On Weierstra{\ss} semigroups at one and two points and their corresponding Poincar\'e series

The aim of this paper is to introduce and investigate the Poincar\'e series associated with the Weierstra{\ss} semigroup of one and two rational points at a (not necessarily irreducible) non-singular projective algebraic curve defined over a finite field, as well as to describe their functional equations in the case of an affine complete intersection.Comment: Beginning of Section 3 and Subsection 3.1 were modifie

Quantum codes from a new construction of self-orthogonal algebraic geometry codes

[EN] We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes. These results demonstrate that there is a lot more scope for constructing self-orthogonal AG codes than was previously known.G. McGuire was partially supported by Science Foundation Ireland Grant 13/IA/1914. The remainder authors were partially supported by the Spanish Government and the EU funding program FEDER, Grants MTM2015-65764-C3-2-P and PGC2018-096446-B-C22. F. Hernando and J. J. Moyano-Fernandez are also partially supported by Universitat Jaume I, Grant UJI-B2018-10.Hernando, F.; Mcguire, G.; Monserrat Delpalillo, FJ.; Moyano-Fernández, JJ. (2020). Quantum codes from a new construction of self-orthogonal algebraic geometry codes. Quantum Information Processing. 19(4):1-25. https://doi.org/10.1007/s11128-020-2616-8S125194Abhyankar, S.S.: Irreducibility criterion for germs of analytic functions of two complex variables. Adv. Math. 74, 190–257 (1989)Abhyankar, S.S.: Algebraic Geometry for Scientists and Engineers. Mathematical Surveys and Monographs, American Mathematical Society, Providence (1990)Ashikhmin, A., Barg, A., Knill, E., Litsyn, S.: Quantum error-detection I: statement of the problem. IEEE Trans. Inf. Theory 46, 778–788 (2000)Ashikhmin, A., Barg, A., Knill, E., Litsyn, S.: Quantum error-detection II: bounds. IEEE Trans. Inf. Theory 46, 789–800 (2000)Ashikhmin, A., Knill, E.: Non-binary quantum stabilizer codes. IEEE Trans. Inf. Theory 47, 3065–3072 (2001)Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symb. Comput. 24, 235–265 (1997)Bierbrauer, J., Edel, Y.: Quantum twisted codes. J. Comb. Des. 8, 174–188 (2000)Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction and orthogonal geometry. Phys. Rev. Lett. 76, 405–409 (1997)Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996)Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via codes over GF(4). IEEE Trans. Inf. Theory 44(4), 1369–1387 (1998)Campillo, A., Farrán, J.I.: Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models. Finite Fields Appl. 6, 71–92 (2000)Duursma, I.M.: Algebraic geometry codes: general theory. In: Advances in Algebraic Geometry Codes, Series of Coding Theory and Cryptology, vol. 5. World Scientific, Singapore (2008)Feng, K.: Quantum error correcting codes. In: Coding Theory and Cryptology, pp. 91–142. Word Scientific (2002)Feng, K., Ma, Z.: A finite Gilbert–Varshamov bound for pure stabilizer quantum codes. IEEE Trans. Inf. Theory 50, 3323–3325 (2004)Galindo, C., Geil, O., Hernando, F., Ruano, D.: On the distance of stabilizer quantum codes from $$J$$-affine variety codes. Quantum Inf. Process 16, 111 (2017)Galindo, C., Hernando, F., Matsumoto, R.: Quasi-cyclic construction of quantum codes. Finite Fields Appl. 52, 261–280 (2018)Galindo, C., Hernando, F., Ruano, D.: Stabilizer quantum codes from $$J$$-affine variety codes and a new Steane-like enlargement. Quantum Inf. Process 14, 3211–3231 (2015)Galindo, C., Hernando, F., Ruano, D.: Classical and quantum evaluation codes at the trace roots. IEEE Trans. Inf. Theory 16, 2593–2602 (2019)Garcia, A.: On AG codes and Artin–Schreier extensions. Commun. Algebra 20(12), 3683–3689 (1992)Goppa, V.D.: Geometry and Codes. Mathematics and its Applications, vol. 24. Kluwer, Dordrecht (1991)Goppa, V.D.: Codes associated with divisors. Probl. Inf. Transm. 13, 22–26 (1977)Gottesman, D.: A class of quantum error-correcting codes saturating the quantum Hamming bound. Phys. Rev. A 54, 1862–1868 (1996)Grassl, M., Rötteler, M.: Quantum BCH codes. In: Proceedings X International Symposium Theory Electrical Engineering, pp. 207–212. Germany (1999)Grassl, M., Beth, T., Rötteler, M.: On optimal quantum codes. Int. J. Quantum Inf. 2, 757–775 (2004)He, X., Xu, L., Chen, H.: New $$q$$-ary quantum MDS codes with distances bigger than $$q/2$$. Quantum Inf. Process. 15(7), 2745–2758 (2016)Hirschfeld, J.W.P., Korchmáros, G., Torres, F.: Algebraic Curves Over a Finite Field. Princeton Series in Applied Mathematics, Princeton (2008)Høholdt, T., van Lint, J., Pellikaan, R.: Algebraic geometry codes. Handb. Coding Theory 1, 871–961 (1998)Jin, L., Xing, C.: Euclidean and Hermitian self-orthogonal algebraic geometry codes and their application to quantum codes. IEEE Trans. Inf. Theory 58, 4489–5484 (2012)Ketkar, A., Klappenecker, A., Kumar, S., Sarvepalli, P.K.: Nonbinary stabilizer codes over finite fields. IEEE Trans. Inf. Theory 52, 4892–4924 (2006)La Guardia, G.G.: Construction of new families of nonbinary quantum BCH codes. Phys. Rev. A 80, 042331 (2009)La Guardia, G.G.: On the construction of nonbinary quantum BCH codes. IEEE Trans. Inf. Theory 60, 1528–1535 (2014)Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications. Cambridge University Press, Cambridge (1994)Matsumoto, R., Uyematsu, T.: Constructing quantum error correcting codes for $$p^m$$ state systems from classical error correcting codes. IEICE Trans. Fund. E83–A, 1878–1883 (2000)McGuire, G., Yılmaz, E.S.: Divisibility of L-polynomials for a family of Artin–Schreier curves. J. Pure Appl. Algebra 223(8), 3341–3358 (2019)Munuera, C., Sepúlveda, A., Torres, F.: Castle curves and codes. Adv. Math. Commun. 3, 399–408 (2009)Munuera, C., Tenório, W., Torres, F.: Quantum error-correcting codes from algebraic geometry codes of castle type. Quantum Inf. Process. 15, 4071–4088 (2016)Pellikaan, R., Shen, B.Z., van Wee, G.J.M.: Which linear codes are algebraic-geometric. IEEE Trans. Inf. Theory 37, 583–602 (1991)Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124–134. IEEE Computer Society Press (1994)Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493 (1995)Steane, A.M.: Multiple-particle interference and quantum error correction. Proc. R. Soc. Lond. Ser. A 452, 2551–2557 (1996)Stichtenoth, H.: Algebraic Function Fields and Codes. Springer, Berlin (2009)Tsfasman, M.A., Vlăduţ, S.G., Zink, T.: Modular curves, Shimura curves and AG codes, better than Varshamov–Gilbert bound. Math. Nachr. 109, 21–28 (1982

El amoniaco en los peces. II. Aspectos tóxicos

A review of much of the existing information about toxic effects of arnmonia in fish is done, making distinction between acute and chronic toxicity. The different noticeable damages in fish, thus environmental and nutritional factors influencing ammonia levels in water are described. Lastly, sorne methods of measure of ammonia concentration are enumerated,even as their utility for fish culturists.Se hace una revisión de la información existente sobre los efectos tóxicos del amoníaco en peces, distinguiendo entre toxicidad crónica y agua. Se describen las distintas alteraciones apreciables, así como los factores ambientales y nutricionales que influyen en la variación de los niveles de amoníaco en el medio. Por último, se enumeran algunos métodos de medida de la concentractón de dicho compuesto en agua y su utilidad para el piscicultor

El amoniaco en los peces. II. Aspectos tóxicos

Se hace una revisión de la información existente sobre los efectos tóxicos del amoníaco en peces, distinguiendo entre toxicidad crónica y agua. Se describen las distintas alteraciones apreciables, así como los factores ambientales y nutricionales que influyen en la variación de los niveles de amoníaco en el medio. Por último, se enumeran algunos métodos de medida de la concentractón de dicho compuesto en agua y su utilidad para el piscicultor.A review of much of the existing information about toxic effects of arnmonia in fish is done, making distinction between acute and chronic toxicity. The different noticeable damages in fish, thus environmental and nutritional factors influencing ammonia levels in water are described. Lastly, sorne methods of measure of ammonia concentration are enumerated,even as their utility for fish culturists

El amoniaco en los peces. I. aspectos metabólicos y excreción

A review of the existing information about metabolic aspects and excretion of ammonia in fish is done. Different metabolic pathways and their respective contribution to total ammoniogenesis are described, thus branchial excretion mecahisms and the different factors affecting it.Se hace una revisión de la información existente sobre los aspectos metabólicos y la excreción de amoníaco en peces. Se describen las distintas vías metabólicas de producción de amoníaco y su contribución a la amoniogénesis total, así como los mecanismos de excreción a nivel branquial y diversos factores que influyen sobre ella

El amoniaco en los peces. I. aspectos metabólicos y excreción

Se hace una revisión de la información existente sobre los aspectos metabólicos y la excreción de amoníaco en peces. Se describen las distintas vías metabólicas de producción de amoníaco y su contribución a la amoniogénesis total, así como los mecanismos de excreción a nivel branquial y diversos factores que influyen sobre ella.A review of the existing information about metabolic aspects and excretion of ammonia in fish is done. Different metabolic pathways and their respective contribution to total arnmoniogenesis are described, thus branchial excretion mecahisms and the different factors affecting it

Angular momentum transport by magnetic fields in main sequence stars with Gamma Doradus pulsators

Context. Asteroseismic studies showed that cores of post main-sequence stars rotate slower than theoretically predicted by stellar models with purely hydrodynamical transport processes. Recent studies on main sequence stars, particularly Gamma Doradus ($\gamma$ Dor) stars, revealed their internal rotation rate for hundreds of stars, offering a counterpart on the main sequence for studies of angular momentum transport. Aims. We investigate whether such a disagreement between observed and predicted internal rotation rates is present in main sequence stars by studying angular momentum transport in $\gamma$ Dor stars. Furthermore, we test whether models of rotating stars with internal magnetic fields can reproduce their rotational properties. Methods. We compute rotating models with the Geneva stellar evolution code taking into account meridional circulation and the shear instability. We also compute models with internal magnetic fields using a general formalism for transport by the Tayler-Spruit dynamo. We then compare these models to observational constraints for $\gamma$ Dor stars that we compiled from the literature, combining so the core rotation rates, projected rotational velocities from spectroscopy, and constraints on their fundamental parameters. Results. We show that combining the different observational constraints available for $\gamma$ Dor stars enable to clearly distinguish the different scenarios for internal angular momentum transport. Stellar models with purely hydrodynamical processes are in disagreement with the data whereas models with internal magnetic fields can reproduce both core and surface constraints simultaneously. Conclusions. Similarly to results obtained for subgiant and red giant stars, angular momentum transport in radiative regions of $\gamma$ Dor stars is highly efficient, in good agreement with predictions of models with internal magnetic fields.Comment: Accepted for publication in Astronomy & Astrophysics. 16 pages, 17 figures, 1 appendi

Nonadditive entropy and nonextensive statistical mechanics - Some central concepts and recent applications

We briefly review central concepts concerning nonextensive statistical mechanics, based on the nonadditive entropy $S_q=k\frac{1-\sum_{i}p_i^q}{q-1} (q \in {\cal R}; S_1=-k\sum_{i}p_i \ln p_i)$. Among others, we focus on possible realizations of the $q$-generalized Central Limit Theorem, including at the edge of chaos of the logistic map, and for quasi-stationary states of many-body long-range-interacting Hamiltonian systems.Comment: 15 pages, 9 figs., to appear in Journal of Physics: Conf.Series (IOP, 2010

On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al

In the present paper we refute the criticism advanced in a recent preprint by Figueiredo et al [1] about the possible application of the $q$-generalized Central Limit Theorem (CLT) to a paradigmatic long-range-interacting many-body classical Hamiltonian system, the so-called Hamiltonian Mean Field (HMF) model. We exhibit that, contrary to what is claimed by these authors and in accordance with our previous results, $q$-Gaussian-like curves are possible and real attractors for a certain class of initial conditions, namely the one which produces nontrivial longstanding quasi-stationary states before the arrival, only for finite size, to the thermal equilibrium.Comment: 2 pages, 2 figures. Short version of the paper, accepted for publication in Europhysics Letters, (2009) in pres