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Academic literature on the topic 'Varieties of sums of powers'

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Published: 14 March 2023

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Journal articles on the topic "Varieties of sums of powers"

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Massarenti, Alex. "Generalized varieties of sums of powers." Bulletin of the Brazilian Mathematical Society, New Series 47, no. 3 (February 24, 2016): 911–34. http://dx.doi.org/10.1007/s00574-016-0196-0.

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Ranstad, K., and F. O. Schreyer. "Varieties of sums of power." Journal für die reine und angewandte Mathematik (Crelles Journal) 2000, no. 525 (August 11, 2000): 147–81. http://dx.doi.org/10.1515/crll.2000.064.

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Massarenti, Alex, and Massimiliano Mella. "Birational aspects of the geometry of Varieties of Sums of Powers." Advances in Mathematics 243 (August 2013): 187–202. http://dx.doi.org/10.1016/j.aim.2013.04.006.

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Iliev, Atanas, and Kristian Ranestad. "Canonical Curves and Varieties of Sums of Powers of Cubic Polynomials." Journal of Algebra 246, no. 1 (December 2001): 385–93. http://dx.doi.org/10.1006/jabr.2001.8942.

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Iliev, Atanas, and Kristian Ranestad. "$K3$ surfaces of genus 8 and varieties of sums of powers of cubic fourfolds." Transactions of the American Mathematical Society 353, no. 4 (October 11, 2000): 1455–68. http://dx.doi.org/10.1090/s0002-9947-00-02629-5.

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Bolognesi, Michele, and Alex Massarenti. "Varieties of sums of powers and moduli spaces of(1, 7)-polarized abelian surfaces." Journal of Geometry and Physics 125 (February 2018): 23–32. http://dx.doi.org/10.1016/j.geomphys.2017.12.004.

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Dolgachev, Igor V. "Dual Homogeneous Forms and Varieties of Power Sums." Milan Journal of Mathematics 72, no. 1 (October 2004): 163–87. http://dx.doi.org/10.1007/s00032-004-0029-2.

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Huang, Hang, Mateusz Michałek, and Emanuele Ventura. "Vanishing Hessian, wild forms and their border VSP." Mathematische Annalen 378, no. 3-4 (September 14, 2020): 1505–32. http://dx.doi.org/10.1007/s00208-020-02080-8.

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Abstract Wild forms are homogeneous polynomials whose smoothable rank is strictly larger than their border rank. The discrepancy between these two ranks is caused by the difference between the limit of spans of a family of zero-dimensional schemes and the span of their flat limit. For concise forms of minimal border rank, we show that the condition of vanishing Hessian is equivalent to being wild. This is proven by making a detour through structure tensors of smoothable and Gorenstein algebras. The equivalence fails in the non-minimal border rank regime. We exhibit an infinite series of minimal border rank wild forms of every degree $$d\ge 3$$ d ≥ 3 as well as an infinite series of wild cubics. Inspired by recent work on border apolarity of Buczyńska and Buczyński, we study the border varieties of sums of powers $$\underline{{\mathrm {VSP}}}$$ VSP ̲ of these forms in the corresponding multigraded Hilbert schemes.
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Heath-Brown, D. R. "Christopher Hooley. 7 August 1928—13 December 2018." Biographical Memoirs of Fellows of the Royal Society 69 (September 9, 2020): 225–46. http://dx.doi.org/10.1098/rsbm.2020.0027.

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Christopher Hooley was one of the leading analytic number theorists of his day, world-wide. His early work on Artin’s conjecture for primitive roots remains the definitive investigation in the area. His greatest contribution, however, was the introduction of exponential sums into every corner of analytic number theory, bringing the power of Deligne’s ‘Riemann hypothesis’ for varieties over finite fields to bear throughout the subject. For many he was a figure who bridged the classical period of Hardy and Littlewood with the modern era. This biographical sketch describes how he succeeded in applying the latest tools to famous old problems.
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Takagi, Hiromichi, and Francesco Zucconi. "Geometries of lines and conics on the quintic del Pezzo 3-fold and its application to varieties of power sums." Michigan Mathematical Journal 61, no. 1 (March 2012): 19–62. http://dx.doi.org/10.1307/mmj/1331222846.

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Dissertations / Theses on the topic "Varieties of sums of powers"

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Patel, Vandita. "Perfect powers that are sums of consecutive like powers." Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/95153/.

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This thesis is concerned with finding integer solutions to certain Diophantine equations. In doing so, we will use a variety of techniques. Unfortunately, we are not able to mention all of them - there are many techniques in solving Diophantine equations! Combining analytic methods with classic and modern algebraic approaches proves fruitful in a number of cases.
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Alsulmi, Badria. "Generalized Jacobi sums modulo prime powers." Diss., Kansas State University, 2016. http://hdl.handle.net/2097/32668.

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Ghidelli, Luca. "On Gaps Between Sums of Powers and Other Topics in Number Theory and Combinatorics." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/40014.

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One main goal of this thesis is to show that for every K it is possible to find K consecutive natural numbers that cannot be written as sums of three nonnegative cubes. Since it is believed that approximately 10% of all natural numbers can be written in this way, this result indicates that the sums of three cubes distribute unevenly on the real line. These sums have been studied for almost a century, in relation with Waring's problem, but the existence of ``arbitrarily long gaps'' between them was not known. We will provide two proofs for this theorem. The first is relatively elementary and is based on the observation that the sums of three cubes have a positive bias towards being cubic residues modulo primes of the form p=1+3k. Thus, our first method to find consecutive non-sums of three cubes consists in searching them among the natural numbers that are non-cubic residues modulo ``many'' primes congruent to 1 modulo 3. Our second proof is more technical: it involves the computation of the Sato-Tate distribution of the underlying cubic Fermat variety {x^3+y^3+z^3=0}, via Jacobi sums of cubic characters and equidistribution theorems for Hecke L-functions of the Eisenstein quadratic number field Q(\sqrt{-3}). The advantage of the second approach is that it provides a nearly optimal quantitative estimate for the size of gaps: if N is large, there are >>\sqrt{log N}/(log log N)^4 consecutive non-sums of three cubes that are less than N. According to probabilistic models, an optimal estimate would be of the order of log N / log log N. In this thesis we also study other gap problems, e.g. between sums of four fourth powers, and we give an application to the arithmetic of cubic and biquadratic theta series. We also provide the following additional contributions to Number Theory and Combinatorics: a derivation of cubic identities from a parameterization of the pseudo-automorphisms of binary quadratic forms; a multiplicity estimate for multiprojective Chow forms, with applications to Transcendental Number Theory; a complete solution of a problem on planar graphs with everywhere positive combinatorial curvature.
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Clark, John. "On a conjecture involving Fermat's Little Theorem." [Tampa, Fla] : University of South Florida, 2008. http://purl.fcla.edu/usf/dc/et/SFE0002485.

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Ye, Lizao. "Faisceau automorphe unipotent pour G₂, nombres de Franel, et stratification de Thom-Boardman." Thesis, Université de Lorraine, 2019. http://www.theses.fr/2019LORR0081/document.

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Dans cette thèse, d’une part, nous généralisons au cas équivariant un résultat de J. Denef et F. Loeser sur les sommes trigonométriques sur un tore ; d’autre part, nous étudions la stratification de Thom-Boardman associée à la multiplication des sections globales des fibrés en droites sur une courbe. Nous montrons une inégalité subtile sur les dimensions de ces strates. Notre motivation vient du programme de Langlands géométrique. En s’appuyant sur les travaux de W. T. Gan, N. Gurevich, D. Jiang et de S. Lysenko, nous proposons, pour le groupe réductif G de type G2, une construction conjecturale du faisceau automorphe dont le paramètre d’Arthur est unipotent et sous-régulier. En utilisant nos deux résultats ci-dessus, nous déterminons les rangs génériques de toutes les composantes isotypiques d’un faisceau S₃-équivariant qui apparaît dans notre conjecture, ce S₃ étant le centralisateur du SL2 sous-régulier dans le groupe dual de Langlands de G
In this thesis, on the one hand, we generalise to the equivariant case a result of J. Denef and F. Loeser about trigonometric sums on tori ; on the other hand, we study the Thom-Boardman stratification associated to the multiplication of global sections of line bundles on a curve. We prove a subtle inequaliity about the dimensions of these strata. Our motivation comes from the geometric Langlands program. Based on works of W. T. Gan, N. Gurevich, D. Jiang and S. Lysenko, we propose, for the reductive group G of type G2, a conjectural construction of the automorphic sheaf whose Arthur parameter is unipotent and sub-regular. Using our two results above, we determine the generic ranks of all isotypic components of an S3-equivaraint sheaf which appears in our conjecture, this S3 being the centraliser of the sub-regular SL2 inside the Langlands dual group of G
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wang, mue ming, and 王牧民. "The dicussions of the sums of the n'th powers over finite fields." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/42203614939865821328.

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Books on the topic "Varieties of sums of powers"

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Reznick, Bruce Arie. Sums of even powers of real linear forms. Providence, R.I: American Mathematical Society, 1992.

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Rodale Press. Shades of lavender: A guide to the healing powers, flavor, and lore of nature's most fragrant herb. [Emmaus, PA]: Rodale, 2000.

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1953-, Campillo Antonio, ed. Zeta functions in algebra and geometry: Second International Workshop on Zeta Functions in Algebra and Geometry, May 3-7, 2010, Universitat de Les Illes Balears, Palma de Mallorca, Spain. Providence, R.I: American Mathematical Society, 2012.

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Alta.) WIN (Conference) (2nd 2011 Banff. Women in Numbers 2: Research directions in number theory : BIRS Workshop, WIN2 - Women in Numbers 2, November 6-11, 2011, Banff International Research Station, Banff, Alberta, Canada. Edited by David Chantal 1964-, Lalín Matilde 1977-, and Manes Michelle 1970-. Providence, Rhode Island: American Mathematical Society, 2013.

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Alladi, Krishnaswami, Frank Garvan, and Ae Ja Yee. Ramanujan 125: International conference to commemorate the 125th anniversary of Ramanujan's birth, Ramanujan 125, November 5--7, 2012, University of Florida, Gainesville, Florida. Providence, Rhode Island: American Mathematical Society, 2014.

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Kleiman, S. L., Anthony Iarrobino, Vassil Kanev, and A. Iarrobino. Power Sums, Gorenstein Algebras, and Determinantal Loci. Springer London, Limited, 2006.

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Iarrobino, Anthony, Vassil Kanev, A. Iarrobino, and S. L. Kleiman. Power Sums, Gorenstein Algebras, and Determinantal Loci. Springer, 2000.

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Becker, E. Sums of Powers in Fields and Artin-Schreier Theory of Orderings of Higher Level (Modern Surveys in Mathematics Series). Springer-Verlag, 1995.

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Dawson, C. Bryan. Calculus Set Free. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895592.001.0001.

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Calculus Set Free: Infinitesimals to the Rescue is a single-variable calculus textbook that incorporates the use of infinitesimals, and more generally the hyperreal numbers. The infinitesimal methods and notation herein were developed with beginning calculus students in mind, resulting in exposition that is more intuitive as well as many calculational procedures that are easier to perform, as compared to both traditional calculus textbooks and earlier attempts at including infinitesimals in calculus. Arithmetic of hyperreal numbers, levels of hyperreal numbers, and approximation in the hyperreals lead to a definition of limit. Limit computations are based directly on that definition. Computation-style proofs of derivative rules use an approximation formula called the “local linearity formula.” The definite integral is developed through the idea of finding area using infinitely many subintervals and right-hand endpoints; the resulting “omega sums” are much easier than Riemann sums as a result of the “sum of powers approximation formula,” which also anticipates the Fundamental Theorem of Calculus by its resemblance to the antiderivative power rule. The limit comparison test is replaced by the “level comparison test,” which is so widely applicable and computationally simple that strategy for testing series is noticeably less difficult. Although infinitesimal methods are used for any mathematical process involving a limit, the remainder of the text uses the standard methods of calculus. Organization is similar to other college-level calculus texts. Features include ample marginal notes, examples, illustrations, and answers to odd-numbered exercises.
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Knobloch, Eberhard. Generality in Leibniz’s mathematics. Edited by Karine Chemla, Renaud Chorlay, and David Rabouin. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780198777267.013.3.

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This article discusses generality in Gottfried Leibniz’s mathematics. In principle, Leibnizian mathematics has a philosophical-theological basis. From the beginning everything that exists is to be found in an orderly relation. The general and inviolable laws of the world are an ontological a priori. The universal harmony of the world consists in the largest possible variety being given the largest possible order so that the largest possible perfection is involved. After considering the relationship between the value of generality and the harmonies that are at the center of Leibniz’s concern, this article explores his view that generality implies beauty as well as conciseness and simplicity. It also examines how the interest in generality relates to notations, taking the examples of determinants and sums of powers, and to utility and fecundity. Finally, it demonstrates how generality is connected with laws of formation.
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Book chapters on the topic "Varieties of sums of powers"

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Kac, Victor, and Pokman Cheung. "Sums of Powers." In Quantum Calculus, 90–91. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0071-7_24.

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Prestel, Alexander, and Charles N. Delzell. "Sums of 2mth Powers." In Springer Monographs in Mathematics, 161–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-662-04648-7_8.

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Bonzio, Stefano, Francesco Paoli, and Michele Pra Baldi. "Płonka Sums and Regular Varieties." In Trends in Logic, 33–70. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04297-3_2.

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Bruin, Nils. "On Powers as Sums of Two Cubes." In Lecture Notes in Computer Science, 169–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/10722028_9.

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Nelson, Randolph. "Sums of the Powers of Successive Integers." In A Brief Journey in Discrete Mathematics, 93–108. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37861-5_7.

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Strick, Heinz Klaus. "Sums of Powers of Consecutive Natural Numbers." In Mathematics is Beautiful, 295–321. Berlin, Heidelberg: Springer Berlin Heidelberg, 2021. http://dx.doi.org/10.1007/978-3-662-62689-4_16.

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Krashen, Daniel, and David J. Saltman. "Severi—Brauer Varieties and Symmetric Powers." In Encyclopaedia of Mathematical Sciences, 59–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05652-3_5.

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Gómez, Amparo. "Causation and Scientific Realism: Mechanisms and Powers without Essentialism." In Varieties of Scientific Realism, 367–83. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51608-0_20.

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Friedenberg, Netanel, Alessandro Oneto, and Robert L. Williams. "Minkowski Sums and Hadamard Products of Algebraic Varieties." In Fields Institute Communications, 133–57. New York, NY: Springer New York, 2017. http://dx.doi.org/10.1007/978-1-4939-7486-3_7.

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Iarrobino, Anthony, and Vassil Kanev. "Sums of powers of linear forms, and gorenstein algebras." In Lecture Notes in Mathematics, 57–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/bfb0093428.

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Conference papers on the topic "Varieties of sums of powers"

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García-Marco, Ignacio, Pascal Koiran, and Timothee Pecatte. "Reconstruction Algorithms for Sums of Affine Powers." In ISSAC '17: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2017. http://dx.doi.org/10.1145/3087604.3087605.

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Comon, Pierre, and B. Mourrain. "Decomposition of quantics in sums of powers." In SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, edited by Franklin T. Luk. SPIE, 1994. http://dx.doi.org/10.1117/12.190826.

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Hanneken, John W., B. N. Narahari Achar, David M. Vaught, James M. Andrews, and Avery T. Carr. "Sums of the Zeros of the Single Parameter Mittag-Leffler Function With the Parameter Equal to One-Half." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86220.

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The sums of the powers of the reciprocals of the non-trivial (non-zero) zeros of the single parameter Mittag-Leffler function with alpha equal to one-half have been investigated. Analytical results for these sums were compared to the results from numerically summing over a billion zeros. Sums for integer powers from 3 to 10 agreed with the predictions of the analytical results but not for powers 1 and 2. The sum of the reciprocals of the zeros diverged in contrast to the analytical result and the sum of the squares of the zeros converged to a different result than predicted. This illustrates that the analytical results for polynomials cannot in general be applied to the infinite series representation of the Mittag-Leffler functions.
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Simsek, Yilmaz. "Identities and relations containing finite sums of powers of binomial coefficients." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026604.

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Tanash, Islam M., and Taneli Riihonen. "Remez Exchange Algorithm for Approximating Powers of the Q-Function by Exponential Sums." In 2021 IEEE 93rd Vehicular Technology Conference (VTC2021-Spring). IEEE, 2021. http://dx.doi.org/10.1109/vtc2021-spring51267.2021.9448807.

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Garg, Ankit, Neeraj Kayal, and Chandan Saha. "Learning sums of powers of low-degree polynomials in the non-degenerate case." In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2020. http://dx.doi.org/10.1109/focs46700.2020.00087.

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Buralli, Dale A., and John R. Rogers. "Use of Gaussian brackets in holographic optical design." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.mj4.

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The ability to factor expressions for the back focal distance and magnification of a multielement optical system in terms of the element powers and separations provides a simple means of investigating the dependence of the first-order optical properties (and their chromatic variations) on the system parameters. The Gaussian bracket expressions for the first-order properties of multielement systems consist of products and sums of the expressions for the elements rather than continued fractions. By examining the structure of the Gaussian bracket expressions for an arbitrary system, conclusions of a general nature may be formed. A rigorous proof is given that any achromatic image of a real object which is formed by an all-holographic imaging system must be virtual regardless of the number of holographic elements in the system. Also, a three-hologram imaging system is derived from the theory, and it Is shown to be the only three-element solution which is corrected for the chromatic difference of magnification and both primary and secondary longitudinal chromatic aberration. Although this solution has previously been found through other means, it was not known to be the only solution.
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Beneyto Falagán, Neus. "Utopía y memoria del territorio: procesos de colonización interior en España a finales del siglo XIX." In Seminario Internacional de Investigación en Urbanismo. Barcelona: Instituto de Arte Americano. Universidad de Buenos Aires, 2013. http://dx.doi.org/10.5821/siiu.5974.

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El presente artículo constituye un acercamiento teórico al urbanismo utópico y los proyectos de colonización interior desarrollados en nuestro país a finales del siglo XIX, a instancias tanto gubernamentales como patronales. La investigación está orientada a revisar las utopías urbanas e identificar alternativas y propuestas en materia de ordenación del territorio y articulación entre los espacios de producción y reproducción, su principio modelador y las estructuras de poder. Con el fin de evaluar el grado de aplicación práctica de los planteamientos utopistas, se han analizado, a modo de estudio de caso, algunas experiencias colonizadoras, en sus variedades industrial, agrícola y minera. This paper is a theoretical approach to utopian urbanism and internal colonization projects developed in Spain in the late nineteenth century, by both governmental and employer bodies. The research aims at reviewing the urban utopias and identifying alternatives and proposals for land planning and coordination between areas of production and reproduction, its spaces modeler principle, and structures of power. In order to assess the degree of practical application of utopian approaches, it explores, as case studies, some colonization experiences, in its industrial, agricultural and mining varieties
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Nanda, Aditya, M. Amin Karami, and Puneet Singla. "Uncertainty Quantification of Energy Harvesting Systems Using Method of Quadratures and Maximum Entropy Principle." In ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/smasis2015-9026.

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This paper uses the method of Quadratures in conjunction with the Maximum Entropy principle to investigate the effect of parametric uncertainties on the mean power output and root mean square deflection of piezoelectric vibrational energy harvesting systems. Uncertainty in parameters of harvesters could arise from insufficient manufacturing controls or change in material properties over time. We investigate bimorph based harvesters that transduce ambient vibrations to electricity via the piezoelectric effect. Three varieties of energy harvesters — Linear, Nonlinear monostable and Nonlinear bistable are considered in this research. This analysis quantitatively shows the probability density function for the mean power and root mean square deflection as a function of the probability densities of the excitation frequency, excitation amplitude, initial deflection of the bimorph and magnet gap of the energy harvester. The method of Quadratures is used for numerically integrating functions by propagating weighted points from the domain and evaluating the integral as a weighted sum of the function values. In this paper, the method of Quadratures is used for evaluating central moments of the distributions of rms deflection and mean harvested power and, then, in conjunction with the principle of Maximum Entropy (MaxEnt) an optimal density function is obtained which maximizes the entropy and satisfies the moment constraints. The The computed nonlinear density functions are validated against Monte Carlo simulations thereby demonstrating the efficiency of the approach. Further, the Maximum Entropy principle is widely applicable to uncertainty quantification of a wide range of dynamic systems.
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Reports on the topic "Varieties of sums of powers"

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Beery, Janet. Sums of Powers of Positive Integers. Washington, DC: The MAA Mathematical Sciences Digital Library, April 2009. http://dx.doi.org/10.4169/loci003284.

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Pengelley, David. Sums of Powers in Discrete Mathematics: Archimedes Sums Squares in the Sand. Washington, DC: The MAA Mathematical Sciences Digital Library, June 2013. http://dx.doi.org/10.4169/loci003986.

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Pengelley, David. Figurate Numbers and Sums of Numerical Powers: Fermat, Pascal, Bernoulli. Washington, DC: The MAA Mathematical Sciences Digital Library, June 2013. http://dx.doi.org/10.4169/loci003987.

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Unal, Hasan, and Hakan Kursat Oral. Extending al-Karaji's Work on Sums of Odd Powers of Integers. Washington, DC: The MAA Mathematical Sciences Digital Library, August 2011. http://dx.doi.org/10.4169/loci003725.

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