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Journal articles on the topic 'Jacobi groups'

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Published: 14 March 2023

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1

Rezaei-Aghdam, Adel, and Mehdi Sephid. "Classical r-matrices of real low-dimensional Jacobi–Lie bialgebras and their Jacobi–Lie groups." International Journal of Geometric Methods in Modern Physics 13, no. 07 (July 25, 2016): 1650087. http://dx.doi.org/10.1142/s0219887816500870.

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In this paper, we obtain the classical [Formula: see text]-matrices of real two- and three-dimensional Jacobi–Lie bialgebras. In this way, we classify all non-isomorphic real two- and three-dimensional coboundary Jacobi–Lie bialgebras and their types (triangular and quasi-triangular). Also, we obtain the generalized Sklyanin bracket formula by use of which, we calculate the Jacobi structures on the related Jacobi–Lie groups. Finally, we present a new method for constructing classical integrable systems using coboundary Jacobi–Lie bialgebras.

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2

Sun, BinYong. "On representations of real Jacobi groups." Science China Mathematics 55, no. 3 (December 24, 2011): 541–55. http://dx.doi.org/10.1007/s11425-011-4333-3.

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3

Celeghini, E., M. Gadella, and M. A. del Olmo. "Groups, Jacobi functions, and rigged Hilbert spaces." Journal of Mathematical Physics 61, no. 3 (March 1, 2020): 033508. http://dx.doi.org/10.1063/1.5138238.

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4

Kohnen, W. "Nonholomorphic Poincaré-Type Series on Jacobi Groups." Journal of Number Theory 46, no. 1 (January 1994): 70–99. http://dx.doi.org/10.1006/jnth.1994.1005.

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5

Macdonald, I. D., and B. H. Neumann. "On commutator laws in groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 45, no. 1 (August 1988): 95–103. http://dx.doi.org/10.1017/s1446788700032304.

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AbstractThere are some well-known laws that the commutator satisfies in groups, and that go by some or all of the names Jacobi, Witt, Hall; and there are also some lesser-known laws. This is an attempt at an axiomatic study of the interdependence and independence of these laws.

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6

Stroffolini, Bianca. "Homogenization of Hamilton-Jacobi equations in Carnot Groups." ESAIM: Control, Optimisation and Calculus of Variations 13, no. 1 (January 2007): 107–19. http://dx.doi.org/10.1051/cocv:2007005.

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7

Kerr, Matt, James D. Lewis, and Stefan Müller-Stach. "The Abel–Jacobi map for higher Chow groups." Compositio Mathematica 142, no. 02 (March 2006): 374–96. http://dx.doi.org/10.1112/s0010437x05001867.

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8

Younes, Laurent. "Jacobi fields in groups of diffeomorphisms and applications." Quarterly of Applied Mathematics 65, no. 1 (February 15, 2007): 113–34. http://dx.doi.org/10.1090/s0033-569x-07-01027-5.

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9

Shao, Jinghai. "Hamilton–Jacobi semi-groups in infinite dimensional spaces." Bulletin des Sciences Mathématiques 130, no. 8 (December 2006): 720–38. http://dx.doi.org/10.1016/j.bulsci.2006.03.001.

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10

Celeghini, Enrico, Mariano A. del Olmo, and Miguel A. Velasco. "Lie groups, algebraic special functions and Jacobi polynomials." Journal of Physics: Conference Series 597 (April 13, 2015): 012023. http://dx.doi.org/10.1088/1742-6596/597/1/012023.

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11

Amirzadeh-Fard, H., Gh Haghighatdoost, and A. Rezaei-Aghdam. "Jacobi-Lie Hamiltonian Systems on Real Low-Dimensional Jacobi-Lie Groups and their Lie Symmetries." Zurnal matematiceskoj fiziki, analiza, geometrii 18, no. 1 (January 25, 2022): 33–56. http://dx.doi.org/10.15407/mag18.01.033.

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12

Amirzadeh-Fard, H., G. Haghighatdoost, P. Kheradmandynia, and A. Rezaei-Aghdam. "Jacobi structures on real two- and three-dimensional Lie groups and their Jacobi–Lie systems." Theoretical and Mathematical Physics 205, no. 2 (November 2020): 1393–410. http://dx.doi.org/10.1134/s004057792011001x.

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13

Nagaoka, S. "On eisenstein series for the Hermitian modular groups and the Jacobi groups." Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 62, no. 1 (December 1992): 117–46. http://dx.doi.org/10.1007/bf02941621.

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14

Macdonald, I. D., and B. H. Neumann. "On commutator laws in groups, 3." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 58, no. 1 (February 1995): 126–33. http://dx.doi.org/10.1017/s1446788700038143.

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AbstractIn this final contribution to the investigation of commutator laws in groups, we answer some of the questions left open in the previous two papers. The principal result is the independence of the Jacobi-Witt-Hall type laws from the so-called standard set of laws. The main results of the earlier papers are summarised. An interlude corrects some of the numerous printing errors in the second of our papers.

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15

Zhang, Bei. "Fourier–Jacobi coefficients of Eisenstein series on unitary groups." Algebra & Number Theory 7, no. 2 (April 25, 2013): 283–337. http://dx.doi.org/10.2140/ant.2013.7.283.

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16

Kerr, Matt, and James D. Lewis. "The Abel–Jacobi map for higher Chow groups, II." Inventiones mathematicae 170, no. 2 (August 1, 2007): 355–420. http://dx.doi.org/10.1007/s00222-007-0066-x.

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17

Hawkins, Thomas. "Jacobi and the birth of Lie's theory of groups." Archive for History of Exact Sciences 42, no. 3 (1991): 187–278. http://dx.doi.org/10.1007/bf00375135.

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18

Sato, Kanetomo. "Abel-Jacobi mappings and finiteness of motivic cohomology groups." Duke Mathematical Journal 104, no. 1 (July 2000): 75–112. http://dx.doi.org/10.1215/s0012-7094-00-10414-0.

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19

Iglesias, David, and Juan C. Marrero. "Generalized Lie bialgebras and Jacobi structures on Lie groups." Israel Journal of Mathematics 133, no. 1 (December 2003): 285–320. http://dx.doi.org/10.1007/bf02773071.

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20

Berceanu, Stefan, and Alexandru Gheorghe. "The Jacobi group and its holomorphic discrete series representations on Siegel–Jacobi domains." Russian Universities Reports. Mathematics, no. 128 (2019): 345–53. http://dx.doi.org/10.20310/2686-9667-2019-24-128-345-353.

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This is the summary of a part of the talk delivered at the workshop held at the Tambov University in September 2012, reporting several results on Jacobi groups and its holomorphic representations published by the authors.

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21

Wang, Wenjie, and Xinxin Dai. "Pseudo-Parallel Characteristic Jacobi Operators on Contact Metric 3 Manifolds." Journal of Mathematics 2021 (July 21, 2021): 1–6. http://dx.doi.org/10.1155/2021/6148940.

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We prove that the characteristic Jacobi operator on a contact metric three manifold is semiparallel if and only if it vanishes. We determine Lie groups of dimension three admitting left invariant contact metric structures such that the characteristic Jacobi operators are pseudoparallel.

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22

Obukhov, Valeriy V. "Algebra of the Symmetry Operators of the Klein–Gordon–Fock Equation for the Case When Groups of Motions G3 Act Transitively on Null Subsurfaces of Spacetime." Symmetry 14, no. 2 (February 9, 2022): 346. http://dx.doi.org/10.3390/sym14020346.

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The algebras of the symmetry operators for the Hamilton–Jacobi and Klein–Gordon–Fock equations are found for a charged test particle, moving in an external electromagnetic field in a spacetime manifold on the isotropic (null) hypersurface, of which a three-parameter groups of motions acts transitively. We have found all admissible electromagnetic fields for which such algebras exist. We have proved that an admissible field does not deform the algebra of symmetry operators for the free Hamilton–Jacobi and Klein–Gordon–Fock equations. The results complete the classification of admissible electromagnetic fields, in which the Hamilton–Jacobi and Klein–Gordon–Fock equations admit algebras of motion integrals that are isomorphic to the algebras of operators of the r-parametric groups of motions of spacetime manifolds if (r≤4).

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23

Rezaei-Aghdam, A., and M. Sephid. "Classification of real low-dimensional Jacobi (generalized)–Lie bialgebras." International Journal of Geometric Methods in Modern Physics 14, no. 01 (December 20, 2016): 1750007. http://dx.doi.org/10.1142/s0219887817500074.

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We describe the definition of Jacobi (generalized)–Lie bialgebras [Formula: see text] in terms of structure constants of the Lie algebras [Formula: see text] and [Formula: see text] and components of their 1-cocycles [Formula: see text] and [Formula: see text] in the basis of the Lie algebras. Then, using adjoint representations and automorphism Lie groups of Lie algebras, we give a method for classification of real low-dimensional Jacobi–Lie bialgebras. In this way, we obtain and classify real two- and three-dimensional Jacobi–Lie bialgebras.

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24

Beals, Richard, Bernard Gaveau, and Peter C. Greiner. "Hamilton–Jacobi theory and the heat kernel on Heisenberg groups." Journal de Mathématiques Pures et Appliquées 79, no. 7 (September 2000): 633–89. http://dx.doi.org/10.1016/s0021-7824(00)00169-0.

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25

Munteanu, Marian Ioan. "Magnetic Geodesic in (Almost) Cosymplectic Lie Groups of Dimension 3." Mathematics 10, no. 4 (February 10, 2022): 544. http://dx.doi.org/10.3390/math10040544.

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In this paper, we study contact magnetic geodesics in a 3-dimensional Lie group G endowed with a left invariant almost cosymplectic structure. We distinguish the two cases: G is unimodular, and G is nonunimodular. We pay a careful attention to the special case where the structure is cosymplectic, and we write down explicit expressions of magnetic geodesics and corresponding magnetic Jacobi fields.

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26

Raskind, Wayne. "Higher $l$ -adic Abel-Jacobi mappings and filtrations on Chow groups." Duke Mathematical Journal 78, no. 1 (April 1995): 33–57. http://dx.doi.org/10.1215/s0012-7094-95-07803-x.

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27

Bertola, Marco. "Frobenius manifold structure on orbit space of Jacobi groups; Part I." Differential Geometry and its Applications 13, no. 1 (July 2000): 19–41. http://dx.doi.org/10.1016/s0926-2245(00)00026-7.

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28

Bertola, Marco. "Frobenius manifold structure on orbit space of Jacobi groups; Part II." Differential Geometry and its Applications 13, no. 3 (November 2000): 213–33. http://dx.doi.org/10.1016/s0926-2245(00)00027-9.

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29

Williams, Brandon. "Higher pullbacks of modular forms on orthogonal groups." Forum Mathematicum 33, no. 3 (March 20, 2021): 631–52. http://dx.doi.org/10.1515/forum-2020-0066.

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Abstract We apply differential operators to modular forms on orthogonal groups O ⁢ ( 2 , ℓ ) {\mathrm{O}(2,\ell)} to construct infinite families of modular forms on special cycles. These operators generalize the quasi-pullback. The subspaces of theta lifts are preserved; in particular, the higher pullbacks of the lift of a (lattice-index) Jacobi form ϕ are theta lifts of partial development coefficients of ϕ. For certain lattices of signature ( 2 , 2 ) {(2,2)} and ( 2 , 3 ) {(2,3)} , for which there are interpretations as Hilbert–Siegel modular forms, we observe that the higher pullbacks coincide with differential operators introduced by Cohen and Ibukiyama.

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30

Chan, Kei Yuen. "Restriction for general linear groups: The local non-tempered Gan–Gross–Prasad conjecture (non-Archimedean case)." Journal für die reine und angewandte Mathematik (Crelles Journal) 2022, no. 783 (December 2, 2021): 49–94. http://dx.doi.org/10.1515/crelle-2021-0066.

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Abstract We prove a local Gan–Gross–Prasad conjecture on predicting the branching law for the non-tempered representations of general linear groups in the case of non-Archimedean fields. We also generalize to Bessel and Fourier–Jacobi models and study a possible generalization to Ext-branching laws.

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31

Green, Mark, Phillip Griffiths, and Matt Kerr. "Néron models and limits of Abel–Jacobi mappings." Compositio Mathematica 146, no. 2 (February 2, 2010): 288–366. http://dx.doi.org/10.1112/s0010437x09004400.

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AbstractWe show that the limit of a one-parameter admissible normal function with no singularities lies in a non-classical sub-object of the limiting intermediate Jacobian. Using this, we construct a Hausdorff slit analytic space, with complex Lie group fibres, which ‘graphs’ such normal functions. For singular normal functions, an extension of the sub-object by a finite group leads to the Néron models. When the normal function comes from geometry, that is, a family of algebraic cycles on a semistably degenerating family of varieties, its limit may be interpreted via the Abel–Jacobi map on motivic cohomology of the singular fibre, hence via regulators onK-groups of its substrata. Two examples are worked out in detail, for families of 1-cycles on CY and abelian 3-folds, where this produces interesting arithmetic constraints on such limits. We also show how to compute the finite ‘singularity group’ in the geometric setting.

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32

Liu, Yifeng. "Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups." Manuscripta Mathematica 145, no. 1-2 (March 9, 2014): 1–69. http://dx.doi.org/10.1007/s00229-014-0666-x.

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33

Gan, Wee Teck, Benedict H. Gross, and Dipendra Prasad. "Branching laws for classical groups: the non-tempered case." Compositio Mathematica 156, no. 11 (November 2020): 2298–367. http://dx.doi.org/10.1112/s0010437x20007496.

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This paper generalizes the Gan–Gross–Prasad (GGP) conjectures that were earlier formulated for tempered or more generally generic L-packets to Arthur packets, especially for the non-generic L-packets arising from Arthur parameters. The paper introduces the key notion of a relevant pair of Arthur parameters that governs the branching laws for ${{\rm GL}}_n$ and all classical groups over both local fields and global fields. It plays a role for all the branching problems studied in Gan et al. [Symplectic local root numbers, central critical L-values and restriction problems in the representation theory of classical groups. Sur les conjectures de Gross et Prasad. I, Astérisque 346 (2012), 1–109] including Bessel models and Fourier–Jacobi models.

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34

Yamana, Shunsuke. "PERIODS OF AUTOMORPHIC FORMS: THE TRILINEAR CASE." Journal of the Institute of Mathematics of Jussieu 17, no. 1 (October 26, 2015): 59–74. http://dx.doi.org/10.1017/s1474748015000377.

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Following Jacquet, Lapid and Rogawski, we regularize trilinear periods. We use the regularized trilinear periods to compute Fourier–Jacobi periods of residues of Eisenstein series on metaplectic groups, which has an application to the Gan–Gross–Prasad conjecture.

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35

Xue, Hang. "Refined global Gan–Gross–Prasad conjecture for Fourier–Jacobi periods on symplectic groups." Compositio Mathematica 153, no. 1 (January 2017): 68–131. http://dx.doi.org/10.1112/s0010437x16007752.

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In this paper, we propose a conjectural identity between the Fourier–Jacobi periods on symplectic groups and the central value of certain Rankin–Selberg $L$-functions. This identity can be viewed as a refinement to the global Gan–Gross–Prasad conjecture for $\text{Sp}(2n)\times \text{Mp}(2m)$. To support this conjectural identity, we show that when $n=m$ and $n=m\pm 1$, it can be deduced from the Ichino–Ikeda conjecture in some cases via theta correspondences. As a corollary, the conjectural identity holds when $n=m=1$ or when $n=2$, $m=1$ and the automorphic representation on the bigger group is endoscopic.

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36

Zou, Yi Ming. "Quantum super spheres and their transformation groups, representations, and little t-Jacobi polynomials." Journal of Algebra 267, no. 1 (September 2003): 178–98. http://dx.doi.org/10.1016/s0021-8693(03)00101-7.

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37

Skopin, A. I. "Jacobi identity and P. Hall's collection formula in two types of transmetabelian groups." Journal of Soviet Mathematics 57, no. 6 (December 1991): 3507–12. http://dx.doi.org/10.1007/bf01100121.

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38

Kohnen, W. "On the uniform convergence of poincaré series of exponential type on Jacobi groups." Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 66, no. 1 (December 1996): 131–34. http://dx.doi.org/10.1007/bf02940798.

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39

Innami, Nobuhiro, and Byung Hak Kim. "Gradient vector fields which characterize warped products." MATHEMATICA SCANDINAVICA 88, no. 2 (June 1, 2001): 182. http://dx.doi.org/10.7146/math.scand.a-14322.

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We find what condition on gradient vector fields characterizes warped products, Riemannian products and round spheres. To do this we apply the theory of Jacobi equations without conjugate points to the differential maps of the local one-parameter groups generated by gradient vector fields.

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40

SOLÉ, PATRICK, and DMITRII ZINOVIEV. "A MACWILLIAMS FORMULA FOR CONVOLUTIONAL CODES." International Journal of Number Theory 03, no. 02 (June 2007): 191–206. http://dx.doi.org/10.1142/s1793042107000869.

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Regarding convolutional codes as polynomial analogues of arithmetic lattices, we derive a Poisson–Jacobi formula for their trivariate weight enumerator. The proof is based on harmonic analysis on locally compact abelian groups as developed in Tate's thesis to derive the functional equation of the zeta function.

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41

Grillo, Sergio, Juan Carlos Marrero, and Edith Padrón. "Extended Hamilton–Jacobi Theory, Symmetries and Integrability by Quadratures." Mathematics 9, no. 12 (June 11, 2021): 1357. http://dx.doi.org/10.3390/math9121357.

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In this paper, we study the extended Hamilton–Jacobi Theory in the context of dynamical systems with symmetries. Given an action of a Lie group G on a manifold M and a G-invariant vector field X on M, we construct complete solutions of the Hamilton–Jacobi equation (HJE) related to X (and a given fibration on M). We do that along each open subset U⊆M, such that πU has a manifold structure and πU:U→πU, the restriction to U of the canonical projection π:M→M/G, is a surjective submersion. If XU is not vertical with respect to πU, we show that such complete solutions solve the reconstruction equations related to XU and G, i.e., the equations that enable us to write the integral curves of XU in terms of those of its projection on πU. On the other hand, if XU is vertical, we show that such complete solutions can be used to construct (around some points of U) the integral curves of XU up to quadratures. To do that, we give, for some elements ξ of the Lie algebra g of G, an explicit expression up to quadratures of the exponential curve expξt, different to that appearing in the literature for matrix Lie groups. In the case of compact and of semisimple Lie groups, we show that such expression of expξt is valid for all ξ inside an open dense subset of g.

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42

Guin, Satyajit, and Bipul Saurabh. "Representations and classification of the compact quantum groups Uq(2) for complex deformation parameters." International Journal of Mathematics 32, no. 04 (February 24, 2021): 2150020. http://dx.doi.org/10.1142/s0129167x21500208.

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In this paper, we obtain a complete list of inequivalent irreducible representations of the compact quantum group [Formula: see text] for nonzero complex deformation parameters [Formula: see text], which are not roots of unity. The matrix coefficients of these representations are described in terms of the little [Formula: see text]-Jacobi polynomials. The Haar state is shown to be faithful and an orthonormal basis of [Formula: see text] is obtained. Thus, we have an explicit description of the Peter–Weyl decomposition of [Formula: see text]. As an application, we discuss the Fourier transform and establish the Plancherel formula. We also describe the decomposition of the tensor product of two irreducible representations into irreducible components. Finally, we classify the compact quantum group [Formula: see text].

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43

Massa, Enrico, and Enrico Pagani. "On the notion of Jacobi fields in constrained calculus of variations." Communications in Mathematics 24, no. 2 (December 1, 2016): 91–113. http://dx.doi.org/10.1515/cm-2016-0007.

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Abstract In variational calculus, the minimality of a given functional under arbitrary deformations with fixed end-points is established through an analysis of the so called second variation. In this paper, the argument is examined in the context of constrained variational calculus, assuming piecewise differentiable extremals, commonly referred to as extremaloids. The approach relies on the existence of a fully covariant representation of the second variation of the action functional, based on a family of local gauge transformations of the original Lagrangian and on a set of scalar attributes of the extremaloid, called the corners' strengths [16]. In dis- cussing the positivity of the second variation, a relevant role is played by the Jacobi fields, defined as infinitesimal generators of 1-parameter groups of diffeomorphisms preserving the extremaloids. Along a piecewise differentiable extremal, these fields are generally discontinuous across the corners. A thorough analysis of this point is presented. An alternative characterization of the Jacobi fields as solutions of a suitable accessory variational problem is established.

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44

BOUWKNEGT, PETER, and DAVID RIDOUT. "PRESENTATIONS OF WESS–ZUMINO–WITTEN FUSION RINGS." Reviews in Mathematical Physics 18, no. 02 (March 2006): 201–32. http://dx.doi.org/10.1142/s0129055x06002620.

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The fusion rings of the Wess–Zumino–Witten models are re-examined. Attention is drawn to the difference between fusion rings over ℤ (which are often of greater importance in applications) and fusion algebras over ℂ. Complete proofs are given by characterizing the fusion algebras (over ℂ) of the SU (r+1) and Sp (2r) models in terms of the fusion potentials, and it is shown that the analagous potentials cannot describe the fusion algebras of the other models. This explains why no other representation-theoretic fusion potentials have been found. Instead, explicit generators are then constructed for general WZW fusion rings (over ℤ). The Jacobi–Trudy identity and its Sp (2r) analogue are used to derive the known fusion potentials. This formalism is then extended to the WZW models over the spin groups of odd rank, and explicit presentations of the corresponding fusion rings are given. The analogues of the Jacobi–Trudy identity for the spinor representations (for all ranks) are derived for this purpose, and may be of independent interest.

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45

Celeghini, Enrico, Manuel Gadella, and Mariano A. del Olmo. "Groups, Special Functions and Rigged Hilbert Spaces." Axioms 8, no. 3 (July 27, 2019): 89. http://dx.doi.org/10.3390/axioms8030089.

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We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special functions serve as bases for infinite dimensional Hilbert spaces supporting linear unitary irreducible representations of a given Lie group. These representations are explicitly given by operators on the Hilbert space H and the generators of the Lie algebra are represented by unbounded self-adjoint operators. The action of these operators on elements of continuous bases is often considered. These continuous bases do not make sense as vectors in the Hilbert space; instead, they are functionals on the dual space, Φ × , of a rigged Hilbert space, Φ ⊂ H ⊂ Φ × . In fact, rigged Hilbert spaces are the structures in which both, discrete orthonormal and continuous bases may coexist. We define the space of test vectors Φ and a topology on it at our convenience, depending on the studied group. The generators of the Lie algebra can often be continuous operators on Φ with its own topology, so that they admit continuous extensions to the dual Φ × and, therefore, act on the elements of the continuous basis. We investigate this formalism for various examples of interest in quantum mechanics. In particular, we consider S O ( 2 ) and functions on the unit circle, S U ( 2 ) and associated Laguerre functions, Weyl–Heisenberg group and Hermite functions, S O ( 3 , 2 ) and spherical harmonics, s u ( 1 , 1 ) and Laguerre functions, s u ( 2 , 2 ) and algebraic Jacobi functions and, finally, s u ( 1 , 1 ) ⊕ s u ( 1 , 1 ) and Zernike functions on a circle.

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46

HAYASHIDA, Shuichi. "RANKIN-SELBERG METHOD FOR JACOBI FORMS OF INTEGRAL WEIGHT AND OF HALF-INTEGRAL WEIGHT ON SYMPLECTIC GROUPS." Kyushu Journal of Mathematics 73, no. 2 (2019): 391–415. http://dx.doi.org/10.2206/kyushujm.73.391.

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47

Achter, Jeffrey D., Sebastian Casalaina-Martin, and Charles Vial. "On descending cohomology geometrically." Compositio Mathematica 153, no. 7 (May 10, 2017): 1446–78. http://dx.doi.org/10.1112/s0010437x17007151.

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In this paper, motivated by a problem posed by Barry Mazur, we show that for smooth projective varieties over the rationals, the odd cohomology groups of degree less than or equal to the dimension can be modeled by the cohomology of an abelian variety, provided the geometric coniveau is maximal. This provides an affirmative answer to Mazur’s question for all uni-ruled threefolds, for instance. Concerning cohomology in degree three, we show that the image of the Abel–Jacobi map admits a distinguished model over the rationals.

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48

Maalaoui, Kamel, and Fouad Zargouni. "The lower and middle Berriasian in Central Tunisia: Integrated ammonite and calpionellid biostratigraphy of the Sidi Kralif Formation." Acta Geologica Polonica 66, no. 1 (March 1, 2016): 43–58. http://dx.doi.org/10.1515/agp-2016-0002.

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Abstract The lower and middle Berriasian sedimentary succession of the Sidi Kralif Formation has been a subject of biostratigraphic study in two key sections in Central Tunisia. Our contribution is an attempt to better define the basal Berriasian interval, between the Berriasella jacobi Zone and the Subthurmannia occitanica Zone. Zonal schemes are established using ammonites and calpionellids, and these permit correlation with other regions of Mediterranean Tethys and beyond. The use of biomarkers afforded by microfossil groups has allowed characterization and direct correlation with four widely accepted calpionellid sub-zones, namely Calpionella alpina, Remaniella, Calpionella elliptica and Tintinopsella longa. The two ammonite zones of Berriasella jacobi and of Subthurmannia occitanica are recognised on the basis of their index species. The parallel ammonite and calpionellid zonations are useful as a tool for correlation and calibration in time and space, thus allowing a better definition of a J/K boundary. The presence of four Berriasian calpionellid bioevents is recognised: (1) the ‘explosion’ of Calpionella alpina, (2) the first occurrence of Remaniella, (3) the first occurrence of Calpionella elliptica and (4) the first occurrence of Tintinopsella longa. The last is here documented as coeval with the presence of Subthurmannia occitanica, which marks the lower/middle Berriasian boundary.

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49

Voineagu, Mircea. "Cylindrical homomorphisms and Lawson homology." Journal of K-Theory 8, no. 1 (June 8, 2010): 135–68. http://dx.doi.org/10.1017/is010004024jkt108.

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AbstractWe use the cylindrical homomorphism and a geometric construction introduced by J. Lewis to study the Lawson homology groups of certain hypersurfaces X ⊂ ℙn + 1 of degree d ℙ n + 1. As an application, we compute the rational semi-topological K-theory of generic cubics of dimensions 5, 6 and 8 and, using the Bloch-Kato conjecture, we prove Suslin's conjecture for these varieties. Using generic cubic sevenfolds, we show that there are smooth projective varieties such that the lowest nontrivial step in their s-filtration is infinitely generated and undetected by the Abel-Jacobi map.

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50

Günther, Paul. "The Poisson Formula for Euclidean Space Groups and some of its Applications II. The Jacobi Transformation for Flat Manifolds." Zeitschrift für Analysis und ihre Anwendungen 4, no. 4 (1985): 341–52. http://dx.doi.org/10.4171/zaa/157.

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