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On representations by Egyptian fractions  [PDF]
Florin Ambro,Mugurel Barcau
Mathematics , 2014,
Abstract: We give a sharp upper bound for the entries of the representations of a rational number as a sum of Egyptian fractions.
The Unsustainable City  [PDF]
Matthias Berger
Sustainability , 2014, DOI: 10.3390/su6010365
Abstract: “Make cities more sustainable” is an omnipresent slogan in architecture and urban planning. This article is a discussion on theoretical and practical boundaries of using the expression “sustainability” with respect to the scientific community, therefore avoiding sustainability becoming a euphemism for “doing good”. By definition, it can be concluded, cities developed as counterparts to the hinterland and, therefore, they axiomatically should be and are as a matter of fact unsustainable. Furthermore, sustainability is a binary, not a gradual concept. Something is either sustainable or not. Aiming to increase the sustainability is consequently a sham battle. It would be necessary to change our perception to acknowledge that cities should be unsustainable in order to become efficient, seen from a global perspective including the hinterland.
Denser Egyptian Fractions  [PDF]
Greg Martin
Mathematics , 1998,
Abstract: An Egyptian fraction is a sum of distinct unit fractions (reciprocals of positive integers). We show that every rational number has Egyptian fraction representations where the number of terms is of the same order of magnitude as the largest denominator, improving a result from an earlier paper to best-possible form. We also settle, in best-possible form, the related problem of how small M_t(r) can be such that there is an Egyptian fraction representation of r with exactly t terms, the denominators of which are all at most M_t(r). We also consider the following problems posed by Erdos and Graham: the set of integers that cannot be the largest denominator of an Egyptian fraction representation of 1 is infinite - what is its order of growth? How about those integers that cannot be the second-largest (third-largest, etc.) denominator of such a representation? In the latter case, we show that only finitely many integers cannot be the second-largest (third-largest, etc.) denominator of such a representation; while in the former case, we show that the set of integers that cannot be the largest denominator of such a representation has density zero, and establish its order of growth. Both results extend to representations of any positive rational number.
Dense Egyptian Fractions  [PDF]
Greg Martin
Mathematics , 1998,
Abstract: Every positive rational number has representations as Egyptian fractions (sums of reciprocals of distinct positive integers) with arbitrarily many terms and with arbitrarily large denominators. However, such representations normally use a very sparse subset of the positive integers up to the largest demoninator. We show that for every positive rational there exist Egyptian fractions whose largest denominator is at most N and whose denominators form a positive proportion of the integers up to N, for sufficiently large N; furthermore, the proportion is within a small factor of best possible.
TP Decoding  [PDF]
Yi Lu,Cyril Measson,Andrea Montanari
Mathematics , 2007,
Abstract: `Tree pruning' (TP) is an algorithm for probabilistic inference on binary Markov random fields. It has been recently derived by Dror Weitz and used to construct the first fully polynomial approximation scheme for counting independent sets up to the `tree uniqueness threshold.' It can be regarded as a clever method for pruning the belief propagation computation tree, in such a way to exactly account for the effect of loops. In this paper we generalize the original algorithm to make it suitable for decoding linear codes, and discuss various schemes for pruning the computation tree. Further, we present the outcomes of numerical simulations on several linear codes, showing that tree pruning allows to interpolate continuously between belief propagation and maximum a posteriori decoding. Finally, we discuss theoretical implications of the new method.
Intra-familial physical violence among Mexican and Egyptian youth
Rivera-Rivera,Leonor; Allen,Betania; Thrasher,James F; Chavez,Ruben; Fernandez-Ortega,Cielo; Galal,Osman; Lazcano-Ponce,Eduardo C;
Revista de Saúde Pública , 2005, DOI: 10.1590/S0034-89102005000500003
Abstract: objective: to determine the prevalence of experiencing intra-familial violence among mexican and egyptian youth and to describe its associated risk factors. methods: data from questionnaires applied to 12,862 mexican and 5,662 egyptian youth, aged 10 to 19, who attended public schools were analyzed. biviarate and logistic regression analysis were used to determine the relationship between socio-demographics, the experience of intra-familial violence and violence perpetration. results: the prevalence of having experienced intra-familial violence was comparable across the mexican and egyptian populations (14% and 17%, respectively). in mexico, young men were more likely to have experienced such violence (or=2.36) than women, whereas in egypt, young women were at slightly greater risk than young men (or=1.25). older age, male gender and urban residence were independent correlates of experiencing intra-familial violence among mexican youth. for egyptian adolescents, in contrast, younger age, female gender and having non-married parents were independent correlates of victimization. intra-familial violence victims were also more likely than non-victims to perpetrate violence (mexico: or=13.13; egypt: or=6.58). conclusions: mexican and egyptian youth experienced intra-familial violence at a relatively low prevalence when compared with youth of other countries. a strong association was found between experiencing intra-familial violence and perpetrating violence.
Decoding of Differential AG Codes  [PDF]
Kwankyu Lee
Mathematics , 2014,
Abstract: The interpolation-based decoding that was developed for general evaluation AG codes is shown to be equally applicable to general differential AG codes. A performance analysis of the decoding algorithm, which is parallel to that of its companion algorithm, is reported. In particular, the decoding capacities of evaluation AG codes and differential AG codes are seen to be nicely interrelated. As an interesting special case, a decoding algorithm for classical Goppa codes is presented.
List Decoding of Burst Errors  [PDF]
Ron M. Roth,Pascal O. Vontobel
Mathematics , 2008,
Abstract: A generalization of the Reiger bound is presented for the list decoding of burst errors. It is then shown that Reed-Solomon codes attain this bound.
New Criteria for Iterative Decoding  [PDF]
Florence Alberge,Ziad Naja,P. Duhamel
Mathematics , 2010, DOI: 10.1109/ICASSP.2009.4960128
Abstract: Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical optimization techniques. We first show that iterative decoding can be rephrased as two embedded minimization processes involving the Fermi-Dirac distance. Based on this new formulation, an hybrid proximal point algorithm is first derived with the additional advantage of decreasing a desired criterion. In a second part, an hybrid minimum entropy algorithm is proposed with improved performance compared to the classical iterative decoding. Even if this paper focus on iterative decoding for BICM, the results can be applied to the large class of turbo-like decoders.
An Egyptian Geographer in Ouessant.
Atef Abdel-Hamid
EspacesTemps.net , 2010,
Abstract: Within less than twenty-four hours, I have moved from Cairo, the capital city of Egypt, with its fifteen-million population, to the Ouessant island, with its less-than-a-thousand population. At the last moment before catching the boat sailing from Brest to Ouessant, I picked up a very impressive touristic map. On board, with a coffee and a cappuccino, I made contact with some French passengers who were coming from Marseille to have a holiday in that remote island. For a na ve Egyptian ...
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