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On rank 2 and rank 3 residually connected geometries for

This implies that G is also transitive on the set of all elements of any chosen type i. If we consider a chamber c 1 ,c 2We now use the above observation to define an incidence structure from a group G together with a set of subgroups G 1 ,G 2By definition the elements of type i are the right cosets of the subgroup G i.

Two cosets are incident if and only if their intersection is not empty. This is an incidence structure which is not necessarily a geometry see Chapter 3 for definitions.

In order to check whether a coset incidence structure is indeed a geometry you can use the command IsFlagTransitiveGeometry which in case it returns true guarantees that the argument is a geometry. This category is a subcategory of IsIncidenceGeometryand contains all coset geometries. Returns: the coset incidence structure defined by the list l of subgroups of the group G. G must be a group and l is a list of subgroups of G. The subgroups in l will be the parabolic subgroups of the coset incidence structure whose rank equals the length of l.

Returns: true if and only if ele1 and ele2 are incident. The Borel subgroup is equal to the stabilizer of a chamber. It corresponds to the intersection of all parabolic subgroups.

Returns: true if and only if the group G defining cg acts flag-transitively. This test can be quite time consuming. You can bind the attribute IsFlagTransitiveGeometry if you are sure the coset geometry is indeed flag-transitive. Returns: the image of the CosetGeometryElement ele under the action of g. The group element g must belong to AmbientGroup AmbientGeometry ele.

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This is an operation which returns the image of elean element of a coset incidence structure, under gan element of AmbientGroup AmbientGeometry ele. This is an operation which returns the image of flga flag of a coset incidence structure, under gan element of AmbientGroup AmbientGeometry flg.First published Preface page i x. Abstract representations p. Permutation representations Includes bibliographical references and indexes.

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Graphs ISBN 4. Geometries and complexes 1. Sporadic groups Mathematics I. The general linear group and its projective geometry QA A83 6. Fiber products of groups l. Involutions 8. Extraspecial groups ISBN hardback 3. Algebras, Codes, and Forms 9. Forms and algebras Codes Derived forms. Syrnplectic 2-Loops 46 Symplectic 2-loops 47 Moufang symplectic Zloops 54 Constructing a 2-local from a loop T h e Discovery, Existence, a n d Uniqueness of the Sporadics 65 History and discovery 65 Existence of the sporadics 70 Uniqueness of the sporadics Steiner systems for the Mathieu groups The Geometry and Structure of MZ4 The Group U4 3 The geometry of M24 U4 3 This implies that G is also transitive on the set of all elements of any chosen type i.

If we consider a chamber c 1 ,c 2We now use the above observation to define an incidence structure from a group G together with a set of subgroups G 1 ,G 2By definition the elements of type i are the right cosets of the subgroup G i.

Two cosets are incident if and only if their intersection is not empty. This is an incidence structure which is not necessarily a geometry see Chapter 4 for definitions.

on rank 2 and rank 3 residually connected geometries for <img alt

Returns: the coset incidence structure defined by the list l of subgroups of the group G. G must be a group and l is a list of subgroups of G. The subgroups in l will be the parabolic subgroups of the coset incidence structure whose rank equals the length of l.

Returns: true if ans only if ele1 and ele2 are incident. The Borel subgroup is equal to the stabilizer of a chamber. It corresponds to the intersection of all parabolic subgroups. Returns: true if and only if the group G defining cg acts flag-transitively.

This test is quite time consuming. You can bind the attribute IsFlagTransitiveGeometry if you are sure the coset geometry is indeed flag-transitive. An incidence geometry is said to be firm if every nonmaximal flag is contained in at least two chambers.

An incidence geometry is said to be tick if every nonmaximal flag is contained in at least three chambers. An incidence geometry is said to be thin if every rank one residue contains exactly 2 elements.

This means that every comaximal flag is contained in exactly 2 chambers.

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A geometry is connected if and only if its incidence graph is connected. A geometry is residually connected if the incidence graphs of all its residues of rank at least 2 are connected. You can bind the attribute IsResiduallyConnected if you are sure the coset geometry is indeed residually connected. The standard chamber just consists of all parabolic subgroups i. The object returned is a FlagOfIncidenceStructure. Returns: element of the defining group of cg which maps fl to the standard chamber of cg.This invention relates to image processing, and, more particularly, to image processing systems and methods wherein information corresponding to a given region or geometric system is systematically recorded and stored in a data bank and then partially retrieved and processed for reproducing images corresponding to selected portions of the geometric system.

Image processing systems have been proposed for permitting controllable display of images corresponding to portions of a quantity of pre-recorded visual or geometric information. In such processing systems it has been proposed to provide reproduction of visual images corresponding to portions of a geographical area, building interior, or the like, but no system has been devised in which images are reproduced in simulated real time with acceptable levels of realism.

A primary application of the present invention is as a visual display for flight simulators employed in pilot training, and the exemplary embodiment disclosed relates to such an application. It will be understood, however, that the system is also useful for various other applications such as the visual simulation of building interiors, city streets, factory interiors, and for various industrial applications such as computer aided design of geometric structures.

Flight simulator systems employed for pilot training have in the past employed visual displays of only limited capacity. Such systems have been incapable of reproducing wide angle views corresponding to a multiplicity of simulated flight positions within a geographical area. A flight simulator capable of reproducing realistic visual images corresponding to all possible scenes which could be viewed from an aircraft flying through a given geographical area must be capable of displaying scenes which would be viewed from the craft along a substantial variety of flight paths and conditions, e.

If the images are to be displayed in simulated "real time" corresponding to an inputed flight path selected by the pilot trainee, it will be apparent to those versed in the art that rapid processing of large amounts of data will be required.

Largely because of these factors, the image processing systems which have been proposed in the past have not been capable of processing the large amounts of data entailed, with sufficient speed. Whereas multiple photographs of high resolution taken at various positions within a geographical area, as from an aircraft traveling along a known pattern of flight paths, may include large amounts of visual information about the area, mere sequential retrieval of such unprocessed photographs does not accurately simulate a flight path selected by the simulator operator unless the selected flight path happens, by an improbable coincidence, to correspond exactly with the flight path of the aircraft from which the pictures were taken.

It is, accordingly, a major object of the present invention to provide an image processing system in which a data bank of high resolution images corresponding to known orientations within a given geometric system is processed to permit retrieval of portions of the images appropriate for simulating a portion of the goemetric system.

A further object is to provide such a system in which retrieval of the images is effected sequentially in response to inputs for simulating movement through the geometric system. A still further object is to provide such a system in which the high resolution images are derived from optically recorded images of a geometrical area and in which the retrieval and display of the images corresponds to simulated movement through the area, in response to commands from an operator, and in which a real-time visual display is provided for simulating movement along the path input by the operator.

A still further objective is to provide a visual flight simulation system having such a controlled data base and operable for reproducing high definition, real- time images of multiple, adjacent views of a given scene along different vectors from a simulated cockpit.

Yet another object is to provide such a system operable to process optically reproduced images derived from multiple views taken along multiple axes of a geometric system, and to integrate the multiple images into a single overall scene representative of a wide angle, hemispherical view of the overall scene.

A still further object is to provide a display processing unit capable of selecting, processing, and displaying appropriate portions of a hemispherical image as required to simulate a view of a portion of the overall scene at and along a particular axis. For clarity of description, a preliminary summary of the major features of the recording and display portions of a preferred embodiment of the system is now provided, after which individual portions of the system will be described in detail.

The disclosed embodiment of the system as an aircraft flight simulator may be termed an "out-the-window" real world visual scene display system, and preferably employs multiple video discs for storing in NTSC TV format the visual information derived from aerial photographs of a "gaming area," i. The use of video discs, or other high capacity storage media, as direct rapid access bulk storage devices is an immportant factor in the system, which employs a series of discrete aerial photographs of the gaming area terrain as an initial data source.

Each picture is electronically scanned and converted to time-base video data, which is processed into a digital television signal, and recorded and stored on video discs.

When needed for display, the data are retrieved, electronically processed and manipulated to display the correct perspective view of terrain relative to the position and attitude of the simulated aircraft.

The data base for the multichannel out-the-cockpit display is thus initially recorded on color film. The technical requirements for deriving real time visual images with multiple fields of view from a data bank comprising multiple images or scenes are substantial, as has been briefly discussed above. To permit real-time processing of visual information, it is advantageous to store the information electronically in multiple storage media, e.

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Source data derived from high resolution photographs is preferred for realism, but the need for processing of the information necessitates its conversion into electrically encoded form.

Technical difficulties are manifold because of the requirement for rapid recall of information in usable form to permit a nominal thirty frames per second reproduction of images for simulating moving scenes corresponding in real time to the path elected by the operator and, at the same time, providing the requisite massive storage of information contained in photographic images of the size and resolution required for scene realism. These techniques entail the selective retrieving, processing, and coherent display of visual images in color, suitably on multiple displays positioned adjacent the operator's seat or "cockpit," as shown in FIG.

Such information includes the "real-time" simulated location of the simulated aircraft or vehicle, its velocity, azimuth, and attitude. The transition from information derived from one photograph, appropriate for a given set of inputs, to that appropriate for the next time sequence is also entailed. The display system includes a plurality of video displays e.

As seen in FIG. As an overview of the visual on-line playback system, and with reference to FIG. The discs contain the entire photograhic data base, i. The video storage system 10 includes control interfacing with the control computer 19 for feeding desired portions of the information to the remainder of the system.

As suggested above, massive amount of information is thus stored on the multiple video discs in standard NTSC television format, and it is not readily processed by electronic circuitry. Such processing is required, as will be understood from the description below, when coordinating the multiple inputs, derived originally from the pilots' controls, to the programmed and displayed images. As will also be understood from the description below, an important aspect of the present invention is its capability of selecting appropriate portions of the stored visual information for rapid processing to provide real-time playback, thus making compatible the requirements for both storage of required amounts of visual information corresponding to the geographical "gaming area," and at the same time, selective rapid processing of portions of the information as required for simulated real-time display.

Under control of a general purpose computer 19, suitably a Harris model series, information from up to three of the video disc playback units, which information corresponds to the photograhic images, is simultaneously selected for retrieval.Fernandes and A.

Ivic-Weiss, Highly symmetric hypertopesAequationes Math. Back to top 1. Connor, Algorithmic enumeration of regular maps. Ars Math. Cameron, M. Fernandes and M. Mixer, String C-groups as transitive subgroups of Sym nJ. Algebra Buekenhout and J. Rodrigues, Linear codes with complementary duals from some strongly regular subgraphs of the McLaughlin graphMath. Algebraic Combin. Connor and J. Connor, An Atlas of subgroup lattices of finite almost simple groups.

Publications

Connor and S. Elliott and E. O'Reilly-Regueiro, Chiral polyhedra and projective linesInt. Connor, C-groups of Suzuki type. Connor and M. Mixer, Abstract regular polytopes for the O'Nan group. International Journal of Algebra and Computation 24nr.

on rank 2 and rank 3 residually connected geometries for <img alt

Hubard, Chiral polytopes and Suzuki simple groupsIn Eds. Connelly, W.Thanks for helping us catch any problems with articles on DeepDyve. We'll do our best to fix them. Check all that apply - Please note that only the first page is available if you have not selected a reading option after clicking "Read Article".

Include any more information that will help us locate the issue and fix it faster for you. We generalize the theory of sheaves to chamber systems. We also prove that, under suitable hypotheses, a sheaf defined over a truncation of can be extended to a sheaf for. In the last section of this paper, we apply these results to a number of special cases. We might wonder if such an extension S really exists forbeing willing to be satisfied with something less than a geometry, namely a chamber system from which the chamber system of can be obtained as a truncation.

More formally, a D-extension of is a pairwhere. Advances in Geometry — de Gruyter. Enjoy affordable access to over 18 million articles from more than 15, peer-reviewed journals. Get unlimited, online access to over 18 million full-text articles from more than 15, scientific journals. See the journals in your area. Continue with Facebook. Sign up with Google. Bookmark this article. You can see your Bookmarks on your DeepDyve Library. Sign Up Log In. Copy and paste the desired citation format or use the link below to download a file formatted for EndNote.

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You can change your cookie settings through your browser. Open Advanced Search. DeepDyve requires Javascript to function. Please enable Javascript on your browser to continue. Extending locally truncated chamber Systems by sheaves Extending locally truncated chamber Systems by sheaves Pasini, Antonio Abstract.

Extending locally truncated chamber Systems by sheaves Pasini, Antonio. Read Article. Download PDF. Share Full Text for Free beta.By clicking on the titles of the papers, you can get an abstract of them. Should you want a copy of any of these, please feel free to contact me.

Click here to have this list by year of publication. Books 1. Buekenhout and M. Belgique, Mem. Residually weakly primitive and locally two-transitive geometries for sporadic groups.

on rank 2 and rank 3 residually connected geometries for <img alt

Chapters in books 3. Incidence Geometry. Bosma and J. Cannon, Handbook of Magma FunctionsVersion 2. Vchapter 82, pp Buekenhout, P. Cara and M. Dehon, Residually weakly primitive geometries of small sporadic and almost simple groups : a synthesis. Hubard, Chiral polytopes and Suzuki simple groupsIn Eds.

Connelly, W. Whitely, A. Fernandes and A. Weiss, Hexagonal extensions of toroidal maps and hypermapsM. Conder et al.

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Papers in international journals 7. Symbolic Comput. Two Nearly Isomorphic Groups. Atti Sem. Modena XLV Beitrage Algebra Geom. Thin geometries for the Suzuki simple group Sz 8.

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Theory Ser. A 85nr.

Publications by year

An Atlas of regular thin geometries for small groups. The rank 3 geometries of the simple Suzuki groups Sz q.

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Note Mat. The Residually weakly primitive geometries of the Dihedral Groups. The Residually Weakly Primitive pre-geometries of the Suzuki simple groups. Percsy, New geometries for finite groups and polytopes.


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