Sucesiones dobles sobre el cuerpo K = R o C y sus aplicaciones

Investiga la construcción y propiedades de las sucesiones dobles en el campo de los números reales R o sobre el campo de los números complejos C. Se considera en la presente investigación la teoría de sucesiones dobles, las relaciones existentes entre la unicidad del límite doble, los límites iterados y el intercambio del orden para la sucesión doble. Se investigó el Criterio de Cauchy para sucesiones dobles, las subsucesiones y los límites dobles monótonas y acotadas. Las sucesiones dobles se aplican a los lmites inversos y continuos enrejados.Tesi

Influence of the Nb and Ba dopands on the properties of the PZT type ceramics

Investigations of an influence of an admixture of ions Ba2+ and Nb5+ on dielectric and piezoelectric properties of the Pb(Zr0:53Ti0:47)O3 (PZT) ceramics were conducted. The PZT type ceramics was synthesized by a conventional method, and compacted by a free sintering method. The PZT type specimens were poling by a low and high temperature method. It was found that there was a positive influence of adding 10mol%Ba and 2mol%Nb simultaneously on a set of dielectric and piezoelectric parameters, which are important for practical applications of this PZT type ceramics.[1] E.G. F e s e n k o, A.Ya. D a n c i g e r, O.N. R o z u -m o v s k a y a, Novye piezokeramicheskye materialy, Izd. RGU, Rostov na Donu, 49-70 (1983). [2] I. F r a n k e, K. R o l e d e r, L. M i t o s e r i u, R. P i t i c e s c u, Z. U j m a, High-temperature macroscopic piezoelectricity in Nb-doped PbZr1 x Ti x O3 ceramics driven by the existence of polar regions, Phys. Rev. B 73, 144114-1-5 (2006). [3] B. J a f f e, W.R. C o o k, H. J a f f e, Piezoelectricheskaya keramica, Izd. “Mir” Moskva, 139-147 (1974). [4] B. N o h e d a, J.A. G o n z a l o, L.E. C r o s s, R. G u o, S.-E. P a r k, D.E. C o x, G. S h i r a n e, Tetragonal-to-monoclinic phase transition in a ferroelectric perovskite: The structure of PbZr0:52Ti 0:48O3, Phys. Rev. B 61, 8687-9695 (2000). [5] J. D u d e k, D. B o c h e n e k, M.F. K u p r i y a n o v, Z. S u r o w i a k, Wpływ składu chemicznego i warunków otrzymywania na stabilność parametrów piezoceramiki typu PZT, Ceramics 65, 93-100 (2001). [6] T. I k e d a, Studies on (Ba-Pb)(Ti-Zr)O3 System, Journal of Physical Society of Japan, 14, 2 168-174 (1959). [7] G. L i, G. H a e r t l i n g, Dielectric, ferroelectric and electric field-induced strain properties of (Pb1 x Bax )(Zr1 y Tiy )O3 ceramics, Ferroelectrics 166, 31 (1995). [8] Z. S u r o w i a k, D. B o c h e n e k, Modyfikowanie składu chemicznego elektroceramiki PZT, Materiały ceramiczne/ Ceramic Materials/, 4, 124-134 (2004). [9] R. Z a c h a r i a s z, D. B o c h e n e k, Properties of the PZT type ceramics admixed with barium and niobium, Archives of Metallurgy and Materials, 54, 895-902 (2009). [10] K. O k a d z a k i, Technologia ceramicznych dielektryków, Izd. “Energia”, Moskva, 233-235 (1976). [11] I. F r a n k e, K. R o l e d e r, J. K l i m o n t k o, A. R a t u s z n a, A. S o s z y ń s k i, Anomalus piezoelectric and elastic properties of a tetragonal PZT ceramic near morfotropic phase boundary, J. Phys. D: Appl. Phys. 38, 749 (2005). [12] J. D u d e k, D. B o c h e n e k, Z. S u r o w i a k, V.G. G a v r i l y c h e n k o, Wpływ warunków technologicznych na stabilność właściwości piezoelektrycznych ceramiki typu PZT, Ceramics, 79, 130-136 (2003). [13] M. A d a m c z y k, Z. U j m a, L. S z y m c z a k, Effect of Nb doping on the relaxor behaviour of (Pb0:75 Ba0:25)(Zr0:70 Ti0:30)O3 ceramics, Journal of the European Ceramic Society, 26, 331-336 (2006)

New Algorithms for Maximum Disjoint Paths Based on Tree-Likeness

We study the classical NP-hard problems of finding maximum-size subsets from given sets of k terminal pairs that can be routed via edge-disjoint paths (MaxEDP) or node-disjoint paths (MaxNDP) in a given graph. The approximability of MaxEDP/NDP is currently not well understood; the best known lower bound is Omega(log^{1/2 - varepsilon} n), assuming NP not subseteq ZPTIME(n^{poly log n}). This constitutes a significant gap to the best known approximation upper bound of O(n^1/2) due to Chekuri et al. (2006) and closing this gap is currently one of the big open problems in approximation algorithms. In their seminal paper, Raghavan and Thompson (Combinatorica, 1987) introduce the technique of randomized rounding for LPs; their technique gives an O(1)-approximation when edges (or nodes) may be used by O(log n/log log n) paths. In this paper, we strengthen the above fundamental results. We provide new bounds formulated in terms of the feedback vertex set number r of a graph, which measures its vertex deletion distance to a forest. In particular, we obtain the following. - For MaxEDP, we give an O(r^0.5 log^1.5 kr)-approximation algorithm. As r<=n, up to logarithmic factors, our result strengthens the best known ratio O(n^0.5) due to Chekuri et al. - Further, we show how to route Omega(opt) pairs with congestion O(log(kr)/log log(kr)), strengthening the bound obtained by the classic approach of Raghavan and Thompson. - For MaxNDP, we give an algorithm that gives the optimal answer in time (k+r)^O(r)n. This is a substantial improvement on the run time of 2^kr^O(r)n, which can be obtained via an algorithm by Scheffler. We complement these positive results by proving that MaxEDP is NP-hard even for r=1, and MaxNDP is W[1]-hard for parameter r. This shows that neither problem is fixed-parameter tractable in r unless FPT = W[1] and that our approximability results are relevant even for very small constant values of r