differ from unity due to the non-uniformity of flow parameters at the nozzle exit and the presence of boundary layer as well.

Euclidean distance geometry an introduction

CERN Document Server

Liberti, Leo

2017-01-01

This textbook, the first of its kind, presents the fundamentals of distance geometry:  theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several.  Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.

Origami, Geometry and Art

Science.gov (United States)

Wares, Arsalan; Elstak, Iwan

2017-01-01

The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…

Spacetime and Euclidean geometry

Science.gov (United States)

Brill, Dieter; Jacobson, Ted

2006-04-01

Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.

Comparative study of the gamma spectrometry method performance in different measurement geometries

International Nuclear Information System (INIS)

Diaconescu, C.; Ichim, C.; Bujoreanu, L.; Florea, I.

2013-01-01

This paper presents the results obtained by gamma spectrometry on aqueous liquid waste sample using different measurement geometries. A liquid waste sample with known gamma emitters content was measured in three different geometries in order to assess the influence of the geometry on the final results. To obtain low measurement errors, gamma spectrometer was calibrated using a calibration standard with the same physical and chemical characteristics as the sample to be measured. Since the calibration was performed with the source at contact with HPGe detector, the waste sample was also measured, for all the three geometries, at the detector contact. The influence of the measurement geometry on the results was evaluated by computing the relative errors. The measurements performed using three different geometries (250 ml plastic vial, Sarpagan box and 24 ml Tricarb vial) showed that all these geometries may be used to quantify the activity of gamma emitters in different type of radioactive waste. (authors)

Numerical optimization of die geometry in open die forging

DEFF Research Database (Denmark)

Christiansen, Peter; Hattel, Jesper Henri; Bay, Niels

2013-01-01

This paper deals with numerical optimization of open die forging of large metallic ingots made by casting implying risk of defects, e.g. central pores. Different material hardening properties and die geometries are combined in order to investigate, which geometry gives rise to maximum closure...

Graph-drawing algorithms geometries versus molecular mechanics in fullereness

Science.gov (United States)

Kaufman, M.; Pisanski, T.; Lukman, D.; Borštnik, B.; Graovac, A.

1996-09-01

The algorithms of Kamada-Kawai (KK) and Fruchterman-Reingold (FR) have been recently generalized (Pisanski et al., Croat. Chem. Acta 68 (1995) 283) in order to draw molecular graphs in three-dimensional space. The quality of KK and FR geometries is studied here by comparing them with the molecular mechanics (MM) and the adjacency matrix eigenvectors (AME) algorithm geometries. In order to compare different layouts of the same molecule, an appropriate method has been developed. Its application to a series of experimentally detected fullerenes indicates that the KK, FR and AME algorithms are able to reproduce plausible molecular geometries.