Geometry Modeling Program Implementation of Human Hip Tissue
Directory of Open Access Journals (Sweden)
WANG Mo-nan
2017-10-01
Full Text Available Abstract:Aiming to design a simulate software of human tissue modeling and analysis，Visual Studio 2010 is selected as a development tool to develop a 3 D reconstruction software of human tissue with language C++.It can be used alone. It also can be a module of the virtual surgery systems. The system includes medical image segmentation modules and 3 D reconstruction modules，and can realize the model visualization. This software system has been used to reconstruct hip muscles，femur and hip bone accurately. The results show these geometry models can simulate the structure of hip tissues.
Geometry Modeling Program Implementation of Human Hip Tissue
Directory of Open Access Journals (Sweden)
WANG Monan
2017-04-01
Full Text Available Aiming to design a simulate software of human tissue modeling and analysis，Visual Studio 2010 is selected as a development tool to develop a 3 D reconstruction software of human tissue with language C++.It can be used alone. It also can be a module of the virtual surgery systems. The system includes medical image segmentation modules and 3 D reconstruction modules，and can realize the model visualization. This software system has been used to reconstruct hip muscles，femur and hip bone accurately. The results show these geometry models can simulate the structure of hip tissues.
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...
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 ...
PDGFRα plays a crucial role in connective tissue remodeling.
Horikawa, Shinjiro; Ishii, Yoko; Hamashima, Takeru; Yamamoto, Seiji; Mori, Hisashi; Fujimori, Toshihiko; Shen, Jie; Inoue, Ran; Nishizono, Hirofumi; Itoh, Hiroshi; Majima, Masataka; Abraham, David; Miyawaki, Toshio; Sasahara, Masakiyo
2015-12-07
Platelet derived growth factor (PDGF) plays a pivotal role in the remodeling of connective tissues. Emerging data indicate the distinctive role of PDGF receptor-α (PDGFRα) in this process. In the present study, the Pdgfra gene was systemically inactivated in adult mouse (α-KO mouse), and the role of PDGFRα was examined in the subcutaneously implanted sponge matrices. PDGFRα expressed in the fibroblasts of Pdgfra-preserving control mice (Flox mice), was significantly reduced in the sponges in α-KO mice. Neovascularized areas were largely suppressed in the α-KO mice than in the Flox mice, whereas the other parameters related to the blood vessels and endothelial cells were similar. The deposition of collagen and fibronectin and the expression of collagen 1a1 and 3a1 genes were significantly reduced in α-KO mice. There was a significantly decrease in the number and dividing fibroblasts in the α-KO mice, and those of macrophages were similar between the two genotypes. Hepatocyte growth factor (Hgf) gene expression was suppressed in Pdgfra-inactivated fibroblasts and connective tissue. The findings implicate the role of PDGFRα-dependent ECM and HGF production in fibroblasts that promotes the remodeling of connective tissue and suggest that PDGFRα may be a relevant target to regulate connective tissue remodeling.
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.
The mother centriole plays an instructive role in defining cell geometry.
Directory of Open Access Journals (Sweden)
Jessica L Feldman
2007-06-01
Full Text Available Centriole positioning is a key step in establishment and propagation of cell geometry, but the mechanism of this positioning is unknown. The ability of pre-existing centrioles to induce formation of new centrioles at a defined angle relative to themselves suggests they may have the capacity to transmit spatial information to their daughters. Using three-dimensional computer-aided analysis of cell morphology in Chlamydomonas, we identify six genes required for centriole positioning relative to overall cell polarity, four of which have known sequences. We show that the distal portion of the centriole is critical for positioning, and that the centriole positions the nucleus rather than vice versa. We obtain evidence that the daughter centriole is unable to respond to normal positioning cues and relies on the mother for positional information. Our results represent a clear example of "cytotaxis" as defined by Sonneborn, and suggest that centrioles can play a key function in propagation of cellular geometry from one generation to the next. The genes documented here that are required for proper centriole positioning may represent a new class of ciliary disease genes, defects in which would be expected to cause disorganized ciliary position and impaired function.
Influence of tissue preservation methods on arterial geometry and echogenicity
DEFF Research Database (Denmark)
Wilhjelm, Jens Erik; Vogt, Katja; Jespersen, Søren Kragh
1997-01-01
Thoracic porcine aortas from 5 pigs were investigated with 7,5-MHz ultrasound in vitro at low and high transmural pressure before and after the following tissue preservation methods were applied: 1, Storage in frozen condition(-12 degrees C) for 24 h followed by thawing; 2, fixation in formalin...
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
Delgado-Ruiz, Rafael Arcesio; Calvo-Guirado, Jose Luis; Abboud, Marcus; Ramirez-Fernandez, Maria Piedad; Maté-Sánchez de Val, José Eduardo; Negri, Bruno; Gomez-Moreno, Gerardo; Markovic, Aleksa
2015-08-01
To describe contact, thickness, density, and orientation of connective tissue fibers around healing abutments of different geometries by means of a new method using coordinates. Following the bilateral extraction of mandibular premolars (P2, P3, and P4) from six fox hound dogs and a 2-month healing period, 36 titanium implants were inserted, onto which two groups of healing abutments of different geometry were screwed: Group A (concave abutments) and Group B (wider healing abutment). After 3 months the animals were sacrificed and samples extracted containing each implant and surrounding soft and hard tissues. Histological analysis was performed without decalcifying the samples by means of circularly polarized light under optical microscope and a system of vertical and horizontal coordinates across all the connective tissue in an area delimited by the implant/abutment, epithelium, and bone tissue. In no case had the connective tissue formed a connection to the healing abutment/implant in the internal zone; a space of 35 ± 10 μm separated the connective tissue fibers from the healing abutment surface. The total thickness of connective tissue in the horizontal direction was significantly greater in the medial zone in Group B than in Group A (p connective tissue thickness. © 2013 Wiley Periodicals, Inc.
Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue
International Nuclear Information System (INIS)
Woodward, Ruth M; Cole, Bryan E; Wallace, Vincent P; Pye, Richard J; Arnone, Donald D; Linfield, Edmund H; Pepper, Michael
2002-01-01
We demonstrate the application of terahertz pulse imaging (TPI) in reflection geometry for the study of skin tissue and related cancers both in vitro and in vivo. The sensitivity of terahertz radiation to polar molecules, such as water, makes TPI suitable for studying the hydration levels in the skin and the determination of the lateral spread of skin cancer pre-operatively. By studying the terahertz pulse shape in the time domain we have been able to differentiate between diseased and normal tissue for the study of basal cell carcinoma (BCC). Basal cell carcinoma has shown a positive terahertz contrast, and inflammation and scar tissue a negative terahertz contrast compared to normal tissue. In vivo measurements on the stratum corneum have enabled visualization of the stratum corneum-epidermis interface and the study of skin hydration levels. These results demonstrate the potential of terahertz pulse imaging for the study of skin tissue and its related disorders, both in vitro and in vivo
Directory of Open Access Journals (Sweden)
Antonio Boccaccio
Full Text Available Functionally Graded Scaffolds (FGSs are porous biomaterials where porosity changes in space with a specific gradient. In spite of their wide use in bone tissue engineering, possible models that relate the scaffold gradient to the mechanical and biological requirements for the regeneration of the bony tissue are currently missing. In this study we attempt to bridge the gap by developing a mechanobiology-based optimization algorithm aimed to determine the optimal graded porosity distribution in FGSs. The algorithm combines the parametric finite element model of a FGS, a computational mechano-regulation model and a numerical optimization routine. For assigned boundary and loading conditions, the algorithm builds iteratively different scaffold geometry configurations with different porosity distributions until the best microstructure geometry is reached, i.e. the geometry that allows the amount of bone formation to be maximized. We tested different porosity distribution laws, loading conditions and scaffold Young's modulus values. For each combination of these variables, the explicit equation of the porosity distribution law-i.e the law that describes the pore dimensions in function of the spatial coordinates-was determined that allows the highest amounts of bone to be generated. The results show that the loading conditions affect significantly the optimal porosity distribution. For a pure compression loading, it was found that the pore dimensions are almost constant throughout the entire scaffold and using a FGS allows the formation of amounts of bone slightly larger than those obtainable with a homogeneous porosity scaffold. For a pure shear loading, instead, FGSs allow to significantly increase the bone formation compared to a homogeneous porosity scaffolds. Although experimental data is still necessary to properly relate the mechanical/biological environment to the scaffold microstructure, this model represents an important step towards
Directory of Open Access Journals (Sweden)
Pascal Joly
Full Text Available To heal tissue defects, cells have to bridge gaps and generate new extracellular matrix (ECM. Macroporous scaffolds are frequently used to support the process of defect filling and thus foster tissue regeneration. Such biomaterials contain micro-voids (pores that the cells fill with their own ECM over time. There is only limited knowledge on how pore geometry influences cell organization and matrix production, even though it is highly relevant for scaffold design. This study hypothesized that 1 a simple geometric description predicts cellular organization during pore filling at the cell level and that 2 pore closure results in a reorganization of ECM. Scaffolds with a broad distribution of pore sizes (macroporous starPEG-heparin cryogel were used as a model system and seeded with primary fibroblasts. The strategies of cells to fill pores could be explained by a simple geometrical model considering cells as tensioned chords. The model matched qualitatively as well as quantitatively by means of cell number vs. open cross-sectional area for all pore sizes. The correlation between ECM location and cell position was higher when the pores were not filled with tissue (Pearson's coefficient ρ = 0.45±0.01 and reduced once the pores were closed (ρ = 0.26±0.04 indicating a reorganization of the cell/ECM network. Scaffold pore size directed the time required for pore closure and furthermore impacted the organization of the fibronectin matrix. Understanding how cells fill micro-voids will help to design biomaterial scaffolds that support the endogenous healing process and thus allow a fast filling of tissue defects.
Connective tissue injury in calf muscle tears and return to play: MRI correlation.
Prakash, Ashutosh; Entwisle, Tom; Schneider, Michal; Brukner, Peter; Connell, David
2017-10-26
The aim of our study was to assess a group of patients with calf muscle tears and evaluate the integrity of the connective tissue boundaries and interfaces. Further, we propose a novel MRI grading system based on integrity of the connective tissue and assess any correlation between the grading score and time to return to play. We have also reviewed the anatomy of the calf muscles. We retrospectively evaluated 100 consecutive patients with clinical suspicion and MRI confirmation of calf muscle injury. We evaluated each calf muscle tear with MRI for the particular muscle injured, location of injury within the muscle and integrity of the connective tissue structure at the interface. The muscle tears were graded 0-3 depending on the degree of muscle and connective tissue injury. The time to return to play for each patient and each injury was found from the injury records and respective sports doctors. In 100 patients, 114 injuries were detected. Connective tissue involvement was observed in 63 out of 100 patients and failure (grade 3 injury) in 18. Mean time to return to play with grade 0 injuries was 8 days, grade 1 tears was 17 days, grade 2 tears was 25 days and grade 3 tears was 48 days (pmuscle tears. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.
Tunable geometry of bacterial inclusion bodies as substrate materials for tissue engineering
Energy Technology Data Exchange (ETDEWEB)
GarcIa-Fruitos, Elena; Seras-Franzoso, JoaquIn; Vazquez, Esther; Villaverde, Antonio [CIBER en BioingenierIa, Biomateriales y Nanomedicina, Bellaterra, 08193 Barcelona (Spain); Institut de Biotecnologia i de Biomedicina and Departament de Genetica i de Microbiologia, Universitat Autonoma de Barcelona, 08193 Bellaterra (Cerdanyola del Valles), Barcelona (Spain)
2010-05-21
A spectrum of materials for biomedical applications is produced in bacteria, and some of them, such as metals or polyhydroxyalkanoates, are straightforwardly obtained as particulate entities. We have explored the biofabrication process of bacterial inclusion bodies, particulate proteinaceous materials (ranging from 50 to 500 nm in diameter) recently recognized as suitable for surface topographical modification and tissue engineering. Inclusion bodies have been widely described as spherical or pseudo-spherical particles with only minor morphological variability, mostly restricted to their size. Here we have identified a cellular gene in Escherichia coli (clpP) that controls the in vivo fabrication process of inclusion bodies. In the absence of the encoded protease, the dynamics of protein deposition is perturbed, resulting in unusual tear-shaped particles with enhanced surface-volume ratios. This fact modifies the ability of inclusion bodies to promote mammalian cell attachment and differentiation upon surface decoration. The implications of the genetic control of inclusion body geometry are discussed in the context of their biological fabrication and regarding the biomedical potential of these protein clusters in regenerative medicine.
Tunable geometry of bacterial inclusion bodies as substrate materials for tissue engineering
International Nuclear Information System (INIS)
GarcIa-Fruitos, Elena; Seras-Franzoso, JoaquIn; Vazquez, Esther; Villaverde, Antonio
2010-01-01
A spectrum of materials for biomedical applications is produced in bacteria, and some of them, such as metals or polyhydroxyalkanoates, are straightforwardly obtained as particulate entities. We have explored the biofabrication process of bacterial inclusion bodies, particulate proteinaceous materials (ranging from 50 to 500 nm in diameter) recently recognized as suitable for surface topographical modification and tissue engineering. Inclusion bodies have been widely described as spherical or pseudo-spherical particles with only minor morphological variability, mostly restricted to their size. Here we have identified a cellular gene in Escherichia coli (clpP) that controls the in vivo fabrication process of inclusion bodies. In the absence of the encoded protease, the dynamics of protein deposition is perturbed, resulting in unusual tear-shaped particles with enhanced surface-volume ratios. This fact modifies the ability of inclusion bodies to promote mammalian cell attachment and differentiation upon surface decoration. The implications of the genetic control of inclusion body geometry are discussed in the context of their biological fabrication and regarding the biomedical potential of these protein clusters in regenerative medicine.
Wang, F; Ding, H; Lin, F
2000-08-01
Based on the modified Lambert-Beer law under scattering media, near infra-red spectroscopy tissue oximeter measures the changes of absorber concentrations (such as oxy-hemoglobin, deoxy-hemoglobin, cytochrome aa3). This is made possible by recording the optical density change under different physiological status. This paper describes the average penetration depth, average photon path-length and spatial sensitive profile in multi-layered tissue model using Monte-Carlo method. The result shows the probe geometry of the sensor, which is the separation between the light source and the detector, has a great influence on the sensitivity of measurement. Increasing this separation properly allows the improvement of the sensitivity of measurement and the increase of the probability of looking at oxygenation deep under the surface tissue. But this improvement is limited by the decrease of signal-noise ratio. Optimum probe spacing should be estimated for special tissue structure.
Feng, W; Haishu, D; Fenghua, T; Jun, Z; Qing, X; Xianwu, T
2001-02-01
In this paper, the influences of overlying tissue and detecting distance between the source and the detector on the measurement of a tissue oximeter were discussed. The signal-noise-ratio of the detector was also examined. A semi-infinite multi-layer Monte Carlo model was induced to simulate the migration of the photons in the skin, adipose and muscle. The thickness of the adipose layer and the separation between the source and the detector in the muscle were changed to simulate the clinical application. Partial pathlength was introduced as a characteristic parameter to evaluate the sensitivity of the oximeter. A two-wavelength (700 and 830 nm) tissue oximeter was developed to verify the results of the simulation. The Monte Carlo simulation results showed that the sensitivity of the near infrared spectroscopy (NIRS) oximeter declined greatly with increasing overlying tissue thickness. Increasing the distance between the light source and the detector improved the sensitivity. However, in order to achieve a sufficiently high signal-to-noise ratio, it was necessary to limit this distance. The results of a bicycle ergometer exercise verified the above results and showed that, for a special adipose thickness (AT), there may be a reasonable range of the emitter-detector separation.
Bone Geometry as a Predictor of Tissue Fragility and Stress Fracture Risk
National Research Council Canada - National Science Library
Jepsen, Karl
2003-01-01
... and bone quality, such that slender bones are associated with more damageable bone tissue. We postulate that a similar reciprocal relationship between bone mass and bone material properties exists in the human skeleton...
Bone Geometry as a Predictor of Tissue Fragility and Stress Fracture Risk
National Research Council Canada - National Science Library
Jepsen, Karl J
2004-01-01
... and bone quality, such that slender bones are associated with more damageable bone tissue. We postulate that a similar reciprocal relationship between bone mass and bone material properties exists in the human skeleton...
Bone Geometry as a Predictor of Tissue Fragility and Stress Fracture Risk
National Research Council Canada - National Science Library
Jepsen, Karl J
2006-01-01
... and bone quality, such that slender bones are associated with more damageable bone tissue. We postulate that a similar reciprocal relationship between bone mass and bone material properties exists in the human skeleton...
Bone Geometry as a Predictor of Tissue Fragility and Stress Fracture Risk
National Research Council Canada - National Science Library
Jepsen, Karl
2002-01-01
... and bone quality, such that slender bones are associated with more damageable bone tissue. We postulate that a similar reciprocal relationship between bone mass and bone material properties exists in the human skeleton...
International Nuclear Information System (INIS)
Canpolat, M.; Mourant, J.R.
2000-01-01
Measurement of light transport in tissue has the potential to be an inexpensive and practical tool for non-invasive tissue diagnosis in medical applications because it can provide information on both morphological and biochemical properties. To capitalize on the potential of light transport as a diagnostic tool, an understanding of what information can be gleaned from light transport measurements is needed. We present data concerning the sensitivity of light transport measurements, made in clinically relevant geometries, to scattering properties. The intensity of the backscattered light at small source-detector separations is shown to be sensitive to the phase function, and furthermore the collected light intensity is found to be correlated with the amount of high-angle scattering in the medium. (author)
Ilyasov, Ildar K.; Prikhodko, Constantin V.; Nevorotin, Alexey J.
1995-01-01
Monte Carlo (MC) simulation model and the thermoindicative tissue phantom were applied for evaluation of a depth of tissue necrosis (DTN) as a result of quasi-cw copper vapor laser (578 nm) irradiation. It has been shown that incident light focusing angle is essential for DTN. In particular, there was a significant rise in DTN parallel to elevation of this angle up to +20 degree(s)C and +5 degree(s)C for both the MC simulation and tissue phantom models, respectively, with no further increase in the necrosis depth above these angles. It is to be noted that the relationship between focusing angles and DTN values was apparently stronger for the real target compared to the MC-derived hypothetical one. To what extent these date are applicable for medical practice can be evaluated in animal models which would simulate laser-assisted therapy for PWS or related dermatologic lesions with converged 578 nm laser beams.
The Influence of Bioreactor Geometry and the Mechanical Environment on Engineered Tissues
Osborne, J. M.; O’ Dea, R. D.; Whiteley, J. P.; Byrne, H. M.; Waters, S. L.
2010-01-01
A three phase model for the growth of a tissue construct within a perfusion bioreactor is examined. The cell population (and attendant extracellular matrix), culture medium, and porous scaffold are treated as distinct phases. The bioreactor system is represented by a two-dimensional channel containing a cell-seeded rigid porous scaffold (tissue construct), which is perfused with a culture medium. Through the prescription of appropriate functional forms for cell proliferation and extracellular matrix deposition rates, the model is used to compare the influence of cell density-, pressure-, and culture medium shear stress-regulated growth on the composition of the engineered tissue. The governing equations are derived in O'Dea et al. "A Three Phase Model for Tissue Construct Growth in a Perfusion Bioreactor," Math. Med. Biol., in which the long-wavelength limit was exploited to aid analysis; here, finite element methods are used to construct two-dimensional solutions to the governing equations and to investigate thoroughly their behavior. Comparison of the total tissue yield and averaged pressures, velocities, and shear stress demonstrates that quantitative agreement between the two-dimensional and long-wavelength approximation solutions is obtained for channel aspect ratios of order 10 -2 and that much of the qualitative behavior of the model is captured in the long-wavelength limit, even for relatively large channel aspect ratios. However, we demonstrate that in order to capture accurately the effect of mechanotransduction mechanisms on tissue construct growth, spatial effects in at least two dimensions must be included due to the inherent spatial variation of mechanical stimuli relevant to perfusion bioreactors, most notably, fluid shear stress, a feature not captured in the long-wavelength limit. Copyright © 2010 by ASME.
The Influence of Bioreactor Geometry and the Mechanical Environment on Engineered Tissues
Osborne, J. M.
2010-01-01
A three phase model for the growth of a tissue construct within a perfusion bioreactor is examined. The cell population (and attendant extracellular matrix), culture medium, and porous scaffold are treated as distinct phases. The bioreactor system is represented by a two-dimensional channel containing a cell-seeded rigid porous scaffold (tissue construct), which is perfused with a culture medium. Through the prescription of appropriate functional forms for cell proliferation and extracellular matrix deposition rates, the model is used to compare the influence of cell density-, pressure-, and culture medium shear stress-regulated growth on the composition of the engineered tissue. The governing equations are derived in O\\'Dea et al. "A Three Phase Model for Tissue Construct Growth in a Perfusion Bioreactor," Math. Med. Biol., in which the long-wavelength limit was exploited to aid analysis; here, finite element methods are used to construct two-dimensional solutions to the governing equations and to investigate thoroughly their behavior. Comparison of the total tissue yield and averaged pressures, velocities, and shear stress demonstrates that quantitative agreement between the two-dimensional and long-wavelength approximation solutions is obtained for channel aspect ratios of order 10 -2 and that much of the qualitative behavior of the model is captured in the long-wavelength limit, even for relatively large channel aspect ratios. However, we demonstrate that in order to capture accurately the effect of mechanotransduction mechanisms on tissue construct growth, spatial effects in at least two dimensions must be included due to the inherent spatial variation of mechanical stimuli relevant to perfusion bioreactors, most notably, fluid shear stress, a feature not captured in the long-wavelength limit. Copyright © 2010 by ASME.
Three-Dimensional Geometry of Collagenous Tissues by Second Harmonic Polarimetry.
Reiser, Karen; Stoller, Patrick; Knoesen, André
2017-06-01
Collagen is a biological macromolecule capable of second harmonic generation, allowing label-free detection in tissues; in addition, molecular orientation can be determined from the polarization dependence of the second harmonic signal. Previously we reported that in-plane orientation of collagen fibrils could be determined by modulating the polarization angle of the laser during scanning. We have now extended this method so that out-of-plane orientation angles can be determined at the same time, allowing visualization of the 3-dimensional structure of collagenous tissues. This approach offers advantages compared with other methods for determining out-of-plane orientation. First, the orientation angles are directly calculated from the polarimetry data obtained in a single scan, while other reported methods require data from multiple scans, use of iterative optimization methods, application of fitting algorithms, or extensive post-optical processing. Second, our method does not require highly specialized instrumentation, and thus can be adapted for use in almost any nonlinear optical microscopy setup. It is suitable for both basic and clinical applications. We present three-dimensional images of structurally complex collagenous tissues that illustrate the power of such 3-dimensional analyses to reveal the architecture of biological structures.
Pauly, Hannah M; Kelly, Daniel J; Popat, Ketul C; Trujillo, Nathan A; Dunne, Nicholas J; McCarthy, Helen O; Haut Donahue, Tammy L
2016-08-01
Electrospun nanofibers are a promising material for ligamentous tissue engineering, however weak mechanical properties of fibers to date have limited their clinical usage. The goal of this work was to modify electrospun nanofibers to create a robust structure that mimics the complex hierarchy of native tendons and ligaments. The scaffolds that were fabricated in this study consisted of either random or aligned nanofibers in flat sheets or rolled nanofiber bundles that mimic the size scale of fascicle units in primarily tensile load bearing soft musculoskeletal tissues. Altering nanofiber orientation and geometry significantly affected mechanical properties; most notably aligned nanofiber sheets had the greatest modulus; 125% higher than that of random nanofiber sheets; and 45% higher than aligned nanofiber bundles. Modifying aligned nanofiber sheets to form aligned nanofiber bundles also resulted in approximately 107% higher yield stresses and 140% higher yield strains. The mechanical properties of aligned nanofiber bundles were in the range of the mechanical properties of the native ACL: modulus=158±32MPa, yield stress=57±23MPa and yield strain=0.38±0.08. Adipose derived stem cells cultured on all surfaces remained viable and proliferated extensively over a 7 day culture period and cells elongated on nanofiber bundles. The results of the study suggest that aligned nanofiber bundles may be useful for ligament and tendon tissue engineering based on their mechanical properties and ability to support cell adhesion, proliferation, and elongation. Copyright © 2016 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Hoflack, Ch.
1999-01-01
The present day dosimetry means for radiations with a strong ionization density cannot fulfill the future radioprotection regulations which will require an individual dosimetry with active dosemeters. The aim of this work is the study and development of an individual dosemeter based on a tissue equivalent proportional counter and with a multi-cellular geometry allowing to reach a sensibility equivalent to environmental dosemeters. A pressure regulation bench has been added to the detector in order to reduce the degassing of the detector parts and to reach a sufficient service life for the implementation of the characterization tests. The hole counter system has been adopted for the first prototypes in order to reduce the sensibility of the wires multiplication system with respect to mechanical vibrations. Tests performed with an internal alpha source have shown that a better electrical efficiency can be reached when more severe mechanical limits are adopted during the construction. The dose equivalent response of the prototype for mono-energy neutrons of 144 keV to 2.5 MeV is analyzed experimentally and by simulation. During experiments with normal incidence neutrons, the prototype fulfills the requirements of the CEI N O 1323 standard for energies comprised between 400 keV and 2.5 MeV, while the simulation indicates a satisfactory response up to 200 keV. A preliminary study of the behaviour of the detector with respect to the neutrons incidence indicates that the multi-cellular geometry is efficient for large angles (the sensibility of the prototype is increased by a factor 3). Finally, simulation studies have to be made to optimize the electrical operation and the geometry of the next prototype. (J.S.)
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.
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.
Vergnon-Miszczycha, Delphine; Lucht, Frédéric; Roblin, Xavier; Pozzetto, Bruno; Paul, Stéphane; Bourlet, Thomas
2015-12-01
The gut associated lymphoid tissue (GALT) is the site of numerous immunological disturbances during HIV-1 infection. It constitutes the largest reservoir for HIV, not or very poorly susceptible to antiretroviral therapy (ART), making it a major obstacle to HIV cure. Moreover, the GALT is involved in systemic immune activation in HIV-infected individuals: intestinal damage due to viral replication and severe CD4(+) T cell depletion in the GALT leads to microbial translocation, a key driver of immune activation, and in turn, disease progression. In this review, we describe the role of the GALT in HIV infection and we discuss therapeutic options to decrease the intestinal viral reservoir and to preserve immune function in the gut of HIV-infected people. Achieving these goals is necessary for a long-term infection control after the interruption of ART. © 2015 médecine/sciences – Inserm.
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)
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
DEFF Research Database (Denmark)
Asmar, Meena; Simonsen, Lene; Asmar, Ali
2016-01-01
CONTEXT AND OBJECTIVE: Glucose-dependent insulinotropic polypeptide (GIP) in combination with hyperinsulinemia increases blood flow and triglyceride (TAG) clearance in subcutaneous (sc) abdominal adipose tissue in lean humans. The present experiments were performed to further investigate the role...... of insulin for the vasoactive effect of GIP in adipose tissue metabolism and whether the vasodilatory effect of GIP is dependent on C-peptide. METHODS: Six lean healthy subjects were studied. The sc abdominal adipose tissue metabolism was assessed by Fick's principle during GIP infusion (1.5 pmol...
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
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.
Rudan, Dusko
2013-12-01
The paper offers a review of the development of the concept of play and playing. The true beginnings of the development of the theories of play are set as late as in the 19th century. It is difficult to define play as such; it may much more easily be defined through its antipode--work. In the beginning, play used to be connected with education; it was not before Freud's theory of psychoanalysis and Piaget's developmental psychology that the importance of play in a child's development began to be explained in more detail. The paper further tackles the role of play in the adult age. Detailed attention is paid to psychodynamic and psychoanalytic authors, in particular D. W. Winnicott and his understanding of playing in the intermediary (transitional) empirical or experiential space. In other words, playing occupies a space and time of its own. The neuroscientific concept of playing is also tackled, in the connection with development as well.
Methods of information geometry
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...
International Nuclear Information System (INIS)
Sadashiva, Satish Rao Bola; Mumbrekar, Kamalesh Dattaram; Venkatesh, Goutham Hassan; Fernandes, Donald Jerard; Bejadi, Vadhiraja Manjunath; Kapaettu, Satyamoorthy
2014-01-01
The ability to predict individual risk of radiotherapy induced normal tissue complications prior to the therapy may give an opportunity to personalize the treatment aiming improved therapeutic effect and quality of life. Therefore, predicting the risk of developing acute reactions before the initiation of radiation therapy may serve as a potential biomarker. DNA double-strand break (DSB) induction and its repair kinetics in lymphocytes of Head-and-Neck (n = 183) and Breast cancer (n = 132) patients undergoing chemoradiation or radiation therapy alone were analyzed by performing γ-H2AX foci, neutral comet and a modified neutral filter elution assay. Candidate radioresponsive genes like DNA repair, antioxidant pathway, profibrotic cytokine genes were screened for the common variants for their association with normal tissue toxicity outcome. Patients were stratified as non-over responders (NOR) and over responders (OR) based on their Radiation Therapy Oncology Group grading for normal tissue adverse reactions. Our results suggest that DSB repair plays a major role in the development of normal tissue adverse reactions in H and N and Breast cancer patients. The cellular (γ-H2AX analysis) and SNP analysis may have the potential to be developed into a clinically useful predictive assay for identifying the normal tissue over reactors
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
Becari, Christiane; Durand, Marina T; Guimaraes, Alessander O; Lataro, Renata M; Prado, Cibele M; de Oliveira, Mauro; Candido, Sarai C O; Pais, Paloma; Ribeiro, Mauricio S; Bader, Michael; Pesquero, Joao B; Salgado, Maria C O; Salgado, Helio C
2017-01-01
In vitro and ex vivo experiments indicate that elastase-2 (ELA-2), a chymotrypsin-serine protease elastase family member 2A, is an alternative pathway for angiotensin II (Ang II) generation. However, the role played by ELA-2 in vivo is unclear. We examined ELA-2 knockout (ELA-2KO) mice compared to wild-type (WT) mice and determined whether ELA-2 played a role in hemodynamics [arterial pressure (AP) and heart rate (HR)], cardiocirculatory sympathovagal balance and baroreflex sensitivity. The variability of systolic arterial pressure (SAP) and pulse interval (PI) for evaluating autonomic modulation was examined for time and frequency domains (spectral analysis), whereas a symbolic analysis was also used to evaluate PI variability. In addition, baroreflex sensitivity was examined using the sequence method. Cardiac function was evaluated echocardiographically under anesthesia. The AP was normal whereas the HR was reduced in ELA-2KO mice (425 ± 17 vs. 512 ± 13 bpm from WT). SAP variability and baroreflex sensitivity were similar in both strains. The LF power from the PI spectrum (33.6 ± 5 vs. 51.8 ± 4.8 nu from WT) and the LF/HF ratio (0.60 ± 0.1 vs. 1.45 ± 0.3 from WT) were reduced, whereas the HF power was increased (66.4 ± 5 vs. 48.2 ± 4.8 nu from WT) in ELA-2KO mice, indicating a shift toward parasympathetic modulation of HR. Echocardiographic examination showed normal fractional shortening and an ejection fraction in ELA-2KO mice; however, the cardiac output, stroke volume, and ventricular size were reduced. These findings provide the first evidence that ELA-2 acts on the sympathovagal balance of the heart, as expressed by the reduced sympathetic modulation of HR in ELA-2KO mice.
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
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
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.
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.
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...
Directory of Open Access Journals (Sweden)
David Morrissey
2012-01-01
Full Text Available Purpose. In vivo gene therapy directed at tissues of mesenchymal origin could potentially augment healing. We aimed to assess the duration and magnitude of transene expression in vivo in mice and ex vivo in human tissues. Methods. Using bioluminescence imaging, plasmid and adenoviral vector-based transgene expression in murine quadriceps in vivo was examined. Temporal control was assessed using a doxycycline-inducible system. An ex vivo model was developed and optimised using murine tissue, and applied in ex vivo human tissue. Results. In vivo plasmid-based transgene expression did not silence in murine muscle, unlike in liver. Although maximum luciferase expression was higher in muscle with adenoviral delivery compared with plasmid, expression reduced over time. The inducible promoter cassette successfully regulated gene expression with maximum levels a factor of 11 greater than baseline. Expression was re-induced to a similar level on a temporal basis. Luciferase expression was readily detected ex vivo in human muscle and tendon. Conclusions. Plasmid constructs resulted in long-term in vivo gene expression in skeletal muscle, in a controllable fashion utilising an inducible promoter in combination with oral agents. Successful plasmid gene transfection in human ex vivo mesenchymal tissue was demonstrated for the first time.
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...
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
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,
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
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
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.
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.
DEFF Research Database (Denmark)
Sicart (Vila), Miguel Angel
? In Play Matters, Miguel Sicart argues that to play is to be in the world; playing is a form of understanding what surrounds us and a way of engaging with others. Play goes beyond games; it is a mode of being human. We play games, but we also play with toys, on playgrounds, with technologies and design......, but not necessarily fun. Play can be dangerous, addictive, and destructive. Along the way, Sicart considers playfulness, the capacity to use play outside the context of play; toys, the materialization of play--instruments but also play pals; playgrounds, play spaces that enable all kinds of play; beauty...
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...
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.)
General Geometry and Geometry of Electromagnetism
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...
DEFF Research Database (Denmark)
Kjaergaard, Jesper; Iversen, Kasper K; Vejlstrup, Niels G
2010-01-01
Pulmonary regurgitation (PR) following repair of right ventricular (RV) outflow obstruction is related to slowly progressive RV dilatation and heart failure and will eventually require surgical intervention, but optimal timing of pulmonary valve replacement is challenging. Tissue Doppler based...
Patil, Ratnadeep Chandrakant
2016-01-01
Dental implants have been offered as favorable options the world over to replace missing teeth and with increasing human life expectancy the need for long-term maintenance of implant- teeth for esthetics and function has become ever so important, especially the soft tissue (gums)formation around
Torsional heterotic geometries
International Nuclear Information System (INIS)
Becker, Katrin; Sethi, Savdeep
2009-01-01
We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.
Abhyankar, Shreeram Shankar
1964-01-01
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from
DEFF Research Database (Denmark)
Åkerstrøm Andersen, Niels; Pors, Justine Grønbæk
2014-01-01
This article studies the implications of current attempts by organizations to adapt to a world of constant change by introducing the notion of playful organizational membership. To this end we conduct a brief semantic history of organizational play and argue that when organizations play, employees...... are expected to engage in playful exploration of alternative selves. Drawing on Niklas Luhmann's theory of time and decision-making and Gregory Bateson's theory of play, the article analyses three empirical examples of how games play with conceptions of time. We explore how games represent an organizational...
Play, Playfulness, Creativity and Innovation
Directory of Open Access Journals (Sweden)
Patrick Bateson
2014-05-01
Full Text Available Play, as defined by biologists and psychologists, is probably heterogeneous. On the other hand, playfulness may be a unitary motivational state. Playful play as opposed to activities that merge into aggression is characterized by positive mood, intrinsic motivation, occurring in a protected context and easily disrupted by stress. Playful play is a good measure of positive welfare. It can occupy a substantial part of the waking-life of a young mammal or bird. Numerous functions for play have been proposed and they are by no means mutually exclusive, but some evidence indicates that those individual animals that play most are most likely to survive and reproduce. The link of playful play to creativity and hence to innovation in humans is strong. Considerable evidence suggests that coming up with new ideas requires a different mindset from usefully implementing a new idea.
Fast, V G; Kléber, A G
1995-05-01
Unidirectional conduction block (UCB) and reentry may occur as a consequence of an abrupt tissue expansion and a related change in the electrical load. The aim of this study was to evaluate critical dimensions of the tissue necessary for establishing UCB in heart cell culture. Neonatal rat heart cell cultures with cell strands of variable width emerging into a large cell area were grown using a technique of patterned cell growth. Action potential upstrokes were measured using a voltage sensitive dye (RH-237) and a linear array of 10 photodiodes with a 15 microns resolution. A mathematical model was used to relate action potential wave shapes to underlying ionic currents. UCB (block of a single impulse in anterograde direction - from a strand to a large area - and conduction in the retrograde direction) occurred in narrow cell strands with a width of 15(SD 4) microns (1-2 cells in width, n = 7) and there was no conduction block in strands with a width of 31(8) microns (n = 9, P multiple rising phases. Mathematical modelling showed that two rising phases were caused by electronic current flow, whereas local ionic current did not coincide with the rising portions of the upstrokes. (1) High resolution optical mapping shows multiphasic action potential upstrokes at the region of abrupt expansion. At the site of the maximum decrement in conduction, these peaks were largely determined by the electrotonus and not by the local ionic current. (2) Unidirectional conduction block occurred in strands with a width of 15(4) microns (1-2 cells).
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
Lawver, Timothy; Blankenship, Kelly
2008-01-01
Play therapy is a treatment modality in which the therapist engages in play with the child. Its use has been documented in a variety of settings and with a variety of diagnoses. Treating within the context of play brings the therapist and the therapy to the level of the child. By way of an introduction to this approach, a case is presented of a six-year-old boy with oppositional defiant disorder. The presentation focuses on the events and interactions of a typical session with an established patient. The primary issues of the session are aggression, self worth, and self efficacy. These themes manifest themselves through the content of the child’s play and narration of his actions. The therapist then reflects these back to the child while gently encouraging the child toward more positive play. Though the example is one of nondirective play therapy, a wide range of variation exists under the heading of play therapy. PMID:19724720
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
DEFF Research Database (Denmark)
Froes, Isabel
these practices, which compose the taxonomy of tablet play. My contribution lies in identifying and proposing a series of theoretical concepts that complement recent theories related to play and digital literacy studies. The data collected through observations informed some noteworthy aspects, including how...... with tablets’ physical and digital affordances shape children’s digital play. This thesis presents how young children’s current practices when playing with tablets inform digital experiences in Denmark and Japan. Through an interdisciplinary lens and a grounded theory approach, I have identified and mapped...... vocabulary in children’s digital play experiences. These early digital experiences set the rules for the playgrounds and assert digital tablets as twenty-first-century toys, shaping young children’s playful literacy....
DEFF Research Database (Denmark)
2003-01-01
The video Playful Interaction describes a future architectural office, and envisions ideas and concepts for playful interactions between people, materials and appliances in a pervasive and augmented working environment. The video both describes existing developments, technologies and designs...... as well as ideas not yet implemented such as playful modes of interaction with an augmented ball. Playful Interaction has been used as a hybrid of a vision video and a video prototype (1). Externally the video has been used to visualising our new ideas, and internally the video has also worked to inspire...
DEFF Research Database (Denmark)
Johansen, Stine Liv
Children’s play must nowadays be understood as a mediatized field in society and culture. Media – understood in a very broad sense - holds severe explanatory power in describing and understanding the practice of play, since play happens both with, through and inspired by media of different sorts........ In this presentation the case of ‘playing soccer’ will be outlined through its different mediated manifestations, including soccer games and programs on TV, computer games, magazines, books, YouTube videos and soccer trading cards....
DEFF Research Database (Denmark)
Karoff, Helle Skovbjerg
2013-01-01
The aim of this article is to develop a view of play as a relation between play practices and play moods based on an empirical study of children's everyday life and by using Bateson's term of ‘framing’ [(1955/2001). In Steps to an ecology of mind (pp. 75–80). Chicago: University of Chicago Press......], Schmidt's notion of ‘commonness’ [(2005). Om respekten. København: Danmarks Pædagogiske Universitets Forlag; (2011). On respect. Copenhagen: Danish School of Education University Press] and Heidegger's term ‘mood’ [(1938/1996). Time and being. Cornwall: Wiley-Blackwell.]. Play mood is a state of being...... in which we are open and ready, both to others and their production of meaning and to new opportunities for producing meaning. This play mood is created when we engage with the world during play practices. The article points out four types of play moods – devotion, intensity, tension and euphorica – which...
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.
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.
Escande, Carlos; Nin, Veronica; Pirtskhalava, Tamar; Chini, Claudia C. S.; Tchkonia, Tamar; Kirkland, James L.; Chini, Eduardo N.
Obesity is often regarded as the primary cause of metabolic syndrome. However, many lines of evidence suggest that obesity may develop as a protective mechanism against tissue damage during caloric surplus and that it is only when the maximum fat accumulation capacity is reached and fatty acid
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
Bashian, Kathleen Ryniker
1993-01-01
Describes a yearlong project at 12 Catholic middle schools in the Diocese of Arlington, Virginia, to incorporate the plays of William Shakespeare into the curriculum. Teachers attended university lectures and directed students in performances of the plays. Concludes that Shakespeare can be understood and enjoyed by middle school students. (BCY)
Escande, Carlos; Nin, Veronica; Pirtskhalava, Tamar; Chini, Claudia C S; Tchkonia, Tamar; Kirkland, James L; Chini, Eduardo N
2015-01-01
Obesity is often regarded as the primary cause of metabolic syndrome. However, many lines of evidence suggest that obesity may develop as a protective mechanism against tissue damage during caloric surplus and that it is only when the maximum fat accumulation capacity is reached and fatty acid spillover occurs into to peripheral tissues that metabolic diseases develop. In this regard, identifying the molecular mechanisms that modulate adipocyte fat accumulation and fatty acid spillover is imperative. Here we identify the deleted in breast cancer 1 (DBC1) protein as a key regulator of fat storage capacity of adipocytes. We found that knockout (KO) of DBC1 facilitated fat cell differentiation and lipid accumulation and increased fat storage capacity of adipocytes in vitro and in vivo. This effect resulted in a "healthy obesity" phenotype. DBC1 KO mice fed a high-fat diet, although obese, remained insulin sensitive, had lower free fatty acid in plasma, were protected against atherosclerosis and liver steatosis, and lived longer. We propose that DBC1 is part of the molecular machinery that regulates fat storage capacity in adipocytes and participates in the "turn-off" switch that limits adipocyte fat accumulation and leads to fat spillover into peripheral tissues, leading to the deleterious effects of caloric surplus. © 2015 by the American Diabetes Association. Readers may use this article as long as the work is properly cited, the use is educational and not for profit, and the work is not altered.
Stochastic geometry and its applications
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
Donaldson, David S.; Else, Kathryn J.
2015-01-01
ABSTRACT Prion diseases are infectious neurodegenerative disorders characterized by accumulations of abnormally folded cellular prion protein in affected tissues. Many natural prion diseases are acquired orally, and following exposure, the early replication of some prion isolates upon follicular dendritic cells (FDC) within gut-associated lymphoid tissues (GALT) is important for the efficient spread of disease to the brain (neuroinvasion). Prion detection within large intestinal GALT biopsy specimens has been used to estimate human and animal disease prevalence. However, the relative contributions of the small and large intestinal GALT to oral prion pathogenesis were unknown. To address this issue, we created mice that specifically lacked FDC-containing GALT only in the small intestine. Our data show that oral prion disease susceptibility was dramatically reduced in mice lacking small intestinal GALT. Although these mice had FDC-containing GALT throughout their large intestines, these tissues were not early sites of prion accumulation or neuroinvasion. We also determined whether pathology specifically within the large intestine might influence prion pathogenesis. Congruent infection with the nematode parasite Trichuris muris in the large intestine around the time of oral prion exposure did not affect disease pathogenesis. Together, these data demonstrate that the small intestinal GALT are the major early sites of prion accumulation and neuroinvasion after oral exposure. This has important implications for our understanding of the factors that influence the risk of infection and the preclinical diagnosis of disease. IMPORTANCE Many natural prion diseases are acquired orally. After exposure, the accumulation of some prion diseases in the gut-associated lymphoid tissues (GALT) is important for efficient spread of disease to the brain. However, the relative contributions of GALT in the small and large intestines to oral prion pathogenesis were unknown. We show that the
Donaldson, David S; Else, Kathryn J; Mabbott, Neil A
2015-09-01
Prion diseases are infectious neurodegenerative disorders characterized by accumulations of abnormally folded cellular prion protein in affected tissues. Many natural prion diseases are acquired orally, and following exposure, the early replication of some prion isolates upon follicular dendritic cells (FDC) within gut-associated lymphoid tissues (GALT) is important for the efficient spread of disease to the brain (neuroinvasion). Prion detection within large intestinal GALT biopsy specimens has been used to estimate human and animal disease prevalence. However, the relative contributions of the small and large intestinal GALT to oral prion pathogenesis were unknown. To address this issue, we created mice that specifically lacked FDC-containing GALT only in the small intestine. Our data show that oral prion disease susceptibility was dramatically reduced in mice lacking small intestinal GALT. Although these mice had FDC-containing GALT throughout their large intestines, these tissues were not early sites of prion accumulation or neuroinvasion. We also determined whether pathology specifically within the large intestine might influence prion pathogenesis. Congruent infection with the nematode parasite Trichuris muris in the large intestine around the time of oral prion exposure did not affect disease pathogenesis. Together, these data demonstrate that the small intestinal GALT are the major early sites of prion accumulation and neuroinvasion after oral exposure. This has important implications for our understanding of the factors that influence the risk of infection and the preclinical diagnosis of disease. Many natural prion diseases are acquired orally. After exposure, the accumulation of some prion diseases in the gut-associated lymphoid tissues (GALT) is important for efficient spread of disease to the brain. However, the relative contributions of GALT in the small and large intestines to oral prion pathogenesis were unknown. We show that the small intestinal
DEFF Research Database (Denmark)
Hammar, Emil
This paper aims to identify an understanding of digital games in virtual environments by using Don Ihde’s (1990) postphenomenological approach to how technology mediates the world to human beings in conjunction with Hans-Georg Gadamer’s (1993) notion of play . Through this tentatively proposed am...... amalgamation of theories I point towards an alternative understanding of the relationship between play and game as not only dialectic, but also as socially and ethically relevant qua the design and implementation of the game as technology....
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.)
DEFF Research Database (Denmark)
Pors, Justine Grønbæk; Åkerstrøm Andersen, Niels
2015-01-01
intact. In its final sections, the article discusses what happens to conditions of decision-making when organisations do not just see undecidability as a given condition, but as a limited resource indispensable for change and renewal. The article advances discussions of organisational play by exploring...
Rogers, Liz; Steffan, Dana
2009-01-01
This article describes how to use clay as a potential material for young children to explore. As teachers, the authors find that their dialogue about the potential of clay as a learning medium raises many questions: (1) What makes clay so enticing? (2) Why are teachers noticing different play and conversation around the clay table as compared to…
Leung, Shuk-kwan S.; Lo, Jane-Jane
2010-01-01
This article features Sweet play math, a "math by the month" activity that involves decorating and making sugar cubes. Teachers may want to substitute straws, paper squares, alphabet blocks, or such commercially made manipulatives as Unifix[R] cubes for the real sweets. Given no allergy concerns, teachers and students alike would enjoy some sweet…
DEFF Research Database (Denmark)
Tychsen, Anders; Hitchens, Michael; Brolund, Thea
2008-01-01
Role-playing games (RPGs) are a well-known game form, existing in a number of formats, including tabletop, live action, and various digital forms. Despite their popularity, empirical studies of these games are relatively rare. In particular there have been few examinations of the effects of the v......Role-playing games (RPGs) are a well-known game form, existing in a number of formats, including tabletop, live action, and various digital forms. Despite their popularity, empirical studies of these games are relatively rare. In particular there have been few examinations of the effects...... of the various formats used by RPGs on the gaming experience. This article presents the results of an empirical study, examining how multi-player tabletop RPGs are affected as they are ported to the digital medium. Issues examined include the use of disposition assessments to predict play experience, the effect...... of group dynamics, the influence of the fictional game characters and the comparative play experience between the two formats. The results indicate that group dynamics and the relationship between the players and their digital characters, are integral to the quality of the gaming experience in multiplayer...
Gilbert, Juan E.
The acceptance of animation technologies is increasing. Video games, such as Sony PlayStation (SONY, 2002), have become part of the culture for young people from kindergarten through undergraduate school. Animation technologies have been implemented into educational systems in the form of animated pedagogical agents (Johnson, 2000). The research…
DEFF Research Database (Denmark)
Bang, Jytte Susanne
2012-01-01
The present article explores the role of music-related artefacts and technologies in children’s lives. More specifically, it analyzes how four 10- to 11-year old girls use CDs and DVD games in their music-play activities and which developmental themes and potentials may accrue from such activitie...
Cline, Jane E.; Smith, Brandy A.
2016-01-01
The inclusion of activities to develop sensory awareness, spatial thinking, and physical dexterity, operationalized through hands-on science lessons such as water play, have long been part of early childhood education. This practical article addresses Next Generation Science Standards K-2 ETS1-3 and K-2 ETS1-2 by having four-year-old…
DEFF Research Database (Denmark)
Houmøller, Ellen; Marchetti, Emanuela
2015-01-01
event called InnoEvent, addressed to students in the fields of multimedia and healthcare. Being interested in studying games and role-play as tools to support independent learning in the field of design thinking and team-building, following Dewey’s (1938) theory of learning experience, we ran two...... workshops based on two classic role-play games: The Silent Game (Brandt, 2006) and The Six Thinking Hats (de Bono, 1985). These games were created to support students in learning design thinking in groups and are assigned positive values in literature, hence we expected a smooth process. However, our...... experience was rather characterized by conflictual negotiations with the students. Data from our observations and from interviews with group representatives show that the students took a discontinuous learning path, characterised by a false start, failure, and a thorough reconsideration of their work...
Needle decompositions in Riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Novianti, T.; Sadikin, M.; Widia, S.; Juniantito, V.; Arida, E. A.
2018-03-01
Development of unidentified specific gene is essential to analyze the availability these genes in biological process. Identification unidentified specific DNA of HIF 1α genes is important to analyze their contribution in tissue regeneration process in lizard tail (Hemidactylus platyurus). Bioinformatics and PCR techniques are relatively an easier method to identify an unidentified gene. The most widely used method is BLAST (Basic Local Alignment Sequence Tools) method for alignment the sequences from the other organism. BLAST technique is online software from website https://blast.ncbi.nlm.nih.gov/Blast.cgi that capable to generate the similar sequences from closest kinship to distant kindship. Gecko japonicus is a species that it has closest kinship with H. platyurus. Comparing HIF 1 α gene sequence of G. japonicus with the other species used multiple alignment methods from Mega7 software. Conserved base areas were identified using Clustal IX method. Primary DNA of HIF 1 α gene was design by Primer3 software. HIF 1α gene of lizard (H. platyurus) was successfully amplified using a real-time PCR machine by primary DNA that we had designed from Gecko japonicus. Identification unidentified gene of HIF 1a lizard has been done successfully with multiple alignment method. The study was conducted by analyzing during the growth of tail on day 1, 3, 5, 7, 10, 13 and 17 of lizard tail after autotomy. Process amplification of HIF 1α gene was described by CT value in real time PCR machine. HIF 1α expression of gene is quantified by Livak formula. Chi-square statistic test is 0.000 which means that there is a different expression of HIF 1 α gene in every growth day treatment.
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...
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.
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)
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)
Foundations of arithmetic differential geometry
Buium, Alexandru
2017-01-01
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is "intrinsically curved"; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
Directory of Open Access Journals (Sweden)
Enrico Euli
2016-07-01
Full Text Available Our society is drenched in the catastrophe; where the growth of financial crisis, environmental cataclysm and militarization represents its gaudiest and mortifying phenomena. Humans struggle with depression, sense of impotence, anguish towards a future considered a threat. A possibility to keep us alive can be represented by the enhancement of our ability in ‘playing Possum’, an exercise of desisting and renitence: to firmly say ‘no’. To say no to a world that proposes just one way of being and living free, that imposes as the only unavoidable possible destiny.
DEFF Research Database (Denmark)
Johansen, Stine Liv; Eriksson, Eva
2013-01-01
In this paper, the design of future services for children in Danish public libraries is discussed, in the light of new challenges and opportunities in relation to new media and technologies. The Danish government has over the last few years initiated and described a range of initiatives regarding...... in the library, the changing role of the librarians and the library space. We argue that intertwining traditional library services with new media forms and engaging play is the core challenge for future design in physical public libraries, but also that it is through new media and technology that new...
Geometry essentials for dummies
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
Arithmetic noncommutative geometry
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...
Quantification of Porcine Vocal Fold Geometry.
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.
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.
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
Algorithms in Algebraic Geometry
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
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
Fundamental concepts of geometry
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.
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.
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.
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.
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
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'…
Tropical geometry of statistical models.
Pachter, Lior; Sturmfels, Bernd
2004-11-16
This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.
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.
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.
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
Complex and symplectic geometry
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.
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
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...
Lectures on Symplectic Geometry
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...
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.
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...
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.
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...
Introduction to tropical geometry
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...
Rudiments of algebraic geometry
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.
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....
Intermediate algebra & analytic geometry
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
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.
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.
Software Geometry in Simulations
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).
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
Global aspects of complex geometry
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.
Sources of hyperbolic geometry
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...
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
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.
Computational synthetic geometry
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...
Discrete and computational geometry
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...
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.
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...
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...
Directory of Open Access Journals (Sweden)
Fang-Fang Mo
2017-11-01
Full Text Available Purpose: To investigate the effect of JTXK granule on the expression pattern of miRNA in pancreatic tissue of KKAy diabetic mice, and to explore the molecular mechanism and pathways of JTXK granule in anti-diabetic effect.Methods: We used high fat diet (HFD to induce the KKAy diabetic mice and screened the differentially expressed miRNAs (DEMs between JTXK-treated group (n = 6 and the diabetic group (n = 6 using MicroRNA (miRNA Microarray. C57BL/6J mice were given a normal diet as the control group (n = 6. Subsequently, miRNA target gene prediction, GO and Pathway analysis were used to explore the function of DEMs. Finally, the mechanism of anti-diabetic effects of JTXK granule was tested by in vitro INS-1 pancreatic β-cell experiment.Results: The blood glucose and body weight of JTXK-treated group was significantly lower compared with the model group. Moreover, a total of 45 miRNAs with significant differences were detected in the model group and the JTXK-treated group (P ≤ 0.05, Fold Change > 2. Further, miRNA-mRNA analysis showed that the differential expression of mmu-miR-192-5p, mmu-miR-291a-3p, mmu-miR-320-3p, mmu-miR-139-5p and mmu-miR-378a-3p are closely related to pancreatic histological changes. In addition, pathway analysis showed that the DEMs were closely related to PI3K-Akt Signaling Pathway. Furthermore, the levels of serine/threonine-protein kinase (Akt, phosphorylated Akt (p-Akt and phosphorylated forkhead transcription factor O1 (p-Foxo1 in INS-1-FOXO1 overexpressing model cells were lower than those in normal group, while JTXK granules could increase the expression of Akt, p-Akt and p-Foxo1.Conclusions: The results showed that JTXK granule could play an anti-diabetic role by regulating the mRNA and miRNAs associated with PI3K-Akt pathway in diabetic mice pancreatic tissue.
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
Designing Out the Play: Accessibility and Playfulness in Inclusive Play.
Holt, Raymond; Beckett, Angharad
2017-01-01
Play is an important part of child development, yet disabled children are often excluded from the opportunity to play, either due to lack of accessible toys and games, or social pressures. This paper presents a case study reflecting on the development of Button Bash: a switch accessible game intended to encourage inclusive play between disabled and non-disabled children. In particular, the paper focuses on how changes intended to make the game more accessible tended to make it less playful, and reflects on the relationship between playfulness and accessibility.
Noncommutative Geometry, Quantum Fields and Motives
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
Architectural Geometry and Fabrication-Aware Design
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.
Network geometry with flavor: From complexity to quantum geometry
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
Computational geometry algorithms and applications
de Berg, Mark; Overmars, Mark; Schwarzkopf, Otfried
1997-01-01
Computational geometry emerged from the field of algorithms design and anal ysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The suc cess of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains--computer graphics, geographic in formation systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modem algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can ...
Conformal geometry and quasiregular mappings
Vuorinen, Matti
1988-01-01
This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook an...
Quantization of the Schwarzschild geometry
International Nuclear Information System (INIS)
Melas, Evangelos
2013-01-01
The conditional symmetries of the reduced Einstein-Hilbert action emerging from a static, spherically symmetric geometry are used as supplementary conditions on the wave function. Based on their integrability conditions, only one of the three existing symmetries can be consistently imposed, while the unique Casimir invariant, being the product of the remaining two symmetries, is calculated as the only possible second condition on the wave function. This quadratic integral of motion is identified with the reparametrization generator, as an implication of the uniqueness of the dynamical evolution, by fixing a suitable parametrization of the r-lapse function. In this parametrization, the determinant of the supermetric plays the role of the mesure. The combined Wheeler – DeWitt and linear conditional symmetry equations are analytically solved. The solutions obtained depend on the product of the two ''scale factors''.
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.
Multiplicity in difference geometry
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.
Spacetime and Euclidean geometry
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.
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
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…
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)
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
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.
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
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.
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.
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
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 ...
Application of Tessellation in Architectural Geometry Design
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.
Porter, Maggie L.; Hernandez-Reif, Maria; Jessee, Peggy
2009-01-01
This article discusses the current issues in play therapy and its implications for play therapists. A brief history of play therapy is provided along with the current play therapy approaches and techniques. This article also touches on current issues or problems that play therapists may face, such as interpreting children's play, implementing…
Multivariate calculus and geometry
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.
Transformational plane geometry
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
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.
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.
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.
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
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)
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.)
Integral geometry and valuations
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.
Introducing geometry concept based on history of Islamic geometry
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.
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)
DEFF Research Database (Denmark)
Feder, Karen
2017-01-01
Abstract The purpose of the new Design for Play initiative is to inspire and educate designers to design for the future of play. To create “play ambassadors” equipped with excellent tools, methods, approaches and mind-sets to design for the playful human being in an ever-changing world. To teach...... and inspire children to grow up to be creative designers of their own life and the world around them. The Design for Play research team will study the interplay between people, processes and products in design for play and support the development of playful designers, playful solutions and playful experiences...
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
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
Dooner, David B
2012-01-01
Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Geometrie verstehen: statisch - kinematisch
Kroll, Ekkehard
Dem Allgemeinen steht begrifflich das Besondere gegenüber. In diesem Sinne sind allgemeine Überlegungen zum Verstehen von Mathematik zu ergänzen durch Untersuchungen hinsichtlich des Verstehens der einzelnen mathematischen Disziplinen, insbesondere der Geometrie. Hier haben viele Schülerinnen und Schüler Probleme. Diese rühren hauptsächlich daher, dass eine fertige geometrische Konstruktion in ihrer statischen Präsentation auf Papier nicht mehr die einzelnen Konstruktionsschritte erkennen lässt; zum Nachvollzug müssen sie daher ergänzend in einer Konstruktionsbeschreibung festgehalten werden.
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
Akopyan, A V
2007-01-01
The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca
2015-01-01
This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric
Graded geometry and Poisson reduction
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
Definition of treatment geometry in radiation therapy
International Nuclear Information System (INIS)
Aaltonen, P.
1996-01-01
When accurate systems for quality assurance and treatment optimization are employed, a precise system for fixation and dosimetric and portal verification are as important as a continued and standardized code of practice for dosimetry and patient follow-up, including registration of tumour responses and acute and late normal tissue reactions. To improve the accuracy of existing dose response relations in order to improve future therapy the treatment geometry and dose delivery concepts have to be accurately defined and uniformly employed. A Nordic working group was set up in 1991 (by Nordic Association of Clinica Physics) to standardize the concepts and quantities used during the whole radiotherapy process in the Nordic countries. Now the group is finalizing its report ''Specification of Dose Delivery in Radiation Therapy''. The report emphasizes that the treatment geometry shall be consistent with the geometry used during the diagnostic work up. The patient fixation is of importance early in the diagnostic phase to ensure that the same reference points and patients position will be used both during the diagnostic work up, simulation and treatment execution. Reference Coordinate System of the patient is a concept based on defined anatomic reference points. This Patient Reference System is a local system which has validity for the tissues, organs and volumes defined during radiotherapy. The reference points of the Patient Reference System should in turn be used for beam set-up. The treatment geometry is then defined by using different concepts describing tissues which are mobile in the Patient Reference System, and finally, volumes which are fixed in this coordinate system. A Set-up Margin has to be considered for movements of the volumes defined in the Reference Coordinate System of the Patient in relation to the radiation beam. The Set-up Margin is dependent on the treatment technique and it is needed in the treatment planning procedure to ensure that the prescribed
Definition of treatment geometry in radiation therapy
Energy Technology Data Exchange (ETDEWEB)
Aaltonen, P [Finnish Centre for Radiation and Nuclear Safety (STUK), Helsinki (Finland)
1996-08-01
When accurate systems for quality assurance and treatment optimization are employed, a precise system for fixation and dosimetric and portal verification are as important as a continued and standardized code of practice for dosimetry and patient follow-up, including registration of tumour responses and acute and late normal tissue reactions. To improve the accuracy of existing dose response relations in order to improve future therapy the treatment geometry and dose delivery concepts have to be accurately defined and uniformly employed. A Nordic working group was set up in 1991 to standardize the concepts and quantities used during the whole radiotherapy process in the Nordic countries. Now the group is finalizing its report ``Specification of Dose Delivery in Radiation Therapy``. The report emphasizes that the treatment geometry shall be consistent with the geometry used during the diagnostic work up. The patient fixation is of importance early in the diagnostic phase to ensure that the same reference points and patients position will be used both during the diagnostic work up, simulation and treatment execution. Reference Coordinate System of the patient is a concept based on defined anatomic reference points. This Patient Reference System is a local system which has validity for the tissues, organs and volumes defined during radiotherapy. The reference points of the Patient Reference System should in turn be used for beam set-up. The treatment geometry is then defined by using different concepts describing tissues which are mobile in the Patient Reference System, and finally, volumes which are fixed in this coordinate system. A Set-up Margin has to be considered for movements of the volumes defined in the Reference Coordinate System of the Patient in relation to the radiation beam. The Set-up Margin is dependent on the treatment technique and it is needed in the treatment planning procedure to ensure that the prescribed dose to the Target Volume is delivered.
DEFF Research Database (Denmark)
Meier Sørensen, Bent; Spoelstra, Sverre
2012-01-01
The interest in organizational play is growing, both in popular business discourse and organization studies. As the presumption that play is dysfunctional for organizations is increasingly discarded, the existing positions may be divided into two camps; one proposes ‘serious play’ as an engine fo...... workplaces engage in play: play as a (serious) continuation of work, play as a (critical) intervention into work and play as an (uninvited) usurpation of work....
DEFF Research Database (Denmark)
Cermak-Sassenrath, Daniel
2018-01-01
and specific ways. For instance, gambling for money, party and drinking games, professional play and show sports, art installations, violent and military propaganda computer games, pervasive/mobile gaming, live-action role playing, festivals, performances, and games such as Ghosting and Planking. It is argued......Everything gets more interesting, challenging, or intense the closer it gets to the edge, and so does play. How edgy can play become and still be play? Based on Huizinga’s notion of play, this chapter discusses how a wide range of playful activities pushes the boundaries of play in different...... that in concert with a number of characteristics that mark an activity as play, play is essentially a subjective perspective and individual decision of the player. Huizinga calls this attitude the play spirit, which informs a player’s actions and is in turn sustained by them. Edgy digital or mobile games do...
Marks-Tarlow, Terry
2012-01-01
The author reviews the role of play within psychotherapy. She does not discuss the formal play therapy especially popular for young children, nor play from the Jungian perspective that encourages the use of the sand tray with adults. Instead, she focuses on the informal use of play during psychotherapy as it is orchestrated intuitively. Because…
Landreth, Garry; Bratton, Sue
Play therapy is based on developmental principles and, thus, provides, through play, developmentally appropriate means of expression and communication for children. Therefore, skill in using play therapy is an essential tool for mental health professionals who work with children. Therapeutic play allows children the opportunity to express…
Schouten, B.A.M.
2011-01-01
Play is seen as an activity that is fun, voluntary, offers escape, and is fundamentally exciting. Play is however, more than that; it is a working model of flexibility! There is a vital link between play, psychological development and learning. Moreover, the importance of play has gained importance
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
Critique of information geometry
International Nuclear Information System (INIS)
Skilling, John
2014-01-01
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples
International Nuclear Information System (INIS)
Correa, Diego H.; Silva, Guillermo A.
2008-01-01
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents
Emergent geometry of membranes
Energy Technology Data Exchange (ETDEWEB)
Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)
2015-11-13
In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.
Geometry through history Euclidean, hyperbolic, and projective geometries
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...
Child's Play: Therapist's Narrative
Reddy, Rajakumari P.; Hirisave, Uma
2014-01-01
Play has been recognized as an essential component to children's healthy development. Schools of play therapy differ philosophically and technically, but they all embrace the therapeutic and developmental properties of play. This case report is an illustration of how a 6-year-old child with emotional disorder was facilitated to express concerns in child-centered play therapy. The paper discusses the therapist's narration of the child's play. PMID:24860228
Differential geometry in string models
International Nuclear Information System (INIS)
Alvarez, O.
1986-01-01
In this article the author reviews the differential geometric approach to the quantization of strings. A seminal paper demonstrates the connection between the trace anomaly and the critical dimension. The role played by the Faddeev-Popov ghosts has been instrumental in much of the subsequent work on the quantization of strings. This paper discusses the differential geometry of two dimensional surfaces and its importance in the quantization of strings. The path integral quantization approach to strings will be carefully analyzed to determine the correct effective measure for string theories. The choice of measure for the path integral is determined by differential geometric considerations. Once the measure is determined, the manifest diffeomorphism invariance of the theory will have to be broken by using the Faddeev-Popov ansatz. The gauge fixed theory is studied in detail with emphasis on the role of conformal and gravitational anomalies. In the analysis, the path integral formulation of the gauge fixed theory requires summing over all the distinct complex structures on the manifold
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.
Higher geometry an introduction to advanced methods in analytic geometry
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
2017-01-01
The social meanings of play sit at odds with norms of responsible and productive adult conduct. To be “caught” playing as an adult therefore risks embarrassment. Still, many designers want to create enjoyable, nonembarrassing play experiences for adults. To address this need, this article reads instances of spontaneous adult play through the lens of Erving Goffman’s theory of the interaction order to unpack conditions and strategies for nonembarrassing adult play. It identifies established frames, segregated audiences, scripts supporting smooth performance, managing audience awareness, role distancing, and, particularly, alibis for play: Adults routinely provide alternative, adult-appropriate motives to account for their play, such as child care, professional duties, creative expression, or health. Once legitimized, the norms and rules of play themselves then provide an alibi for behavior that would risk being embarrassing outside play.
Effects of Macroion Geometry and Charge Discretization in Charge Reversal
Mukherjee, Arup K.
2008-01-01
The effects of discrete macroion surface charge distribution and valences of these surface charges and counterions on charge reversal have been studied for macroions of three different geometries and compared with those of continuous surface charge distributions. The geometry of the macroion has been observed to play an important role in overcharging in these cases. The interplay of valences of discrete microions and counterions have noticeable effects on overcharging efficiency. For some val...
The Kerr geometry, complex world lines and hyperbolic strings
International Nuclear Information System (INIS)
Burinskii, A.Ya.
1994-01-01
In the Lind-Newman representation the Kerr geometry is created by a source moving along an analytical complex world line. An equivalence of the complex world line and complex (hyperbolic) string is considered. Therefore the hyperbolic string may play the role of the complex source of the Kerr geometry. The Kerr solution with the complex string source acquires Regge behavior of the angular momentum. (orig.)
An introduction to incidence geometry
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...
The effect of micro-ECoG substrate footprint on the meningeal tissue response
Schendel, Amelia A.; Nonte, Michael W.; Vokoun, Corinne; Richner, Thomas J.; Brodnick, Sarah K.; Atry, Farid; Frye, Seth; Bostrom, Paige; Pashaie, Ramin; Thongpang, Sanitta; Eliceiri, Kevin W.; Williams, Justin C.
2014-08-01
Objective. There is great interest in designing implantable neural electrode arrays that maximize function while minimizing tissue effects and damage. Although it has been shown that substrate geometry plays a key role in the tissue response to intracortically implanted, penetrating neural interfaces, there has been minimal investigation into the effect of substrate footprint on the tissue response to surface electrode arrays. This study investigates the effect of micro-electrocorticography (micro-ECoG) device geometry on the longitudinal tissue response. Approach. The meningeal tissue response to two micro-ECoG devices with differing geometries was evaluated. The first device had each electrode site and trace individually insulated, with open regions in between, while the second device had a solid substrate, in which all 16 electrode sites were embedded in a continuous insulating sheet. These devices were implanted bilaterally in rats, beneath cranial windows, through which the meningeal tissue response was monitored for one month after implantation. Electrode site impedance spectra were also monitored during the implantation period. Main results. It was observed that collagenous scar tissue formed around both types of devices. However, the distribution of the tissue growth was different between the two array designs. The mesh devices experienced thick tissue growth between the device and the cranial window, and minimal tissue growth between the device and the brain, while the solid device showed the opposite effect, with thick tissue forming between the brain and the electrode sites. Significance. These data suggest that an open architecture device would be more ideal for neural recording applications, in which a low impedance path from the brain to the electrode sites is critical for maximum recording quality.
International Nuclear Information System (INIS)
Buescher, R.
2005-01-01
Casimir interactions are interactions induced by quantum vacuum fluctuations and thermal fluctuations of the electromagnetic field. Using a path integral quantization for the gauge field, an effective Gaussian action will be derived which is the starting point to compute Casimir forces between macroscopic objects analytically and numerically. No assumptions about the independence of the material and shape dependent contributions to the interaction are made. We study the limit of flat surfaces in further detail and obtain a concise derivation of Lifshitz' theory of molecular forces. For the case of ideally conducting boundaries, the Gaussian action will be calculated explicitly. Both limiting cases are also discussed within the framework of a scalar field quantization approach, which is applicable for translationally invariant geometries. We develop a non-perturbative approach to calculate the Casimir interaction from the Gaussian action for periodically deformed and ideally conducting objects numerically. The obtained results reveal two different scaling regimes for the Casimir force as a function of the distance between the objects, their deformation wavelength and -amplitude. The results confirm that the interaction is non-additive, especially in the presence of strong geometric deformations. Furthermore, the numerical approach is extended to calculate lateral Casimir forces. The results are consistent with the results of the proximity-force approximation for large deformation wavelengths. A qualitatively different behaviour between the normal and lateral force is revealed. We also establish a relation between the boundary induced change of the of the density of states for the scalar Helmholtz equation and the Casimir interaction using the path integral method. For statically deformed boundaries, this relation can be expressed as a novel trace formula, which is formally similar to the so-called Krein-Friedel-Lloyd formula. While the latter formula describes the
Planetary Image Geometry Library
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
Geometry simulation and physics with the CMS forward pixel detector
Energy Technology Data Exchange (ETDEWEB)
Parashar, N [Purdue University Calumet, Hammond, Indiana (United States)], E-mail: Neeti@fnal.gov
2008-06-15
The Forward Pixel Detector of CMS is an integral part of the Tracking system, which will play a key role in addressing the full physics potential of the collected data. It has a very complex geometry that encompasses multilayer structure of its detector modules. This presentation describes the development of geometry simulation for the Forward Pixel Detector. A new geometry package has been developed, which uses the detector description database (DDD) interface for the XML (eXtensive Markup Language) to GEANT simulation. This is necessary for digitization and GEANT4 reconstruction software for tracking. The expected physics performance is also discussed.
Geometry simulation and physics with the CMS forward pixel detector
International Nuclear Information System (INIS)
Parashar, N
2008-01-01
The Forward Pixel Detector of CMS is an integral part of the Tracking system, which will play a key role in addressing the full physics potential of the collected data. It has a very complex geometry that encompasses multilayer structure of its detector modules. This presentation describes the development of geometry simulation for the Forward Pixel Detector. A new geometry package has been developed, which uses the detector description database (DDD) interface for the XML (eXtensive Markup Language) to GEANT simulation. This is necessary for digitization and GEANT4 reconstruction software for tracking. The expected physics performance is also discussed
Initiation to global Finslerian geometry
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
DEFF Research Database (Denmark)
Elkind, David; Rinaldi, Carla; Flemmert Jensen, Anne
Proceedings from the conference "Children, Time, and Play". Danish University of Education, January 30th 2003.......Proceedings from the conference "Children, Time, and Play". Danish University of Education, January 30th 2003....
Wyn, Mark A.; Stegink, Steven J.
2000-01-01
Introduces a role playing activity that actively engages students in the learning process of mitosis. Students play either chromosomes carrying information, or cells in the cell membrane. (Contains 11 references.) (Author/YDS)
... Teachers' Questionnaire MRI Play MRI the Magnetic Miracle Game About the game In the MRI imaging technique, strong magnets and ... last will in Paris. Play the Blood Typing Game Try to save some patients and learn about ...
... Questionnaire Tuberculosis Play Tuberculosis Experiments & Discoveries About the game Discover and experience some of the classic methods ... last will in Paris. Play the Blood Typing Game Try to save some patients and learn about ...
Play the Electrocardiogram Game
... and Work Teachers' Questionnaire Electrocardiogram Play the ECG Game About the game ECG is used for diagnosing heart conditions by ... last will in Paris. Play the Blood Typing Game Try to save some patients and learn about ...
Directory of Open Access Journals (Sweden)
Šárka Nedomová
2013-01-01
Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.
Nonperturbative quantum geometries
International Nuclear Information System (INIS)
Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara
1988-01-01
Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)
Bhatia, Rajendra
2013-01-01
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Gold, Katharina; Grothues, Dirk; Leitzmann, Michael; Gruber, Hans; Melter, Michael
2012-01-01
The following article presents an overview of current research studies on play therapy in the hospital. It highlights individual diagnoses for which play therapy has shown reasonable success. The aim of this review is to describe the current status of the scientific debate on play therapy for sick children in order to allow conclusions regarding the indications for which play therapy is or might be useful.
Giesbrecht, Sheila
2012-01-01
Play is important. Environmental educators Sobel and Louv write about the relationship between children and outside play and suggest that early transcendental experiences within nature allow children to develop empathetic orientations towards the natural world. Children who play out-of-doors develop an appreciation for the environment and…
DEFF Research Database (Denmark)
Fogh, Rune; Johansen, Asger
2013-01-01
In this paper we propose The Play Grid, a model for systemizing different play types. The approach is psychological by nature and the actual Play Grid is based, therefore, on two pairs of fundamental and widely acknowledged distinguishing characteristics of the ego, namely: extraversion vs. intro...
... and Work Teachers' Questionnaire Malaria Play the Mosquito Game Play the Parasite Game About the games Malaria is one of the world's most common ... last will in Paris. Play the Blood Typing Game Try to save some patients and learn about ...
DEFF Research Database (Denmark)
Tosca, Susana; Marquez, Israel
2017-01-01
In this paper we introduce and describe the phenomenon of videogame street art as a specific kind of street art. We consider its materiality and significance, and conceptualize it in the light of a double manifestation of play: the playful appropriation of the city by the artist and the fact...... that street art encapsulates the act of playing videogames in a visual form. Digital play spills out of our computer screens and occupies the urban space with the explicit intention of involving spectators, who are invited to play in symbolic ways that actualize nostalgic memories of gaming and can be related...
Playing with social identities
DEFF Research Database (Denmark)
Winther-Lindqvist, Ditte Alexandra
2013-01-01
as pretence, children’s play is understood as an activity involving rules of the social order (roles and positions) as well as identification processes (imagined situations). The theoretical argumentation builds on empirical examples obtained in two different Danish day-care centres. The chapter is informed...... by ethnographic observations and draws on illustrative examples with symbolic group play as well as game-play with rules (soccer) among 5 year old boys. Findings suggest that day-care children’s play, involves negotiation of roles, positioning and identification, and rules – and that these negotiations......This chapter offers support for Vygotsky’s claim that all play involves both an imagined situation as well as rules. Synthesising Schousboe’s comprehensive model of spheres of realities in playing (see Chapter 1, this volume) with Lev Vygotskys insight that all playing involve rules as well...
GPS: Geometry, Probability, and Statistics
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…
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....
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
A prediction for bubbling geometries
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.
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 ...
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...
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
The geometry of elementary particles
International Nuclear Information System (INIS)
Lov, T.R.
1987-01-01
A new model of elementary particles based on the geometry of Quantum deSitter space QdS = SU (3,2)/(SU(3,1) x U(1)) is introduced and studied. QdS is a complexification of quantization of anti-de Sitter space, AdS = SO(3,2)/SO(3,1), which in recent years had played a pivotal role in supergravity. The nontrival principle fiber bundle has total space SU(3,2), fiber SU(3,1) x U(1) and base QdS. In this setting, the standard recipes for Yang-Mills fields don't work. These require connections and the associated covariant derivatives. Here it is shown that the Lie derivatives, not the covariant derivatives are important in quantization. In this setting, the no-go theorems are not valid. This new quantum mechanics leads to a model of elementary particles as vertical vector fields in the bundle with interaction via the Lie bracket. There are five physical interactions modelled by the bracket interaction. The quantum numbers are identified as the roots of su(3,2) and are preserved under the bracket interaction. The model explains conservation of charge, baryon number, lepton number, parity and the heirarchy problem. Since the bracket is the curvature of a homogeneous space, particles are then the curvature of QdS. This model for particles is consistent with the requirements of General Relativity. Furthermore, since the curvature tensor is built from the quantized wave functions, the curvature tensor is quantized and this is quantum theory of gravity
Geometry and Mechanics of Chiral Pod Opening
Sharon, Eran; Armon, Shahaf; Efrati, Efi; Kupferman, Raz
2012-02-01
We study the geometry and mechanics that drive the opening of Bauhinia seeds pods. The pod valve wall consists of two fibrous layers oriented at ± 45^o with respect to the pod axis. Upon drying, each of the layers shrinks uniaxially, perpendicularly to the fibers orientation. This active deformation turn the valve into an incompatible sheet with reference saddle-like curvature tensor and a flat (Euclidean) reference metric. These two intrinsic properties are incompatible. The shape is, therefore, selected by a stretching-bending competition. Strips cut from the valve tissue and from synthetic model material adopt various helical configurations. We provide analytical expressions for these configurations in the bending and stretching dominated regimes. Surface measurements show the transition from minimal surfaces (narrow limit) to cylindrical ones (wide limit). Finally, we show how plants use these mechanical principles using different tissue architectures.
Condensation in complex geometries
International Nuclear Information System (INIS)
Lauro, F.
1975-01-01
A mathematical evaluation of the condensation exchange coefficient can only succeds for well specified cases: small upright or inclined plates, horizontal tubes, small height vertical tubes. Among the main hypotheses accounted for this mathematical development in the case of the condensate, a laminar flow and uniform surface temperature are always considered. In practice certain shapes of surfaces significantly increase the heat transfer during the vapor condensation on a surface wet by the condensate. Such surfaces are rough surfaces such as the condensate is submitted to surface tension effects, negligeable for plane or large curvature surfaces, and the nature of the material may play an important role (temperature gradients). Results from tests on tubes with special shapes, performed in France or out of France, are given [fr
DEFF Research Database (Denmark)
Toft, Herdis
2018-01-01
in a play culture where children recycle them in transmitted, transformed and transgressive modes. His fairy tales function as raw materials – trash – for play-production, and these contemporary children muddle, mingle, remix their formulas and elements with other materials and adjust them to a play context......Hans Christian Andersen is a cultural icon in the Danish community, and his fairy tales are canonized as treasured Danish cultural heritage. However, situated as they are today in a crosscultural mix between folklore, booklore and medialore, they also may be analysed as useful, treasured trash...... through improvisations. So they perform what we shall name FairyPlay - just like Hans Christian Andersen himself did. We show Hans Christian Andersen as an intimate connoisseur of play culture, a homo ludens, a trash-sculptor and a thing-finder, like Pippi Longstocking and like children in play. Examples...
Directory of Open Access Journals (Sweden)
Stan A. Kuczaj
2014-05-01
Full Text Available Play is an important aspect of dolphin life, perhaps even an essential one. Play provides opportunities for dolphin calves to practice and perfect locomotor skills, including those involved in foraging and mating strategies and behaviors. Play also allows dolphin calves to learn important social skills and acquire information about the characteristics and predispositions of members of their social group, particularly their peers. In addition to helping dolphin calves learn how to behave, play also provides valuable opportunities for them to learn how to think. The ability to create and control play contexts enables dolphins to create novel experiences for themselves and their playmates under relatively safe conditions. The behavioral variability and individual creativity that characterize dolphin play yield ample opportunities for individual cognitive development as well as social learning, and sometimes result in innovations that are reproduced by other members of the group. Although adults sometimes produce innovative play, calves are the primary source of such innovations. Calves are also more likely to imitate novel play behaviors than are adults, and so calves contribute significantly to both the creation and transmission of novel play behaviors within a group. Not unexpectedly, then, the complexity of dolphin play increases with the involvement of peers. As a result, the opportunity to observe and/or interact with other dolphin calves enhances the effects of play on the acquisition and maintenance of flexible problem solving skills, the emergence and strengthening of social and communicative competencies, and the establishment of social relationships. It seems that play may have evolved to help young dolphins learn to adapt to novel situations in both their physical and social worlds, the beneficial result being a set of abilities that increases the likelihood that an individual survives and reproduces.
Burrows, J.; Johnson, V.; Henckel, D.
2016-01-01
Work Hard / Play Hard was a participatory performance/workshop or CPD experience hosted by interdisciplinary arts atelier WeAreCodeX, in association with AntiUniversity.org. As a socially/economically engaged arts practice, Work Hard / Play Hard challenged employees/players to get playful, or go to work. 'The game changes you, you never change the game'. Employee PLAYER A 'The faster the better.' Employer PLAYER B
Takikawa, Hirohide
2012-01-01
After the demise of the social contract theory, the argument from fair play, which employs the principle of fair play, has been widely acknowledged as one of the most promising ways of justifying political obligation. First, I articulate the most promising version of the principle of fair play. Then, I show that free riders play fair, that is, that their moral fault lies not in unfairness but in the violation of a rule by appealing to the example of three-in-a-boat. Finally, I conclude that e...
DEFF Research Database (Denmark)
Pichlmair, Martin; Mech, Lena; Sicart, Miguel Angel
2017-01-01
This paper is concerned with designing for immediate play, the experience that a player has when joining a game designed for being played without particular preparation. Museum games, urban games, casual sports, and ad-hoc multiplayer video games are kinds of games that facilitate immediate play...... offer using examples and expert opinions. While most practices and game examples mentioned in this paper are from non-digital games, a special focus is put on the role of technology in immediately playable experiences. Still, the examined design dimensions are independent of the technological foundation...... of the game. This paper provides a starting point for designing better immediate play situations....
DEFF Research Database (Denmark)
Karoff, Helle Skovbjerg
2008-01-01
and the Danish University of Education (among others) have been working with different kind of products, all referred to as PlAYWARE. Playware combines modern technology and knowledge about play culture in order to produce playful experiences for its players. This paper will exemplify how the concept of play can...... from one generation to the next. Because older children are no longer present as younger children grow up, the traditional "cultural leaders" are gone. They have taken with them much of the inspiration for play as well as important knowledge about how to organise a game. In that sense we can say...
Complex analysis and CR geometry
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...
Holt, Jim
2007-01-01
"On seing the Alps for the first time, Dorothy Parket is reputed to have said, "They're beautiful, but they're dumb". Near the foot of Mont Blanc, the greatest of the alpine peaks, another sizable object is taking shape, also quite beautiful in its way, yet not at all dumb. In fact, its pristine geometries may be instrumental in revealing what have hitherto been some of nature's deepest secrets." (2 pages)
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
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
Differential geometry curves, surfaces, manifolds
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.
DEFF Research Database (Denmark)
Marchetti, Emanuela; Petersson, Eva
2011-01-01
What does it mean to design a playful learning tool? What is needed for a learning tool to be perceived by potential users as playful? These questions emerged reflecting on a Participatory Design process aimed at enhancing museum-learning practice from the perspective of primary school children...
Reelsen, Alexander
2015-01-01
This book is aimed at advanced developers who are looking to harness the power of Play 2.x. This book will also be useful for professionals looking to dive deeper into web development. Play 2 .x is an excellent framework to accelerate your learning of advanced topics.
DEFF Research Database (Denmark)
Abildgaard, Mette Simonsen; Birkbak, Andreas; Jensen, Torben Elgaard
2017-01-01
An advantage of the playground metaphor is that it comes with the activity of going out on ‘play dates’ and developing friendships. In such playful relationships, there is always something at stake, but the interaction is also fun and inherently exploratory. In the following, we take a tour of five...
Communication in Symbolic Play.
Umek, Ljubica Marjanovic; Musek, Petra Lesnik; Kranjc, Simona
2001-01-01
Analyzed records of Slovene children's speech from a linguistic point of view and established differences in communication patterns with regard to the children's ages and the type of symbolic play. Found a shift in play from make-believe with regard to objects to roleplay related to social context. The older the child, the more language functions…
DEFF Research Database (Denmark)
Froes, Isabel Cristina G.; Walker, Kevin
2011-01-01
Play is a key element in cultural development, according to the Dutch historian Johan Huizinga. Nowadays many of us interact with other people in online games and social networks, through multiple digital devices. But harnessing playful activities for museum learning is mostly undeveloped. In thi...
Ramsey, Gaynor
1978-01-01
Play your part is a collection of then situations in which students have to take on the roles of particular people and express their opinions, feelings or arguments about the situation. Play your part is intended for use with advanced students of English.
Mangan, Marianne
2013-01-01
Call it physical activity, call it games, or call it play. Whatever its name, it's a place we all need to return to. In the physical education, recreation, and dance professions, we need to redesign programs to address the need for and want of play that is inherent in all of us.
Advances in discrete differential geometry
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, ...
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...
An introduction to differential geometry
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.
Symplectic geometry and Fourier analysis
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.
Topology and geometry for physicists
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
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)
Playful Collaboration (Or Not)
DEFF Research Database (Denmark)
Bogers, Marcel; Sproedt, Henrik
2012-01-01
This article explores how playing games can be used to teach intangible social interaction across boundaries, in particular within open collaborative innovation. We present an exploratory case study of how students learned from playing a board game in a graduate course of the international...... and interdisciplinary Innovation and Business master's program in Denmark. We identify several important themes related to the process of learning through playing and the social dynamics of open collaborative innovation, while we also highlight possible caveats of “playing” and practicing open innovation. Our findings...
Primes, Geometry and Condensed Matter
Directory of Open Access Journals (Sweden)
Al Rabeh R. H.
2009-07-01
Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some "the elementary particles of arithmetic" as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called "the elementary particles of physics" too. This study considers the problem of closely packing similar circles/spheres in 2D/3D space. This is in effect a discretization process of space and the allowable number in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This "number/physical" stability idea applies to bigger collections made from smaller (prime units leading to larger stable prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show convincingly that the growth of prime numbers and that of the masses of
Primes, Geometry and Condensed Matter
Directory of Open Access Journals (Sweden)
Al Rabeh R. H.
2009-07-01
Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some “the elementary particles of arithmetic” as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called “the elementary particles of physics” too. This study considers the problem of closely packing similar circles / spheres in 2D / 3D space. This is in effect a discretization process of space and the allowable num- ber in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This “number / physical” stability idea applies to bigger collections made from smaller (prime units leading to larger sta- ble prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show con- vincingly that the growth of prime numbers and that
DEFF Research Database (Denmark)
Hammar, Emil
Through the theories of play by Gadamer (2004) and Henricks (2006), I will show how the relationship between play and game can be understood as dialectic and disruptive, thus challenging understandings of how the procedures of games determine player activity and vice versa. As such, I posit some...... analytical consequences for understandings of digital games as procedurally fixed (Boghost, 2006; Flannagan, 2009; Bathwaite & Sharp, 2010). That is, if digital games are argued to be procedurally fixed and if play is an appropriative and dialectic activity, then it could be argued that the latter affects...... and alters the former, and vice versa. Consequently, if the appointed procedures of a game are no longer fixed and rigid in their conveyance of meaning, qua the appropriative and dissolving nature of play, then understandings of games as conveying a fixed meaning through their procedures are inadequate...
DEFF Research Database (Denmark)
Eichberg, Henning
2015-01-01
Can play be defined? There is reason to raise critical questions about the established academic demand that at phenomenon – also in humanist studies – should first of all be defined, i.e. de-lineated and by neat lines limited to a “little box” that can be handled. The following chapter develops....... Human beings can very well understand play – or whatever phenomenon in human life – without defining it....
Variable geometry Darrieus wind machine
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.
Euclidean geometry and its subgeometries
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...
Guide to Computational Geometry Processing
DEFF Research Database (Denmark)
Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François
be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...
Electrodynamics and Spacetime Geometry: Foundations
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
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
DEFF Research Database (Denmark)
Karoff, Helle Skovbjerg; Ejsing-Duun, Stine; Hanghøj, Thorkild
2013-01-01
The paper develops an approach of playing and gaming activities through the perspective of both activities as mood activities . The point of departure is that a game - is a tool with which we, through our practices, achieve different moods. This based on an empirical study of children's everyday...... lives, where the differences emerge through actual practices, i.e. through the creation of meaning in the specific situations. The overall argument is that it is not that important whether it is a playing or a gaming activity - it is however crucial to be aware of how moods occur and what their optimal...... dimensions: practices and moods. Practice is the concept of all the doing in the activities. Moods are the particular concept of sense and feeling of being, which is what we are drawn to when we are playing or gaming....
Directory of Open Access Journals (Sweden)
Angela Vargas
2008-05-01
Full Text Available This work tries to contemplate on playing, leaving of the observations on the children's games accomplished during the apprenticeship and the articulation of those with some theoretical ones that have been dedicating if to the study of the game, of the childhood and of the Infantile Education. It was possible, through the apprenticeship registrations and of the observations to live many moments in that the two groups, 3A and 3B, they played incorporating objects and creating characters in your games. He/she gave way, we sought focar the game of the do-of-bill, contemplating on your importance for the children in the first childhood, and that possibilities she brings us in the amplification of the infantile experiences. Another important aspect in this article is to contemplate on the teacher's practice in the Infantile Education, and, through our observations on playing of the children noticed the teachers' involvement in the children's games.
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
Genesereth, Michael
2014-01-01
General game players are computer systems able to play strategy games based solely on formal game descriptions supplied at ""runtime"" (n other words, they don't know the rules until the game starts). Unlike specialized game players, such as Deep Blue, general game players cannot rely on algorithms designed in advance for specific games; they must discover such algorithms themselves. General game playing expertise depends on intelligence on the part of the game player and not just intelligence of the programmer of the game player.GGP is an interesting application in its own right. It is intell
Motivation, Creativity, Play & Learning
DEFF Research Database (Denmark)
Petersson, Eva
2005-01-01
on their needs and desires. This paper presents results from SoundScapes body of research which is utilising technology in assistive (re)habilitation from Virtual Interactive Space (VIS); furthermore the paper describes what emerges in play scenarios that utilise enabling technology. The involved study exhibits...... implementation of robotic physical movement synchronously manipulated from sourced data movement information of a human. SoundScapes is a concept based on non-verbal communication and stimulation through interactive play with sounds and images, which is being realised in the production of a non-wearable sensor...
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
Lectures on Algebraic Geometry I
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
Combinatorial geometry in the plane
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
Modern differential geometry for physicists
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
Comparison theorems in Riemannian geometry
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
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.
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...
Introduction to topology and geometry
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
Algebraic geometry and theta functions
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
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
Topology, Geometry, and Mechanics of Z -Plasty
Matsumoto, Elisabetta A.; Liang, Haiyi; Mahadevan, L.
2018-02-01
Reconstructive surgeries often use topological manipulation of tissue to minimize postoperative scarring. The most common version of this, Z -plasty, involves modifying a straight line cut into a Z shape, followed by a rotational transposition of the resulting triangular pedicle flaps, and a final restitching of the wound. This locally reorients the anisotropic stress field and reduces the potential for scarring. We analyze the planar geometry and mechanics of the Z -plasty to quantify the rotation of the overall stress field and the local forces on the restitched cut using theory, simulations, and simple physical Z -plasty experiments with foam sheets that corroborate each other. Our study rationalizes the most typical surgical choice of this angle, and opens the way for a range of surgical decisions by characterizing the stresses along the cut.
PREFACE: Algebra, Geometry, and Mathematical Physics 2010
Stolin, A.; Abramov, V.; Fuchs, J.; Paal, E.; Shestopalov, Y.; Silvestrov, S.
2012-02-01
This proceedings volume presents results obtained by the participants of the 6th Baltic-Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25-30, 2010. The Baltic-Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic-Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic-Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers. The PDF also contains the following: List of AGMP workshops and other AGMP activities Main topics discussed at AGMP-6 Review of AGMP-6 proceedings Acknowledgments List of Conference Participants
DEFF Research Database (Denmark)
The power of play, so central to psychoanalytic theory and practice, is conjoined to the social psychological or socio-politically coloured concept of power, giving rise to many fruitful discussions of how these concepts manifest themselves in clinical work with children, groups and adults...
Sandberg, Anette; Heden, Rebecca
2011-01-01
The purpose of this study is to contribute knowledge on and gain an understanding of elementary school teachers' perspectives on the function of play in children's learning processes. The study is qualitative with a hermeneutical approach and has George Herbert Mead as a theoretical frame of reference. Interviews have been carried out with seven…
Richard-Foy, Julien
2014-01-01
This book targets Java and Scala developers who already have some experience in web development and who want to master Play framework quickly and efficiently. This book assumes you have a good level of knowledge and understanding of efficient Java and Scala code.
African Journals Online (AJOL)
User
Life-skills of Children Under Difficult Circumstances: The. Case of Two ... Goodman's Strengths and Difficulties Questionnaire-a standardized instrument) were obtained from 17 ... From a developmental point of view, play ... preventing mild problems becoming worse, .... records) and a socially withdrawn child-for example ...
DEFF Research Database (Denmark)
Pichlmair, Martin
This paper presents Activity Theory as a framework for understanding the action of playing games with the intention of building a foundation for the creation of new game design tools and methods. Activity Theory, an epistemological framework rooted in Soviet psychology of the first half of the 20...
DEFF Research Database (Denmark)
context. Contributors: Per Brask, Dario Fo, Jette Barnholdt Hansen, Pil Hansen, Sven Åke Heed, Ulla Kallenbach, Sofie Kluge, Annelis Kuhlmann, Kela Kvam, Anna Lawaetz, Bent Flemming Nielsen, Franco Perrelli, Magnus Tessing Schneider, Antonio Scuderi. stage/page/play is published as a festschrift...
The Idea of Order at Geometry Class.
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…
Canonical quantization of static spherically symmetric geometries
International Nuclear Information System (INIS)
Christodoulakis, T; Dimakis, N; Terzis, P A; Doulis, G; Grammenos, Th; Melas, E; Spanou, A
2013-01-01
The conditional symmetries of the reduced Einstein–Hilbert action emerging from a static, spherically symmetric geometry are used as supplementary conditions on the wave function. Based on their integrability conditions, only one of the three existing symmetries can be consistently imposed, while the unique Casimir invariant, being the product of the remaining two symmetries, is calculated as the only possible second condition on the wave function. This quadratic integral of motion is identified with the reparametrization generator, as an implication of the uniqueness of the dynamical evolution, by fixing a suitable parametrization of the r-lapse function. In this parametrization, the determinant of the supermetric plays the role of the mesure. The combined Wheeler – DeWitt and linear conditional symmetry equations are analytically solved. The solutions obtained depend on the product of the two ''scale factors''
Categorification in geometry, topology, and physics
Beliakova, Anna
2017-01-01
The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorification is a powerful tool for relating various branches of mathematics and exploiting the commonalities between fields. It provides a language emphasizing essential features and allowing precise relationships between vastly different fields. This volume focuses on the role categorification plays in geometry, topology, and physics. These articles illustrate many important trends for the field including geometric representation theory, homotopical methods in link homology, interactions between higher representation theory and gauge theory, and double affine Hecke algebra approaches to link homology. The companion volume (Contemporary Mathematics, Volume 683) is devoted to categorification and higher representation theory.
Analogical Reasoning in Geometry Education
Magdas, Ioana
2015-01-01
The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…
Normal forms in Poisson geometry
Marcut, I.T.
2013-01-01
The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric
Exploring Bundling Theory with Geometry
Eckalbar, John C.
2006-01-01
The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
Matter in toy dynamical geometries
Konopka, T.J.
2009-01-01
One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect
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.
Granular flows in constrained geometries
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.
General Relativity: Geometry Meets Physics
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Learners engaging with transformation geometry
African Journals Online (AJOL)
participants engaged in investigative semi-structured interviews with the resear- chers. ... Keywords: analysis; conversions; transformation geometry; transformations; treatments .... semiotic systems of representation is not only to designate mathematical objects or to com- municate but also to ... Research design. We believe ...
Multivariable calculus and differential geometry
Walschap, Gerard
2015-01-01
This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.
College geometry a unified development
Kay, David C
2011-01-01
""The book is a comprehensive textbook on basic geometry. … Key features of the book include numerous figures and many problems, more than half of which come with hints or even complete solutions. Frequent historical comments add to making the reading a pleasant one.""-Michael Joswig, Zentralblatt MATH 1273
Mahaffey, Michael L.
One of a series of experimental units for children at the preschool level, this booklet deals with geometric concepts. A unit on volume and a unit on linear measurement are covered; for each unit a discussion of mathematical objectives, a list of materials needed, and a sequence of learning activities are provided. Directions are specified for the…
DEFF Research Database (Denmark)
Byg din egen boomerang, kast den, se den flyve, forstå hvorfor og hvordan den vender tilbage, og grib den. Det handler om opdriften på vingerne når du flyver, men det handler også og allermest om den mærkværdige gyroskop-effekt, du bruger til at holde balancen, når du kører på cykel. Vi vil bruge...
Discrete differential geometry. Consistency as integrability
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 ...
DEFF Research Database (Denmark)
Lieberoth, Andreas; Pedersen, Mads Kock; Sherson, Jacob
2015-01-01
Crowdscience games may hold unique potentials as learning opportunities compared to games made for fun or education. They are part of an actual science problem solving process: By playing, players help scientists, and thereby interact with real continuous research processes. This mixes the two...... worlds of play and science in new ways. During usability testing we discovered that users of the crowdscience game Quantum Dreams tended to answer questions in game terms, even when directed explicitly to give science explanations. We then examined these competing frames of understanding though a mixed...... correlational and grounded theory analysis. This essay presents the core ideas of crowdscience games as learning opportunities, and reports how a group of players used “game”, “science” and “conceptual” frames to interpret their experience. Our results suggest that oscillating between the frames instead...
DEFF Research Database (Denmark)
Leino, Olli Tapio
2009-01-01
Researchers interested in player’s experience would assumedly, across disciplines, agree that the goal behind enquiries into player’s experience is to understand the how games’ features end up affecting the player’s experience. Much of the contemporary interdisciplinary research into player......’s experience leans toward the empirical-scientific, in the forms (neuro)psychology, sociology and cognitive science, to name a few. In such approaches, for example demonstrating correlation between physiological symptoms and an in-game event may amount to ‘understanding’. However, the experience of computer...... game play is a viable topic also for computer game studies within the general tradition of humanities. In such context, the idea of ‘understanding an experience’ invites an approach focusing on the experienced significance of events and objects within computer game play. This focus, in turn, suggests...
Directory of Open Access Journals (Sweden)
Deborah Bird Rose
2011-09-01
Full Text Available ‘We were driving through Death Valley, an American-Australian and two Aussies, taking the scenic route from Las Vegas to Santa Cruz.’ This multi-voiced account of multispecies encounters along a highway takes up the challenge of playful and humorous writing that is as well deeply serious and theoretically provocative. Our travels brought us into what Donna Haraway calls the contact zone: a region of recognition and response. The contact zone is a place of significant questions: ‘Who are you, and so who are we? Here we are, and so what are we to become?’ Events were everything in this ecology of play, in which the movements of all the actors involved the material field in its entirety. We were brought into dances of approach and withdrawal, dances emerging directly, to paraphrase Brian Massumi, from the dynamic relation between a myriad of charged particles.
Playful Collaboration (or Not)
DEFF Research Database (Denmark)
Bogers, Marcel
2011-01-01
This paper explores how games and play, which are deeply rooted in human beings as a way to learn and interact, can be used to teach certain concepts and practices related to open collaborative innovation. We discuss how playing games can be a source of creativity, imagination and fun, while it can...... also be conducive to deep learning. As such, a game can engage different dimensions of learning and embed elements of active, collaborative, cooperative and problem-based learning. Building on this logic, we present an exploratory case study of the use of a particular board game in a class of a course...... collaboration at the cost of individual performance and possible long-term collective performance as well....
DEFF Research Database (Denmark)
Sproedt, Henrik
study were to better understand the theoretical foundations and practical implications of complex social interaction in organizational innovation settings. As I did not find any existing models or hypotheses that I was interested in testing I set out to discover how I could grasp complex social...... evidence that play and games could be interesting perspectives to take in order to understand complex social interaction. I come to the conclusion that – in innovation settings – the social dynamics that affect the process are essentially about transformation of knowledge across boundaries. I propose......„Play. Learn. Innovate. – Grasping the Social Dynamics of Participatory Innovation“ the title of this thesis describes how the complex interplay of unexpected events led to some burning questions and eventually to this thesis, which one could call an innovation*1*. During several years...
DEFF Research Database (Denmark)
Ejsing-Duun, Stine; Skovbjerg, Helle Marie
2015-01-01
Abstract: This article explores how student behavior and interactions change when teachers use “producing games” as a primary pedagogical strategy (Papert, 1980; Ejsing-Duun and Karoff, 2014). Based on student and teacher actions and responses, as well as on students' production—observed during f...... fieldwork—this paper emphasizes the importance of understanding how students explore creativity and playfulness while producing in learning situations....
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)
Nonlinear Methods in Riemannian and Kählerian Geometry
Jost, Jürgen
1991-01-01
In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps ...
Control of nonholonomic systems from sub-Riemannian geometry to motion planning
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.
Play and playfulness, basic features of early childhood education
Singer, E.
2013-01-01
This article argues that play and playfulness are basic features in early childhood education, but that play curricula can have serious drawbacks. The starting point is the play theory of the Dutch historian Johan Huizinga, a radical critic of the focus on the educational benefits of play. According
Code subspaces for LLM geometries
Berenstein, David; Miller, Alexandra
2018-03-01
We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.
Euclidean distance geometry an introduction
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.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
The geometry of celestial mechanics
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.
Differential geometry and mathematical physics
Rudolph, Gerd
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
Foliation theory in algebraic geometry
McKernan, James; Pereira, Jorge
2016-01-01
Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classificati...
Groups and Geometries : Siena Conference
Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria
1998-01-01
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...
DEFF Research Database (Denmark)
Aarhus, Rikke; Grönvall, Erik; Larsen, Simon Bo
2011-01-01
participants generally found physical training both fun and socially engaging, and experienced improved fitness. We also argue that embodied gaming motivates seniors to do more than they think themselves capable of, and allows seniors with different mental and physical capabilities to play together. However......, there are also certain barriers, when seniors interact with the system. Speed and complexity of what is displayed on the screen are examples of barriers that affect the seniors’ satisfactory use of the technology. Based on these findings, we discuss how physical rehabilitation may be facilitated by computer...
DEFF Research Database (Denmark)
This book poses the inconvenient question whether he European Union has become a secondary actor on the global arena, or whether it has perhaps for a long time already been playing second fiddle without wishing to admit it. What indicators would today, after a prolonged economic and socio......-political crisis in the Eurozone, imply that the EU can challenge the United States, China, or for that matter Russia, and take a position as a true global powerhouse? Has the train already left the station for what is still a very unique experiment, the European Union? Four different visions of Europes’s future...
Robertson, Susan J; Leonard, Jane; Chamberlain, Alex J
2010-08-01
A 16-year-old boy presented with a number of asymptomatic pigmented macules on the volar aspect of his index fingers. Dermoscopy of each macule revealed a parallel ridge pattern of homogenous reddish-brown pigment. We propose that these lesions were induced by repetitive trauma from a Sony PlayStation 3 (Sony Corporation, Tokyo, Japan) vibration feedback controller. The lesions completely resolved following abstinence from gaming over a number of weeks. Although the parallel ridge pattern is typically the hallmark for early acral lentiginous melanoma, it may be observed in a limited number of benign entities, including subcorneal haematoma.
Celadon Figurines Play Instruments
Institute of Scientific and Technical Information of China (English)
1995-01-01
This group of figurines, each 0.15m tall, were unearthed from a Tang Dynasty tomb in Changsha in 1977. Music was very developed in the Tang Dynasty. Colorful musical instruments and dances were popular both among the people and in the palace. These vivid-looking figurines wear pleated skirts with small sleeves and open chest, a style influenced by the non-Han nationalities living in the north and west of China. Some of the musical instruments were brought from the Western Regions. The figurines are playing the xiao (a vertical bamboo flute), the konghou (an
DEFF Research Database (Denmark)
Knudsen, Hanne; Andersen, Niels Åkerstrøm
2014-01-01
Over the past 10–15 years, state-funded schools have begun to require parents to assume an undefined and infinite personal responsibility. In this article, we investigate how schools organize responsibility games to respond to this challenge and how these games affect the concept of responsibility....... We point to a dislocation in the way parents are assigned responsibility, because the definition of responsibility is not only a question of formulating rules or providing advice. We argue that what emerges is a kind of playful hyper responsibility that identifies responsibility as the participation...
Systematics of IIB spinorial geometry
Gran, U.; Gutowski, J.; Papadopoulos, G.; Roest, D.
2005-01-01
We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of [hep-th/0503046] to IIB supergravity. We give the expressions of the Killing spinor equations on all five types of spinors. In this way, the Killing spinor equations become a linear system for the fluxes, geometry and spacetime derivatives of...
Geometry Dependence of Stellarator Turbulence
International Nuclear Information System (INIS)
Mynick, H.E.; Xanthopoulos, P.; Boozer, A.H.
2009-01-01
Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes
Superbanana orbits in stellarator geometries
International Nuclear Information System (INIS)
Derr, J.A.; Shohet, J.L.
1979-04-01
The presence of superbanana orbit types localized to either the interior or the exterior of stellarators and torsatrons is numerically investigated for 3.5 MeV alpha particles. The absence of the interior superbanana in both geometries is found to be due to non-conservation of the action. Exterior superbananas are found in the stellarator only, as a consequence of the existence of closed helical magnetic wells. No superbananas of either type are found in the torsatron
Turtle geometry the Python way
Battle, S.
2014-01-01
An introduction to coding using Python’s on-screen ‘turtle’ that can be commanded with a few simple instructions including forward, backward, left and right. The turtle leaves a trace that can be used to draw geometric figures. This workshop is aimed at beginners of all ages. The aim is to learn a smattering of programming and a little bit of geometry in a fun way.
Topics in modern differential geometry
Verstraelen, Leopold
2017-01-01
A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
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
Number theory III Diophantine geometry
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
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...
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)
Aspects of differential geometry II
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...
Algebraic Geometry and Number Theory Summer School
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.
Geometry success in 20 minutes a day
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
Krachler, Anne Marie; Ham, Hyeilin; Orth, Kim
2012-01-01
Pathogen attachment to host tissues is one of the initial and most crucial events during the establishment of bacterial infections and thus interference with this step could be an efficient strategy to fight bacterial colonization. Our recent work has identified one of the factors involved in initial binding of host cells by a wide range of Gram-negative pathogens, Multivalent Adhesion Molecule (MAM) 7. Interference with MAM7-mediated attachment, for example by pre-incubation of host cells with recombinant MAM7, significantly delays the onset of hallmarks of infection, such as pathogen-mediated cytotoxicity or the development of other adhesive structures such as actin pedestals. Thus, we are trying to develop tools based on MAM7 that can be used to prevent or diminish certain Gram-negative bacterial infections. Herein, we describe the use of bead-coupled MAM7 as an inhibitor of infection with the clinically relevant pathogen Pseudomonas aeruginosa. PMID:22086133
DEFF Research Database (Denmark)
Papadopoulos, Pantelis M.; Ibrahim, Zeinab; Karatsolis, Andreas
2015-01-01
This paper presents the use of educational games in the context of the “Arabiyyatii” research project, a three-year project funded through Qatar National Research Fund. The scope of the project is teaching Modern Standard Arabic (MSA) to kindergarten students (5-6 years old) that are native...... speakers of the Qatari dialect. Part of the new curriculum envisioned in the project includes the use of simple educational games, specifically designed and developed for tabletop surface computers. The paper presents a naturalistic study design, following the activities of 18 students for a period of 9...... weeks in the project. The paper presents three of the most played games by the students, along with analysis on collected data, focusing on students’ performance and attitudes towards the new curriculum. Results analysis provided an encouraging image, suggesting that the conducted activity was able...
Cassidy, David C.
2013-03-01
It's July 1945. Germany is in defeat and the atomic bombs are on their way to Japan. Under the direction of Samuel Goudsmit, the Allies are holding some of the top German nuclear scientists-among them Heisenberg, Hahn, and Gerlach-captive in Farm Hall, an English country manor near Cambridge, England. As secret microphones record their conversations, the scientists are unaware of why they are being held or for how long. Thinking themselves far ahead of the Allies, how will they react to the news of the atomic bombs? How will these famous scientists explain to themselves and to the world their failure to achieve even a chain reaction? How will they come to terms with the horror of the Third Reich, their work for such a regime, and their behavior during that period? This one-act play is based upon the transcripts of their conversations as well as the author's historical work on the subject.
DEFF Research Database (Denmark)
Ungruhe, Christian
2017-01-01
So far, academic contributions have widely framed football in Africa as a means for migration from a western point of view. At a time, they presented particular and one-dimensional understandings of transnational links in the realm of football migration between Africa and Europe. Macro......-level perspective there is still an analytical gap between the ambitions and experiences of migrating players and economic power relations at play on the one hand and the socio-cultural embedding of the transnational connections in football migration on the other. In order to understand why and how football...... mobilities are indeed linked to ‘the transnational’ in migration there is a need to localize the phenomenon and investigate how local understandings of migration and mobility are lived and expressed in a transnational sport like football. By taking data from fieldwork among West African football migrants...
Observations of needle-tissue interactions
Misra, Sarthak; Reed, Kyle B.; Ramesh, K.T.; Okamura, Allison M.
2009-01-01
Needles with asymmetric bevel tips naturally bend when they are inserted into soft tissue. In this study, we present an analytical model for the loads developed at the bevel tip during needle-tissue interaction. The model calculates the loads based on the geometry of the bevel edge and gel material
Božović Ratko R.
2008-01-01
Free time and play are mutually dependent categories that are always realized together. We either play because we have free time or we have free time because we play (E. Fink). Play, no matter whether it is children's or artistic play or a spontaneous sports game (excluding professional sports) most fully complements human existence and thereby realizes free time as a time in freedom and freedom of time. Therefore, free time exists and is most prominent in play. Moreover, one game releases it...
Impact of radiofrequency ablation geometry on electrical conduction
Rivas, Rhiana N.; Lye, Theresa H.; Hendon, Christine P.
2018-02-01
The gold standard of current treatment for atrial fibrillation is radiofrequency ablation (RFA). Single RFA procedures have low long-term, single-procedure success rates, which can be attributed to factors including inability to measure and visualize lesion depth in real time and incomplete knowledge of how atrial fibrillation manifests and persists. One way to address this problem is to develop a heart model that accurately fits lesion dimensions and depth using OCT to extract structural information. Twenty-three lesions of varying transmurality in left and right swine atrial tissue have been imaged with a Thorlabs OCT system with 6.5-micron axial resolution and a custom Ultra High Resolution system with 2.5-micron axial resolution. The boundaries of the ablation lesions were identified by the appearance of the birefringence artifact to identify areas of un-ablated tissue, as well as by changes to depth penetration and structural features, including decreased contrast between the endocardium and myocardium and disappearance of collagen fibers within the ablation lesion. Using these features, the lateral positions of the lesion boundaries were identified. An algorithm that fit ellipses to the lesion contours modeled the ablation geometry in depth. Lesion dimensions and shape were confirmed by comparison with trichrome histological processing. Finite-element models were fitted with these parameters and electrophysiological simulations were run with the Continuity 6 package. Next steps include correlating lesion geometry to conduction velocity, and including further tissue complexity such as varying tissue composition and fiber orientation. Additional models of linear lesions with gaps and adjacent lesions created with non-perpendicular contact will be created. This work will provide insight into how lesion geometry, tissue composition, and fiber organization impact electrophysiological propagation.
A Whirlwind Tour of Computational Geometry.
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)
Optimizing solar-cell grid geometry
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.
Imagination, Playfulness, and Creativity in Children's Play with Different Toys
Mo????ller, Signe?? Juhl?
2015-01-01
Based on a four-month experimental study of preschool children's play with creative-construction and social-fantasy toys, the author examines the in?uence of both types of toys on the play of preschool children. Her comparative analysis considers the impact of transformative play on the development of imagination during play activities and…
Word Play: Scaffolding Language Development through Child-Directed Play
Wasik, Barbara A.; Jacobi-Vessels, Jill L.
2017-01-01
Play is an important activity in young children's lives. It is how children explore their world and build knowledge. Although free play, which is play that is totally child directed, contributes to children's learning, self-regulation and motivation, adults' participation in children's play is critical in their development, especially their…
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.)
Stochastic geometry for image analysis
Descombes, Xavier
2013-01-01
This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.
Magnetoelectrostatic thruster physical geometry tests
Ramsey, W. D.
1981-01-01
Inert gas tests are conducted with several magnetoelectrostatic containment discharge chamber geometries. The configurations tested include three discharge chamber lengths; three boundary magnet patterns; two different flux density magnet materials; hemispherical and conical shaped thrusters having different surface-to-volume ratios; and two and three grid ion optics. Argon mass utilizations of 60 to 79% are attained at 210 to 280 eV/ion in different test configurations. Short hemi thruster configurations are found to produce 70 to 92% xenon mass utilization at 185 to 220 eV/ion.
Programming system for analytic geometry
International Nuclear Information System (INIS)
Raymond, Jacques
1970-01-01
After having outlined the characteristics of computing centres which do not comply with engineering tasks, notably the time required by all different tasks to be performed when developing a software (assembly, compilation, link edition, loading, run), and identified constraints specific to engineering, the author identifies the characteristics a programming system should have to suit engineering tasks. He discussed existing conversational systems and their programming language, and their main drawbacks. Then, he presents a system which aims at facilitating programming and addressing problems of analytic geometry and trigonometry
The geometry of special relativity
International Nuclear Information System (INIS)
Parizet, Jean
2008-01-01
This book for students in mathematics or physics shows the interest of geometry to understand special relativity as a consequence of invariance of Maxwell equations and of constancy of the speed of light. Space-time is actually provided with a geometrical structure and a physical interpretation: at each observer are associated his own time and his own physical space in which occur events he is concerned with. This leads to a natural approach to special relativity. The Lorentz group and its algebra are then studied by using matrices and the Pauli algebra. Quaternions are also addressed
Moduli spaces in algebraic geometry
International Nuclear Information System (INIS)
Goettsche, L.
2000-01-01
This volume of the new series of lecture notes of the Abdus Salam International Centre for Theoretical Physics contains the lecture notes of the School on Algebraic Geometry which took place at the Abdus Salam International Centre for Theoretical Physics from 26 July to 13 August 1999. The school consisted of 2 weeks of lecture courses and one week of conference. The topic of the school was moduli spaces. More specifically the lectures were divided into three subtopics: principal bundles on Riemann surfaces, moduli spaces of vector bundles and sheaves on projective varieties, and moduli spaces of curves
Worldsheet geometries of ambitwistor string
Energy Technology Data Exchange (ETDEWEB)
Ohmori, Kantaro [Department of Physics, the University of Tokyo,Hongo, Bunkyo-ku, Tokyo 133-0022 (Japan)
2015-06-12
Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.
Porous media geometry and transports
Adler, Pierre
1992-01-01
The goal of ""Porous Media: Geometry and Transports"" is to provide the basis of a rational and modern approach to porous media. This book emphasizes several geometrical structures (spatially periodic, fractal, and random to reconstructed) and the three major single-phase transports (diffusion, convection, and Taylor dispersion).""Porous Media"" serves various purposes. For students it introduces basic information on structure and transports. Engineers will find this book useful as a readily accessible assemblage of al the major experimental results pertaining to single-phase tr
Geometry of physical dispersion relations
International Nuclear Information System (INIS)
Raetzel, Dennis; Rivera, Sergio; Schuller, Frederic P.
2011-01-01
To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements that local matter field dynamics must be predictive and allow for an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible. Dispersion relations passing the simple algebraic checks derived here correspond to physically admissible Finslerian refinements of Lorentzian geometry.
Projective geometry and projective metrics
Busemann, Herbert
2005-01-01
The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.Topics include the projective plane, polarities and conic sectio
Geometry of supersymmetric gauge theories
International Nuclear Information System (INIS)
Gieres, F.
1988-01-01
This monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-Poincare group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism
Clustering in Hilbert simplex geometry
Nielsen, Frank
2017-04-03
Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.
An invitation to noncommutative geometry
Marcolli, Matilde
2008-01-01
This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s). A Walk in the Noncommutative Garden (1,639 KB). Contents: A Walk in the Noncommutative Garden (A Connes & M Marcolli); Renormalization of Noncommutative Quantum Field Theory (H Grosse & R Wulke
Trends and developments in computational geometry
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
Global affine differential geometry of hypersurfaces
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.
"WGL," a Web Laboratory for Geometry
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…
International Nuclear Information System (INIS)
Majewski, O.
1999-01-01
Dr. Otto Majewski, Chief Executive Officer of the Bayernwerk AG utility, in his capacity as Chairman of the European Nuclear Council pointed out at ENC 98 in Nice that national energy policies constituted a major danger to the use of nuclear power. At the same time, he indicated ways and means by which to evade that danger. The decisions taken in Sweden and in the Federal Republic of Germany to opt out of the use of nuclear power show that national energy policies can seriously jeopardize the use of nuclear power. Bayernwerk CEO Dr. Majewski urged nuclear power plant operators to counteract these tendencies by playing the European card. Nuclear power anyway was a classical topic of European cooperation which, in the past, had resulted in higher safety standards and in the development of the EPR. It should also be attempted, by working on European institutions, to strengthen the use of nuclear power, even on a national level. He invoked economic arguments against nuclear opponents, especially the preservation of competitiveness by means of lower electricity prices, and arguments of climate protection. (orig.) [de
Tearing modes in toroidal geometry
International Nuclear Information System (INIS)
Connor, J.W.; Cowley, S.C.; Hastie, R.J.; Hender, T.C.; Hood, A.; Martin, T.J.
1988-01-01
The separation of the cylindrical tearing mode stability problem into a resistive resonant layer calculation and an external marginal ideal magnetohydrodynamic (MHD) calculation (Δ' calculation) is generalized to axisymmetric toroidal geometry. The general structure of this separation is analyzed and the marginal ideal MHD information (the toroidal generalization of Δ') required to discuss stability is isolated. This can then, in principle, be combined with relevant resonant layer calculations to determine tearing mode growth rates in realistic situations. Two examples are given: the first is an analytic treatment of toroidally coupled (m = 1, n = 1) and (m = 2, n = 1) tearing modes in a large aspect ratio torus; the second, a numerical treatment of the toroidal coupling of three tearing modes through finite pressure effects in a large aspect ratio torus. In addition, the use of a coupling integral approach for determining the stability of coupled tearing modes is discussed. Finally, the possibility of using initial value resistive MHD codes in realistic toroidal geometry to determine the necessary information from the ideal MHD marginal solution is discussed
Geometry of isotropic convex bodies
Brazitikos, Silouanos; Valettas, Petros; Vritsiou, Beatrice-Helen
2014-01-01
The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lov�sz-Simonovits conjecture. This book prov...
Differential geometry of group lattices
International Nuclear Information System (INIS)
Dimakis, Aristophanes; Mueller-Hoissen, Folkert
2003-01-01
In a series of publications we developed ''differential geometry'' on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first-order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of ''bicovariant'' Cayley graphs with the property ad(S)S subset of S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first-order calculi extend to higher orders and then allow us to introduce further differential geometric structures. Furthermore, we explore the properties of ''discrete'' vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analog of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained
Geometry of anisotropic CO outflows
International Nuclear Information System (INIS)
Liseau, R.; Sandell, G.; Helsinki Univ., Observatory, Finland)
1986-01-01
A simple geometrical model for the space motions of the bipolar high-velocity CO outflows in regions of recent, active star formation is proposed. It is assumed that the velocity field of the neutral gas component can be represented by large-scale uniform motions. From observations of the spatial distribution and from the characteristics of the line shape of the high-velocity molecular gas emission the geometry of the line-emitting regions can be inferred, i.e., the direction in space and the collimating angle of the flow. The model has been applied to regions where a check on presently obtained results is provided by independent optical determinations of the motions of Herbig-Haro objects associated with the CO flows. These two methods are in good agreement and, furthermore, the results obtained provide convincingly strong evidence for the physical association of CO outflows and Herbig-Haro objects. This also supports the common view that a young stellar central source is responsible for the active phenomena observed in its environmental neighborhood. It is noteworthy that within the framework of the model the determination of the flow geometry of the high-velocity gas from CO measurements is independent of the distance to the source and, furthermore, can be done at relatively low spatial resolution. 32 references
Playful Learning and Montessori Education
Lillard, Angeline S.
2013-01-01
Although Montessori education is often considered a form of playful learning, Maria Montessori herself spoke negatively about a major component of playful learning--pretend play, or fantasy--for young children. In this essay, the author discusses this apparent contradiction: how and why Montessori education includes elements of playful learning…
Play Therapy in Elementary Schools
Landreth, Garry L.; Ray, Dee C.; Bratton, Sue C.
2009-01-01
Because the child's world is a world of action and activity, play therapy provides the psychologist in elementary-school settings with an opportunity to enter the child's world. In the play therapy relationship, toys are like the child's words and play is the child's language. Therefore, children play out their problems, experiences, concerns, and…
Enhanced reality live role playing
Söderberg, Jonas; Waern, Annika; Åkesson, Karl-Petter; Björk, Staffan; Falk, Jennica
2004-01-01
Live role-playing is a form of improvisational theatre played for the experience of the performers and without an audience. These games form a challenging application domain for ubiquitous technology. We discuss the design options for enhanced reality live role-playing and the role of technology in live role-playing games.
The Upside of Videogame Playing.
Jackson, Linda A
2012-12-01
In our research on the relationship between videogame playing and cognitive outcomes we found that children (n=481, 12 year olds) who played videogames more were more creative than those who played them less. Here we summarize these findings and propose new research to identify mediating cognitive factors influenced by videogame playing.
Play and playfulness in early childhood education and care.
Directory of Open Access Journals (Sweden)
Singer E.
2015-06-01
Full Text Available Play and playfulness are basic features in early childhood education. The elements of play are pleasure, a sense of freedom, and the co-construction of shared meaning through the use of rules or rhythms. Play and learning are closely related in early childhood. But when the focus on the educational benefits of play becomes too strong, the most essential feature of play is lost: children’s pleasure. Young children in group settings often have to adapt to the teachers’ demands related to security, hygiene, and social norms and values. But the playfulness of the teachers helps to overcome differences in power in the caregiver-child relationship and prevents young children from becoming overburdened with strict rules and group discipline. Play and playfulness are a resource of shared pleasure and creativity in learning processes.
Ouroboros - Playing A Biochemical
Directory of Open Access Journals (Sweden)
D. T. Rodrigues
2014-08-01
Full Text Available Ouroboros: Playing A Biochemical RODRIGUES,D.T.1,2;GAYER, M.C.1,2; ESCOTO, D.F.1; DENARDIN, E.L.G.2, ROEHRS, R.1,2 1Interdisciplinary Research Group on Teaching Practice, Graduate Program in Biochemistry, Unipampa, RS, Brazil 2Laboratory of Physicochemical Studies and Natural Products, Post Graduate Program in Biochemistry, Unipampa, RS, Brazil Introduction: Currently, teachers seek different alternatives to enhance the teaching-learning process. Innovative teaching methodologies are increasingly common tools in educational routine. The use of games, electronic or conventional, is an effective tool to assist in learning and also to raise the social interaction between students. Objective: In this sense our work aims to evaluate the card game and "Ouroboros" board as a teaching and learning tool in biochemistry for a graduating class in Natural Sciences. Materials and methods: The class gathered 22 students of BSc in Natural Sciences. Each letter contained a question across the board that was drawn to a group to answer within the allotted time. The questions related concepts of metabolism, organic and inorganic chemical reactions, bioenergetics, etc.. Before the game application, students underwent a pre-test with four issues involving the content that was being developed. Soon after, the game was applied. Then again questions were asked. Data analysis was performed from the ratio of the number of correct pre-test and post-test answers. Results and discussion: In the pre-test 18.1% of the students knew all issues, 18.1% got 3 correct answers, 40.9% answered only 2 questions correctly and 22.7% did not hit any. In post-test 45.4% answered all the questions right, 31.8% got 3 questions and 22.7% got 2 correct answers. The results show a significant improvement of the students about the field of content taught through the game. Conclusion: Generally, traditional approaches of chemistry and biochemistry are abstract and complex. Thus, through games
Differential Geometry Based Multiscale Models
Wei, Guo-Wei
2010-01-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that
Differential geometry based multiscale models.
Wei, Guo-Wei
2010-08-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are
Fisher, John P; Bronzino, Joseph D
2007-01-01
Increasingly viewed as the future of medicine, the field of tissue engineering is still in its infancy. As evidenced in both the scientific and popular press, there exists considerable excitement surrounding the strategy of regenerative medicine. To achieve its highest potential, a series of technological advances must be made. Putting the numerous breakthroughs made in this field into a broad context, Tissue Engineering disseminates current thinking on the development of engineered tissues. Divided into three sections, the book covers the fundamentals of tissue engineering, enabling technologies, and tissue engineering applications. It examines the properties of stem cells, primary cells, growth factors, and extracellular matrix as well as their impact on the development of tissue engineered devices. Contributions focus on those strategies typically incorporated into tissue engineered devices or utilized in their development, including scaffolds, nanocomposites, bioreactors, drug delivery systems, and gene t...
Lewis, Phillip L; Green, Richard M; Shah, Ramille N
2018-03-15
Three dimensional (3D) printing is highly amenable to the fabrication of tissue-engineered organs of a repetitive microstructure such as the liver. The creation of uniform and geometrically repetitive tissue scaffolds can also allow for the control over cellular aggregation and nutrient diffusion. However, the effect of differing geometries, while controlling for pore size, has yet to be investigated in the context of hepatocyte function. In this study, we show the ability to precisely control pore geometry of 3D-printed gelatin scaffolds. An undifferentiated hepatocyte cell line (HUH7) demonstrated high viability and proliferation when seeded on 3D-printed scaffolds of two different geometries. However, hepatocyte specific functions (albumin secretion, CYP activity, and bile transport) increases in more interconnected 3D-printed gelatin cultures compared to a less interconnected geometry and to 2D controls. Additionally, we also illustrate the disparity between gene expression and protein function in simple 2D culture modes, and that recreation of a physiologically mimetic 3D environment is necessary to induce both expression and function of cultured hepatocytes. Three dimensional (3D) printing provides tissue engineers the ability spatially pattern cells and materials in precise geometries, however the biological effects of scaffold geometry on soft tissues such as the liver have not been rigorously investigated. In this manuscript, we describe a method to 3D print gelatin into well-defined repetitive geometries that show clear differences in biological effects on seeded hepatocytes. We show that a relatively simple and widely used biomaterial, such as gelatin, can significantly modulate biological processes when fabricated into specific 3D geometries. Furthermore, this study expands upon past research into hepatocyte aggregation by demonstrating how it can be manipulated to enhance protein function, and how function and expression may not precisely correlate in
Hopf algebras in noncommutative geometry
International Nuclear Information System (INIS)
Varilly, Joseph C.
2001-10-01
We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)
Integrable systems, geometry, and topology
Terng, Chuu-Lian
2006-01-01
The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. The article by Burstall gives a beautiful exposition on isothermic surfaces and their relations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu, and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of ...
Tarski Geometry Axioms. Part III
Directory of Open Access Journals (Sweden)
Coghetto Roland
2017-12-01
Full Text Available In the article, we continue the formalization of the work devoted to Tarski’s geometry - the book “Metamathematische Methoden in der Geometrie” by W. Schwabhäuser, W. Szmielew, and A. Tarski. After we prepared some introductory formal framework in our two previous Mizar articles, we focus on the regular translation of underlying items faithfully following the abovementioned book (our encoding covers first seven chapters. Our development utilizes also other formalization efforts of the same topic, e.g. Isabelle/HOL by Makarios, Metamath or even proof objects obtained directly from Prover9. In addition, using the native Mizar constructions (cluster registrations the propositions (“Satz” are reformulated under weaker conditions, i.e. by using fewer axioms or by proposing an alternative version that uses just another axioms (ex. Satz 2.1 or Satz 2.2.
Applied geometry and discrete mathematics
Sturm; Gritzmann, Peter; Sturmfels, Bernd
1991-01-01
This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, th...
Introduction to global variational geometry
Krupka, Demeter
2015-01-01
The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational se...
Some Progress in Conformal Geometry
Directory of Open Access Journals (Sweden)
Sun-Yung A. Chang
2007-12-01
Full Text Available This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the $sigma_2$-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes.
Seesaw mechanism in warped geometry
International Nuclear Information System (INIS)
Huber, S.J.; Shafi, Q.
2003-09-01
We show how the seesaw mechanism for neutrino masses can be realized within a five dimensional (5D) warped geometry framework. Intermediate scale standard model (SM) singlet neutrino masses, needed to explain the atmospheric and solar neutrino oscillations, are shown to be proportional to M P1 .exp((2c-1)πkR), where c denotes the coefficient of the 5D Dirac mass term for the singlet neutrino which also has a Planck scale Majorana mass localized on the Planck-brane, and kR∼11 in order to resolve the gauge hierarchy problem. The case with a bulk 5D Majorana mass term for the singlet neutrino is briefly discussed. (orig.)
Seesaw mechanism in warped geometry
International Nuclear Information System (INIS)
Huber, Stephan J.; Shafi, Qaisar
2004-01-01
We show how the seesaw mechanism for neutrino masses can be realized within a five-dimensional (5D) warped geometry framework. Intermediate scale standard model (SM) singlet neutrino masses, needed to explain the atmospheric and solar neutrino oscillations, are shown to be proportional to M Pl exp((2c-1)πkR), where c denotes the coefficient of the 5D Dirac mass term for the singlet neutrino which also has a Planck scale Majorana mass localized on the Planck-brane, and kR∼11 in order to resolve the gauge hierarchy problem. The case with a bulk 5D Majorana mass term for the singlet neutrino is briefly discussed
Spin, statistics, and geometry of random walks
International Nuclear Information System (INIS)
Jaroszewicz, T.; Kurzepa, P.S.
1991-01-01
The authors develop and unify two complementary descriptions of propagation of spinning particles: the directed random walk representation and the spin factor approach. Working in an arbitrary number of dimensions D, they first represent the Dirac propagator in terms of a directed random walk. They then derive the general and explicit form of the gauge connection describing parallel transport of spin and investigate the resulting quantum-mechanical problem of a particle moving on a sphere in the field of a nonabelian SO(D-1) monopole. This construction, generalizing Polyakov's results, enables them to prove the equivalence of the random walk and path-integral (spin factor) representation. As an alternative, they construct and discuss various Wess-Zumino-Witten forms of the spin factor. They clarify the role played by the coupling between the particle's spin and translational degrees of freedom in establishing the geometrical properties of particle's paths in spacetime. To this end, they carefully define and evaluate Hausdorff dimensions of bosonic and fermionic sample paths, in the covariant as well as nonrelativistic formulations. Finally, as an application of the developed formalism, they give an intuitive spacetime interpretation of chiral anomalies in terms of the geometry of fermion trajectories
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 ...
Convection in Slab and Spheroidal Geometries
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.
Solar proton exposure of an ICRU sphere within a complex structure Part I: Combinatorial geometry.
Wilson, John W; Slaba, Tony C; Badavi, Francis F; Reddell, Brandon D; Bahadori, Amir A
2016-06-01
The 3DHZETRN code, with improved neutron and light ion (Z≤2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency. Published by Elsevier Ltd.
Solar Proton Transport within an ICRU Sphere Surrounded by a Complex Shield: Combinatorial Geometry
Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.
2015-01-01
The 3DHZETRN code, with improved neutron and light ion (Z (is) less than 2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency.
Parental Involvement In Play Therapy
Ohlson, E. Lamonte
1976-01-01
Play therapy acts as a medium of expression for children. The purpose of this article is to outline a methodological approach as well as to emphasize the necessity of including the parent in the play therapy situation. (Author)
Learning, Play, and Your Newborn
... Staying Safe Videos for Educators Search English Español Learning, Play, and Your Newborn KidsHealth / For Parents / Learning, ... Some Other Ideas Print What Is My Newborn Learning? Play is the chief way that infants learn ...
Problematic game play: the diagnostic value of playing motives, passion, and playing time in men.
Kneer, Julia; Rieger, Diana
2015-04-30
Internet gaming disorder is currently listed in the DSM-not in order to diagnose such a disorder but to encourage research to investigate this phenomenon. Even whether it is still questionable if Internet Gaming Disorder exists and can be judged as a form of addiction, problematic game play is already very well researched to cause problems in daily life. Approaches trying to predict problematic tendencies in digital game play have mainly focused on playing time as a diagnostic criterion. However, motives to engage in digital game play and obsessive passion for game play have also been found to predict problematic game play but have not yet been investigated together. The present study aims at (1) analyzing if obsessive passion can be distinguished from problematic game play as separate concepts, and (2) testing motives of game play, passion, and playing time for their predictive values for problematic tendencies. We found (N = 99 males, Age: M = 22.80, SD = 3.81) that obsessive passion can be conceptually separated from problematic game play. In addition, the results suggest that compared to solely playing time immersion as playing motive and obsessive passion have added predictive value for problematic game play. The implications focus on broadening the criteria in order to diagnose problematic playing.
Problematic Game Play: The Diagnostic Value of Playing Motives, Passion, and Playing Time in Men
Directory of Open Access Journals (Sweden)
Julia Kneer
2015-04-01
Full Text Available Internet gaming disorder is currently listed in the DSM—not in order to diagnose such a disorder but to encourage research to investigate this phenomenon. Even whether it is still questionable if Internet Gaming Disorder exists and can be judged as a form of addiction, problematic game play is already very well researched to cause problems in daily life. Approaches trying to predict problematic tendencies in digital game play have mainly focused on playing time as a diagnostic criterion. However, motives to engage in digital game play and obsessive passion for game play have also been found to predict problematic game play but have not yet been investigated together. The present study aims at (1 analyzing if obsessive passion can be distinguished from problematic game play as separate concepts, and (2 testing motives of game play, passion, and playing time for their predictive values for problematic tendencies. We found (N = 99 males, Age: M = 22.80, SD = 3.81 that obsessive passion can be conceptually separated from problematic game play. In addition, the results suggest that compared to solely playing time immersion as playing motive and obsessive passion have added predictive value for problematic game play. The implications focus on broadening the criteria in order to diagnose problematic playing.
Play Therapy: Basics and Beyond.
Kottman, Terry
This book provides an atheoretical orientation to basic concepts involved in play therapy and an introduction to different skills used in play therapy. The demand for mental professionals and school counselors who have training and expertise in using play as a therapeutic tool when working with children has increased tremendously. In response to…
Play Therapy in School Counseling
Trice-Black, Shannon; Bailey, Carrie Lynn; Kiper Riechel, Morgan E.
2013-01-01
Play therapy is an empirically supported intervention used to address a number of developmental issues faced in childhood. Through the natural language of play, children and adolescents communicate feelings, thoughts, and experiences. Schools provide an ideal setting for play therapy in many ways; however, several challenges exist in implementing…
Play Memories and Place Identity.
Sandberg, Anette
2003-01-01
This retrospective study examined play memories from childhood to adulthood of 478 university students between ages 20 and 62 as exhibited in drawings of play memories and questionnaire responses. The study focused on the role of the physical environment and place identity in play memories and individual identity development. Findings showed that…
Pretend Play and Creative Processes
Russ, Sandra W.; Wallace, Claire E.
2013-01-01
The authors contend that many cognitive abilities and affective processes important in creativity also occur in pretend play and that pretend play in childhood affects the development of creativity in adulthood. They discuss a variety of theories and observations that attempt to explain the importance of pretend play to creativity. They argue that…
... are 4 basic types of tissue: connective tissue, epithelial tissue, muscle tissue, and nervous tissue. Connective tissue supports ... binds them together (bone, blood, and lymph tissues). Epithelial tissue provides a covering (skin, the linings of the ...
Connections between algebra, combinatorics, and geometry
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...
Second International workshop Geometry and Symbolic Computation
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. ...
Pin Tool Geometry Effects in Friction Stir Welding
Querin, J. A.; Rubisoff, H. A.; Schneider, J. A.
2009-01-01
In friction stir welding (FSW) there is significant evidence that material can take one of two different flow paths when being displaced from its original position in front of the pin tool to its final position in the wake of the weld. The geometry of the pin tool, along with the process parameters, plays an important role in dictating the path that the material takes. Each flow path will impart a different thermomechanical history on the material, consequently altering the material microstructure and subsequent weld properties. The intention of this research is to isolate the effect that different pin tool attributes have on the flow paths imparted on the FSWed material. Based on published weld tool geometries, a variety of weld tools were fabricated and used to join AA2219. Results from the tensile properties and microstructural characterization will be presented.
Commutative algebra with a view toward algebraic geometry
Eisenbud, David
1995-01-01
Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algeb...
A vector space approach to geometry
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.
Classical geometry Euclidean, transformational, inversive, and projective
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
Introduction to non-Euclidean geometry
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
Applications of Affine and Weyl geometry
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
Morphing methods to parameterize specimen-specific finite element model geometries.
Sigal, Ian A; Yang, Hongli; Roberts, Michael D; Downs, J Crawford
2010-01-19
Shape plays an important role in determining the biomechanical response of a structure. Specimen-specific finite element (FE) models have been developed to capture the details of the shape of biological structures and predict their biomechanics. Shape, however, can vary considerably across individuals or change due to aging or disease, and analysis of the sensitivity of specimen-specific models to these variations has proven challenging. An alternative to specimen-specific representation has been to develop generic models with simplified geometries whose shape is relatively easy to parameterize, and can therefore be readily used in sensitivity studies. Despite many successful applications, generic models are limited in that they cannot make predictions for individual specimens. We propose that it is possible to harness the detail available in specimen-specific models while leveraging the power of the parameterization techniques common in generic models. In this work we show that this can be accomplished by using morphing techniques to parameterize the geometry of specimen-specific FE models such that the model shape can be varied in a controlled and systematic way suitable for sensitivity analysis. We demonstrate three morphing techniques by using them on a model of the load-bearing tissues of the posterior pole of the eye. We show that using relatively straightforward procedures these morphing techniques can be combined, which allows the study of factor interactions. Finally, we illustrate that the techniques can be used in other systems by applying them to morph a femur. Morphing techniques provide an exciting new possibility for the analysis of the biomechanical role of shape, independently or in interaction with loading and material properties. Copyright 2009 Elsevier Ltd. All rights reserved.
Adipose tissue-derived stem cells in oral mucosa tissue engineering ...
African Journals Online (AJOL)
Jane
2011-10-10
Oct 10, 2011 ... stem cells (ADSCs) may play an important role in this field. In this research ..... Adipose tissue is derived from embryonic mesodermal precursors and .... Clonogenic multipotent stem cells in human adipose tissue differentiate ...
Special Geometry and Automorphic Forms
Berglund, P; Wyllard, N; Berglund, Per; Henningson, Mans; Wyllard, Niclas
1997-01-01
We consider special geometry of the vector multiplet moduli space in compactifications of the heterotic string on $K3 \\times T^2$ or the type IIA string on $K3$-fibered Calabi-Yau threefolds. In particular, we construct a modified dilaton that is invariant under $SO(2, n; Z)$ T-duality transformations at the non-perturbative level and regular everywhere on the moduli space. The invariant dilaton, together with a set of other coordinates that transform covariantly under $SO(2, n; Z)$, parameterize the moduli space. The construction involves a meromorphic automorphic function of $SO(2, n; Z)$, that also depends on the invariant dilaton. In the weak coupling limit, the divisor of this automorphic form is an integer linear combination of the rational quadratic divisors where the gauge symmetry is enhanced classically. We also show how the non-perturbative prepotential can be expressed in terms of meromorphic automorphic forms, by expanding a T-duality invariant quantity both in terms of the standard special coord...
Geometry of lattice field theory
International Nuclear Information System (INIS)
Honan, T.J.
1986-01-01
Using some tools of algebraic topology, a general formalism for lattice field theory is presented. The lattice is taken to be a simplicial complex that is also a manifold and is referred to as a simplicial manifold. The fields on this lattice are cochains, that are called lattice forms to emphasize the connections with differential forms in the continuum. This connection provides a new bridge between lattice and continuum field theory. A metric can be put onto this simplicial manifold by assigning lengths to every link or I-simplex of the lattice. Regge calculus is a way of defining general relativity on this lattice. A geometric discussion of Regge calculus is presented. The Regge action, which is a discrete form of the Hilbert action, is derived from the Hilbert action using distribution valued forms. This is a new derivation that emphasizes the underlying geometry. Kramers-Wannier duality in statistical mechanics is discussed in this general setting. Nonlinear field theories, which include gauge theories and nonlinear sigma models are discussed in the continuum and then are put onto a lattice. The main new result here is the generalization to curved spacetime, which consists of making the theory compatible with Regge calculus
Latent geometry of bipartite networks
Kitsak, Maksim; Papadopoulos, Fragkiskos; Krioukov, Dmitri
2017-03-01
Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.
Fractal Geometry and Stochastics V
Falconer, Kenneth; Zähle, Martina
2015-01-01
This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott, Michał Rams, Pablo Shmerkin, and András Te...
Stochastic geometry in PRIZMA code
International Nuclear Information System (INIS)
Malyshkin, G. N.; Kashaeva, E. A.; Mukhamadiev, R. F.
2007-01-01
The paper describes a method used to simulate radiation transport through random media - randomly placed grains in a matrix material. The method models the medium consequently from one grain crossed by particle trajectory to another. Like in the Limited Chord Length Sampling (LCLS) method, particles in grains are tracked in the actual grain geometry, but unlike LCLS, the medium is modeled using only Matrix Chord Length Sampling (MCLS) from the exponential distribution and it is not necessary to know the grain chord length distribution. This helped us extend the method to media with randomly oriented arbitrarily shaped convex grains. Other extensions include multicomponent media - grains of several sorts, and polydisperse media - grains of different sizes. Sort and size distributions of crossed grains were obtained and an algorithm was developed for sampling grain orientations and positions. Special consideration was given to medium modeling at the boundary of the stochastic region. The method was implemented in the universal 3D Monte Carlo code PRIZMA. The paper provides calculated results for a model problem where we determine volume fractions of modeled components crossed by particle trajectories. It also demonstrates the use of biased sampling techniques implemented in PRIZMA for solving a problem of deep penetration in model random media. Described are calculations for the spectral response of a capacitor dose detector whose anode was modeled with account for its stochastic structure. (authors)
The geometry of population genetics
Akin, Ethan
1979-01-01
The differential equations which model the action of selection and recombination are nonlinear equations which are impossible to It is even difficult to describe in general the solve explicitly. Recently, Shahshahani began using qualitative behavior of solutions. differential geometry to study these equations [28]. with this mono graph I hope to show that his ideas illuminate many aspects of pop ulation genetics. Among these are his proof and clarification of Fisher's Fundamental Theorem of Natural Selection and Kimura's Maximum Principle and also the effect of recombination on entropy. We also discover the relationship between two classic measures of 2 genetic distance: the x measure and the arc-cosine measure. There are two large applications. The first is a precise definition of the biological concept of degree of epistasis which applies to general (i.e. frequency dependent) forms of selection. The second is the unexpected appearance of cycling. We show that cycles can occur in the two-locus-two-allele...
Topics in Cubic Special Geometry
Bellucci, Stefano; Roychowdhury, Raju
2011-01-01
We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbit...
Bradshaw, John W S; Pullen, Anne J; Rooney, Nicola J
2015-01-01
Among the Carnivora, play behaviour is usually made up of motor patterns characteristic of predatory, agonistic and courtship behaviour. Domestic dogs are unusual in that play is routinely performed by adults, both socially, with conspecifics and with humans, and also asocially, with objects. This enhanced playfulness is commonly thought to be a side effect of paedomorphosis, the perpetuation of juvenile traits into adulthood, but here we suggest that the functions of the different types of play are sufficiently distinct that they are unlikely to have arisen through a single evolutionary mechanism. Solitary play with objects appears to be derived from predatory behaviour: preferred toys are those that can be dismembered, and a complex habituation-like feedback system inhibits play with objects that are resistant to alteration. Intraspecific social play is structurally different from interspecific play and may therefore be motivationally distinct and serve different goals; for example, dogs often compete over objects when playing with other dogs, but are usually more cooperative when the play partner is human. The majority of dogs do not seem to regard competitive games played with a human partner as "dominance" contests: rather, winning possession of objects during games appears to be simply rewarding. Play may be an important factor in sociality, since dogs are capable of extracting social information not only from games in which they participate, but also from games that they observe between third parties. We suggest that the domestic dog's characteristic playfulness in social contexts is an adaptive trait, selected during domestication to facilitate both training for specific purposes, and the formation of emotionally-based bonds between dog and owner. Play frequency and form may therefore be an indicator of the quality of dog-owner relationships. Copyright © 2014 Elsevier B.V. All rights reserved.
Quantum groups: Geometry and applications
International Nuclear Information System (INIS)
Chu, C.S.
1996-01-01
The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge
Geometry and physics of branes
International Nuclear Information System (INIS)
Gal'tsov, D V
2003-01-01
The book brings together the contents of lecture courses delivered at the school 'Geometry and Physics of Branes' which took place at the Center 'Alessandro Volta' (Como, Italy) in the spring of 2001. The purpose of the school was to provide an introduction to some lines of research, related to the notion of branes in superstring theory, which are in the focus of attention both in the physical and mathematical communities. The book is structured into three parts: the first contains an elementary introduction to branes, the second is devoted to physical aspects (conformal field theory on open and unoriented surfaces and topics in string tachyon dynamics), and the last contains some more formal mathematical developments. An introduction to branes is given in a remarkably lucid contribution by A Lerda. It opens with a construction of p-brane solutions in classical IIA and IIB supergravities with particular emphasis on the 'fundamental string' solution, the NS5-brane and the D3-brane. Then, the quantum description of D-branes is discussed in terms of boundary states of the closed superstring, which is an alternative to the more common description in terms of open strings with Dirichlet boundary conditions in the transverse to the brane directions. When a constant gauge field is present in the D-brane worldvolume, the boundary states are coherent states of the string oscillators depending on the field strength tensor. The couplings of the brane to the bulk fields - the graviton, the dilaton, and the Kalb-Ramond fields - are then extracted and shown to be precisely the ones that are produced by the Dirac-Born-Infeld action governing the low-energy dynamics of the D-brane derived using the open strings formalism. It is also shown that in the classical limit, the boundary states correctly reproduce the parameters of the corresponding classical solutions. The second part of the book starts with a contribution by Y S Stanev devoted to the two-dimensional conformal field
Cabrera, Natasha J; Roggman, Lori
2017-11-01
Both mothers and fathers play with their children, but research on parent-child play interactions is conducted with mothers three times more often than it is with fathers. The articles in this special issue address this gap by focusing on the nature and quality of father-child play, across cultural contexts, and considering whether father play offers something unique and special for early human development, in infancy or early childhood. The studies show that fathers can be just as developmentally supportive as are mothers in terms of being playful and engaged with their children in ways that are related to greater child socioemotional competence, emotion regulation, and vocabulary, and to less aggression, anxiety, and negativity. We encourage future research to examine the cultural influences, family system dynamics, and specificity of timing and types of father-child play in relation to children's developmental competence. © 2017 Michigan Association for Infant Mental Health.
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....
Increasing insightful thinking in analytic geometry
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.
Symposium on Differential Geometry and Differential Equations
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.
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
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
Quantification of variability in bedform geometry
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.
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.)
The Geometry of the Universe: Part 2
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…
Poisson geometry from a Dirac perspective
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.
An approach for management of geometry data
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.
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 .
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 ...
The design of geometry teaching: learning from the geometry textbooks of Godfrey and Siddons
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...
Well Played: The Origins and Future of Playfulness
Gordon, Gwen
2014-01-01
In this article, the author synthesizes research from several disciplines to shed light on play's central role in healthy development. Gordon builds on research in attachment theory that correlates secure attachment in infancy with adult well-being to demonstrate how playfulness might be a lifelong outcome of secure attachment and a primary…
Playing with the Multiple Intelligences: How Play Helps Them Grow
Eberle, Scott G.
2011-01-01
Howard Gardner first posited a list of "multiple intelligences" as a liberating alternative to the assumptions underlying traditional IQ testing in his widely read study "Frames of Mind" (1983). Play has appeared only in passing in Gardner's thinking about intelligence, however, even though play instructs and trains the verbal, interpersonal,…
The Power of Outdoor Play and Play in Natural Environments
Kemple, Kristen M.; Oh, JiHyun; Kenney, Elizabeth; Smith-Bonahue, Tina
2016-01-01
Young children's outdoor play serves important and diverse purposes, including physical exercise and opportunities for growth in all developmental areas. Unfortunately, the amount of time that children spend engaged in unstructured, child-directed outdoor play has diminished significantly in the past generation. In this article, the authors…
DEFF Research Database (Denmark)
Van Leemput, Koen; Puonti, Oula
2015-01-01
Computational methods for automatically segmenting magnetic resonance images of the brain have seen tremendous advances in recent years. So-called tissue classification techniques, aimed at extracting the three main brain tissue classes (white matter, gray matter, and cerebrospinal fluid), are now...... well established. In their simplest form, these methods classify voxels independently based on their intensity alone, although much more sophisticated models are typically used in practice. This article aims to give an overview of often-used computational techniques for brain tissue classification...
Multispecies methods, technologies for play
DEFF Research Database (Denmark)
Jørgensen, Ida Kathrine Hammeleff; Wirman, Hanna
2016-01-01
This article discusses methodological considerations of user-centred design for non-human animals. These considerations are illustrated through a design research project that aims to apply digital technology to build games for orangutans’ enrichment. The article argues that design for other species......-human contributions in design. This method applies play as an interspecies co-creative act and can be used as a starting point for addressing questions of difference in play and designing games that allow for ambiguous play....
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
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.
Machine learning spatial geometry from entanglement features
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).
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.
Special metrics and group actions in geometry
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.
DEFF Research Database (Denmark)
Skovbjerg, Helle Marie
2017-01-01
Based on a field study in a kindergarten among children in Denmark, this paper explores playing activities on a digital swing, the SON-X Octavia (SON-X) and its Applause application. SON-X is an interactive sound unit that can be attached to any swing chain. Here, I explore the relationship between...... to highlight the features of swing play that children develop using the SON-X technology in terms of the danger-safety continuum. The feedback provided, it is found, enables children to independently manage risk and security within the limits of their playing activities; the digital swing supports play...
Directory of Open Access Journals (Sweden)
Kristina Horback
2014-05-01
Full Text Available The predominant method of measuring welfare in swine focuses on overt physical ailments, such as skin lesions, lameness, and body condition. An alternative metric for assessing welfare in swine can be to measure the frequency and duration of positive behavioral states, such as play. Given that play occurs only when an animal's primary needs (food, comfort, safety, etc. have been satisfied, it has been suggested that play may be a sensitive indicator for assessing the welfare of non-human animals. Play has primarily been described in young piglets and is assessed via the occurrence of specific play markers. These play markers include overt bursts of energy like scamper, or more subtle social behaviors like nose-to-body contact. This review describes four areas of play for swine: locomotor, object, sow-piglet, and, peer play. From sporadic leaping to combative wrestling, play behavior allows for the fine-tuning of reflexive behavior which can enhance physical development, enrich cognitive abilities, and facilitate the maintenance of social bonds.
The Internet of Playful Things
DEFF Research Database (Denmark)
Wyeth, Peta; Brereton, Margot; Roe, Paul
2015-01-01
This one-day workshop brings together researchers and practitioners to share knowledge and practices on how people can connect and interact with the Internet of Things in a playful way. Open to participants with a diverse range of interests and expertise, and by exploring novel ways to playfully...... will be a road map to support the development of a Model of Playful Connectedness, focusing on how best to design and make playful networks of things, identifying the challenges that need to be addressed in order to do so....
Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry
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…
Drawing Dynamic Geometry Figures Online with Natural Language for Junior High School Geometry
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…
Modeling flow for modified concentric cylinder rheometer geometry
Ekeruche, Karen; Connelly, Kelly; Kavehpour, H. Pirouz
2016-11-01
Rheology experiments on biological fluids can be difficult when samples are limited in volume, sensitive to degradation, and delicate to extract from tissues. A probe-like geometry has been developed to perform shear creep experiments on biological fluids and to use the creep response to characterize fluid material properties. This probe geometry is a modified concentric cylinder setup, where the gap is large and we assume the inner cylinder rotates in an infinite fluid. To validate this assumption we perform shear creep tests with the designed probe on Newtonian and non-Newtonian fluids and vary the outer cylinder container diameter. We have also created a numerical model based on the probe geometry setup to compare with experimental results at different outer cylinder diameters. A creep test is modeled by applying rotation to the inner cylinder and solving for the deformation of the fluid throughout the gap. Steady state viscosity values are calculated from creep compliance curves and compared between experimental and numerical results.
Extracellular matrix and tissue engineering applications
Fernandes, H.A.M.; Moroni, Lorenzo; van Blitterswijk, Clemens; de Boer, Jan
2009-01-01
The extracellular matrix is a key component during regeneration and maintenance of tissues and organs, and it therefore plays a critical role in successful tissue engineering as well. Tissue engineers should recognise that engineering technology can be deduced from natural repair processes. Due to
A study of complexity of oral mucosa using fractal geometry
Directory of Open Access Journals (Sweden)
S R Shenoi
2017-01-01
Full Text Available Background: The oral mucosa lining the oral cavity is composed of epithelium supported by connective tissue. The shape of the epithelial-connective tissue interface has traditionally been used to describe physiological and pathological changes in the oral mucosa. Aim: The aim is to evaluate the morphometric complexity in normal, dysplastic, well-differentiated, and moderately differentiated squamous cell carcinoma (SCC of the oral mucosa using fractal geometry. Materials and Methods: A total of 80 periodic acid–Schiff stained histological images of four groups: normal mucosa, dysplasia, well-differentiated SCC, and moderately differentiated SCC were verified by the gold standard. These images were then subjected to fractal analysis. Statistical Analysis: ANOVA and post hoc test: Bonferroni was applied. Results: Fractal dimension (FD increases as the complexity increases from normal to dysplasia and then to SCC. Normal buccal mucosa was found to be significantly different from dysplasia and the two grades of SCC (P < 0.05. ANOVA of fractal scores of four morphometrically different groups of buccal mucosa was significantly different with F (3,76 = 23.720 and P< 0.01. However, FD of dysplasia was not significantly different from well-differentiated and moderately differentiated SCC (P = 1.000 and P = 0.382, respectively. Conclusion: This study establishes FD as a newer tool in differentiating normal tissue from dysplastic and neoplastic tissue. Fractal geometry is useful in the study of both physiological and pathological changes in the oral mucosa. A new grading system based on FD may emerge as an adjuvant aid in cancer diagnosis.
Porosity, Mineralization, Tissue Type and Morphology Interactions at the Human Tibial Cortex
Hampson, Naomi A.
Prior research has shown a relationship between tibia robustness (ratio of cross-sectional area to bone length) and stress fracture risk, with less robust bones having a higher risk, which may indicate a compensatory increase in elastic modulus to increase bending strength. Previous studies of human tibiae have shown higher ash content in slender bones. In this study, the relationships between variations in volumetric porosity, ash content, tissue mineral density, secondary bone tissue, and cross sectional geometry, were investigated in order to better understand the tissue level adaptations that may occur in the establishment of cross-sectional properties. In this research, significant differences were found between porosity, ash content, and tissue type around the cortex between robust and slender bones, suggesting that there was a level of co-adaption occurring. Variation in porosity correlated with robustness, and explained large parts of the variation in tissue mineral density. The nonlinear relationship between porosity and ash content may support that slender bones compensate for poor geometry by increasing ash content through reduced remodeling, while robust individuals increase porosity to decrease mass, but only to a point. These results suggest that tissue level organization plays a compensatory role in the establishment of adult bone mass, and may contribute to differences in bone aging between different bone phenotypes. The results suggest that slender individuals have significantly less remodeled bone, however the proportion of remodeled bone was not uniform around the tibia. In the complex results of the study of 38% vs. 66% sites the distal site was subject to higher strains than the 66% site, indicating both local and global regulators may be affecting overall remodeling rates and need to be teased apart in future studies. This research has broad clinical implications on the diagnosis and treatment of fragility fractures. The relationships that
Children's expression through play therapy
Directory of Open Access Journals (Sweden)
Ljubomirović Nataša
2015-01-01
Full Text Available Play as a child's expression, is a skill through which children speaks to adults. Play therapy is a broad field of therapeutic intervention based on the play in order to help the child to cope with problems. Through play, children learn to communicate with others, to express their feelings. Through play they learn and can improve their cognitive, emotional and social capabilities. Play therapy is a nondirective technique focused on the child. It is not focused on the problem, at present even the past, but focused on the expression of the child feelings, accepting the child, rather than correction. The focus has been on the wisdom of a child, not on expertise therapists, guiding the child through play rather than instructing. The aim of play therapy is to encourage healthy growth and development, developing skills in problem solving, reduction of undesirable behavior, confidence building and the development of self-control. This method is effective for a wide range of children's problems, such as the state of stress, anxiety, problem behavior, hyperkinetic syndrome, depression, loss, trauma, the problem of bonding situations parents divorced, somatic disorders, autism spectrum disorders, social problems.
Carlsson-Paige, Nancy; Levin, Diane E.
1988-01-01
In a recent survey of parents and early childhood professionals the prevalence of war play among children and an increase in the amount of violence in children's play was noted. Outlines how the deregulation of children's television during the Reagan administration has affected children's exposure to violence in children's television programming.…
Solitary Play: Some Functional Reconsiderations
Moore, Nancy V.; And Others
1974-01-01
Solitary play in six kindergarten children was observed and coded for frequency and type in order to resolve iscrepancies in a Sex Birth Order interaction. Several facts concerning solitary play as indicative of independence and maturity are noted. (Author/ED)
Playful Interfaces : Introduction and History
Nijholt, Anton; Nijholt, A.
2014-01-01
In this short survey we have some historical notes about human-computer interface development with an emphasis on interface technology that has allowed us to design playful interactions with applications. The applications do not necessarily have to be entertainment applications. We can have playful
Geometry and physics of branes
Energy Technology Data Exchange (ETDEWEB)
Gal' tsov, D V
2003-03-21
The book brings together the contents of lecture courses delivered at the school 'Geometry and Physics of Branes' which took place at the Center 'Alessandro Volta' (Como, Italy) in the spring of 2001. The purpose of the school was to provide an introduction to some lines of research, related to the notion of branes in superstring theory, which are in the focus of attention both in the physical and mathematical communities. The book is structured into three parts: the first contains an elementary introduction to branes, the second is devoted to physical aspects (conformal field theory on open and unoriented surfaces and topics in string tachyon dynamics), and the last contains some more formal mathematical developments. An introduction to branes is given in a remarkably lucid contribution by A Lerda. It opens with a construction of p-brane solutions in classical IIA and IIB supergravities with particular emphasis on the 'fundamental string' solution, the NS5-brane and the D3-brane. Then, the quantum description of D-branes is discussed in terms of boundary states of the closed superstring, which is an alternative to the more common description in terms of open strings with Dirichlet boundary conditions in the transverse to the brane directions. When a constant gauge field is present in the D-brane worldvolume, the boundary states are coherent states of the string oscillators depending on the field strength tensor. The couplings of the brane to the bulk fields - the graviton, the dilaton, and the Kalb-Ramond fields - are then extracted and shown to be precisely the ones that are produced by the Dirac-Born-Infeld action governing the low-energy dynamics of the D-brane derived using the open strings formalism. It is also shown that in the classical limit, the boundary states correctly reproduce the parameters of the corresponding classical solutions. The second part of the book starts with a contribution by Y S Stanev devoted to the two
Hyperunified field theory and gravitational gauge-geometry duality
International Nuclear Information System (INIS)
Wu, Yue-Liang
2018-01-01
A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D h - 1). The dimension D h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)
Hyperunified field theory and gravitational gauge-geometry duality
Energy Technology Data Exchange (ETDEWEB)
Wu, Yue-Liang [International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); Chinese Academy of Sciences, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences (UCAS), Beijing (China)
2018-01-15
A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D{sub h} - 1). The dimension D{sub h} of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)
Steady three-fluid coronal expansion for nonspherical geometries
International Nuclear Information System (INIS)
Joselyn, J.; Holzer, T.E.
1978-01-01
A steady three-fluid model of the solar coronal expansionk in which 4 He ++ ions (alphas) are treated as a nonminor species, is developed for nonspherically symmetric flow geometries of the general sort thought to be characteristic of coronal holes. It is found that the very high mass fluxes in the low corona, which are associated with rapidly diverging flow geometries, lead to a locally enhanced frictional coupling between protons and alphas and consequently to a significant reduction of the He/H abundance ratio in the lower corona from that normally predicted by multifluid models. In the models considered, the frictional drag on the protons by the alphas (a process neglected in most studies) is found to play an important role near the sun. Heavy ions, other than alphas, are treated as minor species and are seen to exhibit varying responses to the rapidly diverging flow geometries, depending on the ion mass and charge. As for the protons, the frictional effect of the alphas on the heavier ions is found to be significant in the models considered
Investigation of Surface Phenomena in Shocked Tin in Converging Geometry
Energy Technology Data Exchange (ETDEWEB)
Rousculp, Christopher L. [Los Alamos National Laboratory; Oro, David Michael [Los Alamos National Laboratory; Griego, Jeffrey Randall [Los Alamos National Laboratory; Turchi, Peter John [Los Alamos National Laboratory; Reinovsky, Robert Emil [Los Alamos National Laboratory; Bradley, Joseph Thomas [Los Alamos National Laboratory; Cheng, Baolian [Los Alamos National Laboratory; Freeman, Matthew Stouten [Los Alamos National Laboratory; Patten, Austin Randall [Los Alamos National Laboratory
2016-03-21
There is great interest in the behavior of the free surface of tin under shock loading. While it is known that meso-scale surface imperfections can seed the Richtmyer- Meshkov Instability (RMI) for a surface that is melted on release, much less is known about a tin surface that is solid, but plastically deforming. Here material properties such as shear and yield strength come into play especially in converging geometry. Previous experiments have been driven by direct contact HE. Usually a thin, flat target coupon is fielded with various single-mode, sinusoidal, machined, profiles on the free surface. The free surface is adjacent to either vacuum or an inert receiver gas. Most of these previous driver/target configurations have been nominal planer geometry. With modern HE it has been straightforward to shock tin into melt on release. However it has been challenging to achieve a low enough pressure for solid state on release. Here we propose to extend the existing base of knowledge to include the behavior of the free surface of tin in cylindrical converging geometry. By shock loading a cylindrical tin shell with a magnetically driven cylindrical liner impactor, the free surface evolution can be diagnosed with proton radiography. With the PHELIX capacitor bank, the drive can easily be varied to span the pressure range to achieve solid, mixed, and liquid states on release. A conceptual cylindrical liner and target is shown in Figure 1.
Hyperunified field theory and gravitational gauge-geometry duality
Wu, Yue-Liang
2018-01-01
A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.
Analysing playing using the note-time playing path.
de Graaff, Deborah L E; Schubert, Emery
2011-03-01
This article introduces a new method of data analysis that represents the playing of written music as a graph. The method, inspired by Miklaszewski, charts low-level note timings from a sound recording of a single-line instrument using high-precision audio-to-MIDI conversion software. Note onset times of pitch sequences are then plotted against the score-predicted timings to produce a Note-Time Playing Path (NTPP). The score-predicted onset time of each sequentially performed note (horizontal axis) unfolds in performed time down the page (vertical axis). NTPPs provide a visualisation that shows (1) tempo variations, (2) repetitive practice behaviours, (3) segmenting of material, (4) precise note time positions, and (5) time spent on playing or not playing. The NTPP can provide significant new insights into behaviour and cognition of music performance and may also be used to complement established traditional approaches such as think-alouds, interviews, and video coding.
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.
A Gyrovector Space Approach to Hyperbolic Geometry
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
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
Information geometry near randomness and near independence
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.
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...
Differential geometry and topology of curves
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.
Digital and discrete geometry theory and algorithms
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
Fractal geometry mathematical foundations and applications
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
Fault geometry and earthquake mechanics
Directory of Open Access Journals (Sweden)
D. J. Andrews
1994-06-01
Full Text Available Earthquake mechanics may be determined by the geometry of a fault system. Slip on a fractal branching fault surface can explain: 1 regeneration of stress irregularities in an earthquake; 2 the concentration of stress drop in an earthquake into asperities; 3 starting and stopping of earthquake slip at fault junctions, and 4 self-similar scaling of earthquakes. Slip at fault junctions provides a natural realization of barrier and asperity models without appealing to variations of fault strength. Fault systems are observed to have a branching fractal structure, and slip may occur at many fault junctions in an earthquake. Consider the mechanics of slip at one fault junction. In order to avoid a stress singularity of order 1/r, an intersection of faults must be a triple junction and the Burgers vectors on the three fault segments at the junction must sum to zero. In other words, to lowest order the deformation consists of rigid block displacement, which ensures that the local stress due to the dislocations is zero. The elastic dislocation solution, however, ignores the fact that the configuration of the blocks changes at the scale of the displacement. A volume change occurs at the junction; either a void opens or intense local deformation is required to avoid material overlap. The volume change is proportional to the product of the slip increment and the total slip since the formation of the junction. Energy absorbed at the junction, equal to confining pressure times the volume change, is not large enongh to prevent slip at a new junction. The ratio of energy absorbed at a new junction to elastic energy released in an earthquake is no larger than P/µ where P is confining pressure and µ is the shear modulus. At a depth of 10 km this dimensionless ratio has th value P/µ= 0.01. As slip accumulates at a fault junction in a number of earthquakes, the fault segments are displaced such that they no longer meet at a single point. For this reason the
Playful biometrics: controversial technology through the lens of play.
Ellerbrok, Ariane
2011-01-01
This article considers the role of play in the context of technological emergence and expansion, particularly as it relates to recently emerging surveillance technologies. As a case study, I consider the trajectory of automated face recognition—a biometric technology of numerous applications, from its more controversial manifestations under the rubric of national security to a clearly emerging orientation toward play. This shift toward “playful” biometrics—or from a technology traditionally coded as “hard” to one now increasingly coded as “soft”—is critical insofar as it renders problematic the traditional modes of critique that have, up until this point, challenged the expansion of biometric systems into increasingly ubiquitous realms of everyday life. In response to this dynamic, I propose theorizing the expansion of face recognition specifically in relation to “play,” a step that allows us to broaden the critical space around newly emerging playful biometrics, as well as playful surveillance more generally. In addition, play may also have relevance for theorizing other forms of controversial technology, particularly given its potential role in processes of obfuscation, normalization, and marginalization.
Geometry optimization of linear and annular plasma synthetic jet actuators
International Nuclear Information System (INIS)
Neretti, G; Seri, P; Taglioli, M; Borghi, C A; Shaw, A; Iza, F
2017-01-01
The electrohydrodynamic (EHD) interaction induced in atmospheric air pressure by a surface dielectric barrier discharge (DBD) actuator has been experimentally investigated. Plasma synthetic jet actuators (PSJAs) are DBD actuators able to induce an air stream perpendicular to the actuator surface. These devices can be used in the field of aerodynamics to prevent or induce flow separation, modify the laminar to turbulent transition inside the boundary layer, and stabilize or mix air flows. They can also be used to enhance indirect plasma treatment effects, increasing the reactive species delivery rate onto surfaces and liquids. This can play a major role in plasma processing and chemical kinetics modelling, where often only diffusive mechanisms are considered. This paper reports on the importance that different electrode geometries can have on the performance of different PSJAs. A series of DBD aerodynamic actuators designed to produce perpendicular jets has been fabricated on two-layer printed circuit boards (PCBs). Both linear and annular geometries were considered, testing different upper electrode distances in the linear case and different diameters in the annular one. An AC voltage supplied at a peak of 11.5 kV and a frequency of 5 kHz was used. Lower electrodes were connected to the ground and buried in epoxy resin to avoid undesired plasma generation on the lower actuator surface. Voltage and current measurements were carried out to evaluate the active power delivered to the discharges. Schlieren imaging allowed the induced jets to be visualized and gave an estimate of their evolution and geometry. Pitot tube measurements were performed to obtain the velocity profiles of the PSJAs and to estimate the mechanical power delivered to the fluid. The optimal values of the inter-electrode distance and diameter were found in order to maximize jet velocity, mechanical power or efficiency. Annular geometries were found to achieve the best performance. (paper)
Playful mediation and virtual sociality
Directory of Open Access Journals (Sweden)
Sihem NAJJAR
2010-01-01
Full Text Available As a space of sociability, virtual games, especially online role playing games, allow us to capture the interest of the playfulness in social life, but they are means by which users are able to experiment their relationship to others. The virtual games as a mediation device, constitute a "pretext" to forge friendships, develop love relationships, improve language skills, discover other cultures, etc. Based on a sociological survey of Tunisian Internet users (both sexes fans of virtual games we try to show how playful mediation is producing a multifaceted virtual sociality inherent in our contemporary societies.
Polynomials in finite geometries and combinatorics
Blokhuis, A.; Walker, K.
1993-01-01
It is illustrated how elementary properties of polynomials can be used to attack extremal problems in finite and euclidean geometry, and in combinatorics. Also a new result, related to the problem of neighbourly cylinders is presented.
Algebra, Geometry and Mathematical Physics Conference
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...
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
Geometry, structure and randomness in combinatorics
Nešetřil, Jaroslav; Pellegrini, Marco
2014-01-01
This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.
The elements of non-Euclidean geometry
Sommerville, D MY
2012-01-01
Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.
The local index formula in noncommutative geometry
International Nuclear Information System (INIS)
Higson, N.
2003-01-01
These notes present a partial account of the local index theorem in non-commutative geometry discovered by Alain Connes and Henri Moscovici. It includes Elliptic partial differential operators, cyclic homology theory, Chern characters, homotopy invariants and the index formulas
Quantum geometry of bosonic strings - revisited
International Nuclear Information System (INIS)
Botelho, Luiz C.L.; Botelho, Raimundo C.L.; Universidade Federal Rural do Rio de Janeiro, RJ
1999-07-01
We review the original paper by A.M. Polyakov (Quantum Geometry of Bosonic Strings) with corrections and improvements the concepts exposed there and following as closely as possible to the original A.M. Polyakov's paper. (author)
Energy Technology Data Exchange (ETDEWEB)
Bejarano, Cecilia; Guzman, Maria Jose [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Ferraro, Rafael [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)
2015-02-01
Null tetrads are shown to be a valuable tool in teleparallel theories of modified gravity. We use them to prove that Kerr geometry remains a solution for a wide family of f(T) theories of gravity. (orig.)