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Journal articles on the topic 'Hilbert serie'

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Author: Grafiati

Published: 9 March 2023

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1

Orús, Román, and Juan Uriagereka. "Sobre álgebra y sintaxis." Revista Española de Lingüística 2, no. 51 (December 18, 2021): 79–92. http://dx.doi.org/10.31810/rsel.51.2.5.

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«Matrix syntax» es un modelo formal de relaciones sintácticas en el lenguaje. La estructura matemática resultante se asemeja a algunos aspectos de la mecánica cuántica. «Matrix syntax» nos permite describir una serie de fenómenos del lenguaje que de otro modo serían muy difíciles de explicar, como las cadenas lingüísticas, y podría decirse que es una teoría del lenguaje más económica que la mayoría de las teorías propuestas en el contexto del programa minimalista en lingüística. En particular, las oraciones se modelan de manera natural como vectores en un espacio de Hilbert con una estructura de producto tensorial, construida a partir de matrices de 2x2.

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2

Himstedt, Frank, and Peter Symonds. "Equivariant Hilbert series." Algebra & Number Theory 3, no. 4 (June 15, 2009): 423–43. http://dx.doi.org/10.2140/ant.2009.3.423.

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3

Iqbal, Zaffar. "Hilbert Series of Positive Braids." Algebra Colloquium 18, spec01 (December 2011): 1017–28. http://dx.doi.org/10.1142/s1005386711000897.

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Deligne proved that the Hilbert series of all Artin monoids are rational functions. We give an algorithm to compute the Hilbert series of the braid monoids [Formula: see text]. We also show that the Hilbert series of the positive words in [Formula: see text] with a given prefix are rational functions.

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4

Jin, Jianjun, and Shuan Tang. "Generalized Hilbert series operators." Filomat 35, no. 13 (2021): 4577–86. http://dx.doi.org/10.2298/fil2113577j.

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In this note we study the generalized Hilbert series operator H?, induced by a positive Bore measure ? on [0,1), between weighted sequence spaces. We characterize the measures ? for which H? is bounded between different sequence spaces. Finally, for certain special measures, we obtain the sharp norm estimates of the operators and establish some new generalized Hilbert series inequalities with the best constant factors.

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5

La Scala, Roberto, and Sharwan K. Tiwari. "Computing noncommutative Hilbert series." ACM Communications in Computer Algebra 52, no. 4 (May 30, 2019): 136–38. http://dx.doi.org/10.1145/3338637.3338645.

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6

Ge, Maorong, Jiayuan Lin, and Yulan Wang. "Hilbert series and Hilbert depth of squarefree Veronese ideals." Journal of Algebra 344, no. 1 (October 2011): 260–67. http://dx.doi.org/10.1016/j.jalgebra.2011.07.027.

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7

Herbig, Hans-Christian, Daniel Herden, and Christopher Seaton. "Hilbert series associated to symplectic quotients by SU2." International Journal of Algebra and Computation 30, no. 07 (July 24, 2020): 1323–57. http://dx.doi.org/10.1142/s0218196720500435.

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We compute the Hilbert series of the graded algebra of real regular functions on the symplectic quotient associated to an [Formula: see text]-module and give an explicit expression for the first nonzero coefficient of the Laurent expansion of the Hilbert series at [Formula: see text]. Our expression for the Hilbert series indicates an algorithm to compute it, and we give the output of this algorithm for all representations of dimension at most [Formula: see text]. Along the way, we compute the Hilbert series of the module of covariants of an arbitrary [Formula: see text]- or [Formula: see text]-module as well as its first three Laurent coefficients.

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8

Zhao, Chang-Jian, and Sum Cheung. "Reverse Hilbert inequalities involving series." Publications de l'Institut Math?matique (Belgrade) 105, no. 119 (2019): 81–92. http://dx.doi.org/10.2298/pim1919081z.

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Some reverse Hilbert's type inequalities involving series of nonnegative terms are established by the use of the technique of real analysis, which provides new estimates on inequalities of these type.

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9

Chardin, Marc, David Eisenbud, and Bernd Ulrich. "Hilbert series of residual intersections." Compositio Mathematica 151, no. 9 (June 9, 2015): 1663–87. http://dx.doi.org/10.1112/s0010437x15007289.

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We give explicit formulas for the Hilbert series of residual intersections of a scheme in terms of the Hilbert series of its conormal modules. In a previous paper, we proved that such formulas should exist. We give applications to the number of equations defining projective varieties and to the dimension of secant varieties of surfaces and three-folds.

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10

Bigatti, Anna M. "Computation of Hilbert-Poincaré series." Journal of Pure and Applied Algebra 119, no. 3 (July 1997): 237–53. http://dx.doi.org/10.1016/s0022-4049(96)00035-7.

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11

Renner, Lex E. "Hilbert series for torus actions." Advances in Mathematics 76, no. 1 (July 1989): 19–32. http://dx.doi.org/10.1016/0001-8708(89)90042-x.

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12

Derksen, Harm. "Hilbert series of subspace arrangements." Journal of Pure and Applied Algebra 209, no. 1 (April 2007): 91–98. http://dx.doi.org/10.1016/j.jpaa.2006.05.032.

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13

Derksen, Harm. "Universal denominators of Hilbert series." Journal of Algebra 285, no. 2 (March 2005): 586–607. http://dx.doi.org/10.1016/j.jalgebra.2004.10.029.

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14

Ryabinin, A. A. "Rademacher series in Hilbert space." Journal of Soviet Mathematics 36, no. 4 (February 1987): 535–40. http://dx.doi.org/10.1007/bf01663467.

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15

Altinok, Selma. "Hilbert series and applications to graded rings." International Journal of Mathematics and Mathematical Sciences 2003, no. 7 (2003): 397–403. http://dx.doi.org/10.1155/s0161171203107090.

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This paper contains a number of practical remarks on Hilbert series that we expect to be useful in various contexts. We use the fractional Riemann-Roch formula of Fletcher and Reid to write out explicit formulas for the Hilbert seriesP(t)in a number of cases of interest for singular surfaces (see Lemma 2.1) and3-folds. IfXis aℚ-Fano3-fold andS∈ |−KX|aK3surface in its anticanonical system (or the general elephant ofX), polarised withD=𝒪S (−KX), we determine the relation betweenPX(t)andPS,D(t). We discuss the denominator∏(1−tai)ofP(t)and, in particular, the question of how to choose a reasonably small denominator. This idea has applications to findingK3surfaces and Fano3-folds whose corresponding graded rings have small codimension. Most of the information about the anticanonical ring of a Fano3-fold orK3surface is contained in its Hilbert series. We believe that, by using information on Hilbert series, the classification ofℚ-Fano3-folds is too close. FindingK3surfaces are important because they occur as the general elephant of aℚ-Fano 3-fold.

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16

Domokos, Mátyás, and Vesselin Drensky. "Rationality of Hilbert series in noncommutative invariant theory." International Journal of Algebra and Computation 27, no. 07 (November 2017): 831–48. http://dx.doi.org/10.1142/s0218196717500394.

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It is a fundamental result in commutative algebra and invariant theory that a finitely generated graded module over a commutative finitely generated graded algebra has a rational Hilbert series, and consequently the Hilbert series of the algebra of polynomial invariants of a group of linear transformations is rational, whenever this algebra is finitely generated. This basic principle is applied here to prove rationality of Hilbert series of algebras of invariants that are neither commutative nor finitely generated. Our main focus is on linear groups acting on certain factor algebras of the tensor algebra that arise naturally in the theory of polynomial identities.

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17

Butzer, Paul L., and Tibor K. Pogány. "A fresh approach to classical Eisenstein series and the newer Hilbert–Eisenstein series." International Journal of Number Theory 13, no. 04 (March 24, 2017): 885–911. http://dx.doi.org/10.1142/s1793042117500464.

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This paper is concerned with new results for the circular Eisenstein series [Formula: see text] as well as with a novel approach to Hilbert–Eisenstein series [Formula: see text], introduced by Michael Hauss in 1995. The latter turns out to be the product of the hyperbolic sinh function with an explicit closed form linear combination of digamma functions. The results, which include differentiability properties and integral representations, are established by independent and different argumentations. Highlights are new results on the Butzer–Flocke–Hauss Omega function, one basis for the study of Hilbert–Eisenstein series, which have been the subject of several recent papers.

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18

Borzì, Alessio, and Alessio D'Alì. "Graded algebras with cyclotomic Hilbert series." Journal of Pure and Applied Algebra 225, no. 12 (December 2021): 106764. http://dx.doi.org/10.1016/j.jpaa.2021.106764.

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19

Maraj, Aida, and Uwe Nagel. "Equivariant Hilbert series for hierarchical Models." Algebraic Statistics 12, no. 1 (April 9, 2021): 21–42. http://dx.doi.org/10.2140/astat.2021.12.21.

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20

Kumar, Arvind, and Rajib Sarkar. "Hilbert series of binomial edge ideals." Communications in Algebra 47, no. 9 (March 26, 2019): 3830–41. http://dx.doi.org/10.1080/00927872.2019.1570241.

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21

Piontkovskii, D. I. "Hilbert series and relations in algebras." Izvestiya: Mathematics 64, no. 6 (December 31, 2000): 1297–311. http://dx.doi.org/10.1070/im2000v064n06abeh000316.

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22

Cameron, Peter, and Natalia Iyudu. "Graphs of relations and Hilbert series." Journal of Symbolic Computation 42, no. 11-12 (November 2007): 1066–78. http://dx.doi.org/10.1016/j.jsc.2007.07.006.

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23

Hanany, Amihay, Noppadol Mekareeya, and Giuseppe Torri. "The Hilbert series of adjoint SQCD." Nuclear Physics B 825, no. 1-2 (January 2010): 52–97. http://dx.doi.org/10.1016/j.nuclphysb.2009.09.016.

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24

La Scala, Roberto, and Sharwan K. Tiwari. "Multigraded Hilbert series of noncommutative modules." Journal of Algebra 516 (December 2018): 514–44. http://dx.doi.org/10.1016/j.jalgebra.2018.08.018.

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25

Sam, Steven V., and Andrew Snowden. "Hilbert series for twisted commutative algebras." Algebraic Combinatorics 1, no. 1 (2018): 147–72. http://dx.doi.org/10.5802/alco.9.

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26

Güntürkün, Sema, and Uwe Nagel. "Equivariant Hilbert series of monomial orbits." Proceedings of the American Mathematical Society 146, no. 6 (February 16, 2018): 2381–93. http://dx.doi.org/10.1090/proc/13943.

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27

de Carvalho Cayres Pinto, Pedro, Hans-Christian Herbig, Daniel Herden, and Christopher Seaton. "The Hilbert series of SL2-invariants." Communications in Contemporary Mathematics 22, no. 07 (March 26, 2019): 1950017. http://dx.doi.org/10.1142/s0219199719500172.

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Let [Formula: see text] be a finite-dimensional representation of the group [Formula: see text] of [Formula: see text] matrices with complex coefficients and determinant one. Let [Formula: see text] be the algebra of [Formula: see text]-invariant polynomials on [Formula: see text]. We present a calculation of the Hilbert series [Formula: see text] as well as formulas for the first four coefficients of the Laurent expansion of [Formula: see text] at [Formula: see text].

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28

Kumari, Moni. "Non-vanishing of Hilbert Poincaré series." Journal of Mathematical Analysis and Applications 466, no. 2 (October 2018): 1476–85. http://dx.doi.org/10.1016/j.jmaa.2018.06.051.

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29

Li, Yingkun. "Restriction of Coherent Hilbert Eisenstein series." Mathematische Annalen 368, no. 1-2 (July 20, 2016): 317–38. http://dx.doi.org/10.1007/s00208-016-1445-7.

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30

Atwill, Timothy W., and Benjamin Linowitz. "Newform theory for Hilbert Eisenstein series." Ramanujan Journal 30, no. 2 (September 6, 2012): 257–78. http://dx.doi.org/10.1007/s11139-012-9418-2.

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31

Yu, Zhou, and Gao Mingzhe. "On Hilbert's Inequality for Double Series and Its Applications." International Journal of Mathematics and Mathematical Sciences 2008 (2008): 1–12. http://dx.doi.org/10.1155/2008/165089.

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This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real functionu(x)and a parameterλ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality inHpfunction are given.

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32

TRAPANI, C. "QUASI *-ALGEBRAS OF OPERATORS AND THEIR APPLICATIONS." Reviews in Mathematical Physics 07, no. 08 (November 1995): 1303–32. http://dx.doi.org/10.1142/s0129055x95000475.

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The main facts of the theory of quasi*-algebras of operators acting in a rigged Hilbert space are reviewed. The particular case where the rigged Hilbert space is generated by a self-adjoint operator in Hilbert space is examined in more details. A series of applications to quantum theories are discussed.

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33

BERGER, ROLAND. "COMBINATORICS AND N-KOSZUL ALGEBRAS." International Journal of Geometric Methods in Modern Physics 05, no. 08 (December 2008): 1205–14. http://dx.doi.org/10.1142/s0219887808003272.

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The numerical Hilbert series combinatorics for quadratic Koszul algebras was extended to N-Koszul algebras by Dubois-Violette and Popov [9]. In this paper, we give a striking application of this extension when the relations of the algebra are all the antisymmetric tensors of degree N over given variables. Furthermore, we present a new type of Hilbert series combinatorics, called comodule Hilbert series combinatorics, and due to Hai, Kriegk and Lorenz [15]. When the relations are all the antisymmetric tensors, a natural generalization of the MacMahon Master Theorem (MMT) is obtained from the comodule level, the original MMT corresponding to N = 2 and to polynomial algebras.

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34

Iqbal, Zaffar, Xiujun Zhang, Mobeen Munir, and Ghina Mubashar. "Hilbert series of mixed braid monoid $ MB_{2, 2} $." AIMS Mathematics 7, no. 9 (2022): 17080–90. http://dx.doi.org/10.3934/math.2022939.

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<abstract><p>Hilbert series is a simplest way to calculate the dimension and the degree of an algebraic variety by an explicit polynomial equation. The mixed braid group $ B_{m, n} $ is a subgroup of the Artin braid group $ B_{m+n} $. In this paper we find the ambiguity-free presentation and the Hilbert series of canonical words of mixed braid monoid $ M\!B_{2, 2} $.</p></abstract>

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35

Lai, Ying-Cheng, and Nong Ye. "Recent Developments in Chaotic Time Series Analysis." International Journal of Bifurcation and Chaos 13, no. 06 (June 2003): 1383–422. http://dx.doi.org/10.1142/s0218127403007308.

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In this paper, two issues are addressed: (1) the applicability of the delay-coordinate embedding method to transient chaotic time series analysis, and (2) the Hilbert transform methodology for chaotic signal processing.A common practice in chaotic time series analysis has been to reconstruct the phase space by utilizing the delay-coordinate embedding technique, and then to compute dynamical invariant quantities of interest such as unstable periodic orbits, the fractal dimension of the underlying chaotic set, and its Lyapunov spectrum. As a large body of literature exists on applying the technique to time series from chaotic attractors, a relatively unexplored issue is its applicability to dynamical systems that exhibit transient chaos. Our focus will be on the analysis of transient chaotic time series. We will argue and provide numerical support that the current delay-coordinate embedding techniques for extracting unstable periodic orbits, for estimating the fractal dimension, and for computing the Lyapunov exponents can be readily adapted to transient chaotic time series.A technique that is gaining an increasing attention is the Hilbert transform method for signal processing in nonlinear systems. The general goal of the Hilbert method is to assess the spectrum of the instantaneous frequency associated with the underlying dynamical process. To obtain physically meaningful results, it is necessary for the signal to possess a proper rotational structure in the complex plane of the analytic signal constructed by the original signal and its Hilbert transform. We will describe a recent decomposition procedure for this task and apply the technique to chaotic signals. We will also provide an example to demonstrate that the methodology can be useful for addressing some fundamental problems in chaotic dynamics.

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36

Homs, Roser, and Anna-Lena Winz. "Canonical Hilbert-Burch matrices for power series." Journal of Algebra 583 (October 2021): 1–24. http://dx.doi.org/10.1016/j.jalgebra.2021.04.021.

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37

Gerritzen, L. "Hilbert series and non-associative Gröbner bases." manuscripta mathematica 103, no. 2 (October 2000): 161–67. http://dx.doi.org/10.1007/pl00022743.

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38

Anick, David J. "Diophantine Equations, Hilbert Series, and Undecidable Spaces." Annals of Mathematics 122, no. 1 (July 1985): 87. http://dx.doi.org/10.2307/1971370.

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39

McCabe, Adam, and Gregory G. Smith. "Log-concavity of asymptotic multigraded Hilbert series." Proceedings of the American Mathematical Society 141, no. 6 (December 20, 2012): 1883–92. http://dx.doi.org/10.1090/s0002-9939-2012-11808-8.

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40

Forcella, Davide, Amihay Hanany, and Alberto Zaffaroni. "Master space, Hilbert series and Seiberg duality." Journal of High Energy Physics 2009, no. 07 (July 6, 2009): 018. http://dx.doi.org/10.1088/1126-6708/2009/07/018.

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41

Enright, T. J., and J. F. Willenbring. "Hilbert series, Howe duality, and branching rules." Proceedings of the National Academy of Sciences 100, no. 2 (January 13, 2003): 434–37. http://dx.doi.org/10.1073/pnas.0136632100.

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42

Ferrarello, Daniela, and Ralf Fröberg. "The Hilbert Series of the Clique Complex." Graphs and Combinatorics 21, no. 4 (December 2005): 401–5. http://dx.doi.org/10.1007/s00373-005-0634-z.

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43

Arenas, Angela, and Jaime-Luis Garcia-Roig. "On Fourier coefficients of Eisenstein–Hilbert series." Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 108, no. 2 (March 17, 2013): 527–39. http://dx.doi.org/10.1007/s13398-013-0124-8.

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44

Bell, Jason P. "The Hilbert series of prime PI rings." Israel Journal of Mathematics 139, no. 1 (December 2004): 1–10. http://dx.doi.org/10.1007/bf02787539.

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45

Ramírez Alfonsín, Jorge L., and Øystein J. Rødseth. "Numerical semigroups: Apéry sets and Hilbert series." Semigroup Forum 79, no. 2 (January 27, 2009): 323–40. http://dx.doi.org/10.1007/s00233-009-9133-5.

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46

Futaki, Akito, Hajime Ono, and Yuji Sano. "Hilbert series and obstructions to asymptotic semistability." Advances in Mathematics 226, no. 1 (January 2011): 254–84. http://dx.doi.org/10.1016/j.aim.2010.06.018.

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47

Piontkovskii, D. I. "Hilbert series and their relations in algebras." Russian Mathematical Surveys 53, no. 6 (December 31, 1998): 1360–61. http://dx.doi.org/10.1070/rm1998v053n06abeh000102.

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48

Broer, B. "A New Method for Calculating Hilbert Series." Journal of Algebra 168, no. 1 (August 1994): 43–70. http://dx.doi.org/10.1006/jabr.1994.1220.

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49

Grundman, H. G. "Defect series and nonrational Hilbert modular threefolds." Mathematische Annalen 300, no. 1 (September 1994): 77–88. http://dx.doi.org/10.1007/bf01450476.

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50

Källström, Rolf, and Yohannes Tadesse. "Hilbert series of modules over Lie algebroids." Journal of Algebra 432 (June 2015): 129–84. http://dx.doi.org/10.1016/j.jalgebra.2015.02.020.

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