Some generalizations of the notion of Lie algebra

We introduce the notion of left (and right) quasi-Loday algebroids and a "universal space" for them, called a left (right) omni-Loday algebroid, in such a way that Lie algebroids, omni-Lie algebras and omni-Loday algebroids are particular substructures.Comment: Second version. 14 pages. Included some comments about previous works related to Leibniz algebras, and updated bibliography. A new example adde

On Lie Algebroids and Poisson Algebras

We introduce and study a class of Lie algebroids associated to faithful modules which is motivated by the notion of cotangent Lie algebroids of Poisson manifolds. We also give a classification of transitive Lie algebroids and describe Poisson algebras by using the notions of algebroid and Lie connections

"It shouldn’t smell like latin language at all". Pedro Simón Abril’s translation of Cicero’s "Letters to Friends" (1589)

En este artículo se examinan los principales recursos técnicos de los que se sirve el humanista Pedro Simón Abril en su traducción de las Epistulae ad familiares de Cicerón (1589), la primera versión completa de esta colección epistolar en España. A través del presente análisis se puede observar cómo estas técnicas de traducción no sólo son fruto de su habilidad y de su experiencia como traductor, sino que responden además a una labor previa de reflexión teórica y a una concepción de la traducción como un proceso esencialmente creativo. Esta necesidad de adaptarse al gusto literario del público lector explica algunas de las características de lengua y estilo de la versión de Simón Abril. Y será en estas cualidades artísticas en las que radique la clave de su éxito y su vigencia por espacio de más de cuatro siglos.The aim of this paper is to revisit the main techniques used by Pedro Simón Abril in his translation of Cicero’s Epistulae ad familiares (1589), the first version of this epistolary collection in Spain. By means of this analysis it can observed that these techniques of translation are the result not only of his skill and translating experience, but also that they respond to a prior work of theoretical reflection and an idea of translation as an essentially creative process. What is more, his adaptation to the literary taste of his readers explains certain peculiarities of the language and the style ofAbril’s translation.And precisely these artistic qualities are the key for the success and the survival of his translation along the last four centuries

On the solvability of groups with four class sizes

It is shown that if the set of conjugacy class sizes of a finite group G is {1,m,n,mn}, where m, n are positive integers which do not divide each other, then G is up to central factors a {p,q}-group. In particular, G is solvable.This research is supported by the Spanish Government, Proyecto MTM2010-19938-C03-02 and by the Valencian Government, Proyecto PROMETEO/2011/30, and the first author is also supported by grant Fundacio Caixa-Castello P11B2010-47.Beltrán, A.; Felipe Román, MJ. (2012). On the solvability of groups with four class sizes. Journal of Algebra and Its Applications. 11(2):1250036-1250043. https://doi.org/10.1142/S0219498811005609S1250036125004311

Class sizes of prime-power order p'-elements and normal subgroups

We prove an extension of the renowned Itô’s theorem on groups having two class sizes in three different directions at the same time: normal subgroups, p′p′-elements and prime-power order elements. Let NN be a normal subgroup of a finite group GG and let pp be a fixed prime. Suppose that |xG|=1|xG|=1 or mm for every qq-element of NN and for every prime q≠pq≠p. Then, NN has nilpotent pp-complements.We are very grateful to the referee, who provided us a significant simplification of the last step of the proof of the main theorem and for many comments which have contributed to improve the paper. C. G. Shao wants to express his deep gratitude for the warm hospitality he has received in the Departamento de Matematicas of the Universidad Jaume I in Castellon, Spain. This research is supported by the Valencian Government, Proyecto PROMETEO/2011/30, by the Spanish Government, Proyecto MTM2010-19938-C03-02. The third author is supported by the research Project NNSF of China (Grant Nos. 11201401 and 11301218) and University of Jinan Research Funds for Doctors (XBS1335 and XBS1336).Beltrán, A.; Felipe Román, MJ.; Shao, C. (2015). Class sizes of prime-power order p'-elements and normal subgroups. Annali di Matematica Pura ed Applicata. 194(5):1527-1533. https://doi.org/10.1007/s10231-014-0432-4S152715331945Akhlaghi, Z., Beltrán, A., Felipe, M.J.: The influence of $$p$$ p -regular class sizes on normal subgroups. J. Group Theory. 16, 585–593 (2013)Alemany, E., Beltrán, A., Felipe, M.J.: Nilpotency of normal subgroups having two $$G$$ G -class sizes. Proc. Am. Math. Soc. 139, 2663–2669 (2011)Alemany, E., Beltrán, A., Felipe, M.J.: Finite groups with two $$p$$ p -regular conjugacy class lengths II. Bull. Aust. Math. Soc. 797, 419–425 (2009)Beltrán, A., Felipe, M.J.: Normal subgroups and class sizes elements of prime-power order. Proc. Am. Math. Soc. 140, 4105–4109 (2012)Beltrán, A.: Action with nilpotent fixed point subgroup. Arch. Math. (Basel) 69, 177–184 (1997)Camina, A.R.: Finite groups of conjugate rank 2. Nagoya Math. J. 53, 47–57 (1974)Casolo, C., Dolfi, S., Jabara, E.: Finite groups whose noncentral class sizes have the same $$p$$ p -part for some prime $$p$$ p . Isr. J. Math. 192, 197–219 (2012)Huppert, B.: Character Theory of Finite groups, vol. 25. De Gruyter Expositions in Mathemathics, Berlin, New York (1998)Kleidman, P., Liebeck, M.: The Subgroup Structure of The Finite Classical Groups. London Mathematical Society Lecture Note Series, 129. Cambridge University Press, Cambridge (1990)Kurzweil, K., Stellmacher, B.: The Theory of Finite Groups. An Introduction. Springer, New York (2004)The GAP Group, GAP—Groups, Algorithms and Programming, Vers. 4.4.12 (2008). http://www.gap-system.orgVasiliev, A.V., Vdovin, E.P.: An adjacency criterion for the prime graph of a finite simple group. Algebra Logic 44(6), 381–406 (2005

Dry cured low-fat rabbit sausage: A much healthier disruptive food that enhances rabbit meat consumption

The main objective of this research was to develop a fuet from rabbit meat with reduced fat and salt content to encourage rabbit consumption and to find out consumer preference for this innovative food compared to retail fuet. Two products were designed: F5, containing fat and F4, where fatty tissue was substituted by konjac gum. In both, salt was partially substituted by KCl. These products, in comparison to commercial ones (pork, chicken and turkey), showed a reduction of at least 40% in the total energy value while protein raised on average 57.81% because of the lower fat content of rabbit and konjac gum use. In addition, there was a decrease in the salt content of approximately 19.50%. The above represents a huge competitive advantage for these new products from a nutritional point of view. The rabbit fuets were characterised by a spicy taste, slightly sour smell, and succulence, lower than in commercial fuets. It could be concluded that the rabbit fuet had a higher protein and lower fat and salt content than commercial fuets. However, they were less juicy and less succulent and therefore consumers preferred the commercial ones. The use of konjac gum does not seem to have any effect on this type of cured product

Influence of Seaweeds on the Quality of Pasta as a Plant-Based Innovative Food

This study evaluated the effect of the incorporation of seaweed on the physicochemical and technological quality of pasta. For this purpose, enriched wheat pastas from different seaweeds (sea lettuce—Ulva lactuca, nori—Porphyra tenera, and wakame—Undaria pinnatifida) were made and compared with durum wheat pasta as a control treatment. Firstly, optimal cooking times were established by visual and instrumental methods. Then, the technological properties of weight gain (WG), swelling index (SI), cooking losses (CL), and moisture (H%) were determined. Protein and fiber analyses, texture profile analysis (TPA), and color measurements were also performed to evaluate the physicochemical properties. Overall, enriched pasta with seaweed revealed slightly shorter optimal cooking times than control pasta. Texture properties were also modified, with a lower value of hardness, and higher values of adhesiveness and resilience. However, due to the low percentages of seaweed (3%), noticeable effects were not appreciated. Moreover, color variations of enriched pasta were relevant due to the difference among seaweeds. Nonetheless, these additions increased the protein content and soluble fiber in these foods. In conclusion, pasta enriched with marine ingredients improved this nutritional profile, and the changes in technological properties did not have a major impact on the product quality

Transforming ‘Bonito del Norte’ Tuna By-Products into Functional Ingredients for Nutritional Enhancement of Cereal-Based Foods

The fishing industry produces a significant number of by-products. This study explored two methods of transforming these by-products: fish protein hydrolysate (FPH) and Fishmeal (FM). Physicochemical characterization of these products was conducted and their potential inclusion in biscuits was investigated due to the lack of high biological value protein and polyunsaturated fatty acids of this product. The results identified colour disparities between FPH and FM, with FM displaying lower brightness and a more reddish hue. In FPH, there was also a noticeable decrease in polyunsaturated fatty acids, probably associated with the temperature reached in spray-drying. While the incorporation of these by-products in biscuits was feasible, there were challenges, particularly the fishy taste and rancid odour, which were more pronounced in FM biscuits due to the higher fat content. This correlated with the oxidation indexes, such as TBARS and acidity index. Nonetheless, FPH biscuit attributes like typical colour or flavour received positive feedback, attributed to the Maillard reaction. Scanning electron microscopy revealed microstructural differences, which correlated with the results of hardness and fracturability, probably due to the higher fat content in FM. This study revealed the possibility of nutritionally enriching cookies with ingredients derived from fish by-products. However, it would be necessary to go a step further and study alternatives that allow better preservation of saturated fatty acids

Low-fat fresh sausage from rabbit meat: An alternative to traditional rabbit consumption

The study aimed at the development of fresh sausages using rabbit exclusively as raw material. The idea was to offer an innovative product to increase rabbit consumption. Also, to meet currently consumers' requirements, a low-fat version was made. Two final formulations, a control sausage and a low-fat version using konjac gum, were developed through an iterative process and stored in a MAP under refrigeration. Sensory, microbiological and physicochemical analyses were carried out on days 1, 6, 8 and 13 after packaging. The shelf-life of the sausages was determined according to a multivariate criterion. Results showed a significant reduction in fat content and energy value. Sensory analysis showed a decrease in characteristic aroma and flavour and an increase in rancid odour, while hardness and fragility decreased in the low-fat treatment. The shelf-life was 7 days for all treatments, concluding that the multivariate method was a powerful technique as physicochemical, microbiological and sensory criteria were considered

Triangles in the graph of conjugacy classes of normal subgroups

[EN] Let G be a finite group and N a normal subgroup of G. We determine the structure of N when the graph G(N), which is the graph associated to the conjugacy classes of G contained in N, has no triangles and when the graph consists in exactly one triangle.The research of the first and second authors is supported by the Valencian Government, Proyecto PROMETEOII/2015/011. The first and the third authors are also partially supported by Universitat Jaume I, Grant P11B2015-77.Beltrán, A.; Felipe Román, MJ.; Melchor, C. (2017). Triangles in the graph of conjugacy classes of normal subgroups. Monatshefte für Mathematik. 182(1):5-21. https://doi.org/10.1007/S00605-015-0866-9S5211821Bertram, E.A., Herzog, M., Mann, A.: On a graph related to conjugacy classes of groups. Bull. London Math. Soc. 22(6), 569-575 (1990)Beltrán, A., Felipe, M.J., Melchor, C.: Graphs associated to conjugacy classes of normal subgroups in finite groups. J. Algebra 443, 335-348 (2015)Camina, A.R.: Arithmetical conditions on the conjugacy class numbers of a finite group. J. London Math. Soc. 2(5), 127-132 (1972)Deaconescu, M.: Classification of finite groups with all elements of prime order. Proc. Am. Math. Soc. 106(3), 625-629 (1989)Doerk, K., Hawkes, T.: Finite soluble groups. de Gruyter Expositions in Mathematics, vol. 4. Walter de Gruyter, Berlin (1992)Fang, M., Zhang, P.: Finite groups with graphs containing no triangles. J. Algebra 264(2), 613-619 (2003)Higman, G.: Finite groups in which every element has prime power order. J. London Math. Soc. 32, 335-342 (1957)Manz, O., Wolf, T.R.: Representations of solvable groups. Cambridge Univ. Press, Cambridge (1993)Riese, U., Shahabi, M.A.: Subgroups which are the union of four conjugacy classes. Commun. Algebra 29(2), 695-701 (2001)Shahryari, M., Shahabi, M.A.: Subgroups which are the union of three conjugate classes. J. Algebra 207(1), 326-332 (1998)The GAP Group.: GAP–groups, algorithms and programming, Vers. 4.4.12. (2008). http://www.gap-system.or