Relevant bibliographies by topics / Trivial zeros

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Trivial zeros'

Author: Grafiati
Published: 30 November 2024

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Journal articles on the topic "Trivial zeros"

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Bayer, Pilar. "La hipòtesi de Riemann: El gran repte pendent." Mètode Revista de difusió de la investigació, no. 8 (June 5, 2018): 35. http://dx.doi.org/10.7203/metode.0.8903.

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The Riemann hypothesis is an unproven statement referring to the zeros of the Riemann zeta function. Bernhard Riemann calculated the first six non-trivial zeros of the function and observed that they were all on the same straight line. In a report published in 1859, Riemann stated that this might very well be a general fact. The Riemann hypothesis claims that all non-trivial zeros of the zeta function are on the the line x = 1/2. The more than ten billion zeroes calculated to date, all of them lying on the critical line, coincide with Riemann’s suspicion, but no one has yet been able to prove that the zeta function does not have non-trivial zeroes outside of this line.
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Lam Kai, Shun. "A Verification of Riemann Non-Trivial Zeros by Complex Analysis by Matlab™ Computation." European Journal of Statistics and Probability 11, no. 1 (January 15, 2023): 69–83. http://dx.doi.org/10.37745/ejsp.2013/vol11n16983.

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With my most recent paper, I tried to prove the Riemann Hypothesis by catching out those contradictory parts of the non-trivial zeros. In the present paper, I will try to verify these known values of Riemann nontrivial zeros by first using U.S.A. Matlab coding with a list of well-organized complex analysis theories. At the same time, as the major core of my verification is just a mono-direction one (i.e. there may be a possibility of the missing non-trivial zeros although the residue value is zero), hence this author try to solve such problem by assuming that there are some other zeros existing between the two known zeros but the contradiction arises – as singularity implies the residue has a value with a multiple of 2πi. In addition, this author also apply the ingenious design (or a hybrid skill) with Feynman technique and Integration by parts to solve a special zeta function integral. Next, this author finds that one may consider those non-trivial zeros as a Fourier transform (or an impulse) between other normal complex numbers. The result is consistent with my previous papers in quantum physics [23], [25] for the electron jumps or reverse. Hence, we may get the (dirac) delta equation for Riemann Zeta. Then we may formulate our quantum circuit & computer. Finally, this author concludes all findings with an algorithm for searching, finer and checking the non-trivial zeros like below: Step 1: Use the computer software with some suitable program codes for an elementary search of feasible non-trivial zeta values among the closed real-complex plane interval – Method Matlab Simulation for searching zeta zeros; Step 2: Substitute back the values laying in the contour interval for zeta as found in Step 1 into the limit of ln(zeta(z))/((zeta'(z)) ) in order to adjust the answer in a finer and accurate way (just like the case of Newton’s method etc) with more decimal digitals – Method Ingenious Design for finer the zeta zero’s values; Step 3: Employ the Cauchy Residue Theorem for a check and hence confirm the previous found non-trivial zeta roots’ uniqueness without any zeta zeros laying in between the two consecutive zeta roots – Method Cauchy’s Residue for checking those already found zeta zeros.
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HASSEN, ABDUL, and HIEU D. NGUYEN. "A ZERO-FREE REGION FOR HYPERGEOMETRIC ZETA FUNCTIONS." International Journal of Number Theory 07, no. 04 (June 2011): 1033–43. http://dx.doi.org/10.1142/s1793042111004678.

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This paper investigates the location of "trivial" zeros of some hypergeometric zeta functions. Analogous to Riemann's zeta function, we demonstrate that they possess a zero-free region on a left-half complex plane, except for infinitely many zeros regularly spaced on the negative real axis.
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Platt, David J. "Isolating some non-trivial zeros of zeta." Mathematics of Computation 86, no. 307 (February 13, 2017): 2449–67. http://dx.doi.org/10.1090/mcom/3198.

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Ghisa, Dorin. "On the Non-Trivial Zeros of Dirichlet Functions." Advances in Pure Mathematics 11, no. 03 (2021): 187–204. http://dx.doi.org/10.4236/apm.2021.113014.

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Silva, Sergio Da. "The Riemann Hypothesis: A Fresh and Experimental Exploration." Journal of Advances in Mathematics and Computer Science 39, no. 4 (April 2, 2024): 100–112. http://dx.doi.org/10.9734/jamcs/2024/v39i41885.

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This research proposes a new approach to the Riemann Hypothesis, focusing on the interplay between prime gaps and the non-trivial zeros of the Riemann Zeta function. Utilizing various statistical models and experimental analysis techniques, three important insights are uncovered: 1) Granger causality tests reveal a predictive relationship in which past non-trivial zeros may predict future prime gaps; 2) Complex, nonlinear interactions between prime gaps and non-trivial zeros are identified, challenging simple linear correlations; and 3) Causal network analysis reveals intricate feedback-loop relationships. These findings contribute to a better understanding of prime number distribution and the Zeta function, opening up novel possibilities for further mathematical research. The study aims to motivate mathematicians towards a proof or disproof of the Riemann Hypothesis.
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Apostol, Tom M. "Note on the Trivial Zeros of Dirichlet L-Functions." Proceedings of the American Mathematical Society 94, no. 1 (May 1985): 29. http://dx.doi.org/10.2307/2044944.

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Rohrlich, David E. "Scarcity and abundance of trivial zeros in division towers." Journal of Algebraic Geometry 17, no. 4 (2008): 643–75. http://dx.doi.org/10.1090/s1056-3911-08-00462-1.

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Benois, Denis. "Trivial zeros of -adic -functions at near-central points." Journal of the Institute of Mathematics of Jussieu 13, no. 3 (September 24, 2013): 561–98. http://dx.doi.org/10.1017/s1474748013000261.

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AbstractUsing the$\ell $-invariant constructed in our previous paper we prove a Mazur–Tate–Teitelbaum-style formula for derivatives of$p$-adic$L$-functions of modular forms at trivial zeros. The novelty of this result is to cover the near-central point case. In the central point case our formula coincides with the Mazur–Tate–Teitelbaum conjecture proved by Greenberg and Stevens and by Kato, Kurihara and Tsuji at the end of the 1990s.
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Apostol, Tom M. "Note on the trivial zeros of Dirichlet $L$-functions." Proceedings of the American Mathematical Society 94, no. 1 (January 1, 1985): 29. http://dx.doi.org/10.1090/s0002-9939-1985-0781049-8.

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Dissertations / Theses on the topic "Trivial zeros"

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Francqueville, Martin. "Fonctions L p-adiques de Rankin-Selberg aux points semistables." Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0225.

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A un couple de formes modulaires, on peut associer une fonction L complexe. Pour étudier cette fonction L complexe, on peut construire une fonction L p-adique interpolant les valeurs de la fonction L complexe, à un facteur près. Il peut cependant arriver que ce facteur s’annule. Dans ce cas, la fonction L p-adique s’annule, et on perd l’information sur la valeur de la fonction L complexe : c’est le phénomène des zéros triviaux. Conjecturalement, il devrait être possible de retrouver l’information sur la valeur de la fonction L complexe en considérant la dérivée cyclotomique de la fonction L p-adique. Dans cette thèse, on se placera dans le cas o`u une forme modulaire est semistable, tandis que l’autre est cristalline. On donnera la formule d’interpolation entre la fonction L complexe et la fonction L p-adique, et on mettra en évidence les conditions pour qu’un zéro trivial apparaisse. Enfin, on montrera une formule donnant la dérivée cyclotomique de la fonction L p-adique en fonction de l’invariant L et de la fonction L complexe
We can associate a complex L-function to a couple of modular forms. To study this complex L-function, we can construct a p-adic L function which interpolates the values of the complex L-function, up to a multiplicative factor. It can happen that this factor vanishes. in this case, the p-adic L function vanishes, and we lose the information on the complex L-function’s value : this is the trivial zero phenomenon. Conjecturally, it should be possible to recover the information on the complex L-function’s value through the p-adic L-functions’s cyclotomic derivative. In this thesis, we consider the case where one modular form is semistable, while the other one is cristalline. We give the interpolation formula between the complex L-function and the p-adic L-function, and we highlight the conditions needed for a trivial zero to appear. finally, we show a formula giving the p-adic L-function’s cyclotomic derivative as a function of the L invariant and the complex L-function
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Alcántara, Bode Julio. "A conjecture about the non-trivial zeroes of the Riemann zeta function." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97185.

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Some heuristic arguments are given in support of the following conjecture: If the Riemann Hypothesis (RH) does not hold then the number of zeroes of the Riemann zeta function with real part σ >  ½ is infinite.
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Bernard, Damien. "Statistique des zéros non-triviaux de fonctions L de formes modulaires." Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2013. http://tel.archives-ouvertes.fr/tel-00922713.

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Cette thèse se propose d'obtenir des résultats statistiques sur les zéros non-triviaux de fonctions L. Dans le cas des fonctions L de formes modulaires, on prouve qu'une proportion positive explicite de zéros non-triviaux se situe sur la droite critique. Afin d'arriver à ce résultat, il nous faut préalablement étendre un théorème sur les problèmes de convolution avec décalage additif en moyenne de manière à déterminer le comportement asymptotique du second moment intégral ramolli d'une fonction L de forme modulaire au voisinage de la droite critique. Une autre partie de cette thèse, indépendante de la précédente, est consacrée à l'étude du plus petit zéro non-trivial d'une famille de fonctions L. Ces résultats sont en particulier appliqués aux fonctions L de puissance symétrique.
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Veronese, Daniel Oliveira [UNESP]. "Medidas não triviais no círculo unitário e polinômios para-ortogonais associados." Universidade Estadual Paulista (UNESP), 2016. http://hdl.handle.net/11449/141955.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Dado um par de sequências reais, sendo uma delas sequência encadeada positiva, podemos considerar uma sequência de polinômios que satisfazem uma relação de recorrência de três termos, de tal modo que os zeros destes polinômios sejam simples e estejam sobre o círculo unitário. Neste trabalho mostramos que é possível obter, a partir dessa fórmula de recorrência, uma única medida não trivial no círculo unitário. Provamos também que a sequência de polinômios gerados por essa relação de recorrência é uma sequência de polinômios para-ortogonais associados à medida obtida. Além disso, obtemos limitantes para os zeros extremos de tais polinômios e fornecemos estimativas para o suporte da medida associada.
Given a pair of real sequences, where one of them is a positive chain sequence, we can associate a sequence of polynomials which satisfy a three term recurrence formula and such that the zeros of these polynomials are simple and lie on the unit circle. In this manuscript, we show that, starting from this three term recurrence formula, it is always possible to obtain a unique nontrivial measure on the unit circle. We also prove that the generated sequence of polynomials is a sequence of para-orthogonal polynomials associated with this measure. Furthermore, we obtain bounds for the extreme zeros of these polynomials and also provide estimates for the support of the associated measure.
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Alvites, José Carlos Valencia. "Hipótese de Riemann e física." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-13042012-084309/.

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Neste trabalho, introduzimos a função zeta de Riemann \'ZETA\'(s), para s \'PERTENCE\' C \\ e apresentamos muito do que é conhecido como justificativa para a hipótese de Riemann. A importância de \'ZETA\' (s) para a teoria analítica dos números é enfatizada e fornecemos uma prova conhecida do Teorema dos Números Primos. No final, discutimos a importância de \'ZETA\'(s) para alguns modelos físicos de interesse e concluimos descrevendo como a hipótese de Riemann pode ser acessada estudando estes sistemas
In this work, we introduce the Riemann zeta function \'ZETA\'(s), s \'IT BELONGS\' C \\ and present much of what is known to support the Riemann hypothesis. The importance of \'ZETA\'(s) to the Analytic number theory is emphasized and a proof for the Prime Number Theorem is reviewed. In the end, we report on the importance of \'ZETA\'(s) to some relevant physical models and conclude by describing how the Riemann Hypothesis can be accessed by studying these systems
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MEDEIROS, Rex Antonio da Costa. "Zero-Error capacity of quantum channels." Universidade Federal de Campina Grande, 2008. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1320.

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Nesta tese, a capacidade erro-zero de canais discretos sem memória é generalizada para canais quânticos. Uma nova capacidade para a transmissão de informação clássica através de canais quânticos é proposta. A capacidade erro-zero de canais quânticos (CEZQ) é definida como sendo a máxima quantidade de informação por uso do canal que pode ser enviada através de um canal quântico ruidoso, considerando uma probabilidade de erro igual a zero. O protocolo de comunicação restringe palavras-código a produtos tensoriais de estados quânticos de entrada, enquanto que medições coletivas entre várias saídas do canal são permitidas. Portanto, o protocolo empregado é similar ao protocolo de Holevo-Schumacher-Westmoreland. O problema de encontrar a CEZQ é reformulado usando elementos da teoria de grafos. Esta definição equivalente é usada para demonstrar propriedades de famílias de estados quânticos e medições que atingem a CEZQ. É mostrado que a capacidade de um canal quântico num espaço de Hilbert de dimensão d pode sempre ser alcançada usando famílias compostas de, no máximo,d estados puros. Com relação às medições, demonstra-se que medições coletivas de von Neumann são necessárias e suficientes para alcançar a capacidade. É discutido se a CEZQ é uma generalização não trivial da capacidade erro-zero clássica. O termo não trivial refere-se a existência de canais quânticos para os quais a CEZQ só pode ser alcançada através de famílias de estados quânticos não-ortogonais e usando códigos de comprimento maior ou igual a dois. É investigada a CEZQ de alguns canais quânticos. É mostrado que o problema de calcular a CEZQ de canais clássicos-quânticos é puramente clássico. Em particular, é exibido um canal quântico para o qual conjectura-se que a CEZQ só pode ser alcançada usando uma família de estados quânticos não-ortogonais. Se a conjectura é verdadeira, é possível calcular o valor exato da capacidade e construir um código de bloco quântico que alcança a capacidade. Finalmente, é demonstrado que a CEZQ é limitada superiormente pela capacidade de Holevo-Schumacher-Westmoreland.
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Books on the topic "Trivial zeros"

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Iliopoulos, John. The Origin of Mass. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198805175.001.0001.

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Why do most ’elementary particles’ which form the constituents of all matter have a non-zero mass? Strange question, apparently in contradiction with our physical intuition. In this little book we attempt to explain that the question is far from being trivial and that the answer can be found in the recent discovery of a new particle in the Large Hadron Collider (LHC) at CERN near Geneva. We offer the reader a guided tour, starting from the tiny fractions of a second after the Big Bang, when all particles have been created, to the present experiments we perform in our laboratories. We show that the Universe follows a profound symmetry principle which seems to determine the structure of the world.
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Whizbooks. Summary of Zero Belly Diet : Lose up to 16 Lbs. in 14 Days!: Trivia/Quiz for Fans. Blurb, 2018.

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Whizbooks. Summary of Zero to One : Notes on Startups, or How to Build the Future: Trivia/Quiz for Fans. Blurb, 2019.

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Book chapters on the topic "Trivial zeros"

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Hassani, Mehdi. "Explicit Bounds Concerning Non-trivial Zeros of the Riemann Zeta Function." In Analytic Number Theory, Approximation Theory, and Special Functions, 69–77. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-0258-3_2.

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Hassani, Mehdi. "On the Means of the Non-trivial Zeros of the Riemann Zeta Function." In Advancements in Complex Analysis, 319–28. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-40120-7_8.

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Cornelissen, Gunther, and Norbert Peyerimhoff. "Spectra, Group Representations and Twisted Laplacians." In Twisted Isospectrality, Homological Wideness, and Isometry, 17–30. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-27704-7_3.

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AbstractIn this chapter, we review basic notions about spectra, group representations, and twisted Laplace operators. We first recall how to define the spectrum and the spectral zeta function for a general symmetric second order elliptic differential operator acting on smooth sections of a Hermitian line bundle. We prove that the non-zero spectrum (i.e., the spectral zeta function) determines the entire spectrum on an odd-dimensional manifold, but also give an example showing that this is not always true for even-dimensional manifolds; the example is obstructed by the non-vanishing of some topological genus. After setting up some notation from representation theory, we discuss G-sets and weak conjugacy (“Gaßmann equivalence”) of subgroups of a group, explaining the interrelations. In the final sections, we introduce twisted Laplacians, corresponding to unitary representations of the fundamental group. After this, we focus on the case of a twisted Laplacian arising from a finite Galois cover of manifolds and we relate the spectrum on the top manifold to that of the induced representation on the bottom manifold. We relate the multiplicity of zero in the spectrum to the multiplicity of the trivial representation in the given representation, and finally we show that, contrary to the general case, the multiplicity of zero in the spectrum of a twisted Laplacian is determined from the non-zero spectrum, provided one also knows the usual Laplace spectrum of the manifold.
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Imai, Hideki, Kirill Morozov, and Anderson C. A. Nascimento. "Efficient Oblivious Transfer Protocols Achieving a Non-zero Rate from Any Non-trivial Noisy Correlation." In Lecture Notes in Computer Science, 183–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10230-1_16.

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Bennett, Charles H. "Logical Depth and Physical Complexity." In The Universal Turing Machine: A Half-Century Survey, 227–58. Oxford University PressOxford, 1990. http://dx.doi.org/10.1093/oso/9780198537748.003.0008.

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Abstract Some mathematical and natural objects (a random sequence, a sequence of zeros, a perfect crystal, a gas) are intuitively trivial, while others (e.g., the human body, the digits of 7r) contain internal evidence of a nontrivial causal history. Persons of Turing’s genius do not shy away from asking big questions, and hoping to see, in advance of the eventual slow progress of science, the essential outlines of the answers. “What is intelligence?” is one such question that clearly fascinated Turing. “How do complicated structures arise in nature?” is another. On this latter question, seeds planted by Turing have begun to mature to an extent that I think would please him.
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Xiaochun, Mei. "A Strict Proof That the Riemann Zeta Function Equation Has No Non-trivial Zeros." In Novel Research Aspects in Mathematical and Computer Science Vol. 2, 74–88. Book Publisher International (a part of SCIENCEDOMAIN International), 2022. http://dx.doi.org/10.9734/bpi/nramcs/v2/6049f.

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Mostepanenko, V. M., N. N. Trunov, and R. L. Znajek. "Vacuum polarization in topologically non-trivial spaces and cosmology." In The Casimir Effect and its Applications, 100–152. Oxford University PressOxford, 1997. http://dx.doi.org/10.1093/oso/9780198539988.003.0004.

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Abstract As has been previously noted, when considering a quantized field in a topologically non-trivial space additional conditions are imposed that are similar to conditions at material boundaries. As a result, in comparison with Minkowski space, the zero-point fluctuation spectrum changes, (for example, from being continuous to being discrete), which leads to the appearance of a non-zero vacuum EMT for the quantized field in that space.
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Chandrasekhar, S. "The rectilinear ascent and descent of bodies." In Newton’s Principia for the Common Reader, 143–64. Oxford University PressOxford, 1995. http://dx.doi.org/10.1093/oso/9780198517443.003.0008.

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Abstract This is an inversion of the common procedure: rectilinear motion in a central field of force is generally (if not always) considered as a special (and a simpler) case that requires a separate treatment since the angular momentum of such motions is zero and there is no constant of areas as a (non-trivial) constraint. Instead, Newton considers rectilinear motion as a limiting case of motion along conic sections and shows how it becomes determinate by an ‘invariant’ form of the law of areas which applies to orbits independently of their eccentricity.
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Gennes, P. G. De, and J. Prost. "Long- And Short-Range Order In Nematics." In The Physics of Liquid Crystals, 41–97. Oxford University PressOxford, 1993. http://dx.doi.org/10.1093/oso/9780198520245.003.0002.

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Abstract The nematic phase has a lower symmetry than the high-temperature isotropic liquid. We express this qualitatively by saying that the nematic phase is ‘more ordered’. To put this on a quantitative basis, we need to define an order parameter that is non-zero in the nematic phase but that vanishes, for symmetry reasons, in the isotropic phase. In some physical systems an adequate choice of the order parameter is obvious. For instance, in a ferromagnet, the order parameter is the magnetization M; this is a vector with three independent components M,,. In a nematic phase the choice is less trivial and we shall have to proceed in successive steps.
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Donaldson, S. k., and P. B. Kronheimer. "Connections." In The Geometry of Four-Manifolds, 31–74. Oxford University PressOxford, 1990. http://dx.doi.org/10.1093/oso/9780198535539.003.0002.

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Abstract In this chapter we begin our study of Yang-Mills theory—the theory of connections-which makes up the core of this book. Classical differential geometry considers, by and large, connections on the tangent bundle of a manifold, the most important being the Levi—Civita connection defined by a Riemannian metric. The key feature of Yang—Mills theory is that it deals with connections on auxiliary bundles, not directly tied to the geometry of the base manifold. After reviewing standard definitions and notation in Section 2.1, we go on to give proofs of two fundamental theorems: the integrability theorem for bolomorphic structures and Uhlenbeck’s theorem on the existence of Coulomb gauges. These are essentially local results. We regard them as extensions of the elementary fact that connections with curvature zero are locally trivial.
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Conference papers on the topic "Trivial zeros"

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Pedrozo, HA, MA Zamarripa, JP Osorio Su�rez, A. Uribe-Rodr�guez, MS Diaz, and LT Biegler. "Impact of surrogate modeling in the formulation of pooling optimization problems for the CO2 point sources." In Foundations of Computer-Aided Process Design, 546–53. Hamilton, Canada: PSE Press, 2024. http://dx.doi.org/10.69997/sct.193976.

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Post-combustion carbon capture technologies have the potential to contribute significantly to achieving the environmental goals of reducing CO2 emissions in the short term. However, these technologies are energy and cost-intensive, and the variability of flue gas represents important challenges. The optimal design and optimization of such systems are critical to reaching the net zero and net negative goals, in this context, the use of computer-aided process design can be very effective in overcoming these issues. In this study, we explore the implementation of carbon capture technologies within an industrial complex, by considering the pooling of CO2 streams. We present an optimization formulation to design carbon capture plants with the goal of enhancing efficiency and minimizing the capture costs. Capital and operating costs are represented via surrogate models (SMs) that are trained using rigorous process models in Aspen Plus, each data point is obtained by solving an optimization problem in Aspen Plus equation-oriented approach. Since selecting the functional form of the surrogate model is crucial for the solution performance; we study different SM approaches (i.e., ALAMO, kriging, radial basis function, polynomials, and artificial neural networks) and analyze their impact on solver performance. Numerical results show the computational advantage of using ALAMO while highlighting the increased complexity of using ANN and kriging to formulate optimization problems. Regarding the pooling of CO2 streams, the optimal designs for the network are not trivial, thus showing the importance of addressing the problem systematically.
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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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Rubio-Sierra, F. J., R. Vazquez, and R. W. Stark. "Transfer Function Analysis of Atomic Force Microscope Cantilevers." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81156.

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Current methods to study atomic force microscope (AFM) cantilever dynamics use model simplification or are based on the non-trivial solution of the equation of motion. As an alternative method, transfer function analysis gives a more complete description of system dynamics. In this work a transfer function study of two different AFM configurations, the point force and base driven cantilever, is presented. Exact analytical expressions of the infinite dimensional transfer function are derived for cantilever deflection and slope along the cantilever. Frequency response and transfer function infinite product expansion are obtained for the case where system outputs are set at the free end of the cantilever. The frequency response reflects the full complexity of cantilever dynamics affected by the presence of an infinite number of poles and zeros. An analytical expression for all the zeros and poles of the system is obtained. From the frequency response and pole-zero investigations it is shown how cantilever actuation and output measurement affect AFM operation and cantilever dynamics modelling. Transfer function analysis of AFM cantilevers opens the possibility of model based AFM operation to increase imaging and manipulation performance.
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Jakob Povšič, Jakob, and Andrej Brodnik. "Zero-Knowledge Authentication." In 7th Student Computer Science Research Conference. University of Maribor Press, 2021. http://dx.doi.org/10.18690/978-961-286-516-0.2.

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Zero-Knowledge proofs (ZKPs) enable proving of mathematical statements, revealing nothing but their validity. We design an authentication sys-tem with a ZKP as a password verification mech-anism within the Extensible Authentication Pro-tocol (EAP) framework. Designing a secure pass-word authentication system requires us to adopt security practices for protecting ourselves against the vulnerabilities of passwords. Integrating said practices is not trivial because of the tight cou-pling with the password verification method.
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Forni, Paolo, Alain Sarlette, Thibault Capelle, Emmanuel Flurin, Samuel Deleglise, and Pierre Rouchon. "Adiabatic Elimination for Multi-Partite Open Quantum Systems with Non-Trivial Zero-Order Dynamics." In 2018 IEEE Conference on Decision and Control (CDC). IEEE, 2018. http://dx.doi.org/10.1109/cdc.2018.8619205.

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Wihstutz, Volker. "Stabilization by Random Vibration." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0332.

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Abstract We consider the control system ẋ = Ax + Bu with stochastic mean zero high gain feedback control u. The classes of stochastic processes which can stabilize the trivial solution x = 0 depend on the rank of B. For rank B = 1 we characterize, in particular, the class of noise which stabilizes the originally unstable equilibrium of the linearized inverted pendulum.
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Yuan, Yuan Y. "Multiple Bifurcations of Synchronized Oscillators With Delays." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84584.

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The synchronized oscillator with two discrete time delays is considered. The local stability of the zero solution of this system is investigated by studying the distributions of the eigenvalues of the system. A complete bifurcation analysis is given by employing the center manifold theorem, normal form method and bifurcation theorem. It is shown that the trivial fixed point may lose stability via a transcritical/pitchfork bifurcation, Hopf bifurcation or Bogdanov-Takens bifurcation. Some numerical simulation examples are given for justify the theoretical results.
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Collins, Nick. "Sonification of the Riemann Zeta Function." In ICAD 2019: The 25th International Conference on Auditory Display. Newcastle upon Tyne, United Kingdom: Department of Computer and Information Sciences, Northumbria University, 2019. http://dx.doi.org/10.21785/icad2019.003.

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The Riemann zeta function is one of the great wonders of mathematics, with a deep and still not fully solved connection to the prime numbers. It is defined via an infinite sum analogous to Fourier additive synthesis, and can be calculated in various ways. It was Riemann who extended the consideration of the series to complex number arguments, and the famous Riemann hypothesis states that the non-trivial zeroes of the function all occur on the critical line 0:5 + ti, and what is more, hold a deep correspondence with the prime numbers. For the purposes of sonification, the rich set of mathematical ideas to analyse the zeta function provide strong resources for sonic experimentation. The positions of the zeroes on the critical line can be directly sonified, as can values of the zeta function in the complex plane, approximations to the prime spectrum of prime powers and the Riemann spectrum of the zeroes rendered; more abstract ideas concerning the function also provide interesting scope.
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Ghayesh, Mergen H., Michael P. Païdoussis, and Marco Amabili. "Nonlinear Planar Dynamics of Fluid-Conveying Cantilevered Extensible Pipes." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-65785.

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This paper for the first time investigates the nonlinear planar dynamics of a cantilevered extensible pipe conveying fluid; the centreline of the pipe is considered to be extensible resulting in coupled longitudinal and transverse equations of motion; specifically, the kinetic and potential energies are obtained in terms of longitudinal and transverse displacements and then the extended version of the Lagrange equations for systems containing non-material volumes is employed to derive the equations of motion. Direct time integration along with the pseudo-arclength continuation method are employed to solve the discretized equations of motion. Bifurcation diagrams of the system are constructed as the flow velocity is increased as the bifurcation parameter. As opposed to the case of an inextensible pipe, an extensible pipe elongates in the axial direction as the flow velocity is increased from zero. At the critical flow velocity, the stability of the system is lost via a supercritical Hopf bifurcation, emerging from the trivial solution for the transverse displacement and non-trivial solution for the longitudinal displacement and leading to a flutter.
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Vedula, Lalit, and N. Sri Namachchivaya. "Stochastic Stability of Linear Gyroscopic Systems: Application to Pipes Conveying Fluid." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-39024.

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In this paper we obtain asymptotic approximations for the moment Lyapunov exponent, g(p), and the Lyapunov exponent,λ, for a two-degree-of-freedom gyroscopic system close to a double zero resonance and subjected to small damping and noisy disturbances. Using a perturbation approach, we show analytically that the moment and the top Lyapunov exponent grow in proportion to ε1/3 when the damping and noise respectively are of O(ε) and O(ε). These results, pertaining to pth moment stability and almost-sure stability of the trivial solution, are applied to study the stochastic stability of a pipe conveying pulsating fluid.
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Reports on the topic "Trivial zeros"

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Roy, Dibyendu, Nilanjan Bondyopadhaya, and Sumanta Tewar. Topologically trivial zero bias conductance peak in semiconductor Majorana wires from boundary e ects. Office of Scientific and Technical Information (OSTI), March 2013. http://dx.doi.org/10.2172/1068217.

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