Trenzas y nudos

El objetivo de este trabajo es mostrar al lector la fuerte relación entre la teoría de trenzas y la teoría de nudos, dos ramas de la topología de baja de dimensión más próximas de lo que parece. La primera parte de este estudio está dedicada a los conceptos y resultados básicos acerca de teoría de trenzas, que nos ayudarán a cumplir nuestro objetivo. En segundo lugar, introduciremos la noción de nudo matemático y explicaremos cómo formarlos a partir de trenzas. En esta sección daremos dos grandes resultados: los Teoremas de Alexander y de Markov. Por último, nos aproximaremos a la construcción original del polinomio de Jones, un invariante de nudos, a partir de grupos de trenzas, lo que pone de manifiesto la estrecha relación entre estas disciplinas

Effects of wet/dry-cycling and plasma treatments on the properties of flax nonwovens intended for composite reinforcing

Producción CientíficaThis research analyzes the effects of different treatments on flax nonwoven (NW) fabrics which are intended for composite reinforcement. The treatments applied were of two different kinds: a wet/dry cycling which helps to stabilize the cellulosic fibers against humidity changes and plasma treatments with air, argon and ethylene gases considering different conditions and combinations, which produce variation on the chemical surface composition of the NWs. The resulting changes in the chemical surface composition, wetting properties, thermal stability and mechanical properties were determined. Variations in surface morphology could be observed by scanning electron microscopy (SEM). The results of the X-ray photoelectron spectroscopy (XPS) showed significant changes to the surface chemistry for the samples treated with argon or air (with more content on polar groups on the surface) and ethylene plasma (with less content of polar groups). Although only slight differences were found in moisture regain and water retention values (WRV), significant changes were found on the contact angle values, thus revealing hydrophilicity for the air-treated and argon-treated samples and hydrophobicity for the ethylene-treated ones. Moreover, for some of the treatments the mechanical testing revealed an increase of the NW breaking force.Ministerio de Educación y Formación Profesional (grants BIA2014-59399-R and FPU12/05869

A new invariant for cyclic orbit flag codes

In the network coding framework, given a prime power $q$ and the vector space $\mathbb{F}_q^n$, a constant type flag code is a set of nested sequences of $\mathbb{F}_q$-subspaces (flags) with the same increasing sequence of dimensions (the type of the flag). If a flag code arises as the orbit under the action of a cyclic subgroup of the general linear group over a flag, we say that it is a cyclic orbit flag code. Among the parameters of such a family of codes, we have its best friend, that is the largest field over which all the subspaces in the generating flag are vector spaces. This object permits to compute the cardinality of the code and estimate its minimum distance. However, as it occurs with other absolute parameters of a flag code, the information given by the best friend is not complete in many cases due to the fact that it can be obtained in different ways. In this work, we present a new invariant, the best friend vector, that captures the specific way the best friend can be unfolded. Furthermore, throughout the paper we analyze the strong underlying interaction between this invariant and other parameters such as the cardinality, the flag distance, or the type vector, and how it conditions them. Finally, we investigate the realizability of a prescribed best friend vector in a vector space

Consistent Flag Codes

In this paper we study flag codes on Fnq, being Fq the finite field with q elements. Special attention is given to the connection between the parameters and properties of a flag code and the ones of a family of constant dimension codes naturally associated to it (the projected codes). More precisely, we focus on consistent flag codes, that is, flag codes whose distance and size are completely determined by their projected codes. We explore some aspects of this family of codes and present examples of them by generalizing the concepts of equidistant and sunflower subspace code to the flag codes setting. Finally, we present a decoding algorithm for consistent flag codes that fully exploits the consistency condition.The authors receive financial support from Ministerio de Ciencia e Innovación (PID2019-108668GB-I00). The second author is supported by Generalitat Valenciana and Fondo Social Europeo (ACIF/2018/196)

On Generalized Galois Cyclic Orbit Flag Codes

Flag codes that are orbits of a cyclic subgroup of the general linear group acting on flags of a vector space over a finite field, are called cyclic orbit flag codes. In this paper, we present a new contribution to the study of such codes, by focusing this time on the generating flag. More precisely, we examine those ones whose generating flag has at least one subfield among its subspaces. In this situation, two important families arise: the already known Galois flag codes, in case we have just fields, or the generalized Galois flag codes in other case. We investigate the parameters and properties of the latter ones and explore the relationship with their underlying Galois flag code.This research was funded by Ministerio de Ciencia e Innovación (grant number PID2019-108668GB-I00) and Generalitat Valenciana y Fondo Social Europeo (Grant number ACIF/2018/196)

Diseño Participativo: Propuesta de Marca Turística del Pueblo de Moixent.

[ES] En este Trabajo Final de Grado se propone una marca turística para el pueblo de Moixent a través del diseño participativo, empleando la metodología del Focus Group. Doce participantes colaboran en el proceso de diseño de la marca en una sesión participativa en la que se llegan a acuerdos colectivos. En esta memoria se recogen los aspectos clave a la hora de realizar este proyecto: el trabajo de investigación, su conceptualización y el desarrollo práctico del mismo. Todo esto llevado a cabo desde una perspectiva funcional, atractiva y actual a través del diseño gráfico, la fotografía y la ilustración. Experimentando y ampliando el proceso creativo y de aprendizaje, se pretende subsanar la falta de una marca turística.[EN] A tourist brand is proposed for the town of Moixent through co-design using the methodology of the Focus Group. Twelve participants collaborate in the branding process, reaching collective agreements by experimenting and expanding the creative and learning process, with the aim to resolve the lack of a tourism brand of the town. This report compiles the main aspects of the project: the research work, its conceptualization and the practical development of it. All this carried out from a functional, attractive and fresh perspective, using graphic design, photography and illustration as the key tools.Navarro Pérez, MÁ. (2020). Diseño Participativo: Propuesta de Marca Turística del Pueblo de Moixent. Universitat Politècnica de València. http://hdl.handle.net/10251/158080TFG

Effects of Cyclodextrin Type on Vitamin C, Antioxidant Activity, and Sensory Attributes of a Mandarin Juice Enriched with Pomegranate and Goji Berries

The effects of the addition of cyclodextrins (CDs), β-CD, or HP-β-CD (1%), on the protection of antioxidant compounds of mandarin juices enriched with pomegranate extract and goji berries juice, was studied. Juices were prepared and after their thermal treatment (98 ◦C, 30 s) they were stored at 4 ◦C during 75 d. Vitamin C content, CIE L∗a∗b∗ color, antioxidant capacity, retinol equivalents, and sensory properties were studied. Losses on vitamin C were higher (6%) for juices with β-CD than juices with HP-β-CD. Retinol equivalents degradation was lower (3.4%) in juices with HP-β-cyclodextrins than in those treated with β-CD. Lower losses were observed for the instrumental and sensory color intensity in juices with HP-β-CD addition. Finally, the antioxidant capacity was also higher in juices treated with HP-β-CD. Finally, the overall sensory quality of juices with HP-β-CD was the best one after 30 d of cold storage. Even though β-CD addition did not cause any improvement compared with control juice (without CD addition), the benefits of adding HP-β-CD to this particular juice were shown in almost all parameters under study.Ciencias de la Alimentació

Flag codes from planar spreads in network coding

In this paper we study a class of multishot network codes given by families of nested subspaces (flags) of a vector space Fnq, being qa prime power and Fqthe finite field of qelements. In particular, we focus on flag codes having maximum distance (optimum distance flag codes). We explore the existence of these codes from spreads, based on the good properties of the latter ones. For n =2k, we show that optimum distance full flag codes with the largest size are exactly those that can be constructed from a planar spread. We give a precise construction of them as well as a decoding algorithm.The first and third authors are partially supported by Projecte AICO/2017/128 of Generalitat Valenciana. The second author is supported by Generalitat Valenciana and Fondo Social Europeo. Grants: ACIF/2018/196 and BEFPI/2019/070. The third author is also supported by the grant BEST/2019/192 of Generalitat Valenciana

An orbital construction of optimum distance flag codes

Flag codes are multishot network codes consisting of sequences of nested subspaces (flags) of a vector space Fnq, where q is a prime power and Fq, the finite field of size q. In this paper we study the construction on F2kq of full flag codes having maximum distance (optimum distance full flag codes) that can be endowed with an orbital structure provided by the action of a subgroup of the general linear group. More precisely, starting from a subspace code of dimension k and maximum distance with a given orbital description, we provide sufficient conditions to get an optimum distance full flag code on F2kq having an orbital structure directly induced by the previous one. In particular, we exhibit a specific orbital construction with the best possible size from an orbital construction of a planar spread on F2kq that strongly depends on the characteristic of the field.The authors receive financial support from Ministerio de Ciencia e Innovación (PID2019-108668GB-I00). The second author is supported by Generalitat Valenciana and Fondo Social Europeo (ACIF/2018/196)