Relevant bibliographies by topics / Arithmetic geometry

Academic literature on the topic 'Arithmetic geometry'

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Published: 4 June 2021
Last updated: 21 February 2023

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Journal articles on the topic "Arithmetic geometry"

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Faltings, Gerd, and Johan de Jong. "Arithmetic Geometry." Oberwolfach Reports 9, no. 3 (2012): 2335–88. http://dx.doi.org/10.4171/owr/2012/38.

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Faltings, Gerd, Johan de Jong, and Peter Scholze. "Arithmetic Geometry." Oberwolfach Reports 13, no. 3 (2016): 2171–224. http://dx.doi.org/10.4171/owr/2016/38.

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Faltings, Gerd, Johan de Jong, and Peter Scholze. "Arithmetic Geometry." Oberwolfach Reports 17, no. 2 (July 1, 2021): 1023–82. http://dx.doi.org/10.4171/owr/2020/20.

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Brown, M. L. "ARITHMETIC GEOMETRY." Bulletin of the London Mathematical Society 19, no. 6 (November 1987): 628–31. http://dx.doi.org/10.1112/blms/19.6.628.

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Rojas, J. Maurice. "Computational Arithmetic Geometry." Journal of Computer and System Sciences 62, no. 2 (March 2001): 216–35. http://dx.doi.org/10.1006/jcss.2000.1728.

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Schwarz, A., and I. Shapiro. "Supergeometry and arithmetic geometry." Nuclear Physics B 756, no. 3 (November 2006): 207–18. http://dx.doi.org/10.1016/j.nuclphysb.2006.08.024.

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Zuo, Kang. "Stability, geometry and arithmetic." Notices of the International Congress of Chinese Mathematicians 7, no. 1 (2019): 100. http://dx.doi.org/10.4310/iccm.2019.v7.n1.a34.

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Jannsen, Uwe. "Weights in arithmetic geometry." Japanese Journal of Mathematics 5, no. 1 (April 2010): 73–102. http://dx.doi.org/10.1007/s11537-010-0947-4.

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Baldwin, John T., and Andreas Mueller. "Autonomy of Geometry." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 11 (February 5, 2020): 5–24. http://dx.doi.org/10.24917/20809751.11.1.

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In this paper we present three aspects of the autonomy of geometry. (1) An argument for the geometric as opposed to the ‘geometric algebraic’ interpretation of Euclid’s Books I and II; (2) Hilbert’s successful project to axiomatize Euclid’s geometry in a first order geometric language, notably eliminating the dependence on the Archimedean axiom; (3) the independent conception of multiplication from a geometric as opposed to an arithmetic viewpoint.
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Scholl, A. J. "CONJECTURES IN ARITHMETIC ALGEBRAIC GEOMETRY." Bulletin of the London Mathematical Society 26, no. 1 (January 1994): 108–11. http://dx.doi.org/10.1112/blms/26.1.108.

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Dissertations / Theses on the topic "Arithmetic geometry"

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Aghasi, Mansour. "Geometry of arithmetic surfaces." Thesis, Durham University, 1996. http://etheses.dur.ac.uk/5270/.

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In this thesis my emphasis is on the resolution of the singularities of fibre products of Arithmetic Surfaces. In chapter one as an introduction to my thesis some elementary concepts related to regular and singular points are reviewed and the concept of tangent cone is defined for schemes over a discrete valuation ring. The concept of arithmetic surfaces is introduced briefly in the end of this chapter. In chapter 2 my new procedures namely the procedure of Mojgan(_1) and the procedure of Mahtab(_2) and a new operator called Moje are introduced. Also the concept of tangent space is defined for schemes over a discrete valuation ring. In chapter 3 the singularities of schemes which are the fibre products of some surfaces with ordinary double points are resolved. It is done in two different methods. The results from both methods are consistent. In chapter 4, I have tried to resolve the singularities of a special class of arithmetic three-folds, namely those which are the fibre product of two arithmetic surfaces, which were very helpful to achieve my final results about the resolution of singularities of fibre products of the minimal regular models of Tate. Chapter 5 includes my final results which are about the resolution of singularities of the fibre product of two minimal regular models of Tate.
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Selander, Björn. "Arithmetic of three-point covers." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7497.

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Any cover of the Riemann sphere with rational branch points is known to be defined over the algebraic numbers. Hence the Galois group of the rationals acts on the category of such branched covers. Particulars about this action are still scarce, even in the simplest non-abelian case, the case with just three branch points. The first paper in this thesis describes a new algorithm, which uses modular form techniques in order to compute the equations for a cover of the Riemann sphere which is hyperelliptic as a curve. Given such equations one may easily determine the Galois orbit to which the cover belongs. We compute and discuss all covers of degree 6 and genus 2, and complete the case of covers of degree 7 and genus 1 as well. The second paper gives a proof of a formula for the number of three-point G-covers with a fixed special G-deformation datum (here G is a finite group which is strictly divisible by a prime number p). Since such a datum is an invariant for the action of the inertia group at p, this gives partial information about the action of this inertia group.
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Morrow, Matthew Thomas. "Investigations in two-dimensional arithmetic geometry." Thesis, University of Nottingham, 2009. http://eprints.nottingham.ac.uk/11016/.

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This thesis explores a variety of topics in two-dimensional arithmetic geometry, including the further development of I. Fesenko's adelic analysis and its relations with ramification theory, model-theoretic integration on valued fields, and Grothendieck duality on arithmetic surfaces. I. Fesenko's theories of integration and harmonic analysis for higher dimensional local fields are extended to an arbitrary valuation field F whose residue field is a local field; applications to local zeta integrals are considered. The integral is extended to F^n, where a linear change of variables formula is proved, yielding a translation-invariant integral on GL_n(F). Non-linear changes of variables and Fubini's theorem are then examined. An interesting example is presented in which imperfectness of a positive characteristic local field causes Fubini's theorem to unexpectedly fail. It is explained how the motivic integration theory of E. Hrushovski and D. Kazhdan can be modified to provide a model-theoretic approach to integration on two-dimensional local fields. The possible unification of this work with A. Abbes and T. Saito's ramification theory is explored. Relationships between Fubini's theorem, ramification theory, and Riemann-Hurwitz formulae are established in the setting of curves and surfaces over an algebraically closed field. A theory of residues for arithmetic surfaces is developed, and the reciprocity law around a point is established. The residue maps are used to explicitly construct the dualising sheaf of the surface.
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Martinez, Metzmeier César. "Two problems in arithmetic geometry. Explicit Manin-Mumford, and arithmetic Bernstein-Kusnirenko." Thesis, Normandie, 2017. http://www.theses.fr/2017NORMC224/document.

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Dans la première partie de cette thèse, on présente des bornes supérieures fines pour le nombre de sous-variétés irréductibles de torsion maximales dans une sous-variété du tore complexe algébrique $(\mathbb{C}^{\times})^n$ et d'une variété abélienne. Dans les deux cas, on donne une borne explicite en termes du degré des polynômes définissants et la variété ambiante. De plus, la dépendance en le degré des polynômes est optimale. Dans le cas du tore complexe, on donne aussi une borne explicite en termes du degré torique de la sous-variété. En conséquence de ce dernier résultat, on démontre les conjectures de Ruppert, et Aliev et Smyth pour le nombre de points de torsion isolés dans une hypersurface. Ces conjectures bornent ce nombre en terme, respectivement, du multi-degré et du volume du polytope de Newton d'un polynôme définissant l'hypersurface.Dans la deuxième partie de cette thèse, on présente une borne supérieure pour la hauteur des zéros isolés, dans le tore, d'un système de polynômes de Laurent sur un corps adélique qui satisfait la formule du produit. Cette borne s'exprime en termes des intégrales mixtes des fonctions toit locales associées à la hauteur choisie et le système des polynômes de Laurent. On montre aussi que cette borne est presque optimale dans quelques familles d'exemples. Ce résultat est un analogue arithmétique du théorème de Bern\v{s}tein-Ku\v{s}nirenko
In the first part of this thesis we present sharp bounds on the number of maximal torsion cosets in a subvariety of a complex algebraic torus $(\mathbb{C}^{\times})^n$ and of an Abelian variety. In both cases, we give an explicit bound in terms of the degree of the defining polynomials and the ambient variety. Moreover, the dependence on the degree of the polynomials is sharp. In the case of the complex torus, we also give an effective bound in terms of the toric degree of the subvariety. As a consequence of the latter result, we prove the conjectures of Ruppert, and Aliev and Smyth on the number of isolated torsion points of a hypersurface. These conjectures bound this number in terms of the multidegree and the volume of the Newton polytope of a polynomial defining the hypersurface, respectively.In the second part of the thesis, we present an upper bound for the height of isolated zeros, in the torus, of a system of Laurent polynomials over an adelic field satisfying the product formula. This upper bound is expressed in terms of the mixed integrals of the local roof functions associated to the chosen height function and to the system of Laurent polynomials. We also show that this bound is close to optimal in some families of examples. This result is an arithmetic analogue of the classical Bern\v{s}tein-Ku\v{s}nirenko theorem
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Paajanen, Pirita Maria. "Zeta functions of groups and arithmetic geometry." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.419325.

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Ji, Shujuan Ramakrishnan Dinakar Ramakrishnan Dinakar. "Arithmetic and geometry on triangular Shimura curves /." Diss., Pasadena, Calif. : California Institute of Technology, 1995. http://resolver.caltech.edu/CaltechETD:etd-10052007-134336.

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Kaba, Mustafa Devrim. "On The Arithmetic Of Fibered Surfaces." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613674/index.pdf.

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In the first three chapters of this thesis we study two conjectures relating arithmetic with geometry, namely Tate and Lang&rsquo
s conjectures, for a certain class of algebraic surfaces. The surfaces we are interested in are assumed to be defined over a number field, have irregularity two and admit a genus two fibration over an elliptic curve. In the final chapter of the thesis we prove the isomorphism of the Picard motives of an arbitrary variety and its Albanese variety.
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Camara, Alberto. "Interaction of topology and algebra in arithmetic geometry." Thesis, University of Nottingham, 2013. http://eprints.nottingham.ac.uk/13247/.

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This thesis studies topological and algebraic aspects of higher dimensional local fields and relations to other neighbouring research areas such as nonarchimedean functional analysis and higher dimensional arithmetic geometry. We establish how a higher local field can be described as a locally convex space once an embedding of a local field into it has been fixed. We study the resulting spaces from a functional analytic point of view: in particular we introduce and study bounded, c-compact and compactoid submodules of characteristic zero higher local fields. We show how these spaces are isomorphic to their appropriately topologized duals and study the implications of this fact in terms of polarity. We develop a sequential-topological study of rational points of schemes of finite type over local rings typical in higher dimensional number theory and algebraic geometry. These rings are certain types of multidimensional complete fields and their rings of integers and include higher local fields. Our results extend the constructions of Weil over (one-dimensional) local fields. We establish the existence of an appropriate topology on the set of rational points of schemes of finite type over the rings considered, study the functoriality of this construction and deduce several properties.
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Yang, Wenzhe. "The arithmetic geometry of mirror symmetry and the conifold transition." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:e55a7b22-a268-4c57-9d98-c0547ecdcef9.

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The central theme of this thesis is the application of mirror symmetry to the study of the arithmetic geometry of Calabi-Yau threefolds. It formulates a conjecture about the properties of the limit mixed Hodge structure at the large complex structure limit of an arbitrary mirror threefold, which is supported by a two-parameter example of a self-mirror Calabi-Yau threefold. It further studies the connections between this conjecture with Voevodsky's mixed motives. This thesis also studies the connections between the conifold transition and Beilinson's conjecture on the values of the L-functions at integral points. It carefully studies the arithmetic geometry of the conifold in the mirror family of the quintic Calabi-Yau threefold and its L-function, which is shown to provide a very interesting example to Beilinson's conjecture.
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Lee, Chih-kuo. "Robust evaluation of differential geometry properties using interval arithmetic techniques." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33565.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 2005.
Includes bibliographical references (p. 79-82).
This thesis presents a robust method for evaluating differential geometry properties of sculptured surfaces by using a validated ordinary differential equation (ODE) system solver based on interval arithmetic. Iso-contouring of curvature of a Bezier surface patch. computation of curvature lines of a Bezier surface patch and computation of geodesics of a Bezier surface patch are computed by the Validated Numerical Ordinary Differential Equations (VNODE) solver which employs rounded interval arithmetic methods. Then. the results generated from the VNODE program are compared with the results from Praxiteles code which uses non-validated ODE solvers operating in double precision floating point arithmetic for the solution of the same problems. From the results of these experiments, we find that the VNODE program performs these computations reliably, but at increased computational cost.
by Chih-kuo Lee.
S.M.
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Books on the topic "Arithmetic geometry"

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Childress, Nancy, and John W. Jones, eds. Arithmetic Geometry. Providence, Rhode Island: American Mathematical Society, 1994. http://dx.doi.org/10.1090/conm/174.

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Colliot-Thélène, Jean-Louis, Peter Swinnerton-Dyer, and Paul Vojta. Arithmetic Geometry. Edited by Pietro Corvaja and Carlo Gasbarri. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15945-9.

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Cornell, Gary, and Joseph H. Silverman, eds. Arithmetic Geometry. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4613-8655-1.

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Gary, Cornell, Silverman Joseph H. 1955-, and Artin Michael, eds. Arithmetic geometry. New York: Springer-Verlag, 1986.

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1965-, Darmon Henri, ed. Arithmetic geometry. Providence, RI: American Mathematical Society, 2009.

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Colliot-Thélène, J. L. Arithmetic algebraic geometry. Edited by Kato K, Vojta Paul 1957-, Ballico E. 1955-, and Centro internazionale matematico estivo. Berlin: Springer-Verlag, 1993.

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Faber, Carel, Gavril Farkas, and Robin de Jong, eds. Geometry and Arithmetic. Zuerich, Switzerland: European Mathematical Society Publishing House, 2012. http://dx.doi.org/10.4171/119.

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van der Geer, G., F. Oort, and J. Steenbrink, eds. Arithmetic Algebraic Geometry. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0457-2.

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Colliot-Thélène, Jean-Louis, Kazuya Kato, and Paul Vojta. Arithmetic Algebraic Geometry. Edited by Edoardo Ballico. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0084727.

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Dieulefait, Luis V., Gerd Faltings, D. R. Heath-Brown, Yu V. Manin, Boris Z. Moroz, and Jean-Pierre Wintenberger, eds. Arithmetic and Geometry. Cambridge: Cambridge University Press, 2015. http://dx.doi.org/10.1017/cbo9781316106877.

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Book chapters on the topic "Arithmetic geometry"

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Stillwell, John. "Arithmetic." In Numbers and Geometry, 1–35. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0687-3_1.

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Faltings, Gerd. "Some Historical Notes." In Arithmetic Geometry, 1–8. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4613-8655-1_1.

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Silverman, Joseph H. "Heights and Elliptic Curves." In Arithmetic Geometry, 253–65. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4613-8655-1_10.

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Artin, M. "Lipman’s Proof of Resolution of Singularities for Surfaces." In Arithmetic Geometry, 267–87. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4613-8655-1_11.

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Chinburg, T. "An Introduction to Arakelov Intersection Theory." In Arithmetic Geometry, 289–307. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4613-8655-1_12.

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Chinburg, T. "Minimal Models for Curves over Dedekind Rings." In Arithmetic Geometry, 309–26. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4613-8655-1_13.

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Gross, Benedict H. "Local Heights on Curves." In Arithmetic Geometry, 327–39. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4613-8655-1_14.

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Vojta, Paul. "A Higher Dimensional Mordell Conjecture." In Arithmetic Geometry, 341–53. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4613-8655-1_15.

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Cornell, Gary, and Joseph H. Silverman. "Erratum to: Erratum." In Arithmetic Geometry, 354. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4613-8655-1_16.

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Faltings, Gerd. "Finiteness Theorems for Abelian Varieties over Number Fields." In Arithmetic Geometry, 9–26. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4613-8655-1_2.

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Conference papers on the topic "Arithmetic geometry"

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Marcolli, Matilde. "Noncommutative Geometry and Arithmetic." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0135.

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Vazquez-Castro, M. A. "Arithmetic geometry of compute and forward." In 2014 IEEE Information Theory Workshop (ITW). IEEE, 2014. http://dx.doi.org/10.1109/itw.2014.6970805.

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Fortune, Steven, and Christopher J. Van Wyk. "Efficient exact arithmetic for computational geometry." In the ninth annual symposium. New York, New York, USA: ACM Press, 1993. http://dx.doi.org/10.1145/160985.161015.

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Brönnimann, Hervé, Christoph Burnikel, and Sylvain Pion. "Interval arithmetic yields efficient dynamic filters for computational geometry." In the fourteenth annual symposium. New York, New York, USA: ACM Press, 1998. http://dx.doi.org/10.1145/276884.276903.

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Duff, Tom. "Interval arithmetic recursive subdivision for implicit functions and constructive solid geometry." In the 19th annual conference. New York, New York, USA: ACM Press, 1992. http://dx.doi.org/10.1145/133994.134027.

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Kalla, Priyank. "Formal verification of arithmetic datapaths using algebraic geometry and symbolic computation." In 2015 Formal Methods in Computer-Aided Design (FMCAD). IEEE, 2015. http://dx.doi.org/10.1109/fmcad.2015.7542240.

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Sun, Xiaojun, Priyank Kalla, Tim Pruss, and Florian Enescu. "Formal Verification of Sequential Galois Field Arithmetic Circuits Using Algebraic Geometry." In Design, Automation and Test in Europe. New Jersey: IEEE Conference Publications, 2015. http://dx.doi.org/10.7873/date.2015.0158.

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Li, Y., D. H. Kim, A. Kostrzewski, and George Eichmann. "Optoelectronic content addressable memory-based modified signed digit arithmetic." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.tumm3.

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The modified signed digit (MSD) number system offers inherent low interdigit dependence for arithmetic processing. Recently, using both optical logic and memory based approaches, various optical MSD arithmetic schemes were proposed. For the logic based optical MSD arithmetic, an existing approach implements a three-stage processing algorithm with either a symbolic substitution processor or some binary logic elements, such as bistable etalons. Because of the use of multiple processing stages, the required computing energy and its speed is sacrificed. The optical memory based approach, on the other hand, utilizes a single-stage content addressable memory (CAM) for a fast MSD arithmetic. However, the existing holographic CAM is difficult to implement. In this talk, a new nonholographic CAM scheme for a single-stage MSD addition processing is proposed and demonstrated. A position encoded 18 × 56 pixel CAM mask is used in an angularly multiplexed geometry for a parallel CAM matching operation. Electronic logic inverters are used as the output devices.
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Yu, Xinguo, Wenbin Gan, and Mingshu Wang. "Understanding explicit arithmetic word problems and explicit plane geometry problems using syntax-semantics models." In 2017 International Conference on Asian Language Processing (IALP). IEEE, 2017. http://dx.doi.org/10.1109/ialp.2017.8300590.

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Milenkovic, V. "Double precision geometry: a general technique for calculating line and segment intersections using rounded arithmetic." In 30th Annual Symposium on Foundations of Computer Science. IEEE, 1989. http://dx.doi.org/10.1109/sfcs.1989.63525.

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Reports on the topic "Arithmetic geometry"

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Schattschneider, Doris. Proof without Words: The Arithmetic Mean-Geometric Mean Inequality. Washington, DC: The MAA Mathematical Sciences Digital Library, February 2010. http://dx.doi.org/10.4169/capsules003370.

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Schattschneider, Doris. Proof without Words: The Arithmetic Mean-Geometric Mean Inequality. Washington, DC: The MAA Mathematical Sciences Digital Library, February 2010. http://dx.doi.org/10.4169/capsules003372.

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Saltus, Christina, Todd Swannack, and S. McKay. Geospatial Suitability Indices Toolbox (GSI Toolbox). Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/41881.

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Habitat suitability models are widely adopted in ecosystem management and restoration, where these index models are used to assess environmental impacts and benefits based on the quantity and quality of a given habitat. Many spatially distributed ecological processes require application of suitability models within a geographic information system (GIS). Here, we present a geospatial toolbox for assessing habitat suitability. The Geospatial Suitability Indices (GSI) toolbox was developed in ArcGIS Pro 2.7 using the Python® 3.7 programming language and is available for use on the local desktop in the Windows 10 environment. Two main tools comprise the GSI toolbox. First, the Suitability Index Calculator tool uses thematic or continuous geospatial raster layers to calculate parameter suitability indices based on user-specified habitat relationships. Second, the Overall Suitability Index Calculator combines multiple parameter suitability indices into one overarching index using one or more options, including: arithmetic mean, weighted arithmetic mean, geometric mean, and minimum limiting factor. The resultant output is a raster layer representing habitat suitability values from 0.0 to 1.0, where zero is unsuitable habitat and one is ideal suitability. This report documents the model purpose and development as well as provides a user’s guide for the GSI toolbox.
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Saltus, Christina, S. McKay, and Todd Swannack. Geospatial suitability indices (GSI) toolbox : user's guide. Engineer Research and Development Center (U.S.), August 2022. http://dx.doi.org/10.21079/11681/45128.

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Habitat suitability models have been widely adopted in ecosystem management and restoration to assess environmental impacts and benefits according to the quantity and quality of a given habitat. Many spatially distributed ecological processes require application of suitability models within a geographic information system (GIS). This technical report presents a geospatial toolbox for assessing habitat suitability. The geospatial suitability indices (GSI) toolbox was developed in ArcGIS Pro 2.7 using the Python 3.7 programming language and is available for use on the local desktop in the Windows 10 environment. Two main tools comprise the GSI toolbox. First, the suitability index (SIC) calculator tool uses thematic or continuous geospatial raster layers to calculate parameter suitability indices using user-specified habitat relationships. Second, the overall suitability index calculator (OSIC) combines multiple parameter suitability indices into one overarching index using one or more options, including arithmetic mean, weighted arithmetic mean, geometric mean, and minimum limiting factor. The result is a raster layer representing habitat suitability values from 0.0–1.0, where zero (0) is unsuitable habitat and one (1) is ideal suitability. This report documents the model purpose and development and provides a user’s guide for the GSI toolbox.
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