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

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Runovska, M. K. "Convergence of series of Gaussian Markov sequences." Theory of Probability and Mathematical Statistics 83 (2011): 149–62. http://dx.doi.org/10.1090/s0094-9000-2012-00848-x.

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12

Ma, Sheng, and Qin Jiang. "The Characteristic of Power Series and its Sum Function on the Convergence Circle." Advanced Materials Research 821-822 (September 2013): 1434–37. http://dx.doi.org/10.4028/www.scientific.net/amr.821-822.1434.

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In the paper, the specific issues is discussed whether or not the points on the convergence circle are the singular point of a sum function of a class of power series. Whats more, the relationship between divergence of the power series on the convergence circle and the pole of its function on the convergence circle is explored. And a new result is obtained that there exists the pole of its function on the convergence circle, the power series has the characteristic of everywhere divergence on the convergence circle.

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13

Laeng, Enrico, and Vittorino Pata. "A convergence–divergence test for series of nonnegative terms." Expositiones Mathematicae 29, no. 4 (2011): 420–24. http://dx.doi.org/10.1016/j.exmath.2011.07.004.

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14

Natkaniec, Tomasz, and Waldemar Sieg. "On convergence of sequences of functions possessing closed graphs." Georgian Mathematical Journal 26, no. 4 (December 1, 2019): 573–82. http://dx.doi.org/10.1515/gmj-2019-2036.

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Abstract In the first part of the paper we study the sets of boundedness and of convergence and divergence to infinity of sequences of real closed-graph functions. Generalization on ideal convergence of such sequences is discussed. Limits and ideal-limits of sequences of functions with closed graphs are considered in the last part of the article.

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15

Abramov, Vyacheslav, Meitner Cadena, and Edward Omey. "A new test for convergence of positive series." Publications de l'Institut Math?matique (Belgrade) 109, no. 123 (2021): 61–76. http://dx.doi.org/10.2298/pim2123061a.

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16

Krushna, A. Vamsi. "Convergence or Divergence Among Indian States: A Study Of New Series Data." IRA-International Journal of Management & Social Sciences (ISSN 2455-2267) 15, no. 1 (April 30, 2019): 1. http://dx.doi.org/10.21013/jmss.v15.n1.p1.

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Till now there is a vast literature available on this subject both theoretically and empirically. All the studies are mostly observing this convergence/divergence nature over a long period of time. To quote some of the researches such as Trivedi (2002), Bandyopadhyay (2002), Michelle, Kirsty and Cassen (2005), Nayyar (2008), Kalra & Sodsriwiboon (2010), Ghosh (2012), Stewart and Moslares (2014), Mishra and Mishra (2017) and Chakraborty and Chakraborty (2018) all are considered long period of time to estimate the presence of convergence/divergence among Indian states. But the long term development of a region depends upon so many factors such as availability of natural resources, human resources, economic policies adopted in the region, political climate etc. Hence, when we are dealing with the issue of convergence/divergence we have to consider the above-said factors. From this point of view, this paper focuses on the short term observing of convergence/divergence particularly with reference to Indian states during the period 2011-12 to 2016-17. High Growth Group States witnessed convergence in PCNSDP while Low Growth Group States and the Total States exhibited divergent trends. The high Growth Group States converged at a rate of 49.8 per cent during the study period. The rate of divergence among the Low Growth Group States is 14.5 per cent. Regarding the Total States, the rate of divergence is observed as 12.4 per cent. Here also the high growth group states are accounted for fewer fluctuations when compared with low growth group states.

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17

Zhou, Xun. "Some Series and Mathematic Constants Arising in Radioactive Decay." Journal of Mathematics Research 11, no. 6 (October 28, 2019): 14. http://dx.doi.org/10.5539/jmr.v11n6p14.

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In this paper we show the construction of 32 infinite series based on the law of decay of radioactive isotopes, which indicates that a radioactive parent isotope is reduced by 1/2 and 1/e of its initial value during each half-life and mean life, respectively. We found that the ratios among the values of the radioactive parent isotope and the radiogenic daughter isotope for each half-life’s and mean life’s decay can be used to construct 16 half-life related (or 2-related) and 16 mean life related (or e-related) infinite series. There are 8 divergent series, 4 previously known convergent series and 2 series converging to the Erdös-Borwein constant. The remaining 18 series are found to converge to 18 mathematical constants and the divergent and alternating mean life related series leads to another 2 mathematical constants. A few interesting mathematical relations exist among these convergent series and 5 sequences are also attained from the convergent half-life related series.

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18

Weniger, Ernst Joachim. "Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series." Computer Physics Reports 10, no. 5-6 (December 1989): 189–371. http://dx.doi.org/10.1016/0167-7977(89)90011-7.

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19

Huang, Feng Li, and Guang Sheng Chen. "Sequences and Series of Functions on Fractal Space." Advanced Materials Research 798-799 (September 2013): 765–68. http://dx.doi.org/10.4028/www.scientific.net/amr.798-799.765.

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20

Khan, Rasul A. "Another Elementary Proof of the Convergence-Divergence of $p$-Series." Missouri Journal of Mathematical Sciences 16, no. 2 (May 2004): 104–7. http://dx.doi.org/10.35834/2004/1602104.

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21

Galvão Jr, A. F., and F. A. Reis Gomes. "Convergence or divergence in Latin America? A time series analysis." Applied Economics 39, no. 11 (June 2007): 1353–60. http://dx.doi.org/10.1080/00036840600606278.

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22

D'yachenko, M. I., and K. S. Kazaryan. "On sets of convergence and divergence of multiple orthogonal series." Sbornik: Mathematics 193, no. 9 (October 31, 2002): 1281–301. http://dx.doi.org/10.1070/sm2002v193n09abeh000678.

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23

Dragovich, Branko, Andrei Khrennikov, and Natasa Misic. "Summation of p-adic functional series in integer points." Filomat 31, no. 5 (2017): 1339–47. http://dx.doi.org/10.2298/fil1705339d.

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Summation of a large class of the functional series, which terms contain factorials, is considered. We first investigated finite partial sums for integer arguments. These sums have the same values in real and all p-adic cases. The corresponding infinite functional series are divergent in the real case, but they are convergent and have p-adic invariant sums in p-adic cases. We found polynomials which generate all significant ingredients of these series and make connection between their real and p-adic properties. In particular, we found connection of one of our integer sequences with the Bell numbers.

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24

Móricz, F. "OnΛ-strong convergence of numerical sequences and Fourier series." Acta Mathematica Hungarica 54, no. 3-4 (September 1989): 319–27. http://dx.doi.org/10.1007/bf01952063.

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25

Cook, Eung-Do. "Linguistic divergence in Fort Chipewyan." Language in Society 20, no. 3 (September 1991): 423–40. http://dx.doi.org/10.1017/s0047404500016560.

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ABSTRACTScollon and Scollon (1979) claimed that the consonantal system of Chipewyan in Fort Chipewyan has been reduced to 16 segments from 39 influenced by Cree, a case of linguistic convergence. This conclusion was based on their incoherent and indiscriminate admixture of variable data. While there is no Chipewyan speaker whose consonantal inventory includes only 16 phonemes, there is ample evidence for the merger of two series of coronal affricates in an innovative system like in other Athapaskan languages that have had no intimate contact with Cree. That is, there is evidence for intralinguistic divergence, but not for interlinguistic convergence. Neither is there any evidence to support another major claim by the Scollons that the sibilant alternations in Chipewyan are correlated with “world views.” All the changes, including sibilant alternations and coronal mergers, recorded in Fort Chipewyan are those frequently observed in other Athapaskan communities. (Language contact, change, convergence, divergence, variability, obsolescence, register, sociolinguistic variable)

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26

F. Bayart, S. V. Konyagin, and H. Queffélec. "Convergence Almost Everywhere and Divergence Everywhere of Taylor and Dirichlet Series." Real Analysis Exchange 29, no. 2 (2004): 557. http://dx.doi.org/10.14321/realanalexch.29.2.0557.

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27

Gát, György, and Ushangi Goginava. "Uniform and 𝐿-Convergence of Logarithmic Means of Double Walsh–Fourier Series." gmj 12, no. 1 (March 2005): 75–88. http://dx.doi.org/10.1515/gmj.2005.75.

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Abstract We discuss some convergence and divergence properties of twodimensional (Nörlund) logarithmic means of two-dimensional Walsh–Fourier series of functions both in the uniform and in the Lebesgue norm. We give necessary and sufficient conditions for the convergence regarding the modulus of continuity of the function, and also the function space.

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28

Endou, Noboru. "Double Series and Sums." Formalized Mathematics 22, no. 1 (March 30, 2014): 57–68. http://dx.doi.org/10.2478/forma-2014-0006.

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Summary In this paper the author constructs several properties for double series and its convergence. The notions of convergence of double sequence have already been introduced in our previous paper [18]. In section 1 we introduce double series and their convergence. Then we show the relationship between Pringsheim-type convergence and iterated convergence. In section 2 we study double series having non-negative terms. As a result, we have equality of three type sums of non-negative double sequence. In section 3 we show that if a non-negative sequence is summable, then the sequence of rearrangement of terms is summable and it has the same sums. In the last section two basic relations between double sequences and matrices are introduced.

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29

Palma, Nuno, and Jaime Reis. "From Convergence to Divergence: Portuguese Economic Growth, 1527–1850." Journal of Economic History 79, no. 2 (April 29, 2019): 477–506. http://dx.doi.org/10.1017/s0022050719000056.

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We construct the first time-series for Portugal’s per capita GDP for 1527–1850, drawing on a new database. Starting in the early 1630s there was a highly persistent upward trend which accelerated after 1710 and peaked 40 years later. At that point, per capita income was high by European standards, though behind the most advanced Western European economies. But as the second half of the eighteenth century unfolded, a phase of economic decline was initiated. This continued into the nineteenth century, and by 1850 per capita incomes were not different from what they had been in the early 1530s.

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30

Tong, Jingcheng. "Kummer's Test Gives Characterizations for Convergence or Divergence of all Positive Series." American Mathematical Monthly 101, no. 5 (May 1994): 450–52. http://dx.doi.org/10.1080/00029890.1994.11996971.

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31

Tong, Jingcheng. "Kummer's Test Gives Characterizations for Convergence or Divergence of all Positive Series." American Mathematical Monthly 101, no. 5 (May 1994): 450. http://dx.doi.org/10.2307/2974907.

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32

Kadak, Uğur, and Hakan Efe. "On Uniform Convergence of Sequences and Series of Fuzzy-Valued Functions." Journal of Function Spaces 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/870179.

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The class of membership functions is restricted to trapezoidal one, as it is general enough and widely used. In the present paper since the utilization of Zadeh’s extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct for a fuzzy-valued function via related trapezoidal membership function. We derive uniform convergence of fuzzy-valued function sequences and series with some illustrated examples. Also we study Hukuhara differentiation and Henstock integration of a fuzzy-valued function with some necessary inclusions. Furthermore, we introduce the power series with fuzzy coefficients and define the radius of convergence of power series. Finally, by using the notions of H-differentiation and radius of convergence we examine the relationship between term by term H-differentiation and uniform convergence of fuzzy-valued function series.

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33

Runovska, M. K. "Convergence of series of elements of multidimensional Gaussian Markov sequences." Theory of Probability and Mathematical Statistics 84 (2012): 139–50. http://dx.doi.org/10.1090/s0094-9000-2012-00857-0.

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34

Buldygin, Valerii V., and Marina K. Runovska. "Almost Sure Convergence of the Series of Gaussian Markov Sequences." Communications in Statistics - Theory and Methods 40, no. 19-20 (October 2011): 3407–24. http://dx.doi.org/10.1080/03610926.2011.581163.

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35

Begunts, A. V. "On the Convergence of Alternating Series Associated with Beatty Sequences." Mathematical Notes 107, no. 1-2 (January 2020): 345–49. http://dx.doi.org/10.1134/s0001434620010344.

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36

Braha, Naim L., and Toufik Mansour. "On Λ2-strong convergence of numerical sequences and Fourier series." Acta Mathematica Hungarica 141, no. 1-2 (February 9, 2013): 113–26. http://dx.doi.org/10.1007/s10474-013-0301-4.

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37

Srivastava, Shailesh Kumar, and Uaday Singh. "On T-Strong Convergence of Numerical Sequences and Fourier Series." Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 88, no. 4 (January 24, 2017): 571–76. http://dx.doi.org/10.1007/s40010-016-0327-4.

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38

Wang, B. "On C-sequences of operators." Studia Scientiarum Mathematicarum Hungarica 40, no. 1-2 (July 1, 2003): 145–50. http://dx.doi.org/10.1556/sscmath.40.2003.1-2.11.

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Invariant results are established for a considerably general multiplier convergence of operator series where the operators are defined on arbitrary topological vector spaces and valued in arbitrary locally convex spaces.

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39

Bodnar, D. I., and I. B. Bilanyk. "Convergence criterion for branched contіnued fractions of the special form with positive elements." Carpathian Mathematical Publications 9, no. 1 (June 8, 2017): 13–21. http://dx.doi.org/10.15330/cmp.9.1.13-21.

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In this paper the problem of convergence of the important type of a multidimensional generalization of continued fractions, the branched continued fractions with independent variables, is considered. This fractions are an efficient apparatus for the approximation of multivariable functions, which are represented by multiple power series. When variables are fixed these fractions are called the branched continued fractions of the special form. Their structure is much simpler then the structure of general branched continued fractions. It has given a possibility to establish the necessary and sufficient conditions of convergence of branched continued fractions of the special form with the positive elements. The received result is the multidimensional analog of Seidel's criterion for the continued fractions. The condition of convergence of investigated fractions is the divergence of series, whose elements are continued fractions. Therefore, the sufficient condition of the convergence of this fraction which has been formulated by the divergence of series composed of partial denominators of this fraction, is established. Using the established criterion and Stieltjes-Vitali Theorem the parabolic theorems of branched continued fractions of the special form with complex elements convergence, is investigated. The sufficient conditions gave a possibility to make the condition of convergence of the branched continued fractions of the special form, whose elements lie in parabolic domains.

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40

Birky, C. William. "Heterozygosity, Heteromorphy, and Phylogenetic Trees in Asexual Eukaryotes." Genetics 144, no. 1 (September 1, 1996): 427–37. http://dx.doi.org/10.1093/genetics/144.1.427.

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Abstract Little attention has been paid to the consequences of long-term asexual reproduction for sequence evolution in diploid or polyploid eukaryotic organisms. Some elementary theory shows that the amount of neutral sequence divergence between two alleles of a protein-coding gene in an asexual individual will be greater than that in a sexual species by a factor of 2tu, where t is the number of generations since sexual reproduction was lost and u is the mutation rate per generation in the asexual lineage. Phylogenetic trees based on only one allele from each of two or more species will show incorrect divergence times and, more often than not, incorrect topologies. This allele sequence divergence can be stopped temporarily by mitotic gene conversion, mitotic crossing-over, or ploidy reduction. If these convergence events are rare, ancient asexual lineages can be recognized by their high allele sequence divergence. At intermediate frequencies of convergence events, it will be impossible to reconstruct the correct phylogeny of an asexual clade from the sequences of protein coding genes. Convergence may be limited by allele sequence divergence and heterozygous chromosomal rearrangements which reduce the homology needed for recombination and result in aneuploidy after crossing-over or ploidy cycles.

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41

García-Máynez, Adalberto, and Adolfo Pimienta Acosta. "A Method to Construct Generalized Fibonacci Sequences." Journal of Applied Mathematics 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/4971594.

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The main purpose of this paper is to study the convergence properties of Generalized Fibonacci Sequences and the series of partial sums associated with them. When the proper values of ans×sreal matrixAare real and different, we give a necessary and sufficient condition for the convergence of the matrix sequenceA,A2,A3,…to a matrixB.

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42

Weniger, Ernst Joachim. "On the derivation of iterated sequence transformations for the acceleration of convergence and the summation of divergent series." Computer Physics Communications 64, no. 1 (April 1991): 19–45. http://dx.doi.org/10.1016/0010-4655(91)90047-o.

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43

Aizpuru, A., A. Gutiérrez-Dávila, and A. Sala. "A Riemann type theorem for series of operators on Banach spaces." Bulletin of the Australian Mathematical Society 68, no. 1 (August 2003): 13–20. http://dx.doi.org/10.1017/s0004972700037370.

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We study Kalton's theorem on the unconditional convergence of series of compact operators and we use some matrix techniques to obtain sufficient conditions, weaker than previous ones, on the convergence and unconditional convergence of series of compact operators. Finally, we characterise weak unconditionally Cauchy series in Cℒ(X, Y) in the terms of certain spaces of vector sequences.

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44

Foster, J. H., and Monika Serbinowska. "On the Convergence of a Class of Nearly Alternating Series." Canadian Journal of Mathematics 59, no. 1 (February 1, 2007): 85–108. http://dx.doi.org/10.4153/cjm-2007-004-1.

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AbstractLet C be the class of convex sequences of real numbers. The quadratic irrational numbers can be partitioned into two types as follows. If α is of the first type and (ck) ∈ C, then ∑(—1)⎿ck⏌ converges if and only if ck log k → 0. If α is of the second type and (ck) ∈ C, then ∑(—1)⎿ck⏌ converges if and only if ∑ ck/k converges. An example of a quadratic irrational of the first type is and an example of the second type is . The analysis of this problem relies heavily on the representation of α as a simple continued fraction and on properties of the sequences of partial sums and double partial sums .

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45

Kórus, Péter. "On Λ^r-strong convergence of numerical sequences and Fourier series." Journal of Classical Analysis, no. 2 (2016): 89–98. http://dx.doi.org/10.7153/jca-09-10.

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46

Móricz, F. "On Λ-strong convergence of double numerical sequences and Fourier series." Acta Mathematica Hungarica 56, no. 1-2 (March 1990): 125–36. http://dx.doi.org/10.1007/bf01903714.

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47

Wijaya, Ronni Andri, Yamasitha Yamasitha, Elfiswandi Elfiswandi, and Lusiana Lusiana. "Relative Strenght Index, Moving Average Convergence-Divergence on Stock Performance and Fundamental Analysis as Moderating." UPI YPTK Journal of Business and Economics 6, no. 2 (August 5, 2021): 27–30. http://dx.doi.org/10.35134/jbe.v6i2.40.

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This study aims to determine the effect of Relative Strength Index (RSI) and Moving Average Convergence-divergence (MACD) on stock performers with Debt to Equity Ratio (DER) as a Moderation variable in Financing companies listed on the Indonesian Stock Exchange (IDX). Sampling in the study using purpose sampling method obtained 14 companies with time series data. The analysis method used in this study is multiple linear regression analysis using eview. The results show that Relative Strenth Index (RSI) partially has a positive and significant effect on stock performance, Moving Average Convergence-divergence (MACD) partially has a positive and significant effect on stock performance, Relative Strenth Index (RSI) has a positive and significant effect on stock performance. which is moderated by Debt to Equity Ratio (DER), Moving Average Convergence-divergence (MACD) has a positive and significant effect on the Performance of Shares moderated by Debt to Equity Ratio (DER).

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48

Wu, Qunying, and Yuanying Jiang. "SOME LIMITING BEHAVIOR FOR ASYMPTOTICALLY NEGATIVE ASSOCIATED RANDOM VARIABLES." Probability in the Engineering and Informational Sciences 32, no. 1 (November 29, 2016): 58–66. http://dx.doi.org/10.1017/s0269964816000437.

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In this paper, we study the almost sure convergence for sequences of asymptotically negative associated (ANA) random variables. As a result, we extend the classical Khintchine–Kolmogorov convergence theorem, Marcinkiewicz strong law of large numbers, and the three series theorem for sequences of independent random variables to sequences of ANA random variables without necessarily adding any extra conditions.

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49

Fondevila, Gustavo, and Ricardo Massa. "Convergence Dynamics of Robbery Rates in Mexico." Crime & Delinquency 64, no. 14 (February 22, 2018): 1925–50. http://dx.doi.org/10.1177/0011128718757738.

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This work presents a time-series convergence (divergence) analysis for robbery rates in Mexico. Two distinctive features, in relation to previous studies, can be identified: first, the use of an autoregressive vector to better estimate the series dynamic compared with single-equation models, and second, the implementation of an escalation/de-escalation analysis is done using two variants of the same crime—high- and low-impact robberies. Our results suggest that modifications to the national security policy in Mexico have a direct—and rapid—effect on robbery crime trends. Moreover, the three phases of the dynamics between the rates coincide with the three major national security policies implemented in recent years: (a) 1997 to 2006, (b) 2007 to 2011, and (c) 2012 to 2018.

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50

Móricz, F. "Walsh-Fourier series with coefficients of generalized bounded variation." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 47, no. 3 (December 1989): 458–65. http://dx.doi.org/10.1017/s144678870003319x.

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AbstractWe extend in different ways the class of null sequences of real numbers that are of bounded variation and study the Walsh-Fourier series of integrable functions on the interval [(0, 1) with such coefficients. We prove almost everywhere convergence as well as convergence in the pseu dometric of Lr(0, 1) for 0 < r < 1.

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