* uschian groups of the first kind * Automorphic forms and functions * Hecke operators and the zeta-functions associated with modular forms * Elliptic curves * Abelian extensions of imaginary quadratic fields and complex multiplication of elliptic curves * Modular functions of higher level * Zeta-functions of algebraic curves and abelian varieties * The cohomology group assoicated with cusp forms * Arithmetic Fuschian groups

Introduction to the arithmetic theory of automorphic functions

State-of-the-art analysis of the environmental benefits of green roofs

https://researchrepository.ucd.ie/bitstream/10197/8711/1/Manuscript_GI_Review_Accepted_Version.pdf

Air pollution abatement performances of green infrastructure in open road and built-up street canyon environments – A review

The abundant availability and accessibility of plant fibres are the major reasons for an emerging new interest in sustainable technology. While focusing on the composite materials, the main points to be considered are environment friendliness and light weight, with high specific properties. This century has witnessed remarkable achievements in green technology in the field of materials science through the development of high-performance materials made from natural resources is increasing worldwide. Plant fibres are a kind of renewable resources, which have been renewed by nature and human ingenuity for thousands of years. The greatest challenge in working with plant fibre reinforced composites (PFRCs) is their large variation in properties and characteristics. A PFRCs properties are influenced by a number of variables, including the fibre type, environmental conditions, processing methods, and modification of the fibre. A detailed systematic review on these sustainable and renewable green materials is presented in this paper. The overall characteristics of plant fibres used in bio-composites, including source, type, structure, composition, as well as properties, will be reviewed. Finally, the review will conclude with recent developments and future trends of PFRCs as well as key issues that need to be addressed and resolved.

Plant fibre based bio-composites: Sustainable and renewable green materials

The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree and given diameter. General upper bounds - called Moore bounds - for the order of such graphs and digraphs are attainable only for certain special graphs and digraphs. Finding better (tighter) upper bounds for the maximum possible number of vertices, given the other two parameters, and thus attacking the degree/diameter problem 'from above', remains a largely unexplored area. Constructions producing large graphs and digraphs of given degree and diameter represent a way of attacking the degree/diameter problem 'from below'. This survey aims to give an overview of the current state-of-the-art of the degree/diameter problem. We focus mainly on the above two streams of research. However, we could not resist mentioning also results on various related problems. These include considering Moore-like bounds for special types of graphs and digraphs, such as vertex-transitive, Cayley, planar, bipartite, and many others, on the one hand, and related properties such as connectivity, regularity, and surface embeddability, on the other hand.

Moore Graphs and Beyond: A survey of the Degree/Diameter Problem

Green vertical systems for buildings as passive systems for energy savings

https://www.irbnet.de/daten/iconda/CIB17433.pdf

Behaviour of green facades in Mediterranean Continental climate

A curve X over [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] is modular if it is dominated by X 1 ( N ) for some N ; if in addition the image of its jacobian in J 1 ( N ) is contained in the new subvariety of J 1 ( N ), then X is called a new modular curve. We prove that for each g ≥ 2, the set of new modular curves over [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] of genus g is finite and computable. For the computability result, we prove an algorithmic version of the de Franchis-Severi Theorem. Similar finiteness results are proved for new modular curves of bounded gonality, for new modular curves whose jacobian is a quotient of J 0 ( N ) new with N divisible by a prescribed prime, and for modular curves (new or not) with levels in a restricted set. We study new modular hyperelliptic curves in detail. In particular, we find all new modular curves of genus 2 explicitly, and construct what might be the complete list of all new modular hyperelliptic curves of all genera. Finally we prove that for each field k of characteristic zero and g ≥ 2, the set of genus- g curves over k dominated by a Fermat curve is finite and computable.

Finiteness results for modular curves of genus at least 2

https://wstein.org/people/goins/lario.pdf

Rational and Elliptic Parametrizations ofQ-Curves

LetBD be the indefinite quaternion algebra overQ of reduced discriminantD=p1· · · · ·p2r for pairwise different prime numbers pi and let XD/Q be the Shimura curve attached to BD. As it was shown by Shimura [23], XD is the coarse moduli space of abelian surfaces with quaternionic multiplication by BD. Let W = {ωm : m | D} ⊆ Aut Q(XD) be the group of Atkin-Lehner involutions. For any m | D, we will denote X D = XD/〈ωm〉, the quotient of the Shimura curve XD, by ωm. The importance of the curves X D is enhanced by their moduli interpretation as curves embedded in Hilbert-Blumenthal surfaces and Igusa’s threefold A2 (cf. [21, 22]). The classical modular case arises when D = 1. In this case, automorphic forms of these curves admit Fourier expansions around the cusp of infinity and we know explicit generators of the field of functions of such curves. Also, explicit methods are known to determine bases of the space of their regular differentials, which are used to compute equations for quotients of modular curves. When D = 1, the absence of cusps has been an obstacle for explicit approaches to Shimura curves. Explicit methods to handle functions and regular differential forms on these curves are less accessible and we refer the reader to [3] for progress in this regard. For this reason, at present, few equations of Shimura curves are known, all of them of genus 0 or 1 (cf. [6, 11, 13]). In addition, in a later work, Kurihara conjectured equations for all Shimura curves of genus two and for several curves of genera three and five, though he was not able to give a proof for his guesses (cf. [14]).

Josep González

Papers

Green vertical systems for buildings as passive systems for energy savings

Behaviour of green facades in Mediterranean Continental climate

Finiteness results for modular curves of genus at least 2

Rational and Elliptic Parametrizations ofQ-Curves

Equations of Shimura Curves of Genus Two