Lebesgue quasi-uniformity on textures

[EN] This is a continuation of the work where the notions of Lebesgue uniformity and Lebesgue quasi uniformity in a texture space were introduced. It is  well known that the quasi uniform space with a compact topology has the Lebesgue property. This result is extended to direlational quasi uniformities and dual dicovering quasi uniformities. Additionally we discuss the completeness of lebesgue di-uniformities and dual dicovering lebesgue di-uniformities.Ozcag, S. (2015). Lebesgue quasi-uniformity on textures. Applied General Topology. 16(2):167-181. doi:10.4995/agt.2015.3323.SWORD167181162Brown, L. M., Ertürk, R., & Dost, Ş. (2004). Ditopological texture spaces and fuzzy topology, I. Basic concepts. Fuzzy Sets and Systems, 147(2), 171-199. doi:10.1016/j.fss.2004.02.009L. M. Brown and M. M. Gohar, Compactness in Ditopological Texture Spaces}, Hacettepe journal of Mathematics and Statistics 38, no. 1 (2009), 21--43.P. Fletcher and W. F. Lindgren, Quasi-uniform spaces, Marcel Dekker, (New York and Basel, 1982).Gantner, T. E., & Steinlage, R. C. (1972). Characterizations of Quasi-Uniformities†. Journal of the London Mathematical Society, s2-5(1), 48-52. doi:10.1112/jlms/s2-5.1.48Hutton, B. (1977). Uniformities on fuzzy topological spaces. Journal of Mathematical Analysis and Applications, 58(3), 559-571. doi:10.1016/0022-247x(77)90192-5J. Marin and S. Romaguera, On quasi uniformly continuous functions and Lebesgue spaces}, Publicationes Mathematicae Debrecen 48 (1996), 347-355.S. Özcag, F. Yildiz and L. M. Brown, Convergence of regular difilters and the completeness of di-uniformities, Hacettepe Journal of mathematics and statistics 34, (2005) 53-68

Sequentially dinormal ditopological texture spaces and dimetrizability

AbstractThe authors extend the bitopological notion of sequential normality to ditopological texture spaces, and use this notion to state and prove a (pseudo-)dimetrizability theorem

Fuzzy topological spaces

(1) We define normality for fuzzy topological spaces, define a fuzzy unit interval, and prove a Urysohn type lemma. (2) We define uniformities on fuzzy lattices, and characterise uniformizability in terms of complete regularity. (3) We define the product of a collection of fuzzy topological spaces. We define compactness and connectedness, and show that the product is compact (connected) iff each factor space is. (4) We place normality and complete regularity within a coherent hierarchy of separation and regularity axioms. We prove the usual implications, and the usual theorems about compactness and products. (5) We give alternative definitions of uniformities and pseudometrics, and show a compact R1 space has a unique uniformity

On MV - topologies

En este trabajo estamos interesados en un tipo particular de topología fuzzy llamada MV-topología, la cual usa operaciones MV-algebraicas para generar abiertos fuzzy. Estos espacios topológicos fuzzy permiten generalizaciones naturales de definiciones y resultados importantes de la topología clásica. En este sentido, desarrollamos algunos conceptos y resultados centrales, con el proprósito de extender los correspondientes de la topología clásica, y al mismo tiempo siguiendo la ruta de la bien conocida teoría de espacios topológicos fuzzy. Mostramos que las MV-topologías son un tipo de topología fuzzy que goza de muy "buen comportamiento" matemático, en el sentido de que la mayoría de definiciones y resultados clásicos de topología general encuentran una extensión o adaptación natural en este marco. Entre otros resultados, también extendemos el concepto de haz para el caso en el que el espacio base es un espacio MV-topológico, y mostramos una representación por "MV-haces" para una clase de MV-álgebras.DoctoradoDOCTOR(A) EN CIENCIAS - MATEMÁTICA

Complete regularity and related concepts in L-uniform spaces

L will denote a completely distributive lattice with an order reversing involution. The concept of an L-uniform space is introduced. An extension theorem concerning L-uniformly continuous functions is proved. A characterisation of L-uniformizability, involving L-complete regularity is given. With respect to L--completely regular spaces it is shown that the topological modification of an L-completely regular space is completely regular. Furthermore it is shown that the topologically generated L-topology of a completely regular space is L-completely regular

A Near-Infrared Search for Silicates in Jovian Trojan Asteroids

We obtained near-infrared (0.8 - 2.5 micron) spectra of seven Jovian Trojan asteroids that have been formerly reported to show silicate-like absorption features near 1 micron. Our sample includes the Trojan (1172) Aneas, which is one of three Trojans known to possess a comet-like 10 micron emission feature, indicative of fine-grained silicates. Our observations show that all seven Trojans appear featureless in high signal-to-noise ratio spectra. The simultaneous absence of the 1 micron band and presence of the 10 micron emission can be understood if the silicates on (1172) Aneas are iron-poor. In addition, we present near infrared observations of five optically grey Trojans, including three objects from the collisionally produced Eurybates family. The five grey Trojans appear featureless in the near infrared with no diagnostic absorption features. The near infrared spectrum of Eurybates can be best fitted with the spectrum of a CM2 carbonaceous chondrite, which hints that the C-type Eurybates family members may have experienced aqueous alteration.Comment: 22 pages, 5 figures, accepted to be published in A

An investigation into the limitations of myocardial perfusion imaging

Myocardial Perfusion Imaging (MPI) plays a very important role in the management of patients with suspected Coronary Artery Disease and its use has grown despite the shortcomings of the technique. Significant progress has been made in identifying the causes of these shortcomings and many solutions been suggested in the literature but the clinical sensitivity and specificity of the technique is still well below optimum. Monte Carlo Simulation is a very useful tool in identifying and guiding the understanding of the existing problems in MPI and this present study utilised this method to establish the basis of the simulations to be used and the way to analyse the results so that many of the causes of the attenuation defects, when using MPI, could be identified. This was achieved by investigating the effect that the different anatomical parts of the thorax have on the attenuation defects caused. A further aspect investigated was the impact that self-absorption in the heart has on these defects. The variability of these defects were further investigated by altering the position and orientation of the heart itself within the thorax and determining the effect it has on the attenuation defects caused. Results indicate that the attenuation caused is a very complicated process, that the self-absorption of the heart plays an extremely important role and the impact of the different positions and orientation of the heart inside the thorax are also significant. The distortion caused on the images by these factors was demonstrated by the intensity losses in the basal part and an over-estimation in the apical parts, which were clearly observable on the final clinical images, with the potential to affect clinical interpretation. Attenuation correction procedures using transmission sources, have been available for some time, but have not been adopted widely, amidst concern that they introduce additional artefacts. This study determined the effectiveness of these methods by establishing the level of correction obtained and whether additional artefacts were introduced. This included the effectiveness of the compensation achieved with the use of the latest commercially available comprehensive correction techniques. The technique investigated was “Flash3D" from Siemens providing transmission based attenuation correction, depth-dependent resolution recovery and scatter correction. The comparison between the defects and intensity losses predicted by the Monte Carlo Simulations and the corrections provided by this commercial correction technique revealed that solution is compensating almost entirely for these problems and therefore do provide substantial progress in overcoming the limitations of MPI. As a result of the improvements gained from applying these commercially available techniques and the accuracy established in this study for the mentioned technique it is strongly recommended that these new techniques be embraced by the wider Nuclear Medicine community so that the limitations in MPI can be reduced in clinical environment. Non-withstanding the above gains made there remains room for improvement by overcoming the of use transmission attenuation correction techniques by replacing them with emission based techniques. In this study two new related emission based attenuation correction techniques have been suggested and investigated and provide a promising prospect of overcoming these limitations

The Brains of Babies: A Surface Based Approach To Study Cortical Development in Term and Preterm Human Infants

Half a million infants are born before term gestation each year in the United States. Although advances in newborn medicine have increased survival rates of very preterm infants to almost 90%, surviving preterm infants are at increased risk for developing lasting neurologic impairments. In order to develop a plausible neuroprotective strategy it is imperative that we improve our understanding of normal cortical development and develop tools to evaluate injury. Using a surface based approach we have characterized normal cortical development in healthy term infants and analyzed abnormalities associated with preterm birth. Accurate cortical surface reconstructions for each hemisphere of 12 healthy term gestation infants and 12 low-risk preterm infants at term equivalent postmenstrual age were generated from structural magnetic resonance imaging data using a novel segmentation algorithm. Data from the 12 term infants were used to establish the first population average surface based atlas of human cerebral cortex at term gestation. Comparing this atlas to a previously established atlas of adult cortex revealed that cortical structure in term infants is similar to the adult in many respects, including the pattern of individual variability and the presence of statistically significant structural asymmetries in lateral temporal cortex, suggesting that that several features of cortical shape are minimally reliant on the postnatal environment. Surprisingly, the pattern of postnatal expansion in surface area is strikingly non-uniform; regions of lateral temporal, parietal, and frontal cortex expand nearly twice as much as other regions in insular and medial occipital cortex. Differential expansion may point to differential sensitivity of cortical circuits to normal or aberrant childhood experiences. The pattern of human postnatal expansion parallels the pattern of evolutionary cortical expansion revealed by comparison between the human and the macaque monkey. Finally, in comparing term and preterm infants, region-specific alterations in cortical folding in the preterm population were found. The most striking shape differences were present in the orbitofrontal and inferior occipital regions with reductions in folding in the insular, lateral temporal, lateral parietal, and lateral frontal cortex. Overall these findings improve our understanding of normal cortical development and help elucidate the potential pathways for cortical injury in preterm infants