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Daten und Fakten zu Migrantenjugendlichen an Sonderschulen in der Bundesrepublik Deutschland Powell, Justin J W ; E-print/Working paper (2001) Zwischen 1965 und 1994 hat sich die Zahl der nichtdeutschen Schüler/innen in der Bundesrepublik Deutschland verzwanzigfacht. Seit dem Jahr 1991 gehen mehr als eine Million Schüler/innen mit ... [more ▼] Zwischen 1965 und 1994 hat sich die Zahl der nichtdeutschen Schüler/innen in der Bundesrepublik Deutschland verzwanzigfacht. Seit dem Jahr 1991 gehen mehr als eine Million Schüler/innen mit ausländischem Pass in (west-)deutsche Schulen; d.h. circa jede/r zehnte Schüler/in hat eine nichtdeutsche Staatsangehörigkeit. Über diese zahlenmäßige Präsens hinaus bieten die Vergleiche zwischen deutschen und nichtdeutschen Schülern/innen allgemein und zwischen deutschen und nichtdeutschen Sonderschülern/innen eine Perspektive, welche die Herausforderungen des Bildungssystems der Bundesrepublik Deutschland in ihrer Institutionalisierung und Expansion darstellt. Gleichzeitig stellen „in der BRD (...) die Ausländerkinder eine Gruppe dar, der im Bildungswesen besondere Aufmerksamkeit gewidmet werden muß, wenn sie nicht schulisch erheblich benachteiligt werden soll“ (Arbeitsgruppe Bildungsbericht am MPIB, 1994: 364). Von 1970 bis 1979 stieg der Anteil nichtdeutscher Schüler/innen an den Sonderschulen im Vergleich zu den Schülern insgesamt kontinuierlich an (Trommer/Köhler 1981: 130). Dieser Trend setzte sich fort, so dass bis 1999 nahezu 15% aller Sonderschüler/innen nichtdeutscher Herkunft waren, obwohl Schüler/innen nichtdeutscher Herkunft nur 9,4% aller Schüler/innen in der Bundesrepublik ausmachten. Das bedeutet für 1999 eine Überrepräsentanz ausländischer Kinder und Jugendlicher an deutschen Sonderschulen von 1,56. Parallel dazu zeigen die folgenden Analysen eine hohe Varianz zwischen den Bundesländern in der Sonderschulzuweisung nichtdeutscher Schüler/innen sowie unter den europäischen Nationalitäten (im Schuljahr 1998/99: von 0,5% bis hin zu 13,6%). Zugleich gibt es historisch Verschiebungen in der Begründung des Förderbedarfs zwischen dem größten Förderschwerpunkt „Lernen“ (von 82% auf 54% zwischen 1970-98) und anderen Kategorien des Förderbedarfs, die an Bedeutung gewonnen haben. Regionale Unterschiede in der Verteilung von Migrantenjugendlichen unter den einzelnen Sonderschularten sind u.a. Ausdruck der Differenzen in der Bildungs- bzw. Schulpolitik der Länder. So existieren große Unterschiede in der Akzeptanz integrativer pädagogischer Ansätze und Konzepte, der Ausbildung der Lehrer/innen und in der historischen Entwicklung verschiedener Schulformen. Die Existenz von Hauptschulen und Sonderschulen als quasi „untere bzw. separate Bildungsgänge“ sowie die Veränderung ihrer Schülerschaft in Folge der Bildungsexpansion und eine allgemein höhere Bildungsbeteiligung resultieren unter anderem darin, dass zwei von zehn nichtdeutschen Schulentlassenen die Schule ohne Hauptschulabschluss verlassen und deren „Misserfolgsquote“ immer noch ca. 2,5-mal so hoch ist wie bei den deutschen Jugendlichen (Solga 2001). Um die ausgewiesenen Ergebnisse zu Jugendlichen mit Migrationshintergrund an deutschen Sonderschulen adäquat einordnen zu können, werden in diesem Arbeitspapier auch ausgewählte Daten und Fakten zur allgemeinen Bildungsbeteiligung von Jugendlichen ausländischer Herkunft dargestellt und es wird auf demographische Schlüsseldaten eingegangen. Insgesamt zeigen die im Folgenden dargestellten Zahlen deutlich, dass—wie es heute in der Politik und den Medien nun endlich reflektiert wird—Jugendliche nichtdeutscher Herkunft im deutschen Bildungssystem benachteiligt sind und man immer noch versucht, ihre „Lernbehinderung“—die zum Großteil auch auf eine gesellschaftliche „Lernblockierung“ zurückgeht—mittels Sonder- bzw. Förderschulen und damit mittels institutioneller Separierung statt Integration zu lösen. [less ▲] Detailed reference viewed: 156 (5 UL)Effets de complémentarité externes et incidence sur la productivité : le cas de l'industrie manufacturière luxembourgeoise Bourgain, Arnaud ; Pieretti, Patrice E-print/Working paper (2001) This article seeks to measure knowledge spillovers between nearby industries. This represents one of types of externality identified in the studies of industry location. A spillover indicator is suggested ... [more ▼] This article seeks to measure knowledge spillovers between nearby industries. This represents one of types of externality identified in the studies of industry location. A spillover indicator is suggested which can explain increasing returns at the aggregate level. It is shown that this indicator is positively related to industry diversity. As applied to data from Luxembourg’s manufacturing industry, this indicator suggests that labor productivity is increasing in industry diversity. [less ▲] Detailed reference viewed: 107 (0 UL)On perfect, amicable, and sociable chains Marichal, Jean-Luc E-print/Working paper (2000) Let $\bfx = (x_0,\ldots,x_{n-1})$ be an $n$-chain, i.e., an $n$-tuple of non-negative integers $< n$. Consider the operator $s: \bfx \mapsto\bfx' = (x'_0,\ldots,x'_{n-1})$, where $x'_j$ represents the ... [more ▼] Let $\bfx = (x_0,\ldots,x_{n-1})$ be an $n$-chain, i.e., an $n$-tuple of non-negative integers $< n$. Consider the operator $s: \bfx \mapsto\bfx' = (x'_0,\ldots,x'_{n-1})$, where $x'_j$ represents the number of $j$'s appearing among the components of $\bfx$. An $n$-chain $\bfx$ is said to be perfect if $s(\bfx) = \bfx$. For example, (2,1,2,0,0) is a perfect 5-chain. Analogously to the theory of perfect, amicable, and sociable numbers, one can define from the operator $s$ the concepts of amicable pair and sociable group of chains. In this paper we give an exhaustive list of all the perfect, amicable, and sociable chains. [less ▲] Detailed reference viewed: 45 (3 UL)Review of a BBS target article Lexical Entries and Rules of Language: A Multidisciplinary Study of German Inflection by Harald Clahsen to appear in BBS (1999) 22 (6) Reuter, Robert E-print/Working paper (1999) Many authors (e.g., Chomsky 1995, Pinker 1984, and Marcus 1998) argue that the architecture of the language faculty contains two separate components: a (structured) lexicon and a computational component ... [more ▼] Many authors (e.g., Chomsky 1995, Pinker 1984, and Marcus 1998) argue that the architecture of the language faculty contains two separate components: a (structured) lexicon and a computational component. Clahsen presents in a current BBS target article (in press) new empirical evidences in favour of such a dual-mechanism model of language processing based on a multidisciplinary study of German inflection. In the following review, I will summarise and discuss the major points of Clahsen's paper. My focus will be on theoretical, methodological and empirical issues presented and discussed in the paper. An important issue will be the bearing of his empirical findings on the current debate in psycholinguistic modelling. I will as well speculate that at least a part of Clahsen's reasoning seems not to hold in the case of a language closely related to German, namely Luxembourgian. [less ▲] Detailed reference viewed: 200 (2 UL)On the function of consciousness:An adaptationist perspective Reuter, Robert E-print/Working paper (1999) Detailed reference viewed: 62 (1 UL)Analyse de l’évolution de la productivité totale des facteurs dans l’industrie luxembourgeoise Bourgain, Arnaud ; Pieretti, Patrice E-print/Working paper (1999) Detailed reference viewed: 68 (0 UL)On linear decompositions of L-valued simple graphs Bisdorff, Raymond E-print/Working paper (1996) In this report we will present a linear decomposition of a given L- valued binary relation into a set of sub-relations of kernel-dimension one. We will apply this theoretical result to the design of a ... [more ▼] In this report we will present a linear decomposition of a given L- valued binary relation into a set of sub-relations of kernel-dimension one. We will apply this theoretical result to the design of a faster algorithm for computing L-valued kernels on general L-valued simple graphs. [less ▲] Detailed reference viewed: 27 (1 UL)Quel est l'intérêt d'une approche multi-dimensionnelle du jugement de préférence ? Bisdorff, Raymond E-print/Working paper (1995) We present, in terms of logic programming, an algorithm for constructing decision rules from an extensional representation of the solutions to a multiple attributes decision problem. The algorithm is ... [more ▼] We present, in terms of logic programming, an algorithm for constructing decision rules from an extensional representation of the solutions to a multiple attributes decision problem. The algorithm is based on the decision tree obtained from a hierarchical decomposition of the decision attributes along their discriminatory power of the decision acts. We illustrate our methodological approach with an application to the cognitive categorization of the human colour vision. [less ▲] Detailed reference viewed: 66 (3 UL)Le français langue seconde dans les écoles maternelles et primaires de la République de Vanuatu (Pacifique Sud), Bilan d’une année d’étude dans le cadre de la « bourse d‘excellence postdoctorale Aupelf-Uref » Ehrhart, Sabine E-print/Working paper (1995) Detailed reference viewed: 71 (2 UL)Quelques réflexions concernant la genèse du tayo en Nouvelle-Calédonie et discussion des éventuels apports venant de l’extérieur, notamment du créole réunionnais, Conférence donnée à l'Université de Münster, 1991 Ehrhart, Sabine E-print/Working paper (1994) Detailed reference viewed: 129 (0 UL)Three-dimensional arithmetic billiards Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 84 (3 UL)Weakening the tight coupling between geometry and simulation in isogeometric analysis: from sub- and super- geometric analysis to Geometry Independent Field approximaTion (GIFT) ; ; Tomar, Satyendra et al E-print/Working paper (n.d.) This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution ... [more ▼] This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main advantage of isogeometric analysis, i.e. preserves the original, exact CAD geometry (for example, given by NURBS), but allows pairing it with an approximation space which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to re-parameterize the domain, and therefore without weakening the link with the CAD model. We demonstrate the use of the method with different choices of the geometry and field splines, and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for non-nested spaces. [less ▲] Detailed reference viewed: 281 (13 UL)Verification of the Quillen conjecture in the rank 2 imaginary quadratic case Rahm, Alexander ; E-print/Working paper (n.d.) We confirm a conjecture of Quillen in the case of the mod 2 cohomology of arithmetic groups SL_2(A[1/2]), where A is an imaginary quadratic ring of integers. To make explicit the free module structure on ... [more ▼] We confirm a conjecture of Quillen in the case of the mod 2 cohomology of arithmetic groups SL_2(A[1/2]), where A is an imaginary quadratic ring of integers. To make explicit the free module structure on the cohomology ring conjectured by Quillen, we compute the mod 2 cohomology of SL_2(Z[sqrt(−2)][1/2]) via the amalgamated decomposition of the latter group. [less ▲] Detailed reference viewed: 75 (1 UL)Effective Kummer Theory for Elliptic Curves ; Tronto, Sebastiano E-print/Working paper (n.d.) Let E be an elliptic curve defined over a number field K, let α ∈ E(K) be a point of infinite order, and let N −1 α be the set of N -division points of α in E(K). We prove strong effective and uniform ... [more ▼] Let E be an elliptic curve defined over a number field K, let α ∈ E(K) be a point of infinite order, and let N −1 α be the set of N -division points of α in E(K). We prove strong effective and uniform results for the degrees of the Kummer extensions [K(E[N ], N −1 α) : K(E[N ])]. When K = Q, and under a minimal (necessary) assumption on α, we show that the inequality [Q(E[N ], N −1 α) : Q(E[N ])] ≥ cN 2 holds with a constant c independent of both E and α. [less ▲] Detailed reference viewed: 71 (9 UL)Four Riddles with Four Brothers Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 52 (1 UL)Deniable Public-Key Authenticated Quantum Key Exchange van Wier, Jeroen ; Atashpendar, Arash ; Roenne, Peter E-print/Working paper (n.d.) In this work, we explore the notion of deniability in public-key authenticated quantum key exchange (QKE), which allows two parties to establish a shared secret key without leaving any evidence that would ... [more ▼] In this work, we explore the notion of deniability in public-key authenticated quantum key exchange (QKE), which allows two parties to establish a shared secret key without leaving any evidence that would bind a session to either party. The deniability property is expressed in terms of being able to simulate the transcripts of a protocol. The ability to deny a message or an action has applications ranging from secure messaging to secure e-voting and whistle-blowing. While quite well-established in classical cryptography, it remains largely unexplored in the quantum setting. Here, we first present a natural extension of classical definitions in the simulation paradigm to the setting of quantum computation and formalize the requirements for a deniable QKE scheme. We then prove that the BB84 variant of QKE, when authenticated using a strong designated verifier signature scheme, satisfies deniability and, finally, propose a concrete instantiation. [less ▲] Detailed reference viewed: 28 (4 UL)The least common multiple of several numbers in terms of greatest common divisors Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 32 (1 UL)Beware proportions Perucca, Antonella ; Ronk, Pit Ferdy E-print/Working paper (n.d.) Detailed reference viewed: 35 (7 UL)Bayesian inference for the stochastic identification of elastoplastic material parameters: Introduction, misconceptions and insights Rappel, Hussein ; Beex, Lars ; Hale, Jack et al E-print/Working paper (n.d.) We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material ... [more ▼] We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material parameters. For this purpose a single spring is considered, for which the stress-strain curves are artificially created. Besides offering a didactic introduction to BI, this paper proposes an approach to incorporate statistical errors both in the measured stresses, and in the measured strains. It is assumed that the uncertainty is only due to measurement errors and the material is homogeneous. Furthermore, a number of possible misconceptions on BI are highlighted based on the purely elastic case. [less ▲] Detailed reference viewed: 371 (106 UL)ON THE (NON-)EQUIVALENCE OF INTEGRAL BINARY QUADRATIC FORMS AND THEIR NEGATIVE FORMS Barthel, Jim Jean-Pierre ; Müller, Volker E-print/Working paper (n.d.) Integral binary quadratic forms have been extensively studied in order to compute the class number of real and complex quadratic ﬁelds. Many studies restricted the equivalence class of quadratic forms or ... [more ▼] Integral binary quadratic forms have been extensively studied in order to compute the class number of real and complex quadratic ﬁelds. Many studies restricted the equivalence class of quadratic forms or identiﬁed speciﬁc forms in order to compute the class number through enumeration of equivalence classes. One often used assumption is that a given form and its negative are equivalent or are synthetically identiﬁed. This document presents a concise Lagrangian approach to integral binary quadratic forms, outlines the equivalence classes in its broadest sense and uses it to develop a general condition when a given integral binary quadratic form and its negative are equivalent. Then, the existence of integral binary quadratic forms which are non-equivalent to their negatives is proven and an elementary algorithm to determine the (non-)equivalence of a given form and its negative is outlined. [less ▲] Detailed reference viewed: 90 (6 UL)Linear smoothed extended finite element method ; ; et al E-print/Working paper (n.d.) The extended finite element method (XFEM) was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to ... [more ▼] The extended finite element method (XFEM) was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to be split by a discontinuity, strong or weak and hence requires the integration of discontinuous functions or functions with discontinuous derivatives over elementary volumes. Moreover, in the case of open surfaces and singularities, special, usually non-polynomial functions must also be integrated.A variety of approaches have been proposed to facilitate these special types of numerical integration, which have been shown to have a large impact on the accuracy and convergence of the numerical solution. The smoothed extended finite element method (SmXFEM) [1], for example, makes numerical integration elegant and simple by transforming volume integrals into surface integrals. However, it was reported in [1, 2] that the strain smoothing is inaccurate when non-polynomial functions are in the basis. This is due to the constant smoothing function used over the smoothing domains which destroys the effect of the singularity. In this paper, we investigate the benefits of a recently developed Linear smoothing procedure [3] which provides better approximation to higher order polynomial fields in the basis. Some benchmark problems in the context of linear elastic fracture mechanics (LEFM) are solved to compare the standard XFEM, the constant-smoothed XFEM (Sm-XFEM) and the linear-smoothed XFEM (LSm-XFEM). We observe that the convergence rates of all three methods are the same. The stress intensity factors (SIFs) computed through the proposed LSm-XFEM are however more accurate than that obtained through Sm-XFEM. To conclude, compared to the conventional XFEM, the same order of accuracy is achieved at a relatively low computational effort. [less ▲] Detailed reference viewed: 136 (3 UL)A conjecture on primes in arithmetic progressions and geometric intervals Barthel, Jim Jean-Pierre ; Müller, Volker E-print/Working paper (n.d.) We conjecture that any interval of the form [q^t ,q^(t+1) ], where q≥ 2 and t≥1 denote positive integers, contains at least one prime from each coprime congruence class. We prove this conjecture first ... [more ▼] We conjecture that any interval of the form [q^t ,q^(t+1) ], where q≥ 2 and t≥1 denote positive integers, contains at least one prime from each coprime congruence class. We prove this conjecture first unconditionally for all 2≤q≤45000 and all t≥1 and second under ERH for almost all q≥2 and all t≥2. Furthermore, we outline heuristic arguments for the validity of the conjecture beyond the proven bounds and we compare it with related long-standing conjectures. Finally, we discuss some of its consequences. [less ▲] Detailed reference viewed: 42 (8 UL)On basis vectors of lattices Barthel, Jim Jean-Pierre ; Müller, Volker E-print/Working paper (n.d.) Integer lattices enjoy increasing interest among mathematicians and cryptographers. However, there are still many elementary open questions, like finding specific vectors or particular bases of a given ... [more ▼] Integer lattices enjoy increasing interest among mathematicians and cryptographers. However, there are still many elementary open questions, like finding specific vectors or particular bases of a given lattice. Our study consists in exhibiting which integer vectors may be chosen as basis vectors of a chosen lattice. The compelling part of our development is that this condition is obtained through an unusual application of Dirichlet's Theorem on primes in arithmetic progressions and that it has a surprising consequence for vectors achieving the successive minima. [less ▲] Detailed reference viewed: 41 (3 UL)Not participating in education, employment or training (NEET): Hope to mitigate new social risks in the UK? Murphy, Emily ; ; E-print/Working paper (n.d.) Young people not participating in education, employment or training (NEET) are a key policy concern in Europe. We examine whether hope, as a form of life course agency, plays a protective role against the ... [more ▼] Young people not participating in education, employment or training (NEET) are a key policy concern in Europe. We examine whether hope, as a form of life course agency, plays a protective role against the risk of being NEET in the context of the British welfare state. Hope is conceptualised as multidimensional: being a temporally embedded, agentic mentality comprised of one’s sense of adaptive decision-making in the present and pathways thinking towards the future. Longitudinal estimations based on the latest Understanding Society microdata (2009-2018) indicate a direct association between higher-hope modes, on average, and a lower likelihood of being NEET. Further, our study assesses whether hopeful agency is moderated by the experience of parental worklessness. Findings indicate that while hope is not more important for those who experienced disadvantages in upbringing, hopeful agency is shown to be equally important in the face of past and present NEET risks. For the UK, building young peoples’ adaptive, agentic mentality towards their future in education or employment over the long-term, may prove one cost-effective policy approach. [less ▲] Detailed reference viewed: 213 (51 UL)The first-digit law Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 69 (0 UL)Rubik's Snakes on a plane Grotto, Francesco ; Perucca, Antonella ; E-print/Working paper (n.d.) Detailed reference viewed: 132 (37 UL)Divisibility conditions on the order of the reductions of algebraic numbers Sgobba, Pietro E-print/Working paper (n.d.) Let K be a number field, and let G be a finitely generated subgroup of K*. Without relying on (GRH) we prove an asymptotic formula for the number of primes \p of K such that the order of (G mod \p) is ... [more ▼] Let K be a number field, and let G be a finitely generated subgroup of K*. Without relying on (GRH) we prove an asymptotic formula for the number of primes \p of K such that the order of (G mod \p) is divisible by a fixed integer. We also provide a rational expression for the natural density of this set. Furthermore, we study the primes \p for which the order is k-free, and those for which the order has a prescribed \ell-adic valuation for finitely many primes \ell. An additional condition on the Frobenius conjugacy class of \p may be considered. In order to establish these results, we prove an unconditional version of the Chebotarev density theorem for Kummer extensions of number fields. [less ▲] Detailed reference viewed: 100 (10 UL)Kummer theory for finite fields and p-adic fields Perissinotto, Flavio ; Perucca, Antonella E-print/Working paper (n.d.) Let K be a finite field or a finite extension of Qp for some prime number p. If G is a finitely generated subgroup of K*, then we can consider the degree of the cyclotomic-Kummer extension K(\zeta_N ... [more ▼] Let K be a finite field or a finite extension of Qp for some prime number p. If G is a finitely generated subgroup of K*, then we can consider the degree of the cyclotomic-Kummer extension K(\zeta_N, \sqrt[n]{G})/K, where n divides N. If K is a finite field, then we give a closed formula for the degree, while if K is a p-adic field, then we describe a strategy to compute the degree. [less ▲] Detailed reference viewed: 58 (2 UL)A Simple Inner-Product Functional Encryption Scheme from the Inverse-DDH Assumption Barthel, Jim Jean-Pierre ; Rosie, Razvan ; Sahu, Rajeev Anand E-print/Working paper (n.d.) Detailed reference viewed: 131 (29 UL)Kummer theory for products of one-dimensional tori Perucca, Antonella ; E-print/Working paper (n.d.) Detailed reference viewed: 77 (27 UL)Correspondences between WZNW models and CFTs with W-algebra symmetry Roenne, Peter Browne ; ; E-print/Working paper (n.d.) Detailed reference viewed: 125 (3 UL)New Constructions of Verifiable Delay Functions Barthel, Jim Jean-Pierre ; Rosie, Razvan E-print/Working paper (n.d.) Detailed reference viewed: 144 (10 UL)The Hardest Logic Puzzle Ever Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 56 (0 UL)Kummer theory for multiquadratic or quartic cyclic number fields Perissinotto, Flavio ; Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 99 (15 UL)A new one point quadrature rule over arbitrary star convex polygon/polyhedron ; ; et al E-print/Working paper (n.d.) The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we ... [more ▼] The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we propose a linearly consistent one point integration scheme which possesses the properties of the LS scheme with three integration points but requires one third of the integration computational time. The essence of the proposed technique is to approximate the strain by the smoothed nodal derivatives that are determined by the discrete form of the divergence theorem. This is done by the Taylor's expansion of the weak form which facilitates the evaluation of the smoothed nodal derivatives acting as stabilization terms. The smoothed nodal derivatives are evaluated only at the centroid of each integration cell. These integration cells are the simplex subcells (triangle/tetrahedron in two and three dimensions) obtained by subdividing the polytope. The salient feature of the proposed technique is that it requires only $n$ integrations for an $n-$ sided polytope as opposed to $3n$ in~\cite{francisa.ortiz-bernardin2017} and $13n$ integration points in the conventional approach. The convergence properties, the accuracy, and the efficacy of the LS with one point integration scheme are discussed by solving few benchmark problems in elastostatics. [less ▲] Detailed reference viewed: 69 (3 UL)Linear smoothed polygonal and polyhedral finite elements ; ; Bordas, Stéphane et al E-print/Working paper (n.d.) It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal ... [more ▼] It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes to deliver improved accuracy and pass the patch test to machine precision. [less ▲] Detailed reference viewed: 464 (10 UL)Kummer theory for products of one-dimensional tori Perissinotto, Flavio ; Perucca, Antonella E-print/Working paper (n.d.) Let T be a finite product of one-dimensional tori defined over a number field K. We consider the torsion-Kummer extension K(T[nt], (1/n)G), where n,t are positive integers and G is a finitely generated ... [more ▼] Let T be a finite product of one-dimensional tori defined over a number field K. We consider the torsion-Kummer extension K(T[nt], (1/n)G), where n,t are positive integers and G is a finitely generated group of K-points on T. We show how to compute the degree of K(T[nt], (1/n)G) over K and how to determine whether T is split over such an extension. If K=Q, then we may compute at once the degree of the above extensions for all n and t. [less ▲] Detailed reference viewed: 56 (6 UL)Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation Bui, Huu Phuoc ; Tomar, Satyendra ; et al E-print/Working paper (n.d.) We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our ... [more ▼] We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our approach enables to control the error in the computation of the displacement and stress fields around the needle tip and needle shaft by suitably refining the mesh, whilst maintaining a coarser mesh in other parts of the domain. We demonstrate through academic and practical examples that our approach increases the accuracy of the displacement and stress fields around the needle without increasing the computational expense. This enables real-time simulations. The proposed methodology has direct implications to increase the accuracy and control the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anesthesia, or cryotherapy and can be essential to the development of robotic guidance. [less ▲] Detailed reference viewed: 530 (34 UL)Prime divisors of the l-Genocchi numbers and the ubiquity of Ramanujan-style congruences of level l ; Sgobba, Pietro E-print/Working paper (n.d.) Let \ell be any fixed prime number. We define the \ell-Genocchi numbers by G_n:=\ell(1-\ell^n)B_n, with B_n the n-th Bernoulli number. They are integers. We introduce and study a variant of Kummer's ... [more ▼] Let \ell be any fixed prime number. We define the \ell-Genocchi numbers by G_n:=\ell(1-\ell^n)B_n, with B_n the n-th Bernoulli number. They are integers. We introduce and study a variant of Kummer's notion of regularity of primes. We say that an odd prime p is \ell-Genocchi irregular if it divides at least one of the \ell-Genocchi numbers G_2,G_4,..., G_{p-3}, and \ell-regular otherwise. With the help of techniques used in the study of Artin's primitive root conjecture, we give asymptotic estimates for the number of \ell-Genocchi irregular primes in a prescribed arithmetic progression in case \ell is odd. The case \ell=2 was already dealt with by Hu, Kim, Moree and Sha (2019). Using similar methods we study the prime factors of (1-\ell^n)B_{2n}/2n and (1+\ell^n)B_{2n}/2n. This allows us to estimate the number of primes p\leq x for which there exist modulo p Ramanujan-style congruences between the Fourier coefficients of an Eisenstein series and some cusp form of prime level \ell. [less ▲] Detailed reference viewed: 54 (3 UL)Non-Fungible Tokens (NFTs): A Review of Pricing Determinants, Applications and Opportunities Kräussl, Roman ; Tugnetti, Alessandro E-print/Working paper (n.d.) This paper provides a review of the development of the non-fungible tokens (NFTs) market, with a particular focus on its pricing determinants, its current applications and future opportunities. We ... [more ▼] This paper provides a review of the development of the non-fungible tokens (NFTs) market, with a particular focus on its pricing determinants, its current applications and future opportunities. We investigate the current state of the NFT markets and highlight the perception and expectations of investors towards these products. We summarize and compare the financial and econometric models that have been used in the literature for the pricing of non-fungible tokens with a special focus on their predictive performance. 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