A family of perfect factorisations of complete bipartite graphs

A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n = p(2) for an odd prime p. We construct a family of (p-1)/2 non-isomorphic perfect 1-factorisations of K-n,K-n. Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin square is pan-Hamiltoilian if the permutation defined by any row relative to any other row is a single Cycle. (C) 2002 Elsevier Science (USA).

Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

Revival resonant scattering, perfect caustics and isotropic transport of pseudospin-1 particles

This work was supported by ONR under Grant No. N00014-16-1-2828.

Enzymatic kinetic resolution of (RS)-1-(Phenyl)ethanols by Burkholderia cepacia lipase immobilized on magnetic nanoparticles

Lipase from Burkholderia cepacia immobilized on superparamagnetic nanoparticles using adsorption and chemisorption methodologies was efficiently applied as recyclable biocatalyst in the enzymatic kinetic resolution of (RS)-1-(phenyl)ethanols via transesterification reactions. (R)-Esters and the remaining (S)-alcohols were obtained with excellent enantiomeric excess (> 99%), which corresponds to a perfect process of enzymatic kinetic resolution (conversion 50%, E > 200). The transesterification reactions catalysed with B. cepacia lipase immobilized by the glutaraldehyde method showed the best results in terms of reusability, preserving the enzyme activity (conversion 50%, E > 200) for at least 8 successive cycles.

Casimir interaction between a perfect conductor and graphene described by the Dirac model

We adopt the Dirac model for graphene and calculate the Casimir interaction energy between a plane suspended graphene sample and a parallel plane perfect conductor. This is done in two ways. First, we use the quantum-field-theory approach and evaluate the leading-order diagram in a theory with 2+1-dimensional fermions interacting with 3+1-dimensional photons. Next, we consider an effective theory for the electromagnetic field with matching conditions induced by quantum quasiparticles in graphene. The first approach turns out to be the leading order in the coupling constant of the second one. The Casimir interaction for this system appears to be rather weak. It exhibits a strong dependence on the mass of the quasiparticles in graphene.

Influência da função distribuição de quebra na modelagem e simulação do circuito de moagem de Carajás - Parte 1 - ajuste de modelos

The perfect mixing model (PMM) is based on parameters derived from the equipment characteristics as well as ore breakage characteristics. Ore characteristics are represented through the appearance function. This function may be determined using JKMRC laboratorial methods or by standard functions. This work describes the model fitting process of the Carajas grinding circuit, using the JKSimMet simulator Two scenarios were used in model fitting exercises: 1) standard appearance function; and 2) appearance fund ion based on testing carried out on samples taken at circuit feed. From this assessment, the appearance function`s influence in the PMM,fit and it`s relation with the breakage rate were determined. The influence of the appearance function on the respective breakage rate distribution was assessed.

Lambda-fold 3-perfect 9-cycle systems

The spectrum for the decomposition of lambda K-v into 3-perfect 9-cycles is found for all lambda > 1. (The case lambda = 1 was dealt with in an earlier paper by the authors and Lindner.) The necessary conditions for the existence of a suitable decomposition turn out to be sufficient.

Será preciso lembrar que o 1º de Maio nasceu em Chicago-EUA?!

É vergonhoso e revoltante que seja o próprio Estado português a promover o despedimento em Portugal, qual país do 3º mundo. Muitas vezes não apenas junto dos trabalhadores do sector privado, mas também junto do próprio sector público. Agora, acreditam que existiram perfeitos ignorantes e idiotas em Portugal que chegaram nos tempos mais recentes a propor o fim deste feriado de cariz mundial?! § Abstract: It is shameful and disgusting that is the very Portuguese State to promote the dismissal in Portugal, which country in the 3rd world. Often not only among private sector employees, but also from the public sector itself. Now, believe that there were ignorant and stupid perfect in Portugal who arrived in recent times to propose the end of this world oriented holiday ?!

The Sticky Information Macro Model: Beyond Perfect Foresight

Sticky information monetary models have been used in the macroeconomic literature to explain some of the observed features regarding inflation dynamics. In this paper, we explore the consequences of relaxing the rational expectations assumption usually taken in this type of model; in particular, by considering expectations formed through adaptive learning, it is possible to arrive to results other than the trivial convergence to a fixed point long-term equilibrium. The results involve the possibility of endogenous cyclical motion (periodic and a-periodic), which emerges essentially in scenarios of hyperinflation. In low inflation settings, the introduction of learning implies a less severe impact of monetary shocks that, nevertheless, tend to last for additional time periods relative to the pure perfect foresight setup.

From perfect strangers to research partners: a study of relationships, resource sharing and perceived benefits within R&D cooperation networks

Doctoral thesis in Marketing and Strategy.

equivalence of almost bent and almost perfect nonlinear functions and their generalizations

Vectorial Boolean function, almost bent, almost perfect nonlinear, affine equivalence, CCZ-equivalence

Crosscorrelation properties between perfect sequences

Binary sequence, perfect sequence, autocorrelation, crosscorrelation, Hadamard transform

Contribution of NFI-C to TGF-β1 signalling and tissue regeneration

Summary : Platelet Derived Growth Factor (PDGF) and Transforming Growth Factor-ß (TGF-ß) are two crucial growth factors in tissue repair and regeneration. They control migration and proliferation of macrophages and fibroblasts, as well as myofibroblast differentiation and synthesis of the new connective tissue. The transcription factor Nuclear Factor I-C (NFI-C) has been implicated in the TGF-ß pathway and regulation of extracellular matrix proteins in vitro. This suggests a possible implication of NFI-C in tissue repair. In this study, our purpose was to identify the NFI-C target genes in TGF-ß1 pathway activation and define the relationship between these two factors in cutaneous wound healing process. High-throughput genomic analysis in wild-type and NFI-C knock-out embryonic fibroblasts indicated that NFI-C acts as a repressor of the expression of genes which transcriptional activity is enhanced by TGF-ß. Interestingly, we found an over representation of genes involved in connective tissue inflammation and repair. In accordance with the genomic analysis, NFI-C-/- mice showed an improvement of skin healing during the inflammatory stage. Analysis of this new phenotype indicated that the expression of PDGFA and PDGF-Ra genes were increased in the wounds of NFI-C-/- mice resulting in early recruitment of macrophages and fibroblasts in the granulation tissue. In correlation with the stimulation effect of TGF-ß on myofibroblast differentiation we found an increased differentiation of these cells in null mice, providing a rationale for rapid wound closure. Thus, in the absence of NFI-C, both TGF-ß and PDGF pathways may be activated, leading to enhanced healing process. Therefore, the inhibition of NFI-C expression could constitute a suitable therapy for healing improvement. In addition, we identified a delay of hair follicle cycle initiation in NFI-C-/- mice. This prompted us to investigate the role of NFI-C in skin appendage. The transition from a quiescent to a proliferative phase requires a perfect timing of signalling modulation, leading to stem cell activation. As a consequence of cycle initiation delay in null mice, the activation of signalling involved in cell proliferation was also retarded. Interestingly, at the crucial moment of cell fate determination, we identified a decrease of CD34 gene in mutant mice. Since CD34 protein is involved in migration of multipotent cells, we suggest that NFI-C may be involved in stem cell mobilisation required for hair follicle renewal. Further investigations of the role of NFI-C in progenitor cell activation will lead to a better understanding of tissue regeneration and raise the possibility of treating alopecia with NFI-C-targeting treatment. In summary, this study demonstrates new regenerative functions of NFI-C in adult mice, which regulates skin repair and hair follicle renewal. Résumé : PDGF et TGF-ß sont des facteurs important du mécanisme de défense immunitaire. Ils influencent la prolifération et migration des macrophages et des fibroblastes, ainsi que la différenciation des myofibroblastes et la formation du nouveau tissu conjonctif. Le facteur de transcription NFI-C a été impliqué dans la voie de signalisation de TGF-ß et dans 1a régulation de l'expression des protéines de la matrice extracellulaire in vitro. Ces études antérieures laissent supposer que NFI-C serait un facteur important du remodelage tissulaire. Cependant le rôle de NFI-C dans un tissu comme la peau n'a pas encore été étudié. Dans ce travail, le but a été de d'identifier la relation qu'il existe entre I~1FI-C et TGF-ßl à un niveau transcriptionnel et dans le processus de cicatrisation cutanée in vivo. Ainsi, une analyse génétique à grande échelle, a permis d'indiquer que NFI-C agit comme un répresseur sur l'expression des gènes dont l'activité transcriptionnelle est activée par TGF-ß. De plus nous avons identifié un groupe de gènes qui controlent le développement et l'inflammation du tissue conjonctif. En relation avec ce résultat, l'absence de NFI-C dans la peau induit une cicatrisation plus rapide pendant la phase inflammatoire. Durant cette période, nous avons montré que les expressions de PDGFA et PDGFRa seraient plus élevées en absence de NFI-C. En conséquence, l'activation de la voie de PDGF induit une infiltration plus importante des macrophages et fibroblastes dans le tissue granuleux des souris mutantes. De plus, en corrélation avec le rôle de TGF-ßl dans la différenciation des myofibroblasts, nous avons observé une différenciation plus importante de ces cellules chez les animaux knock-out, ce qui peut expliquer une contraction plus rapide de la plaie. De plus, nous avons découvert que NFI-C est impliqué dans l'initiation du cycle folliculaire. La caractérisation de ce nouveau phénotype a montré un ralentissement de la transition telogène-anagène des souris NFI-C-/-. Or, un événement clé de cette transition est la modulation de plusieurs signaux moléculaires aboutissant à' l'activation des cellules souches. En corrélation avec le decalage du cycle, l'activation de ces signaux est également décalée dans les souris NFI-C-/-. Ainsi, au commencement de l'anagène, la prolifération des keratinocytes,NFI-C-/- est retardée et corrèle avec une diminution de l'expression de CD34, une protéine responsable de la détermination du migration des cellules multipotentes. Ainsi, NFI-C semble être impliqué dans la mobilisation des cellules souches qui sont nécessaires au renouvellement folliculaire. En résumé, NFI-C est impliqué dans la régulation des signaux moléculaires nécessaires à la réparation tissulaire et son inhibition pourrait constituer un traitement de la cicatrisation. L'analyse de son rôle dans l'activation des cellules souches permettrait de mieux comprendre le renouvellement tissulaire et, à long terme, d'améliorer les techniques de greffe des cellules souches épithéliales ou consituter une cible pour le traitement de l'alopecie.

A mathematical excursion: From the three-door problem to a Cantor-type perfect set

We start with a generalization of the well-known three-door problem:the n-door problem. The solution of this new problem leads us toa beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions will take us to some metrical properties of sets defined through the Pierce expansions of its elements. Finally, these metrical properties will enable us to present 'strange' sets, similar to the classical Cantor set.