999 resultados para Mandelbrot, Benoit B. 1924
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[Traditions. Asie. Inde. État du Maharashtra. Dhule]
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[Traditions. Asie. Inde. Madhya Pradesh. Chhattisgarh]
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[Traditions. Asie. Inde. État du Maharashtra. Dhule]
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[Traditions. Asie. Inde. État du Karnataka. Bjâpur]
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The present study on chaos and fractals in general topological spaces. Chaos theory originated with the work of Edward Lorenz. The phenomenon which changes order into disorder is known as chaos. Theory of fractals has its origin with the frame work of Benoit Mandelbrot in 1977. Fractals are irregular objects. In this study different properties of topological entropy in chaos spaces are studied, which also include hyper spaces. Topological entropy is a measures to determine the complexity of the space, and compare different chaos spaces. The concept of fractals can’t be extended to general topological space fast it involves Hausdorff dimensions. The relations between hausdorff dimension and packing dimension. Regular sets in Metric spaces using packing measures, regular sets were defined in IR” using Hausdorff measures. In this study some properties of self similar sets and partial self similar sets. We can associate a directed graph to each partial selfsimilar set. Dimension properties of partial self similar sets are studied using this graph. Introduce superself similar sets as a generalization of self similar sets and also prove that chaotic self similar self are dense in hyper space. The study concludes some relationships between different kinds of dimension and fractals. By defining regular sets through packing dimension in the same way as regular sets defined by K. Falconer through Hausdorff dimension, and different properties of regular sets also.
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Resumen tomado de la publicación
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von Max Freudenthal
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im Auftrage des Kuratoriums bearb. u. hrsg. von Josef Rosenthal
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BACKGROUND This first-in-human proof-of-concept study aimed to check whether safety and preclinical results obtained by intratumoral administration of BQ788, an endothelin receptor B (EDNRB) antagonist, can be repeated in human melanoma patients. METHODS Three patients received a single intralesional BQ788 application of 3 mg. After 3-7 days, the lesions were measured and removed for analysis. The administered dose was increased to a cumulative dosage of 8 mg in patient 4 (4 × 2.0 mg, days 0-3; lesion removed on day 4) and to 10 mg in patient 5 (3 × 3.3 mg, days 0, 3, and 10; lesion removed after 14 days). Control lesions were simultaneously treated with phosphate-buffered saline (PBS). All samples were processed and analyzed without knowledge of the clinical findings. RESULTS No statistical evaluation was possible because of the number of patients (n = 5) and the variability in the mode of administration. No adverse events were observed, regardless of administered dose. All observations were in accordance with results obtained in preclinical studies. Accordingly, no difference in degree of tumor necrosis was detected between BQ788- and PBS-treated samples. In addition, both EDNRB and Ki67 showed decreased expression in patients 2 and 5 and, to a lesser extent, in patient 1. Similarly, decreased expression of EDNRB mRNA in patients 2 and 5 and of BCL2A1 and/or PARP3 in patients 2, 3, and 5 was found. Importantly, semiquantitatively scored immunohistochemistry for CD31 and CD3 revealed more blood vessels and lymphocytes, respectively, in BQ788-treated tumors of patients 2 and 4. Also, in all patients, we observed inverse correlation in expression levels between EDNRB and HIF1A. Finally, in patient 5 (the only patient treated for longer than 1 week), we observed inhibition in lesion growth, as shown by size measurement. CONCLUSION The intralesional applications of BQ788 were well tolerated and showed signs of directly and indirectly reducing the viability of melanoma cells.
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ʻAzīz Jang.
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Plates, accompanied by unnumbered leaf, laid in.