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Journal articles on the topic 'Bernstein'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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1

Rodman, Howard A. "Remembering Walter Bernstein." Film Quarterly 74, no. 4 (2021): 43–47. http://dx.doi.org/10.1525/fq.2021.74.4.43.

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Screenwriter Howard Rodman offers a poignant appreciation of Walter Bernstein, the blacklisted screenwriter and director who died in January 2021 at the age of 101. Bernstein had been a fixture in Rodman’s life since the 1950s, when Rodman’s father served as a “front” for Bernstein’s television work. Bernstein would later use that experience as inspiration for The Front (dir. Martin Ritt, 1977), his trenchant and mordantly funny account of life on the blacklist. Rodman surveys Bernstein’s long career, from his years as a journalist for the US Army publication Yank and The New Yorker, to his post-blacklist work of the 1960s and 1970s, to his work at the Sundance Screenwriting Lab, where he and Rodman both served as advisors, closing the circle.

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2

Bielak, Jan. "Testament Leonarda Bernsteina – The Unanswered Question w świetle zagadnień dyrygenckich." Kwartalnik Młodych Muzykologów UJ, no. 52 (1) (2022): 23–40. http://dx.doi.org/10.4467/23537094kmmuj.22.002.15646.

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Leonard Bernstein’s Testament — The Unanswered Question in the Light of Conducting Issues In 1973, Leonard Bernstein gave a series of six lectures at Harvard University, entitled The Unanswered Question: Six talks at Harvard. This interdisciplinary course, drawing on Noam Chomsky's theory of transformational-generative grammar, presented an original conception of music as a universal language based on tonality and outlined the history of its development, concluding with Bernstein’s personal credo regarding its future. The argumentation used, although encompassing fields as diverse as linguistics, literary studies, philosophy and art history, was based primarily on musical analyses presented at the piano, supplemented by recordings of the symphonic works being discussed, performed under the baton of Bernstein himself. The Harvard lectures thus represent the summa of his aesthetic reflections and performance experiences, providing a unique insight into his views on music and its interpretation. This paper focuses on synthesising these views, subjecting them to factual verification, and then showing their influence on Bernstein's art of conducting through the example of the recordings used in The Unanswered Question series, focusing in particular on the issue of expression.

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3

MASSEY, DREW. "Leonard Bernstein and the Harvard Student Union: In Search of Political Origins." Journal of the Society for American Music 3, no. 1 (January 15, 2009): 67–84. http://dx.doi.org/10.1017/s1752196309090051.

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AbstractIn spite of the publicity generated at times by the politics of the mature Leonard Bernstein, the roots of his entanglement with political causes have been little-explored. As part of a larger collaborative project investigating Bernstein's ties to Boston, this article traces his role in the Harvard Student Union's theatrical productions. These shows were important because they represented some of Bernstein's earliest efforts at writing and directing for the theater. Bernstein worked on two shows sponsored by the Union: the production of Marc Blitzstein'sCradle Will Rockin 1939, during Bernstein's senior year at Harvard, and that of Aristophanes' playPeacein 1941, two years after he graduated. Although the Harvard Student Union was a major progressive political force on campus, Bernstein's relationship with the group appears to have been surprisingly casual. Examination of archival materials surrounding the productions, as well as selected interviews from the larger collaborative Bernstein project of which this article is but one part, reveals Bernstein as a man who was primarily interested in the Harvard Student Union insofar as it was an organization amenable to supporting his musical activities. As the heat of Bernstein's celebrity cools with time, such findings are an important aid in avoiding drawing overly deterministic conclusions about the significance of Bernstein's affiliations while ignoring his own immediate aims, political or otherwise.

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4

Feng, Yi. "The Epiphany of Language: The Connotation of Zen-Taoism in Charles Bernstein's Echopoetics." boundary 2 48, no. 4 (November 1, 2021): 163–83. http://dx.doi.org/10.1215/01903659-9382243.

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Abstract As a prominent representative figure of American Language poetry, Charles Bernstein has incorporated many themes concerning “nothingness” into his poetry. Contrary to the traditional Western philosophy that defines the concept of “nothingness” as meaninglessness and agnosticism, “nothingness” in Bernstein's poetics is endowed with profound poetic and aesthetic implications. Bernstein studied the works of Zen-Taoist philosophy in his early years. Understanding the Zen-Taoist connotations of “nothingness” is an important new dimension in interpreting Bernstein's echopoetics. Bernstein integrates the anti-traditional ideas in Zen-Taoist philosophy and aesthetics with the experiment of American avant-garde poetry. “The transformation between Xu (emptiness) and Shi (Being),” the beauty of “speechlessness,” and the expression of “defamiliarization” show the “epiphany” of language and the “nature” of language. The Chinese traditional Zen-Taoist philosophy is an important part of Bernstein's echopoetics.

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5

Bernstein, Charles. "Interview with Alí Calderón." boundary 2 48, no. 4 (November 1, 2021): 79–82. http://dx.doi.org/10.1215/01903659-9382074.

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Abstract In 2018, Mexican poet Alí Calderón interviewed Charles Bernstein for his influential web magazine Círculo de poesía. The interview is published here in English for the first time. Bernstein addresses the poetics of “hybridity” and the possibilities for poetic disruption. The discussion ends with Bernstein's then new poem, written for John Ashbery on the day he died.

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6

Resnikoff, Ariel. "A Source Which Is Also a Translation: Toward an Expanded- Yiddish Poetics, with Special Reference to Charles Bernstein." boundary 2 48, no. 4 (November 1, 2021): 184–214. http://dx.doi.org/10.1215/01903659-9382257.

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Abstract The present essay contextualizes the poet, scholar, editor, and translator Charles Bernstein (b. 1950), as an artist and practitioner working within a speculative translingual (language-crossing) field and tradition of expanded Yiddish. Reading Bernstein in relation to other expanded-Yiddish figures, such as his elders, Hannah Weiner (1928–77) and Jerome Rothenberg (b. 1931), and ancestor, Walter Benjamin (1892–1940), among others, this essay makes a case for Bernstein as a writer who works from a position of antinomian Jewish translational originlessness, and a diasporic poetics of “need” (à la Charles Reznikoff), in which every source can be understood as a translation and every translation might be treated as a potential source. The coda of the essay addresses the stakes of Bernstein's praxes from the perspective of widespread modern and contemporary anti-Semitism and Jewish self-hatred and concludes with the first ever translation of Bernstein's poetry into Yiddish proper.

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7

Lang, Abigail. "Bail Out Poetry." boundary 2 48, no. 4 (November 1, 2021): 129–37. http://dx.doi.org/10.1215/01903659-9382187.

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Abstract Originally written as an afterword to a book-length translation of poems by Charles Bernstein, this piece was meant to introduce his recent poetry and poetics to a French audience. It does so by pondering the twin economic and nautical senses contained in the title Bernstein suggested for the collection: Poetry Bailout (in French, Renflouer la poésie). What is the value of poetry? What are its uses? These are questions which have underpinned Bernstein's work. In an early essay, adapting a statement by Simone Weil, Bernstein posited that poetry draws its social—or antisocial—power from the fact that “it is ceaselessly creating a scale of values ‘that is not of this world.’” One way it does that is by intensifying the experience of reading. Placing his recent poetics under the aegis of Poe, Bernstein has managed to balance poetry's social and aesthetic functions by cultivating the uses of aesthetics, reconciling pragmatism with unabashed aestheticism.

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8

Probstein, Ian. "Charles Bernstein: Avant-Garde Is a Constant Renewal." boundary 2 48, no. 4 (November 1, 2021): 215–30. http://dx.doi.org/10.1215/01903659-9382271.

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Abstract The essay explores the work of Charles Bernstein in light of constant renewal. John Ashbery, as one of the brightest representatives of the New York School, and Charles Bernstein, as a representative of the language (L = A = N = G = U = A = G = E), have similar attitudes toward language. They have much in common in terms of poetics: in the rejection of loud phrases, prophetic statements, emotions, confessionalism, and certain self-centeredness. Poetry is a private matter for both. Both have poetics built on the “oddness that stays odd,” as Bernstein himself put it, paraphrasing Pound's “news that stays news.” Both are aimed at renovating the language, and the verses of both are built on fragmentation, collage, moving from one statement to another without preparation. However, in Ashbery, whose poems are surreal, these transitions are smoother, based on an apparent connection, what Bernstein calls “hypotaxis” or “associative parataxis.” In contrast, Bernstein's poetry is built on parataxis; it is “bumpy,” in the poet's own words.

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9

Sirotkina, I. E. "Futurist in Physiology: In Celebration of the 120th Birthday of Nikolai Aleksandrovich Bernstein." Cultural-Historical Psychology 12, no. 4 (2016): 39–47. http://dx.doi.org/10.17759/chp.2016120404.

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The paper is dedicated to the 120th birthday of Nikolai Aleksandrovich Bernstein (1896—1966), a prominent Russian physiologist who contributed also to other fields of knowledge, for instance, cognitive sciences and modeling of biological systems. This study is based on the analysis of various publications and archive materials, including interviews with Bernstein’s disciples conducted by the author in the late 1980s. The paper outlines the ideas and concepts of Bernstein that were well ahead of their time, anticipating research on movement control by at least a hundred years. It also analyses the differences between Bernstein’s theory of movement construction and Pavlov’s theory of conditioned reflex and gives a brief review of the development of Bernstein’s ideas in modern Russian neuroscience. As it is shown, the now popular concept of “kinesthetic imagination” obviously corresponds with Bernstein’s concepts of “movement task” and “model of the desired future”.

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10

Perloff, Marjorie. "Introduction to Charles Bernstein's Distinguished Wenqin Yao Lectures at Zhejiang University, Hangzhou, Fall 2019." boundary 2 48, no. 4 (November 1, 2021): 85–89. http://dx.doi.org/10.1215/01903659-9382102.

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Abstract This brief introduction to Charles Bernstein's work, given in Hangzhou, China, in November 2019, on the occasion of Bernstein's Distinguished Lectureship, discusses the basic principles of Language poetics as put forward in the early books Content's Dream and A Poetics. From the first, Bernstein emphasized the idea that poetry is not the expression of feeling but a constructivist art in which language is taken out of its normal context and recharged. In “Artifice of Absorption,” Bernstein insists that the poet uses all the tools at his command to create a new kind of absorption, arresting the reader's attention. Difficulty is thus inherent to poetry—a difficulty challenging the reader to rise to the challenge of what it means to read poetry. A few examples like “Standing Target” are discussed briefly.

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11

Wachbrit, Augustus. "Problems of Framing." Stance: an international undergraduate philosophy journal 13, no. 1 (April 14, 2020): 118–29. http://dx.doi.org/10.33043/s.13.1.118-129.

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In “Fatalism and Time,” Mark Bernstein argues against the notion that the B-theory of time is fatalistic. However, when he frames the differences between the A-theory of time and the B-theory of time, I argue that Bernstein imports some troublesome conceptual baggage in the form of what he calls “atemporal truths,” which, in the end, dooms the B-theory to fatalism, the consequence he sought to avoid. From my examination of Bernstein’s framing of the B-theory of time, I suggest that, given the proper framing of that theory, it is not doomed to fatalism.

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12

Latash, Mark L., and Vera L. Talis. "Bernstein’s Philosophy of Time: An Unknown Manuscript by Nikolai Bernstein (1949)." Motor Control 25, no. 2 (April 1, 2021): 315–36. http://dx.doi.org/10.1123/mc.2020-0114.

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The authors have presented an unpublished manuscript by Nikolai Aleksandrovich Bernstein written in the form of a diary in 1949. Bernstein focused on the concept of time as a coordinate in four-dimensional space and discussed a variety of issues, including the definition of time, its measurement, time travel, asymmetry of the past and future, and even linguistics. In particular, he offered a definition of life tightly linked to the concept of time. Overall, this manuscript offers a glimpse into Bernstein’s thinking, his sense of humor, and his sarcasm, intimately coupled with the very serious attitude to scientific discourse.

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13

Wachbrit, Augustus. "Problems of Framing." Stance: An International Undergraduate Philosophy Journal 13 (2020): 118–29. http://dx.doi.org/10.5840/stance20201310.

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In “Fatalism and Time,” Mark Bernstein argues against the notion that the B-theory of time is fatalistic. However, when he frames the differences between the A-theory of time and the B-theory of time, I argue that Bernstein imports some troublesome conceptual baggage in the form of what he calls “atemporal truths,” which, in the end, dooms the B-theory to fatalism, the consequence he sought to avoid. From my examination of Bernstein’s framing of the B-theory of time, I suggest that, given the proper framing of that theory, it is not doomed to fatalism.

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14

Hrubý, Karel. "Masaryk and Bernstein." Czech Sociological Review 34, no. 4 (August 1, 1998): 437–52. http://dx.doi.org/10.13060/00380288.1998.34.4.06.

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15

Braverman, Alexander, and David Kazhdan. "Bernstein components via the Bernstein center." Selecta Mathematica 22, no. 4 (October 2016): 2313–23. http://dx.doi.org/10.1007/s00029-016-0277-3.

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16

Atkinson, Paul. "Book Reviews: Reading Bernstein, Researching Bernstein." Sociological Review 53, no. 2 (May 2005): 380–82. http://dx.doi.org/10.1111/j.1467-954x.2005.00518_10.x.

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17

Büscher-Ulbrich, Dennis. "“Nothing tires a vision more than sundry attacks / in the manner of enclosure”: An Afterword to Angriff der Schwierigen Gedichte." boundary 2 48, no. 4 (November 1, 2021): 107–12. http://dx.doi.org/10.1215/01903659-9382159.

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Abstract The following text was published in German as an afterword to the bilingual poetry collection Charles Bernstein: Angriff der Schwierigen Gedichte (München: luxbooks, 2014). Originally intended as a critical survey and introduction for German-language readers, it traces Bernstein's work as a radical modernist poet, distinguished scholar, and critical theorist in his own right from the late 1960s to the early 2010s. From his early poetry to L = A = N = G = U = A = G = E magazine, from his major books of poetry and collective avant-garde performances to his essays on poetics, Bernstein, I argue, consistently articulated with wit and precision why and how radical modernism affects what Jacques Rancière has called the “distribution of the sensible.”

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18

ADAMS, SARAH, CAROL J. OJA, and KAY KAUFMAN SHELEMAY. "Leonard Bernstein's Jewish Boston: An Introductory Note." Journal of the Society for American Music 3, no. 1 (January 15, 2009): 1–2. http://dx.doi.org/10.1017/s1752196309090014.

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Leonard Bernstein (1918–90)—the now-legendary composer and conductor—had deep roots among Eastern European Jewish immigrants in Boston. This volume of essays explores aspects of that personal and sociocultural experience as revealed through an intensive team-research seminar at Harvard University during the spring semester of 2006. Titled “Before West Side Story: Leonard Bernstein's Boston,” the course positioned Bernstein within interlocking local networks, primarily during the 1930s and early 1940s. Its aim was not to prepare a standard biographical narrative, but rather to interrogate the synergy between an individual and supportive communities, whether religious, ethnic, educational, or musical. Carol J. Oja and Kay Kaufman Shelemay designed and team-taught the seminar, guiding a group of nineteen graduate and undergraduate students in both fieldwork and archival research, and they timed it to precede “Leonard Bernstein: Boston to Broadway,” a major international festival and conference about Bernstein, which took place at Harvard in October 2006. By drawing on complementary methodologies and capitalizing on the multiple layers of activity made possible by such a large group of researchers, the students covered an extraordinary amount of turf in a short time, and they did so in innovative ways. As their work unfolded, intriguing insights emerged about the powerful, ongoing role played by Boston's Jewish immigrant community in shaping the identity and character of a man who was to become one of America's most illustrious musicians.

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19

Rehman, Mutti-Ur, Jehad Alzabut, Nahid Fatima, and Tulkin H. Rasulov. "The Stability Analysis of Linear Systems with Cauchy—Polynomial-Vandermonde Matrices." Axioms 12, no. 9 (August 28, 2023): 831. http://dx.doi.org/10.3390/axioms12090831.

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The numerical approximation of both eigenvalues and singular values corresponding to a class of totally positive Bernstein–Vandermonde matrices, Bernstein–Bezoutian structured matrices, Cauchy—polynomial-Vandermonde structured matrices, and quasi-rational Bernstein–Vandermonde structured matrices are well studied and investigated in the literature. We aim to present some new results for the numerical approximation of the largest singular values corresponding to Bernstein–Vandermonde, Bernstein–Bezoutian, Cauchy—polynomial-Vandermonde and quasi-rational Bernstein–Vandermonde structured matrices. The numerical approximation for the reciprocal of the largest singular values returns the structured singular values. The new results for the numerical approximation of bounds from below for structured singular values are accomplished by computing the largest singular values of totally positive Bernstein–Vandermonde structured matrices, Bernstein–Bezoutian structured matrices, Cauchy—polynomial-Vandermonde structured matrices, and quasi-rational Bernstein–Vandermonde structured matrices. Furthermore, we present the spectral properties of totally positive Bernstein–Vandermonde structured matrices, Bernstein–Bezoutian structured matrices, Cauchy—polynomial-Vandermonde structured matrices, and structured quasi-rational Bernstein–Vandermonde matrices by computing the eigenvalues, singular values, structured singular values and its lower and upper bounds and condition numbers.

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20

O'Halloran, Kay L. "A Review of: “Reading Bernstein, Researching Bernstein”." Pedagogies: An International Journal 2, no. 1 (May 10, 2007): 49–51. http://dx.doi.org/10.1080/15544800701343745.

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21

Huang, Yunte. "Ten Plus Ways of Reading Charles Bernstein: Improvisations on Aphoristic Cores." boundary 2 48, no. 4 (November 1, 2021): 255–78. http://dx.doi.org/10.1215/01903659-9382300.

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Abstract Composed as a series of improvisations, this is a modular essay that examines, ponders, and responds to the radical poetics of Charles Bernstein's work from multiple perspectives, including dysraphism, aphorism, wit, and echopoetics. It also situates Bernstein in the long tradition of innovative American poetics extending from Ezra Pound and Gertrude Stein to Charles Olson and Susan Howe.

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22

Kim, Taekyun, Lee-Chae Jang, and Heungsu Yi. "A Note on the Modifiedq-Bernstein Polynomials." Discrete Dynamics in Nature and Society 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/706483.

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We propose the modifiedq-Bernstein polynomials of degreenwhich are differentq-Bernstein polynomials of Phillips (1997). From these modifiedq-Bernstein polynomials of degreen, we derive some recurrence formulae for the modifiedq-Bernstein polynomials.

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23

Rahman, Shagufta, M. Mursaleen, and Ali Alkhaldi. "Convergence of iterates of q-Bernstein and (p,q)-Bernstein operators and the Kelisky-Rivlin type theorem." Filomat 32, no. 12 (2018): 4351–64. http://dx.doi.org/10.2298/fil1812351r.

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Recently, Radu [Note on the iterates of q and (p,q)-Bernstein operators, Scientific Studies and Research, Series Mathematics and Informatics, 26(2) (2016) 83-94] has investigated the convergence of iterates of q-Bernstein polynomial and (p,q)-Bernstein polynomial with the aids of weakly Picard operators theory. In this article, we establish Kelisky-Rivlin type theorem on the power of the q-Bernstein operators for two dimensional case, (p,q)-Bernstein operators and bivariate (p,q)-Bernstein operators by using contraction principle.

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24

Renner, Adrian. "Ödipus’ Söhne. : Männliche Genealogien bei Gerhart Hauptmann und Elsa Bernstein (,,Vor Sonnenaufgang“, ,,Das Friedensfest“, ,,Dämmerung“)." Zeitschrift für Germanistik 33, no. 2 (January 1, 2023): 295–311. http://dx.doi.org/10.3726/92174_295.

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Abstract Zahlreiche naturalistische Dramen der 1890er Jahre verhandeln scheiternde Familiengründungen, in denen Töchter und Söhne in als unentrinnbar geschilderten Familienbeziehungen gefangen bleiben. Der Aufsatz zeigt, wie die frühen Dramen Gerhart Hauptmanns und Elsa Bernsteins als Verhandlungen einer sozialen Determinierung von Männlichkeit aus dem genealogischen Übergang von der Position des Sohnes zu der des Vaters begriffen werden können. Die Darstellung krisenhafter Genealogien bei Hauptmann und Bernstein speist sich aus bisher nur als formale Anleihen diskutierten Bezügen zu Sophokles’ König Ödipus.Various naturalistic dramas written in the 1890s depict failing attempts at establishing new families in which sons and daughters cannot escape their ruinous and dysfunctional family backgrounds. The article shows how naturalistic dramas highlight the social determination of masculinity through a genealogical understanding of the family structure and the transition from son to father. The theme of genealogy can be traced to evocations of Sophocles’ Oedipus Rex in plays by Gerhart Hauptmann and Elsa Bernstein; a link that has previously only been discussed in terms of formal analogies.

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25

Burnham, Patricia M. "Theresa Bernstein." Woman's Art Journal 9, no. 2 (1988): 22. http://dx.doi.org/10.2307/1358316.

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26

Secrest, Meryle. "Leonard Bernstein." Musical Times 132, no. 1780 (June 1991): 279. http://dx.doi.org/10.2307/966532.

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27

Bernad, Catherine. "Antoinette Bernstein." Double jeu, no. 14 (December 31, 2017): 33–55. http://dx.doi.org/10.4000/doublejeu.372.

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28

Parham, David. "Jay Bernstein." Pediatric and Developmental Pathology 12, no. 4 (July 2009): 311. http://dx.doi.org/10.2350/09-03-0624.1.

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29

Adams, Byron, Humphrey Burton, and William Westbrook Burton. "Leonard Bernstein." American Music 15, no. 3 (1997): 409. http://dx.doi.org/10.2307/3052332.

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30

Bernstein, Charles, and Hélène Aji. "Charles Bernstein." Po&sie N°169, no. 3 (2019): 43. http://dx.doi.org/10.3917/poesi.169.0043.

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31

McCandless, Bret. "Leonard Bernstein." Music Reference Services Quarterly 22, no. 1-2 (April 3, 2019): 97–98. http://dx.doi.org/10.1080/10588167.2019.1601658.

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32

Limb, Peter. "Hilda Bernstein." ASA News 40, no. 1 (January 2007): 4. http://dx.doi.org/10.1017/s0278221900070322.

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33

Roytwarf, N., and Yosef Yomdin. "Bernstein classes." Annales de l’institut Fourier 47, no. 3 (1997): 825–58. http://dx.doi.org/10.5802/aif.1582.

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34

Dryer, Murray, Harold Leinbach, and Sami Cuperman. "William Bernstein." Physics Today 52, no. 8 (August 1999): 81. http://dx.doi.org/10.1063/1.882796.

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35

Schappacher, Norbert. "Felix Bernstein." International Statistical Review 73, no. 1 (January 15, 2007): 3–7. http://dx.doi.org/10.1111/j.1751-5823.2005.tb00247.x.

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36

Kaiserling, K. "Baltischer Bernstein." Der Pathologe 22, no. 4 (July 1, 2001): 285–86. http://dx.doi.org/10.1007/s002920100467.

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37

Linda Wang. "Bruce Bernstein." C&EN Global Enterprise 99, no. 15 (April 26, 2021): 32. http://dx.doi.org/10.1021/cen-09915-obits2.

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38

W�rz-Busekros, Angelika. "Bernstein algebras." Archiv der Mathematik 48, no. 5 (May 1987): 388–98. http://dx.doi.org/10.1007/bf01189631.

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39

Al-Sa'di, Sa'ud, and Salti Samarah. "Bernstein and Bernstein-Like Inequalities for Modulation Spaces." International Journal of Emerging Multidisciplinaries: Mathematics 1, no. 1 (January 14, 2022): 91–101. http://dx.doi.org/10.54938/ijemdm.2022.01.1.3.

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It is shown that the modulation spaces Mwp can be characterized by the approximation behavior of their elements using Local Fourier bases. In analogy to the Local Fourier bases, we show that the modulation spaces can also be characterized by the approximation behavior of their elements using Gabor frames. We derive direct and inverse approximation theorems that describe the best approximation by linear combinations of N terms of a given function using its modulates and translates.

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40

Haynes, Robert H. "Aging, Sex, and DNA Repair.Carol Bernstein , Harris Bernstein." Quarterly Review of Biology 69, no. 2 (June 1994): 262–64. http://dx.doi.org/10.1086/418563.

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41

Xu, Xiao-Wei, and Ron Goldman. "On Lototsky–Bernstein operators and Lototsky–Bernstein bases." Computer Aided Geometric Design 68 (January 2019): 48–59. http://dx.doi.org/10.1016/j.cagd.2018.12.004.

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42

Kim, T., J. Choi, and Y. H. Kim. "-Bernstein Polynomials Associated with -Stirling Numbers and Carlitz's -Bernoulli Numbers." Abstract and Applied Analysis 2010 (2010): 1–11. http://dx.doi.org/10.1155/2010/150975.

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Recently, Kim (2011) introduced -Bernstein polynomials which are different -Bernstein polynomials of Phillips (1997). In this paper, we give a -adic -integral representation for -Bernstein type polynomials and investigate some interesting identities of -Bernstein type polynomials associated with -extensions of the binomial distribution, -Stirling numbers, and Carlitz's -Bernoulli numbers.

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43

Prolla, João B. "A generalized Bernstein approximation theorem." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 2 (September 1988): 317–30. http://dx.doi.org/10.1017/s030500410006549x.

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A celebrated theorem of Weierstrass states that any continuous real-valued function f defined on the closed interval [0, 1] ⊂ ℝ is the limit of a uniformly convergent sequence of polynomials. One of the most elegant and elementary proofs of this classic result is that which uses the Bernstein polynomials of fone for each integer n ≥ 1. Bernstein's Theorem states that Bn(f) → f uniformly on [0, 1] and, since each Bn(f) is a polynomial of degree at most n, we have as a consequence Weierstrass' theorem. See for example Lorentz [9]. The operator Bn, defined on the space C([0, 1]; ℝ) with values in the vector subspace of all polynomials of degree at most n has the property that Bn(f) ≥ 0 whenever f ≥ 0. Thus Bernstein's Theorem also establishes the fact that each positive continuous real-valued function on [0, 1] is the limit of a uniformly convergent sequence of positive polynomials. This raises the following natural question: consider a compact Hausdorff space X and the convex cone C+(X):= {f ∈ C(X; ℝ); f ≥ 0}. Now the analogue of Bernstein's Theorem would be a theorem stating when a convex cone contained in C+(X) is dense in it. More generally, one raises the question of describing the closure of a convex cone contained in C(X; ℝ), and, in particular, the closure of A+:= {f ∈ A; f ≥ 0}, where A is a subalgebra of C(X; ℝ).

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44

Rababah, Abedallah. "Transformation of Chebyshev–Bernstein Polynomial Basis." Computational Methods in Applied Mathematics 3, no. 4 (2003): 608–22. http://dx.doi.org/10.2478/cmam-2003-0038.

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AbstractIn this paper, we derive a matrix of transformation of Chebyshev polynomials of the first kind into Bernstein polynomials and vice versa. We also study the stability of these linear maps and show that the Chebyshev–Bernstein basis conversion is remarkably well-conditioned, allowing one to combine the superior least-squares performance of Chebyshev polynomials with the geometrical insight of the Bernstein form. We also compare it to other basis transformations such as Bernstein-Hermite, power-Hermite, and Bernstein–Legendre basis transformations.

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Wang, Yali, and Yinying Zhou. "Shape Preserving Properties forq-Bernstein-Stancu Operators." Journal of Mathematics 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/603694.

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We investigate shape preserving forq-Bernstein-Stancu polynomialsBnq,α(f;x)introduced by Nowak in 2009. Whenα=0,Bnq,α(f;x)reduces to the well-knownq-Bernstein polynomials introduced by Phillips in 1997; whenq=1,Bnq,α(f;x)reduces to Bernstein-Stancu polynomials introduced by Stancu in 1968; whenq=1,α=0, we obtain classical Bernstein polynomials. We prove that basicBnq,α(f;x)basis is a normalized totally positive basis on[0,1]andq-Bernstein-Stancu operators are variation-diminishing, monotonicity preserving and convexity preserving on[0,1].

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Kadak, Uğur, and Faruk Özger. "A numerical comparative study of generalized Bernstein-Kantorovich operators." Mathematical Foundations of Computing 4, no. 4 (2021): 311. http://dx.doi.org/10.3934/mfc.2021021.

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<p style='text-indent:20px;'>In this paper, a new generalization of the Bernstein-Kantorovich type operators involving multiple shape parameters is introduced. Certain Voronovskaja and Grüss-Voronovskaya type approximation results, statistical convergence and statistical rate of convergence of proposed operators are obtained by means of a regular summability matrix. Some illustrative graphics that demonstrate the convergence behavior, accuracy and consistency of the operators are given via Maple algorithms. The proposed operators are comprehensively compared with classical Bernstein, Bernstein-Kantorovich and other new modifications of Bernstein operators such as <inline-formula><tex-math id="M1">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>-Bernstein, <inline-formula><tex-math id="M2">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>-Bernstein-Kantorovich, <inline-formula><tex-math id="M3">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula>-Bernstein and <inline-formula><tex-math id="M4">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula>-Bernstein-Kantorovich operators.</p>

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Simsek, Yilmaz, and Mehmet Acikgoz. "A New Generating Function of (q-) Bernstein-Type Polynomials and Their Interpolation Function." Abstract and Applied Analysis 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/769095.

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The main object of this paper is to construct a new generating function of the (q-) Bernstein-type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and derivative of the (q-) Bernstein-type polynomials. We also give relations between the (q-) Bernstein-type polynomials, Hermite polynomials, Bernoulli polynomials of higher order, and the second-kind Stirling numbers. By applying Mellin transformation to this generating function, we define interpolation of the (q-) Bernstein-type polynomials. Moreover, we give some applications and questions on approximations of (q-) Bernstein-type polynomials, moments of some distributions in Statistics.

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SARNA, JONATHAN D. "Leonard Bernstein and the Boston Jewish Community of His Youth: The Influence of Solomon Braslavsky, Herman Rubenovitz, and Congregation Mishkan Tefila." Journal of the Society for American Music 3, no. 1 (January 15, 2009): 35–46. http://dx.doi.org/10.1017/s1752196309090038.

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AbstractThis essay will place Leonard Bernstein within the context of the Boston Jewish community in which he was raised. It was at Boston's Congregation Mishkan Tefila, the family's synagogue, where Bernstein first encountered serious music. The essay places special emphasis on the role of Prof. Solomon Gregory Braslavsky, the music director and organist of Mishkan Tefila, whose influence on the young Bernstein was far greater than scholars have imagined. In 1973 Bernstein wrote to Braslavsky “[I] never forget the tremendous influence you and your music made on me when I was a youngster.” Bernstein, I contend, meant what he said.

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Jakubík, Ján. "Cantor-Bernstein theorem for lattices." Mathematica Bohemica 127, no. 3 (2002): 463–71. http://dx.doi.org/10.21136/mb.2002.134062.

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Wang, Jianjun, Chan-Yun Yang, and Shukai Duan. "Approximation Order for Multivariate Durrmeyer Operators with Jacobi Weights." Abstract and Applied Analysis 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/970659.

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Using the equivalence relation betweenK-functional and modulus of smoothness, we establish a strong direct theorem and an inverse theorem of weak type for multivariate Bernstein-Durrmeyer operators with Jacobi weights on a simplex in this paper. We also obtain a characterization for multivariate Bernstein-Durrmeyer operators with Jacobi weights on a simplex. The obtained results not only generalize the corresponding ones for Bernstein-Durrmeyer operators, but also give approximation order of Bernstein-Durrmeyer operators.

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