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Academic literature on the topic 'Convergence and divergence of series and sequences'

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Published: 4 June 2021

Last updated: 15 February 2022

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Journal articles on the topic "Convergence and divergence of series and sequences"

Abalo, Elom K., and Kokou Y. Abalo. "Convergence ofp-series revisited with applications." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–8. http://dx.doi.org/10.1155/ijmms/2006/53408.

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We construct two adjacent sequences that converge to the sum of a given convergentp-series. In case of a divergentp-series, lower and upper bounds of the(kn)th partial sum are constructed. In either case, we extend the results obtained by Hansheng and Lu (2005) to any integerk≥2. Some numerical examples are given.

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Bloshanskii, I. L., and O. V. Lifantseva. "Maximal sets of convergence and unbounded divergence of multiple fourier series with J κ -lacunary sequence of partial sums." Mathematical Notes 86, no. 5-6 (December 2009): 883–86. http://dx.doi.org/10.1134/s0001434609110315.

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Bloshanskii, I. L., and O. V. Lifantseva. "Structural and geometric characteristics of sets of convergence and divergence of multiple Fourier series with J k -lacunary sequence of rectangular partial sums." Analysis Mathematica 39, no. 2 (June 2013): 93–121. http://dx.doi.org/10.1007/s10476-013-0202-3.

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Khan, Rasul A. "Convergence-Divergence of p-Series." College Mathematics Journal 32, no. 3 (May 2001): 206. http://dx.doi.org/10.2307/2687474.

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Wang, Xianfu. "Convergence-Divergence of p-Series." College Mathematics Journal 33, no. 4 (September 2002): 314. http://dx.doi.org/10.2307/1559055.

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Pakes, Anthony G. "Convergence and Divergence of Random Series." Australian New Zealand Journal of Statistics 46, no. 1 (March 2004): 29–40. http://dx.doi.org/10.1111/j.1467-842x.2004.00309.x.

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Jones, Roger L., and Mate Wierdl. "Convergence and divergence of ergodic averages." Ergodic Theory and Dynamical Systems 14, no. 3 (September 1994): 515–35. http://dx.doi.org/10.1017/s0143385700008002.

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AbstractIn this paper we consider almost everywhere convergence and divergence properties of various ergodic averages. A general method is given which can be used to construct averages for which a.e. convergence fails, and to show divergence (and in some cases ‘strong sweeping out’) for large classes of ergodic averages. We also show that there are sequences with the gaps between successive terms converging to zero, but such that the Cesaro averages obtained by sampling a flow along these sequences of times converge a.e. for all f∈L1(X).

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Clark Kimberling and Kenneth B. Stolarsky. "Slow Beatty Sequences, Devious Convergence, and Partitional Divergence." American Mathematical Monthly 123, no. 3 (2016): 267. http://dx.doi.org/10.4169/amer.math.monthly.123.3.267.

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Bayart, Frédéric. "Convergence and divergence of wavelet series: multifractal aspects." Proceedings of the London Mathematical Society 119, no. 2 (March 6, 2019): 547–78. http://dx.doi.org/10.1112/plms.12239.

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Córdoba, Antonio, and Pablo Fernández. "Convergence and Divergence of Decreasing Rearranged Fourier Series." SIAM Journal on Mathematical Analysis 29, no. 5 (September 1998): 1129–39. http://dx.doi.org/10.1137/s0036141097320705.

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Dissertations / Theses on the topic "Convergence and divergence of series and sequences"

Colna, Kaitlyn E. "Latitudinal Position and Trends of the Intertropical Convergence Zone (ITCZ) and its Relationship with Upwelling in the Southern Caribbean Sea and Global Climate Indices." Thesis, University of South Florida, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10262701.

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The Intertropical Convergence Zone (ITCZ) is a feature that results from the ocean-atmosphere interactions in the tropics around the world. The ITCZ is characterized by surface wind convergence, tall storm clouds, and it forms a belt of high time-averaged precipitation around the globe. The ITCZ undergoes seasonal migrations between 5°S and 15°N roughly following the subsolar point on Earth with the seasons, with a mean annual position located slightly above the Equator, between 2° and 5°N.

This study tested the hypothesis that there was a northward shift in the median position of the ITCZ in the first decade of the 2000’s relative to the 1900’s. This hypothesis has been posed in the literature given a weakening in the intensity of the Trade Winds observed in the southern Caribbean Sea during the first decade of the 2000’s, with concomitant ecological impacts due to weakening in coastal wind-driven upwelling. The hypothesis was tested by analyzing variations in the monthly latitudinal position of the ITCZ over the Atlantic Ocean relative to the median position computed for the period 1987–2011. The position of the ITCZ was derived from satellite-derived ocean surface wind measurements collected from 1987 to 2011. A Mann-Kendall analysis and a Monte Carlo simulation were used to test for trends in the median cross-basin latitudinal position of the ITCZ. The study included an analysis of regional changes across the tropical central Atlantic (50°W to 15°W), the Western Atlantic (50°W to 30°W), and the Eastern Atlantic (30°W to 15°W) within the tropics. The results show a slight southward trend in the median position of the ITCZ over the central Atlantic and also in the Eastern Atlantic in the first decade of the 2000’s relative to the 1990’s. While this trend is barely significant, it is likely simply due to interannual variation in the average annual position of the ITCZ.

The data were also examined for the timing and persistence of a double ITCZ in the Atlantic. The double ITCZ over the Atlantic appeared every year in February or March, with the largest separation between the northern and southern branches of the ITCZ observed in June and July.

The possible effects of changes in the average latitudinal position of the ITCZ on the upwelling in the Cariaco Basin (southeastern Caribbean Sea off Venezuela) were also examined. Anomalies of the median of the latitudinal position of the ITCZ in the Atlantic were compared with anomalies of in-situ temperature collected during the 1990’s and the first decade of the 2000’s by the CARIACO Ocean Time-Series program and with anomalies of satellite SST (from the Advanced Very High Resolution Radiometer satellite; AVHRR) from 1995 to 2016. Correlation analysis were performed between anomalies of water temperatures at various depths and anomalies of satellite SST with anomalies of the monthly mean ITCZ position with lags up to 3 months for the time series, and also just for the Cariaco basin upwelling months (December-April).

For the whole Cariaco time series there were no significant correlations between the anomalies of the ITCZ position and anomalies in subsurface temperatures in the Cariaco Basin. However, during the upwelling period, the central Atlantic and Western Atlantic ITCZ position anomalies were directly correlated with Cariaco Basin temperature anomalies with no-lag (r = 0.20), and the central and Eastern Atlantic ITCZ position anomalies were inversely correlated with Cariaco Basin temperatures (r ~ -0.22 to -0.28) with ITCZ leading Cariaco temperatures by 3 months. However, these correlations were low, indicating that other factors than the position of ITCZ latitudinal position play bigger role on the Cariaco basin upwelling variability.

Interannual variability in oceanographic and meteorological characteristics of the Atlantic Ocean are expected as a result of large-scale changes in other regions of the world, including due to changes such as the El Niño Southern Oscillation (ENSO) and the Atlantic Multidecadal Oscillation (AMO). Six oceanic-atmospheric variables are used to monitor ENSO over the tropical Pacific, while the AMO is determined by monitoring SST over the Atlantic. Correlations with lags of up to ± 6 months were conducted with those climate indices and the anomalies of the median monthly latitudinal position of the ITCZ. Significant direct correlations with ENSO (Multivariate ENSO Index) were seen in the Atlantic and Western Atlantic (r = 0.15), with ENSO leading the position of the ITCZ anomalies by 3 months. This implies that within three months after an El Niño event (warm ENSO anomaly in the Pacific) the ITCZ over the mid-Atlantic and Western Atlantic Ocean tends to shift to a more northerly position. The AMO also had a direct influence on the anomalies of the ITCZ position (r = 0.13) in the Central and the Western Atlantic, with the AMO leading ITCZ anomalies by 1 month (i.e. a warming of the North Atlantic led to a northward shift in the ITCZ one month later). Correlations between AMO and the ITCZ anomalies in the Eastern Atlantic were also direct but with no lag. Although significant, these correlations were low.

An inverse correlation (~ -0.35) was found between ENSO and anomalies of water temperature of the Cariaco Basin. ENSO lagged ocean temperature anomalies by 3 to 4 months for both the whole Cariaco time series and for the upwelling months of CARIACO data. Correlations with AMO were direct (~ 0.4); for the whole time series AMO led Cariaco temperature anomalies by 3 months, but for the upwelling months AMO lagged Cariaco temperature anomalies by one month.

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Passos, Rokenedy Lima. "Séries de Fourier e o Teorema de Equidistribuição de Weyl." Universidade Federal de Sergipe, 2017. https://ri.ufs.br/handle/riufs/6497.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work is treated in two parts. The first is to find sufficient conditions for a function so that its Fourier series distributions become common and uniform, as well as an approach to Fejér’s Theorem, an interesting and useful result of no Fourier Series study. A second part of the application of the Fourier Series, Weyl equidistribution theorem. A problem that lies at the frontier of Dynamic Systems with a Theory of Numbers. The same refers to the distribution of irrational numbers in the range [0, 1).
Este trabalho é tratado em duas partes. A primeira consiste em encontrar condições suficientes sobre uma dada função para que sua expansão em Série de Fourier convirja pontualmente e uniformemente, como também uma abordagem ao Teorema de Fejér, resultado interessante e útil no estudo de Séries de Fourier. A segunda parte uma aplicação provenientes das Séries de Fourier, o Teorema de equidistribuição de Weyl. Um problema que se encontra na fronteira dos Sistemas Dinâmicos com a Teoria dos Números. O mesmo refere-se à distribuição de números irracionais no intervalo [0, 1).

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Paditz, Ludwig. "Beiträge zur expliziten Fehlerabschätzung im zentralen Grenzwertsatz." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-115105.

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In der Arbeit wird das asymptotische Verhalten von geeignet normierten und zentrierten Summen von Zufallsgrößen untersucht, die entweder unabhängig sind oder im Falle der Abhängigkeit als Martingaldifferenzfolge oder stark multiplikatives System auftreten. Neben der klassischen Summationstheorie werden die Limitierungsverfahren mit einer unendlichen Summationsmatrix oder einer angepaßten Folge von Gewichtsfunktionen betrachtet. Es werden die Methode der charakteristischen Funktionen und besonders die direkte Methode der konjugierten Verteilungsfunktionen weiterentwickelt, um quantitative Aussagen über gleichmäßige und ungleichmäßige Restgliedabschätzungen in zentralen Grenzwertsatz zu beweisen. Die Untersuchungen werden dabei in der Lp-Metrik, 1
In the work the asymptotic behavior of suitably centered and normalized sums of random variables is investigated, which are either independent or occur in the case of dependence as a sequence of martingale differences or a strongly multiplicative system. In addition to the classical theory of summation limiting processes are considered with an infinite summation matrix or an adapted sequence of weighting functions. It will be further developed the method of characteristic functions, and especially the direct method of the conjugate distribution functions to prove quantitative statements about uniform and non-uniform error estimates of the remainder term in central limit theorem. The investigations are realized in the Lp metric, 1

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Paditz, Ludwig. "Beiträge zur expliziten Fehlerabschätzung im zentralen Grenzwertsatz." Doctoral thesis, 1988. https://tud.qucosa.de/id/qucosa%3A26930.

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In der Arbeit wird das asymptotische Verhalten von geeignet normierten und zentrierten Summen von Zufallsgrößen untersucht, die entweder unabhängig sind oder im Falle der Abhängigkeit als Martingaldifferenzfolge oder stark multiplikatives System auftreten. Neben der klassischen Summationstheorie werden die Limitierungsverfahren mit einer unendlichen Summationsmatrix oder einer angepaßten Folge von Gewichtsfunktionen betrachtet. Es werden die Methode der charakteristischen Funktionen und besonders die direkte Methode der konjugierten Verteilungsfunktionen weiterentwickelt, um quantitative Aussagen über gleichmäßige und ungleichmäßige Restgliedabschätzungen in zentralen Grenzwertsatz zu beweisen. Die Untersuchungen werden dabei in der Lp-Metrik, 1In the work the asymptotic behavior of suitably centered and normalized sums of random variables is investigated, which are either independent or occur in the case of dependence as a sequence of martingale differences or a strongly multiplicative system. In addition to the classical theory of summation limiting processes are considered with an infinite summation matrix or an adapted sequence of weighting functions. It will be further developed the method of characteristic functions, and especially the direct method of the conjugate distribution functions to prove quantitative statements about uniform and non-uniform error estimates of the remainder term in central limit theorem. The investigations are realized in the Lp metric, 1

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Books on the topic "Convergence and divergence of series and sequences"

(Victor), Vinnikov V., ed. Foundations of free noncommutative function theory. Providence, Rhode Island: American Mathematical Society, 2014.

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Regularised integrals, sums, and traces: An analytic point of view. Providence, R.I: American Mathematical Society, 2012.

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Saff, E. B., Douglas Patten Hardin, Brian Z. Simanek, and D. S. Lubinsky. Modern trends in constructive function theory: Conference in honor of Ed Saff's 70th birthday : constructive functions 2014, May 26-30, 2014, Vanderbilt University, Nashville, Tennessee. Providence, Rhode Island: American Mathematical Society, 2016.

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Bourchtein, Andrei, and Ludmila Bourchtein. Counterexamples on Uniform Convergence: Sequences, Series, Functions, and Integrals. Wiley & Sons, Incorporated, John, 2017.

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Bourchtein, Andrei, and Ludmila Bourchtein. Counterexamples on Uniform Convergence: Sequences, Series, Functions, and Integrals. Wiley & Sons, Incorporated, John, 2017.

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Chen-Wishart, Mindy, Alexander Loke, and Stefan Vogenauer, eds. Formation and Third Party Beneficiaries. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198808114.001.0001.

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Studies in the Contract Laws of Asia provides an authoritative account of the contract law regimes of selected Asian jurisdictions, including the major centres of commerce where limited critical commentaries have been published in the English language. Each volume in the series aims to offer an insider’s perspective into specific areas of contract law—remedies, formation, parties, contents, vitiating factors, change of circumstances, illegality, and public policy—and explores how these diverse jurisdictions address common problems encountered in contractual disputes. A concluding chapter draws out the convergences and divergences, and other themes. All the Asian jurisdictions examined have inherited or adopted the common law or civil law models of European legal systems. Scholars of legal transplant will find a mine of information on how received law has developed after the initial adaptation and transplant process, including the influences affecting and mechanisms of these developments. The many points of convergence and divergence (in both form and in substance) emerge. These provide good starting points for regional harmonization projects. Volume II of this series deals with contract formation and contracts for the benefit of third parties in the laws of China, India, Japan, Korea, Taiwan, Singapore, Malaysia, Hong Kong, Korea, Vietnam, Cambodia, Thailand, Myanmar, and Indonesia. Typically, each jurisdiction is covered in two chapters; the first deals with contract formation, while the second deals with contracts for the benefit of third parties.

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Chen-Wishart, Mindy, and Stefan Vogenauer, eds. Contents of Contracts and Unfair Terms. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198850427.001.0001.

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Studies in the Contract Laws of Asia provides an authoritative account of the contract law regimes of selected Asian jurisdictions, including the major centres of commerce where limited critical commentaries have been published in the English language. Each volume in the series aims to offer an insider’s perspective into specific areas of contract law—remedies, formation, parties, contents, vitiating factors, change of circumstances, illegality, and public policy—and explores how these diverse jurisdictions address common problems encountered in contractual disputes. A concluding chapter draws out the convergences and divergences, and other themes. All the Asian jurisdictions examined have inherited or adopted the common law or civil law models of European legal systems. Scholars of legal transplant will find a mine of information on how received law has developed after the initial adaptation and transplant process, including the influences affecting and mechanisms of these developments. The many points of convergence and divergence (in both form and in substance) emerge. These provide good starting points for regional harmonization projects. Volume III of this series deals with the contents of contracts and unfair terms in the laws of China, Hong Kong, India, Indonesia, Japan, Korea, Malaysia, Myanmar, the Philippines, Singapore, Taiwan, Thailand, and Vietnam. Typically, each jurisdiction is covered in two chapters; the first deals with the contents of contracts, while the second deals with unfair terms.

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Book chapters on the topic "Convergence and divergence of series and sequences"

Ponnusamy, S. "Sequences: Convergence and Divergence." In Foundations of Mathematical Analysis, 23–70. Boston, MA: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8292-7_2.

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Ponnusamy, S. "Series: Convergence and Divergence." In Foundations of Mathematical Analysis, 147–207. Boston, MA: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8292-7_5.

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Pinsky, Mark A. "Endpoint convergence of Legendre series." In Analysis of Divergence, 79–85. Boston, MA: Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-2236-1_7.

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Ruckle, William H. "Series summability of complete biorthogonal sequences." In Analysis of Divergence, 27–40. Boston, MA: Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-2236-1_3.

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Celia, C. W., A. T. F. Nice, and K. F. Elliott. "Sequences and series: convergence." In Advanced Mathematics 3, 186–231. London: Macmillan Education UK, 1985. http://dx.doi.org/10.1007/978-1-349-06711-4_6.

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Goldblatt, Robert. "Convergence of Sequences and Series." In Graduate Texts in Mathematics, 61–73. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0615-6_6.

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Deng, Zongyi, S. Gopinathan, and Christine Kim-Eng Lee. "The Singapore Curriculum: Convergence, Divergence, Issues and Challenges." In Education Innovation Series, 263–75. Singapore: Springer Singapore, 2013. http://dx.doi.org/10.1007/978-981-4451-57-4_15.

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Mursaleen, M., and S. A. Mohiuddine. "Double Series and Convergence Tests." In Convergence Methods for Double Sequences and Applications, 149–66. New Delhi: Springer India, 2014. http://dx.doi.org/10.1007/978-81-322-1611-7_9.

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Radożycki, Tomasz. "Investigating the Convergence of Sequences and Series of Functions." In Solving Problems in Mathematical Analysis, Part I, 341–65. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35844-0_15.

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Isaev, Alexander. "Morera’s Theorem. Sequences and Series of Functions. Uniform Convergence Inside a Domain. Power Series. Abel’s Theorem. Disk of Convergence. Radius of Convergence." In Springer Undergraduate Mathematics Series, 87–95. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68170-2_11.

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Conference papers on the topic "Convergence and divergence of series and sequences"

Imron, Moch Aruman. "Some convergence of double sine series and convergence p-Supremum bounded variation double sequences." In 2ND INTERNATIONAL CONFERENCE AND WORKSHOP ON MATHEMATICAL ANALYSIS 2016 (ICWOMA2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4972163.

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BLOSHANSKII, I. L. "STRUCTURAL AND GEOMETRIC CHARACTERISTICS OF SETS OF CONVERGENCE AND DIVERGENCE OF MULTIPLE FOURIER SERIES OF FUNCTIONS WHICH EQUAL ZERO ON SOME SET." In Proceedings of the Third International Conference on WAA. World Scientific Publishing Company, 2003. http://dx.doi.org/10.1142/9789812796769_0030.

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Bakhshaei, Hani, Luc Mongeau, and Rosaire Mongrain. "Numerical Assessment of the Quasi-Steady Approximation in Glottal Air Flow." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30593.

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Voice production involves air flow through the glottis and its interaction with the deformable vocal folds. The quasi-steady approximation involves modeling the complex unsteady flow through the glottis as a sequence of steady flows through rigid orifices, which is numerically less expensive. Theoretical and experimental assessments of the quasi-steady approximation have been attempted, but contradictions in previously reported results prompt further analysis. To investigate the validity of the quasi-steady approximation, a two-dimensional dynamic simulation of air flow through an idealized glottal orifice with moving walls was performed for different pressure gradients and oscillation frequencies. A series of steady flow simulations for configurations of the vocal folds and flow boundary conditions that instantaneously coincide with data from the dynamic simulations were performed. Dynamic and static simulations were performed using the COMSOL multiphysics® software. Both stationary and non-stationary geometries were created based on the M5 model with the orifice profile alternating between convergent and divergent included angles (−40° to 40°). The distance between the vocal cord tip and the centerline was established to maintain a constant vocal fold volume, thereby eliminating spurious monopole sources. The results include the fluid flow rate, the pressure drop across the glottis, the shear stress on the glottis walls, and the orifice coefficient. Comparison between these variables for both dynamic and static sets of data allowed the assessment of the accuracy of the quasi-steady approximation to predict the fluid flow in the glottis. The importance of time-dependent terms over short intervals during glottal opening and closure was scrutinized. The results may contribute to the general goal of creating flow models that are optimal for laryngeal orifice coefficient and sound pressure determination.

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Koh, Sung K., Gregory S. Chirikjian, and G. K. Ananthasuresh. "A Jacobian-Based Algorithm for the Attitude Control of a Rigid Body Undergoing Fully-Reversed Sequences of Rotations." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34927.

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Jacobian-based control algorithms for the attitude control of a rigid body undergoing a series of forward and reverse rotations are proposed in this paper. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is singular as well as a null matrix at the identity that makes the conventional Jacobian formulation break down. In order to handle the singularities involved in FR rotations, the Jacobian algorithm is reformulated and implemented so as to synthesize the FR rotation for a desired orientation change. We introduce the single-step and multiple-step Jacobian methods in this paper. The single-step Jacobian method synthesizes a specific FR rotation that enables the rigid body to reach a given desired orientation through a single step. The multiple-step Jacobian method synthesizes physically feasible FR rotations on an incremental optimal path to a desired orientation. A comparison with existing control algorithms for FR motions verifies the fast convergence property of the Jacobian-based algorithm and the accuracy of the solutions.

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Koh, Sung, and Wankyun Chung. "Jacobian-Based Algorithm for Motion Planning for Underactuated Systems Undergoing Forward and Reverse Rotations." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-49413.

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A Jacobian-based algorithm for motion planning for an underactuated system that is a rigid-body operated by two input-rotations is discussed in this paper. The rigid body undergoes a four-rotation fully-reversed (FR) sequence of rotations which consists of a series of initial two rotations about the axes of a coordinate frame attached to the rigid body and subsequent two rotations that undo the proceeding rotations. Due to the insufficient degrees of freedom of four-rotation FR sequences required to achieve all possible orientations, the rigid body cannot achieve some orientations. In order to best approximate these infeasible orientations, the Jacobian-based algorithm is implemented in the sense of least squares. As some orientations can never be attained by a single four-rotation FR sequence, two different four-rotation FR sequences are exploited alternately to ensure the convergence of the proposed algorithm. Assuming the orientation is supposed to be manipulated using three input-rotations, the switching-Jacobian algorithm proposed in this paper has significant practical importance for motion planning for aerospace and underwater vehicles maneuvered using only two input-rotations due to the failure of one of torque-generation mechanisms.

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Lee, M. H., J. H. Lee, and G. H. Jang. "Stability Analysis of a Whirling Rigid Rotor Supported by FDBs Considering Five Degrees of Freedom of a General Rotor-Bearing System." In ASME 2014 Conference on Information Storage and Processing Systems. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/isps2014-6932.

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A rotor supported by fluid dynamic bearings (FDBs) has a whirling motion by centrifugal force due to the mass unbalance or by the flexibility of shaft. This whirling motion also generates periodic time-varying oil-film reaction and dynamic coefficients even in case of the stationary grooved FDBs. This paper proposes a method to determine the stability of a whirling rotor supported by stationary grooved FDBs considering five degrees of freedom of a general rotor-bearing system. Dynamic coefficients are calculated by using the finite element method and the perturbation method, and they are represented as periodic harmonic functions by considering whirling motion. Because of the periodic time-varying dynamic coefficients, the equations of motion of the rotor supported by FDBs can be represented as a parametrically excited system. The solution of the equations of motion can be assumed as the Fourier series so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Hill’s infinite determinant is calculated by using these algebraic equations in order to determine the stability. The stability of the FDBs decreases with the increase of rotational speed. The stability of the FDBs increases with the increase of whirl radius, because the average and variation of Cxx increase faster than those of Kxx. The proposed method is verified by solving the equations of motion by using the forth Runge-Kutta method to determine the convergence and divergence of whirl radius.

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Singai, Chetan, T. R. Kumaraswamy, and Ajay Chandra. "Reforming Higher Education in India: In Pursuit of Excellence." In Sixth International Conference on Higher Education Advances. Valencia: Universitat Politècnica de València, 2020. http://dx.doi.org/10.4995/head20.2020.11237.

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Higher education has emerged as one of the most critical factors for the Nation’s economic, political, social and cultural growth and development. Reforming the higher education sector has become an emergent norm across the globe, especially in the developing world. India is one such emerging nation, witnessing a major shift in its ideological, pragmatic and policy directions in the last few years. The higher education sector in India has witnessed unprecedented expansion. However, given the distinctive social-political-economic context and its complexity in India, expansion in higher education is often linked with ensuring equity and access. Whereas in the developed world, expansion is often associated with quality or excellence in higher education i.e. creating world-class universities. Further, excellence in higher education is arguably the most critical component for the survival, sustenance and growth of the sector. To this end, the paper examines the convergence and divergence in policies and practices related to the pursuit of excellence in higher education and its institutions in India vis-à-vis the dominant global reforms in higher education. Erstwhile policies related to quality in higher education and the current draft National Education Policy-2019, provide a reference to the local-distinctive strategies for seeking excellence at the systemic and the institutional level, with an aspiration for global reputation. For instance, National Institutional Ranking Framework, University Grants Commission’s graded autonomy, Institutional restructuring, National Accreditation and Assessment Council and Quacquarelli Symonds- India rating and so on. The paper also sets direction on how Local strategies for global aspirations could unpack a series of issues regarding the reforms in education and delineate in what ways that these emerging global reforms, strategies are effective and appropriate to the local higher education system and its institutions.

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