Relevant bibliographies by topics / A K Ramanujan

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Academic literature on the topic 'A K Ramanujan'

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Published: 18 May 2024

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Journal articles on the topic "A K Ramanujan"

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Dr. Rituraj Trivedi. "A. K. Ramanujan: A Leading Indo-Anglican Poet." Creative Launcher 7, no. 2 (April 30, 2022): 115–21. http://dx.doi.org/10.53032/tcl.2022.7.2.15.

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Ramanujan is one of the prominent Indo-Anglican Poets. Some critics consider him to be one of the three great Indo-Anglican poets, the other two being Nissim Ezekiel and Kamala Das. Ramanujan’s poetry is largely autobiographical and thought-provoking. The themes Ramanujan considers in his poetry are limited in scope, but some other passages of his poetry largely compensate for that inadequacy. Inversely important as a theme in Ramanujan’s poetry is his Hindu heritage. Ramanujan has shown a sharp and intense textual sensitivity in his poetry. Ramanujan is one of the most competent and professed craftsmen in Indo-Anglican poetry. Among the silent features of Ramanujan’s poetry is its cerebral literalism. His poetry abounds in boons of world and expression. Ramanujan generally writes in free verse without the importance of punctuation, but he does relatively frequently introduce rhyme and assonance into his poems. Another striking point of Ramanujan’s poetry is the ascendance in it of irony. Irony too is a device that is employed by nearly every Indo-Anglican poet, but Ramanujan makes use of this device in nearly every poem. Ramanujan’s poetry contains distinctive and distinguishable imagery from the imagery of other Indo-Anglican Poets.
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Bernd, Bruce C., and Heng Huat Chan. "Some Values for the Rogers-Ramanujan Continued Fraction." Canadian Journal of Mathematics 47, no. 5 (October 1, 1995): 897–914. http://dx.doi.org/10.4153/cjm-1995-046-5.

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AbstractIn his first and lost notebooks, Ramanujan recorded several values for the Rogers-Ramanujan continued fraction. Some of these results have been proved by K. G. Ramanathan, using mostly ideas with which Ramanujan was unfamiliar. In this paper, eight of Ramanujan's values are established; four are proved for the first time, while the remaining four had been previously proved by Ramanathan by entirely different methods. Our proofs employ some of Ramanujan's beautiful eta-function identities, which have not been heretofore used for evaluating continued fractions.
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Anamika Kumari. "The Poetry of A. K. Ramanujan: In Search of Self." Creative Launcher 4, no. 6 (February 29, 2020): 71–76. http://dx.doi.org/10.53032/tcl.2020.4.6.12.

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Self at the centre of all kinds of search manifests itself in Ramanujan’s art from the very beginning of his creative life and the artist has all through assumed an elusive character till his vision clears; well, but his vision is gained through experience. His vision of the self permeates most of his elusive poems, the poems which have so far been faulted on one count or another. First, perhaps is “The Stridess” which is not by chance, the first poem of Ramanujan’s first volume of poems, and this volume The Striders is also entitled after this poem. Ramanujan concern with the self and hence his idea of the individuality of beings is very much there but misted with an uncanny subject like waterbug and mare, gone veiled under an objectivist style of the moderns.
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Anamika Kumari. "Diasporic Concerns in A. K. Ramanujan’s Writings." Creative Launcher 4, no. 2 (June 30, 2019): 39–43. http://dx.doi.org/10.53032/tcl.2019.4.2.06.

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Ramanujan appears to be poised and perched between two worlds. The world in which he is born and the other which he has acquired. It then becomes very obvious that the perception of Ramanujan “is not just that of Hindu or merely an Indian in the sense that he sees only those. His perceptive eye roves wider and the limit of his perception is encompassing wider area.” His perception is pluralistic absorbing other culture. This does not Point towards assimilation or integration of the others into the Indian or the Indian into the global. Ramanujan used to describe his position as “being the hyphen in Indian-American Identifying with E. M Forester’s great urge to “connect” Ramanujan also makes his greatest work out of disconnections. His life's mission seems to be “to keep the dialogues and corals alive and to make something of them.” His aim is to achieve a synthesis between warring cultural coordinates, “It looks as if I live between things all the time two (or more) languages, two countries, and two disciplines. In all his writing translations, critical essays or poetic compositions, there is an invisible thread which lends homogeneity to his writings. In his encounter with different cultures, Ramanujan feels “himself translated a little in each encounter” and learns “a good deal about myself and about Indian arts”.
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Chen, Kwang-Wu. "Median Bernoulli Numbers and Ramanujan’s Harmonic Number Expansion." Mathematics 10, no. 12 (June 12, 2022): 2033. http://dx.doi.org/10.3390/math10122033.

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Ramanujan-type harmonic number expansion was given by many authors. Some of the most well-known are: Hn∼γ+logn−∑k=1∞Bkk·nk, where Bk is the Bernoulli numbers. In this paper, we rewrite Ramanujan’s harmonic number expansion into a similar form of Euler’s asymptotic expansion as n approaches infinity: Hn∼γ+c0(h)log(q+h)−∑k=1∞ck(h)k·(q+h)k, where q=n(n+1) is the nth pronic number, twice the nth triangular number, γ is the Euler–Mascheroni constant, and ck(x)=∑j=0kkjcjxk−j, with ck is the negative of the median Bernoulli numbers. Then, 2cn=∑k=0nnkBn+k, where Bn is the Bernoulli number. By using the result obtained, we present two general Ramanujan’s asymptotic expansions for the nth harmonic number. For example, Hn∼γ+12log(q+13)−1180(q+13)2∑j=0∞bj(r)(q+13)j1/r as n approaches infinity, where bj(r) can be determined.
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Dharwadker, Vinay. "A. K. Ramanujan: Author, Translator, Scholar." World Literature Today 68, no. 2 (1994): 279. http://dx.doi.org/10.2307/40150143.

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McIntosh, Richard J. "The H and K Family of Mock Theta Functions." Canadian Journal of Mathematics 64, no. 4 (August 1, 2012): 935–60. http://dx.doi.org/10.4153/cjm-2011-066-0.

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AbstractIn his last letter to Hardy, Ramanujan defined 17 functionsF(q), |q| < 1, which he calledmockθ-functions. He observed that asqradially approaches any root of unity ζ at whichF(q) has an exponential singularity, there is aθ-functionTζ(q) withF(q) −Tζ(q) =O(1). Since then, other functions have been found that possess this property. These functions are related to a functionH(x,q), wherexis usuallyqrore2πirfor some rational numberr. For this reason we refer toHas a “universal” mockθ-function. Modular transformations ofHgive rise to the functionsK,K1,K2. The functionsKandK1appear in Ramanujan's lost notebook. We prove various linear relations between these functions using Appell–Lerch sums (also called generalized Lambert series). Some relations (mock theta “conjectures”) involving mockθ-functions of even order andHare listed.
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Chidambaraswamy, J., and P. V. Krishnaiah. "An identity for a class of arithmetical functions of two variables." International Journal of Mathematics and Mathematical Sciences 11, no. 2 (1988): 351–54. http://dx.doi.org/10.1155/s0161171288000419.

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For a positive integerr, letr∗denote the quotient ofrby its largest squarefree divisor(1∗=1). Recently, K. R. Johnson proved that(∗)∑d|n|C(d,r)|=r∗∏pa‖nr∗p+r(a+1)∏pa‖nr∗p|r(a(p−1)+1) or 0according asr∗|nor not whereC(n,r)is the well known Ramanujan's sum. In this paper, using a different method, we generalize(∗)to a wide class of arithmetical functions of2variables and deduce as special cases(∗)and similar formulae for several generalizations of Ramanujan''s sum.
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G., E., Vinay Dharwadker, and A. K. Ramanujan. "The Collected Essays of A. K. Ramanujan." Journal of the American Oriental Society 121, no. 3 (July 2001): 537. http://dx.doi.org/10.2307/606720.

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YAMADA, TOMOHIRO. "A GENERALIZATION OF THE RAMANUJAN–NAGELL EQUATION." Glasgow Mathematical Journal 61, no. 03 (August 22, 2018): 535–44. http://dx.doi.org/10.1017/s0017089518000344.

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AbstractWe shall show that, for any positive integer D &gt; 0 and any primes p1, p2, the diophantine equation x2 + D = 2sp1kp2l has at most 63 integer solutions (x, k, l, s) with x, k, l ≥ 0 and s ∈ {0, 2}.
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Dissertations / Theses on the topic "A K Ramanujan"

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Skees, James. "Bounds on k-Regular Ramanujan Graphs and Separator Theorems." TopSCHOLAR®, 2007. http://digitalcommons.wku.edu/theses/379.

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Expander graphs are a family of graphs that are highly connected. Finding explicit examples of expander graphs which are also sparse is a difficult problem. The best type of expander graph in a. certain sense is a Ramanujan graph. Families of graphs that have separator theorems fail to be Ramanujan if the vertex set gets sufficiently large. Using separator theorems to get an estimate on the expanding constant of graphs, we get bounds 011 the number of vertices for such fc-regular graphs in order for them to be Ramanujan.
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Das, Sukriti. "A Study of A K Ramanujans poetry in relation to themes and images." Thesis, University of North Bengal, 2002. http://hdl.handle.net/123456789/1161.

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Ortolan, Manuela <1981&gt. "Mirrors and Fragments. An Investigation into A. K. Ramanujan's Poetry." Master's Degree Thesis, Università Ca' Foscari Venezia, 2017. http://hdl.handle.net/10579/9404.

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My work will be concerned with the life and works of A. K. Ramanujan (1929-1993), I will especially take into account his poetry works. A. K. Ramanujan is an Indian writer who belongs to that fundamental generation of poets who set the basis to what we now call Indian post-colonial literature in English language. Beyond being a writer and a poet, he was a translator, an essayist, a folklorist. He was professor of linguistics in the University of Chicago and lived the most part of his life in the U.S. Being born in an Indian environment and having spent his life in a Western context made him developed a list of alienations that will form the main themes of his poems. From his first publication he reveals his high sensibility about his Indian experience where family subjects and private memories converge, but he also shows conflict and a sense of detachment from his familial environment. Memory is one of the recurring themes in his poems which he handles with both sense of irony and scepticism. His poems are also about fears, anxieties, personal experience and the search for the self swinging between an alien land and a distant home. I will also briefly compare his work as a translator with that of a poet, and trace those elements that influenced his poetry output. I will conclude summing up the points that make A. K. Ramanujan a post-colonial and a postmodern poet.
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Books on the topic "A K Ramanujan"

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India) International Conference "Ramanujan Rediscovered" (2009 Bangalore. Ramanujan rediscovered: Proceedings of a conference on Elliptic functions, Partitions, and q-Series in memory of K. Venkatachaliengar, Bangalore (1-5 June, 2009). Mysore: Ramanujan Mathematical Society, 2010.

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Contemporary Indian poetry in English: With special emphasis on Nissim Ezekiel, Kamala Das, R. Parthasarathy, and A.K. Ramanujan : other poets assessed are Kolatkar, Shiv K. Kumar, Keki Daruwala, Jayanta Mahapatra, and Arvind Krishna Mehrotra. New Delhi: Reliance Pub. House, 1990.

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The poetry of A. K. Ramanujan. New Delhi: Atlantic Publishers & Distributors, 2002.

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Ramanujan, A. K. The Collected Essays of A. K. Ramanujan. Oxford University Press, USA, 2004.

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Ramanujan Rediscovered: Proceedings of a Conference on Elliptic Functions, Partitions, and Q-Series in Memory of K. Venkatachaliengar, Bangalore, June 2009. International Press of Boston, Incorporated, 2012.

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McDonald, Peter D. Against Naturalization. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198725152.003.0009.

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Seen in the context of the analogy UNESCO draws between cultural and biological diversity, this chapter reflects on the leading contemporary Indian poet Arvind Krishna Mehrotra’s choice of English as a literary medium and on his practice as a poet-translator. Like a number of other major poets of the post-independence era, including Arun Kolatkar, A. K. Ramanujan, and Adil Jussawalla, and following in a path Joyce pioneered, Mehrotra refused naturalism in two ways: first, he declined to write in his ‘mother tongue’ (Hindi); second, he chose not to indigenize English as an Indian language. Instead, he chose a number of foreignizing and, for him, denaturalizing strategies, including Americanization. The chapter, which also considers the significance of these strategies given the terms of the Indian constitution, ranges widely across Mehrotra’s oeuvre, focusing on The Absent Traveller (1991) and Songs of Kabir (2001).
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Nagarajan, Vijaya. Beginnings. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780195170825.003.0001.

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Before dawn each day, millions of Hindu women in Tamil Nadu, India, create a kōlam, a sacred ritual art form, on the thresholds of homes, temples, and businesses. It is usually made of rice flour and therefore is ephemeral. Drawing on her extensive ethnographic research, the author seeks to understand the wide range of meanings attributed to the kōlam, such as beauty; auspiciousness; the god Ganesha; the goddesses Lakshmi, Mūdevi, and Bhūdevi; the evil eye; competition; designs; mathematics; ecology; and the idea of “feeding a thousand souls.” This chapter (along with Chapters 2 and 3) lays the foundation for the book. The author describes how her research was influenced by Ivan Illich, A. K. Ramanujan, and Chandralekha. She braids together the diasporic with the home culture, integrating philosophical underpinnings of women’s knowledge systems and oral traditions.
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When Mirrors Are Windows: A View of A. K. Ramanujans Poetics. Oxford University Press India, 2016.

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Book chapters on the topic "A K Ramanujan"

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Simon, Sherry. "A. K. Ramanujan." In Benjamins Translation Library, 161–74. Amsterdam: John Benjamins Publishing Company, 2009. http://dx.doi.org/10.1075/btl.86.14sim.

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Bery, Ashok. "Indian Palimpsests: The Poetry of A. K. Ramanujan." In Cultural Translation and Postcolonial Poetry, 132–55. London: Palgrave Macmillan UK, 2007. http://dx.doi.org/10.1057/9780230286283_7.

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Cooper, Shaun. "Level 10: Ramanujan’s Function k." In Ramanujan's Theta Functions, 523–51. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56172-1_11.

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Annapoorni, S. "Chapter 11. Translation as the interplay of the familiar and the exotic in A. K. Ramanujan’s Poems of Love and War." In FILLM Studies in Languages and Literatures, 173–87. Amsterdam: John Benjamins Publishing Company, 2019. http://dx.doi.org/10.1075/fillm.12.11ann.

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"A. K. Ramanujan 1929–1993." In Name Me a Word, 170–78. Yale University Press, 2019. http://dx.doi.org/10.12987/9780300235654-021.

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"At Home or Nowhere: A. K. Ramanujan." In Worlds Woven Together, 40–54. Columbia University Press, 2022. http://dx.doi.org/10.7312/ravi20274-005.

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Hasan, Anjum. "Ambiguous Journeys and Halfway Homes in Ramanujan, Narayan, Karnad, and Ananthamurthy." In The Oxford Handbook of Modern Indian Literatures, C28P1—C28P85. Oxford University Press, 2023. http://dx.doi.org/10.1093/oxfordhb/9780197647912.013.28.

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Abstract This chapter is a reading of the ambivalent, playful, and embodied relationship to the binaries of tradition and modernity, rural and urban, past and present, in four great Karnataka writers and contemporaries—A. K. Ramanujan (1929–1993), R. K. Narayan (1906–2001), U. R. Ananthamurthy (1932–2014), and Girish Karnad (1938–2019). Using Ashis Nandy’s idea of the journey between the village and city (and back) as the archetypal anxiety of Indian civilization, the chapter analyzes how this bind has been a creative source for the fiction, playwriting, and poetry of these four writers. Their works reveal the possibility of an Indian sensibility highly attuned to its own contradictions, both rooted and open minded. With the hardening in public life of the divide between liberal and conservative views of culture, this secular slant, as poetics rather than only politics, is losing appeal. This also brings into question where these four might have failed to create the new paradigms, forms, and idioms that could have anticipated, if not helped forestall, the ideological battles of the present.
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Patke, Rajeev S. "Recurrent motifs: voyage and translation." In Postcolonial Poetry in english, 207–36. Oxford University PressOxford, 2006. http://dx.doi.org/10.1093/oso/9780199298884.003.0009.

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Abstract Colonialism bred three kinds of willing voyager—adventurer, explorer, colonist; one type of partially willing voyager—the indentured labourer; and one type of unwilling voyager—the slave. Postcolonial history adds two more types to this motley: the migrant, and the exile; in them, as in the indentured labourer, the distinction between willing and involuntary displacement is blurred. Postcolonial writing proliferates with symbolic voyages that are meant to ameliorate the displacement caused by diaspora. One kind of poet tackles the voyage in a collective spirit, as an individual rooted in imagined community, as when Walcott and Brathwaite appear to head away from home, only for their poetry to discover ways of revising their view of the birthplace. The second type of traveller suffers a more literal relocation through migration or self-exile, as illustrated by A. K. Ramanujan, Agha Shahid Ali, and Ee Tiang Hong. Their work shuttles between an emotional anchorage in a home left behind, and the attempt to grow new roots in a place that the poet strives to accept as home.
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Martin, Nancy M. "Embodying Devotion in a Woman’s Body." In Mirabai, 21–70. Oxford University PressNew York, 2023. http://dx.doi.org/10.1093/oso/9780195153897.003.0002.

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Abstract The earliest references to the Hindu woman saint Mirabai are found in the songs of other saints and the hagiographic literature of devotional Hinduism (bhakti) during the sixteenth and seventeenth centuries in India. This chapter examines these references in the context of the life stories of other bhakti saints, highlighting both shared and distinctive elements of her life and character, with attention to gender and the specific challenges of practicing bhakti and becoming a recognized saint for women. Mira’s life story reflects in varied ways the patterns identified by A. K. Ramanujan in women saints’ lives, including their early childhood devotion, avoidance of or escape from marriage, challenge to social norms of caste and/or gender, initiation by a guru, and merger with the divine, and also depicts a relationship of royal patronage with Akbar in contrast to male saints’ relations with the Mughal Emperor and other rulers. Passages relating to Mirabai in Nabhadas’s 1600 CE Bhaktamal (Garland of Devotees) and Priyadas’s 1712 CE commentary are translated and analyzed in detail, including the impact of the religious and political contexts in which they were composed, and the subsequent literary tradition of bhaktamals and commentaries that they inspired. Comparisons are made to dramatically different portrayals of the saint in the Pushtimargi Varta literature and the 1693 CE Sikh Prem Ambodh (Ocean of Love).
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Edixhoven, Bas. "Computing coefficients of modular forms." In Computational Aspects of Modular Forms and Galois Representations. Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691142012.003.0015.

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This chapter applies the main result on the computation of Galois representations attached to modular forms of level one to the computation of coefficients of modular forms. It treats the case of the discriminant modular form, that is, the computation of Ramanujan's tau-function at primes, and then deals with the more general case of forms of level one and arbitrary weight k, reformulated as the computation of Hecke operators Tⁿ as ℤ-linear combinations of the Tᵢ with i < k = 12. The chapter gives an application to theta functions of even, unimodular positive definite quadratic forms over ℤ.
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Conference papers on the topic "A K Ramanujan"

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Gupta, Sushmita, Sanjukta Roy, Saket Saurabh, and Meirav Zehavi. "When Rigging a Tournament, Let Greediness Blind You." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/38.

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A knockout tournament is a standard format of competition, ubiquitous in sports, elections and decision making. Such a competition consists of several rounds. In each round, all players that have not yet been eliminated are paired up into matches. Losers are eliminated, and winners are raised to the next round, until only one winner exists. Given that we can correctly predict the outcome of each potential match (modelled by a tournament D), a seeding of the tournament deterministically determines its winner. Having a favorite player v in mind, the Tournament Fixing Problem (TFP) asks whether there exists a seeding that makes v the winner. Aziz et al. [AAAI’14] showed that TFP is NP-hard. They initiated the study of the parameterized complexity of TFP with respect to the feedback arc set number k of D, and gave an XP-algorithm (which is highly inefficient). Recently, Ramanujan and Szeider [AAAI’17] showed that TFP admits an FPT algorithm, running in time 2^{ O(k^2 log k)} n ^{O(1)}. At the heart of this algorithm is a translation of TFP into an algebraic system of equations, solved in a black box fashion (by an ILP solver). We present a fresh, purely combinatorial greedy solution. We rely on new insights into TFP itself, which also results in the better running time bound of 2^{ O(k log k)} n^{ O(1)} . While our analysis is intricate, the algorithm itself is surprisingly simple.
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