Los Bombardeos de la aviación italiana sobre Burriana (Castellon) durante los años 1937 y 1938

This paper unveils the unpublished material recovered in Italy on aerial bombardments over the city of Burriana (Castellón) by “Legionary” Italian aviation between 1937 and 1938. The graphic material is supplemented with historical documentation unpublished also help to understand these events those never had been analyzed previously.En este artículo damos a conocer material inédito recuperado en Italia sobre los bombardeos aéreos realizados sobre el término municipal de Burriana (Castellón) por la aviación legionaria italiana entre los años 1937 y 1938. Además del material grafico se complementa la documentación con datos históricos también inéditos que ayudan a entender estos acontecimientos

Evaluation codes defined by finite families of plane valuations at infinity

We construct evaluation codes given by weight functions defined over polynomial rings in m a parts per thousand yen 2 indeterminates. These weight functions are determined by sets of m-1 weight functions over polynomial rings in two indeterminates defined by plane valuations at infinity. Well-suited families in totally ordered commutative groups are an important tool in our procedureSupported by Spain Ministry of Education MTM2007-64704 and Bancaixa P1-1B2009-03. The authors thank to the referees for their valuable suggestions.Galindo Pastor, C.; Monserrat Delpalillo, FJ. (2014). Evaluation codes defined by finite families of plane valuations at infinity. Designs, Codes and Cryptography. 70(1-2):189-213. https://doi.org/10.1007/s10623-012-9738-7S189213701-2Abhyankar S.S.: Local uniformization on algebraic surfaces over ground field of characteristic p ≠ 0. Ann. Math. 63, 491–526 (1956)Abhyankar S.S.: On the valuations centered in a local domain. Am. J. Math. 78, 321–348 (1956)Abhyankar S.S.: Lectures on expansion techniques in algebraic geometry. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 57. Tata Institute of Fundamental Research, Bombay (1977).Abhyankar S.S.: On the semigroup of a meromorphic curve (part I). In: Proceedings of the International Symposium on Algebraic Geometry (Kyoto) Kinokunio Tokio, pp. 249–414 (1977).Abhyankar S.S., Moh T.T.: Newton-Puiseux expansion and generalized Tschirnhausen transformation (I). J. Reine Angew. Math. 260, 47–83 (1973)Abhyankar S.S., Moh T.T.: Newton-Puiseux expansion and generalized Tschirnhausen transformation (II). J. Reine Angew. Math. 261, 29–54 (1973)Berlekamp E.R.: Algebraic Coding Theory. McGraw-Hill, New York (1968)Campillo A., Farrán J.I.: Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models. Finite Fields Appl. 6, 71–92 (2000)Carvalho C., Munuera C., Silva E., Torres F.: Near orders and codes. IEEE Trans. Inf. Theory 53, 1919–1924 (2007)Decker W., Greuel G.M., Pfister G., Schöenemann H.: Singular 3.1.3, a computer algebra system for polynomial computations (2011) http://www.singular.uni-kl.de .Feng G.L., Rao T.R.N.: Decoding of algebraic geometric codes up to the designed minimum distance. IEEE Trans. Inf. Theory 39, 37–45 (1993)Feng G.L., Rao T.R.N.: A simple approach for construction of algebraic-geometric codes from affine plane curves. IEEE Trans. Inf. Theory 40, 1003–1012 (1994)Feng G.L., Rao T.R.N.: Improved geometric Goppa codes, part I: basic theory. IEEE Trans. Inf. Theory 41, 1678–1693 (1995)Fujimoto M., Suzuki M.: Construction of affine plane curves with one place at infinity. Osaka J. Math. 39(4), 1005–1027 (2002)Galindo C.: Plane valuations and their completions. Commun. Algebra 23(6), 2107–2123 (1995)Galindo C., Monserrat F.: δ-sequences and evaluation codes defined by plane valuations at infinity. Proc. Lond. Math. Soc. 98, 714–740 (2009)Galindo C., Monserrat F.: The Abhyankar-Moh theorem for plane valuations at infinity. Preprint 2010. ArXiv:0910.2613v2.Galindo C., Sanchis M.: Evaluation codes and plane valuations. Des. Codes Cryptogr. 41(2), 199–219 (2006)Geil O.: Codes based on an $${\mathbb{F}_q}$$ -algebra. PhD Thesis, Aalborg University, June (2000).Geil O., Matsumoto R.: Generalized Sudan’s list decoding for order domain codes. Lecture Notes in Computer Science, vol. 4851, pp. 50–59 (2007)Geil O., Pellikaan R.: On the structure of order domains. Finite Fields Appl. 8, 369–396 (2002)Goppa V.D.: Codes associated with divisors. Probl. Inf. Transm. 13, 22–26 (1997)Goppa V.D.: Geometry and Codes. Mathematics and Its Applications, vol. 24. Kluwer, Dordrecht (1991).Greco S., Kiyek K.: General elements in complete ideals and valuations centered at a two-dimensional regular local ring. In: Algebra, Arithmetic, and Geometry, with Applications, pp. 381–455. Springer, Berlin (2003).Høholdt T., van Lint J.H., Pellikaan R.: Algebraic geometry codes. In: Handbook of Coding Theory, vol. 1, pp. 871–961. Elsevier, Amsterdam (1998).Jensen C.D.: Fast decoding of codes from algebraic geometry. IEEE Trans. Inf. Theory 40, 223–230 (1994)Justesen J., Larsen K.J., Jensen H.E., Havemose A., Høholdt T.: Construction and decoding of a class of algebraic geometric codes. IEEE Trans. Inf. Theory 35, 811–821 (1989)Justesen J., Larsen K.J., Jensen H.E., Høholdt T.: Fast decoding of codes from algebraic plane curves. IEEE Trans. Inf. Theory 38, 111–119 (1992)Massey J.L.: Shift-register synthesis and BCH decoding. IEEE Trans. Inf. Theory 15, 122–127 (1969)Matsumoto R.: Miura’s generalization of one point AG codes is equivalent to Høholdt, van Lint and Pellikaan’s generalization. IEICE Trans. Fundam. E82-A(10), 2007–2010 (1999)Moghaddam M.: Realization of a certain class of semigroups as value semigroups of valuations. Bull. Iran. Math. Soc. 35, 61–95 (2009)O’Sullivan M.E.: Decoding of codes defined by a single point on a curve. IEEE Trans. Inf. Theory 41, 1709–1719 (1995)O’Sullivan M.E.: New codes for the Belekamp-Massey-Sakata algorithm. Finite Fields Appl. 7, 293–317 (2001)Pinkham H.: Séminaire sur les singularités des surfaces (Demazure-Pinkham-Teissier), Course donné au Centre de Math. de l’Ecole Polytechnique (1977–1978).Sakata S.: Extension of the Berlekamp-Massey algorithm to N dimensions. Inf. Comput. 84, 207–239 (1990)Sakata S., Jensen H.E., Høholdt T.: Generalized Berlekamp-Massey decoding of algebraic geometric codes up to half the Feng-Rao bound. IEEE Trans. Inf. Theory 41, 1762–1768 (1995)Sakata S., Justesen J., Madelung Y., Jensen H.E., Høholdt T.: Fast decoding of algebraic geometric codes up to the designed minimum distance. IEEE Trans. Inf. Theory 41, 1672–1677 (1995)Sathaye A.: On planar curves. Am. J. Math. 99(5), 1105–1135 (1977)Shannon C.E.: A mathematical theory of communication. Bell Syst. 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Finite families of plane valuations: value semigroup, graded algebra and Poincaré series

[EN] In this paper, the authors are interested in some applications of valuation theory to algebraic geometry and, particularly, to singularity theory. The aim of this paper is to provide a concise survey of some aspects of the theory of plane valuations, adding some comments upon more general valuations when it is possible. For those valuations, authors describe value semigroup, graded algebra and Poincar ¿e series emphasizing on the recent study of the same algebraic objects for finite families of valuations and their relation with the corresponding ones for reduced germs of plane curvesSupported by Spain Ministry of Education MTM2007-64704 and Bancaixa P1-1B2009-03.Monserrat Delpalillo, FJ.; Galindo Pastor, C. (2012). Finite families of plane valuations: value semigroup, graded algebra and Poincaré series. Contemporary Mathematics. 566:189-212. https://doi.org/10.1090/conm/566/1122118921256

Experiential restaurants: Playing while eating

The goal of this project was analysing if a restaurant based on experiential dinning would succeed in the city of Zaragoza. Having this objective in mind it was necessary to develop a market research. There were two basic ideas proposed, one for the long-run experience (Dynamism) and the other one for the short-run (Playing while eating). In order to cover the need of opinions and direct information, a focus group was made. The results form this technique made us split the research in two parts, one for each topic. At the end, we decided to follow the Playing while eating topic as there were more information available. After that decision, in order to go in depth with the topic we developed another focus group fully oriented to the playing topic. From that focus group we gathered a lot of useful information that had to be checked and compared using a representative sample, which made us develop a survey. Thanks to this survey we could analyse the data in a mathematical way (using averages and percentages) that allowed us to develop the final conclusions of the research and guided us to think about some recommendations for a future. The general conclusion of the research is that depending of the initial investment and the will to organize (as it would be complex) this project would succeed or not (following some of the recommendations of the project).<br /

The Spanish-Muslim fortification of the Burriana’s medina (Castellón)

[EN] This communication aims to publicize the latest archeological findings related to the Spanish-Muslim wall of Burriana, obtained thanks to the interventions carried out throughout the twenty-first century, in which new sectors and towers of the wall have been evidenced, and that they also clarify some ancient historical and archaeological news about the fortification. We highlight the documentation of the construction technique of the wall, which provides interesting data on its chronology, recently established around the eleventh century. The relationship between the defensive structure and other recent archaeological findings associated with this period are examined, such as some necropolis and elements of the urban plot. Finally, an analysis of the historical and territorial context of the defensive structure and the Spanish-Muslim city will be carried out, since Burriana’s medina was an important administrative and commercial center, a stopping point on the land route between Tortosa and Valencia, and cited as an amal that also had a seaport, according to some sources. We do not forget that the madīna is also a prominent enclave in the historical events related to the Christian razzias of the eleventh and twelfth centuries, and in the subsequent process of conquest of the kingdom of Valencia at the beginning of the thirteenth century, as reflected in the chronicles of the time.Melchor Monserrat, J. (2020). La fortificación hispanomusulmana de la madīna de Burriana (Castellón). Editorial Universitat Politècnica de València. 139-146. https://doi.org/10.4995/FORTMED2020.2020.11344OCS13914

On the classification of exceptional planar functions over F_p

The final publication is available at Springer via http://dx.doi.org/10.1007/s10711-013-9926-2We will present many strong partial results towards a classification of exceptional planar/PN monomial functions on finite fields. The techniques we use are the Weil bound, Bézout’s theorem, and Bertini’s theorem.This research was partially supported by MINECO under Grant No. MTM2012-36917-C03-03 (Spain). Research of the second author supported by the Claude Shannon Institute, Science Foundation Ireland Grant 06/MI/006.Hernando, F.; Mcguire, G.; Monserrat Delpalillo, FJ. (2014). On the classification of exceptional planar functions over F_p. Geometriae Dedicata. 173(1):1-35. https://doi.org/10.1007/s10711-013-9926-2S1351731Beauville, A.: Complex Algebraic Surfaces, London Math. Society, Student Texts 34. Cambridge University Press, Cambridge (1996)Bodin, A.: Reducibility of rational functions in several variables. Israel J. Math. 164, 333–347 (2008)Campillo, A., Gonzalez-Sprinberg, G., Monserrat, F.: Configurations of infinitely near points. Sao Paulo J. Math. Sci. 3(1), 115–160 (2009)Coulter, R., Matthews, R.: Planar functions and planes of Lenz–Barlotti class II. Des. Codes Cryptogr. 10, 167–184 (1997)Coulter, R.: Private communication pointed out by R. Coulter in a private communicationDembowski, P., Ostrom, T.G.: Planes of order $$n$$ n with collineation groups of order $$n^2$$ n 2 . Math. Z. 103, 239–258 (1968)Eisenbud, D., Harris, J.: The Geometry of Schemes, Grad. Texts Math., vol. 197. Springer, New York (1999)Fulton, W.: Algebraic Curves. Benjamin, New York (1969)Guralnick, R., Rosenberg, J., Zieve, M.: A new family of exceptional polynomials in characteristic two. Ann. Math. 172, 1361–1390 (2010)Hartshorne, R.: Algebraic Geometry, Grad. Texts Math., vol. 52. Springer, New York (1977)Hernando, F., McGuire, G.: Proof of a conjecture on the sequence of exceptional numbers, classifying cyclic codes and APN functions. J. Algebra 343, 78–92 (2011)Hernando, F., McGuire, G.: Proof of a conjecture of Segre and Bartocci on monomial hyperovals in projective planes. Des. Codes Cryptogr. 65(3), 275–289 (2012)Iitaka, S.: Algebraic Geometry. Grad. Texts Math., vol. 76. Springer, New York (1982)Janwa, H., McGuire, G., Wilson, R.M.: Double-error-correcting cyclic codes and absolutely irreducible polynomials over GF(2). J. Algebra 178(2), 665–676 (1995)Kleiman, S.L.: Bertini and his two fundamental theorems. Studies in the history of modern mathematics. III. Rend. Circ. Mat. Palermo (2) Suppl. no. 55, 9–37 (1998)Kopparty, S., Yekhanin, S.: Detecting rational points on hypersurfaces over finite fields. In: 23rd Annual IEEE Conference Computational Complexity 2008, CCC ’08, pp. 311–320 (2008)Leducq, E.: Functions which are PN on infinitely many extensions of $$F_p, p$$ F p , p odd. http://arxiv.org/abs/1006.2610Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications. Revision of the 1986 first edition. Cambridge University Press, Cambridge, xii+416 pp (1994)Nyberg, K., Knudsen, L.R.: Provable Security Against Differential Cryptanalysis, Advances in Cryptology CRYPTO92, LNCS 740. Springer, Berlin (1992