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Dzhalilov A.,Turin Polytechnic University in Tashkent | Mayer D.,Clausthal University of Technology | Safarov U.,National University of Uzbekistan
Nonlinearity | Year: 2015

Let fi, i = 1, 2, be orientation preserving circle homeomorphisms with a finite number of break points , at which the first derivatives Dfi have jumps, and whose irrational rotation numbers coincide. Denote by the jump ratio of fi at a break point and by its total jump ratio, given by the product of the jump ratios over all break points. We prove that, for two such circle homeomorphisms fi, i = 1, 2, which on each interval of continuity of Dfi are C2+ε, ε > 0, and whose total jump ratios and do not coincide, the map h conjugating f1 and f2 is a singular function. © 2015 IOP Publishing Ltd & London Mathematical Society. Source


Fernandes H.R.,University of Aveiro | Tulyaganov D.U.,University of Aveiro | Tulyaganov D.U.,Turin Polytechnic University in Tashkent | Goel A.,Pacific Northwest National Laboratory | Ferreira J.M.F.,University of Aveiro
Journal of the European Ceramic Society | Year: 2012

Glass compositions with formula (71.78-x)SiO2-2.63Al2O3-(2.63+x)K2O-23.7Li2O (mol.%, x=0-10) and SiO2/Li2O molar ratios far beyond that of stoichiometric lithium disilicate (Li2Si2O5) were prepared by conventional melt-quenching technique to investigate the influence of K2O content on structural transformations and devitrification behaviour of glasses in the Li2O-SiO2 system. The scanning electron microscopy (SEM) examination of as cast non-annealed glasses revealed the presence of nanosized droplets in glassy matrices suggesting occurrence of liquid-liquid phase separation. An overall trend towards depolymerization of the silicate glass network with increasing K2O content was demonstrated by employing magic angle spinning-nuclear magnetic resonance (MAS-NMR) spectroscopy. The distribution of structural units in the experimental glasses was estimated using 29Si MAS-NMR spectroscopy suggesting the appearance of Q2, enhancement of Q3 and diminishing of Q4 groups with increasing K2O contents. X-ray diffraction (XRD) and differential thermal analysis (DTA) were used to assess the influence of K2O on devitrification process and formation of lithium disilicate (Li2Si2O5) and/or lithium metasilicate (Li2SiO3) crystalline phases. © 2011 Elsevier Ltd. Source


Kansal I.,University of Aveiro | Goel A.,Pacific Northwest National Laboratory | Tulyaganov D.U.,Turin Polytechnic University in Tashkent | Santos L.F.,University of Lisbon | Ferreira J.M.F.,University of Aveiro
Journal of Materials Chemistry | Year: 2011

We report on the structure, apatite-forming ability and physicochemical degradation of glasses along the fluorapatite [FA; Ca5(PO 4)3F]-diopside (Di; CaMgSi2O6) join. A series of glasses with varying FA/Di ratio have been synthesised by melt-quenching technique. The amorphous glasses could be obtained only for compositions up to 40 wt.% of FA. The detailed structural analysis of the glasses has been made by infrared spectroscopy (FTIR), Raman spectroscopy and magic angle spinning-nuclear magnetic resonance spectroscopy (MAS-NMR). Silicon was predominantly present as Q2 (Si) species while phosphorus was found in an orthophosphate type environment in all the investigated glasses. The apatite forming ability of glasses was investigated by immersion of the glass powders in simulated body fluid (SBF) for times varying between 1 h-28 days. An extensive precipitation of calcite (CaCO3) after immersion in SBF was found in all the glasses, which considerably masked the formation of hydroxyapatite [HA; Ca5(PO4)3OH]. The possible mechanism favouring the formation of calcite instead of HA has been explained on the basis of experimental results obtained for the structure of the glasses, leaching profile of glass powders in SBF solution and pH variation in SBF solution. Furthermore, the physico-chemical degradation of the glasses has been studied in accordance with ISO 10993-14 "Biological evaluation of medical devices - Part 14: Identification and quantification of degradation products from ceramics" in Tris HCl and citric acid buffer. All the FA containing glasses exhibited a weight gain (instead of weight loss) after immersion in citric acid buffer due to the formation of different crystalline products. © 2011 The Royal Society of Chemistry. Source


Kansal I.,University of Aveiro | Goel A.,Pacific Northwest National Laboratory | Tulyaganov D.U.,Turin Polytechnic University in Tashkent | Rajagopal R.R.,University of Aveiro | Ferreira J.M.F.,University of Aveiro
Journal of the European Ceramic Society | Year: 2012

The influence of varying the CaO/MgO ratio on the structure and thermal properties of CaO-MgO-SiO 2-P 2O 5-CaF 2 glasses was studied in a series of eight glass compositions in the glass forming region of diopside (CaMgSi 2O 6)-fluorapatite [Ca 5(PO 4) 3F]-wollastonite (CaSiO 3) ternary system. The melt-quenched glasses were characterized for their structure by infrared spectroscopy (FTIR) and magic angle spinning (MAS)-nuclear magnetic resonance (NMR) spectroscopy. Silicon is predominantly present as Q 2 (Si) species, while phosphorus tends to coordinate in orthophosphate environment. The sintering and crystallization parameters of the glasses were obtained from differential thermal analysis (DTA) while crystalline phase fractions in the sintered glass-ceramics were analyzed by X-ray diffraction adjoined with Rietveld refinement. Diopside, fluorapatite, wollastonite and pseudowollastonite crystallized as the main crystalline phases in all the glass-ceramics with their content varying with respect to variation in CaO/MgO ratio in glasses. The implications of structure and sintering behaviour of glasses on their bioactivity were discussed. © 2011. Source


Masuda S.,James Franck Institute | Masuda S.,Tohoku University | Nakamura K.,Turin Polytechnic University in Tashkent | Nakamura K.,Osaka City University | Del Campo A.,Los Alamos National Laboratory
Physical Review Letters | Year: 2014

A protocol is proposed for the rapid coherent loading of a Bose-Einstein condensate into the ground state of an optical lattice, without residual excitation associated with the breakdown of adiabaticity. The driving potential required to assist the rapid loading is derived using the fast-forward technique, and generates the ground state in any desired short time. We propose an experimentally feasible loading scheme using a bichromatic lattice potential, which approximates the fast-forward driving potential with high fidelity. © 2014 American Physical Society. Source

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