498 research outputs found
On a rank-unimodality conjecture of Morier-Genoud and Ovsienko
No full textLet α=(a,b,…) be a composition. Consider the associated poset F(α), called a fence, whose covering relations are x1◁x2◁…◁xa+1▷xa+2▷…▷xa+b+1◁xa+b+2◁…. We study the associated distributive lattice L(α) consisting of all lower order ideals of F(α). These lattices are important in the theory of cluster algebras and their rank generating functions can be used to define q-analogues of rational numbers. In particular, we make progress on a recent conjecture of Morier-Genoud and Ovsienko that L(α) is rank unimodal. We show that if one of the parts of α is greater than the sum of the others, then the conjecture is true. We conjecture that L(α) enjoys the stronger properties of having a nested chain decomposition and having a rank sequence which is either top or bottom interlacing, the latter being a recently defined property of sequences. We verify that these properties hold for compositions with at most three parts and for what we call d-divided posets, generalizing work of Claussen and simplifying a construction of Gansner
Catholicism and the making of politics in Central Mozambique, 1940-1986
No full textThis book is concerned with the internal diversity and complexity of the Roman Catholic Church. It aims at exploring, unpacking, and explaining how the Roman Catholic institution works, how its politics are made, and how the latter impact its environment. Using the diocese of Beira in central Mozambique as a case study, and following insights by Max Weber, author Eric Morier-Genoud takes the novel "horizontal" approach of looking at congregations within the Church as a series of autonomous entities, rather than focusing on the hierarchical structure of the institution.Between 1940 and 1980, the diocese of Beira was home to some fifteen different congregations ranging from Jesuits to Franciscans, from Burgos to Picpus fathers. As in many areas of the world, the 1960s brought conflict to Catholic congregations in central Mozambique, with African nationalism and the reforms of Vatican II playing a part. The conflict manifested in many ways: a bishop's flight from his diocese, a congregation abandoning the territory in protest against the collusion between church and state, and a declaration of class struggle in the church. All of these events, occurring against the backdrop of the war for Mozambican independence, make the region an especially fruitful location for the pioneering analysis proffered in this important study
Passively mode-locked diode-pumped surface-emitting diode laser
No full textWe demonstrate to our knowledge the first passively mode-locked surface-emitting semiconductor laser. We used a 3-W high-brightness diode laser as pump source and a semiconductor saturable absorber mirror (SESAM [1,2]) as modelocker. The laser generates two stably mode-locked output beams with 11 mW average power each, 26ps pulse duration, and a repetition rate of 4.4 GHz. In contrast to edge-emitting semiconductor optically pumped semiconductor vertical external cavity surface emitting lasers [OPS-VECSELs) allow one to scale up the mode area in order to generate a high average power and high pulse energies, while the external cavity enforces a diffraction-limited output. A diffraction-limited output with >0.5 W in cw operation has been demonstrated for a similar kind of device [3]. Thus our concept promises to be scalable to much higher average and peak powers than can be obtained from electrically pumped surface-emitting mode-locked diode lasers or from edge emitting diode lasers. Only synchronously pumped surface emitting semiconductor lasers have generated pulses with high average power and pulse energy, but these require a powerful pulsed pump source [4]. Compared to mode-locked laser based on ion-doped crystals or glasses. mode-locked semiconductor lasers can generate high repetition rate (multi-GHz) pulse trains without Q-switching instabilities [5]. Their broad amplification bandwidth is sufficient for pulse durations in the femtosecond regime. <br/
Frieze patterns and Farey complexes
No full textFrieze patterns have attracted significant attention recently, motivated by
their relationship with cluster algebras. A longstanding open problem has been
to provide a combinatorial model for frieze patterns over the ring of integers
modulo akin to Conway and Coxeter's celebrated model for positive integer
frieze patterns. Here we solve this problem using the Farey complex of the ring
of integers modulo ; in fact, using more general Farey complexes we provide
combinatorial models for frieze patterns over any rings whatsoever.
Our strategy generalises that of the first author and of Morier-Genoud et al.
for integers and that of Felikson et al. for Eisenstein integers. We also
generalise results of Singerman and Strudwick on diameters of Farey graphs, we
recover a theorem of Morier-Genoud on enumerating friezes over finite fields,
and we classify those frieze patterns modulo that lift to frieze patterns
over the integers in terms of the topology of the corresponding Farey
complexes.Comment: 40 pages, 10 figure
EXTREMAL SET THEORY, CUBIC FORMS ON F n 2 AND HURWITZ SQUARE IDENTITIES
No full textInternational audienceWe study cubic forms on F n 2 using the Hurwitz-Radon theory of square identities. As an application, we obtain the following elementary statement. Given a family F of subsets of an n-set such that the cardinality of the symmetric di↵erence of any two elements F, F 0 2 F is not a multiple of 4, the maximal size of F is bounded by 2n, unless n ⌘ 3 mod 4 when it is bounded by 2n + 2. We also apply this theory to obtain some information about Boolean cubic forms and so-called additive quadruples
Recommended from our members
Frieze patterns and Farey complexes
No full textFrieze patterns have attracted significant attention recently, motivated by their relationship with cluster algebras. A longstanding open problem has been to provide a combinatorial model for frieze patterns over the ring of integers modulo N akin to Conway and Coxeter's celebrated model for positive integer frieze patterns. Here we solve this problem using the Farey complex of the ring of integers modulo N; in fact, using more general Farey complexes we provide combinatorial models for frieze patterns over any rings whatsoever.
Our strategy generalises that of the first author and of Morier-Genoud et al. for integers and that of Felikson et al. for Eisenstein integers. We also generalise results of Singerman and Strudwick on diameters of Farey graphs, we recover a theorem of Morier-Genoud on enumerating friezes over finite fields, and we classify those frieze patterns modulo N that lift to frieze patterns over the integers in terms of the topology of the corresponding Farey complexes
Review of Mark F. Chingono. The State, Violence and Development. The Political Economy of War in Mozambique, 1975–1992.
No full textBook review of: Mark F. Chingono. The State, Violence and Development. The Political Economy of War in Mozambique, 1975–1992. Avebury (Aldershot, Brookfield USA, Hong Kong, Singapore, Sydney), 1996. 291 pp. Foreword by Keith Hart. Tables. Appendix. Selected Bibliography. Index. £42.00. $71.95. Cloth
Passively mode-locked diode-pumped surface-emitting semiconductor laser
No full textA surface-emitting semiconductor laser has been passively mode locked in an external cavity incorporating a semiconductor saturable absorber mirror. The gain medium consists of a stack of 12 InGaAs-GaAs strained quantum wells, grown above a Bragg mirror structure, and pumped optically by a high-brightness diode laser. The mode-locked laser emits pulses of 22 ps full-width at half maximum duration at 1030 nm, with a repetition rate variable around 4.4 GHz
High power femtosecond source based on passively mode-locked 1055nm VECSEL and Yb-fibre power amplifier
No full textWe report 5 ns pulses at 160 W average power and 910 repetition rate from a passively mode-locked VECSEL source seeding an Yb-doped fibre power amplifier. The amplified pulses were compressed to 291 fs duration
- …
