Srinivas Ramanujan: An Indigenous Mathematician

The paper undertaken for the deliberation of International stature on December 22, 2020 rivets attention on the topic of THE CONTRIBUTION OF RAMANUJAN in the arena of MATHEMATICS. He is remembered for India’s greatest mathematical genii. He made significant contribution to the analytical theory of numbers elliptical functions, continued fractions and infinite series. Ramanujan left a slew of unpublished note books enfolding theorems that future generation of mathematical world have been exploring continuously. He is an icon of a self-studied, self learnt, self-taught mathematical genius who is a living legend and ennobling soul for the posterity. He is known as child prodigy. Owing to his ingenuous acumen and surprising accomplishments in the field of Mathematics, Indian govt. decided to celebrate his birthday 22nd December as National Mathematics Day.

LEV V. PUMPYANSKII ON GUSTAVE FLAUBERT

The article addresses the views of Lev Vasil’evich Pumpyanskii (1891-1940), the prominent philologist and thinker, the friend and colleague of M.M. Bakhtin, on the artistic method of G. Flaubert. L.V. Pumpyanskii in his work «Turgenev and Flaubert» (1930) as well as in his unpublished book «Literature of Modern West and Amerika: 1920-1929» (1930) and unpublished note (1928) about K.A. Fedin’s novel The Brothers describes the artistic method of G. Flaubert as artisticism. For L.V. Pumpyanskii artisticism means the existence of strict creative distance, orientation on someone else’s word, stylization, particular objective world, and evocative method of description. According to L.V. Pumpyanskii Flaubert’s artisticism formed a whole epoch in the history of European literature and had a great influence on Pumpyanskii’s highly estimated Henry James and Thomas Mann.

Rothbard on the Economics of Slavery

Murray Rothbard wrote an unpublished note in the early 1960s on the economics of antebellum slavery. Essentially, it was a criticism of the methodology of the New Economic History, or cliometrics, of which Conrad and Meyer (1958a) was the breakthrough application, on the topic of the profitability of slavery. Rothbard points out that their procedure in no way supports their conclusion that slavery was profitable or their ideological conclusion that the Civil War was necessary to end American slavery.

Mickey Mouse: Utopian and Barbarian

This chapter explores Walter Benjamin’s writings on Mickey Mouse, focussing especially on the unpublished note ‘Mickey Mouse’ (1931), ‘Experience and Poverty’ (1933), and ‘The Work of Art in the Age of Its Technological Reproducibility’ (1935–1939). These texts are read in conjunction with other essays from the period, such as ‘The Destructive Character’ (1931) and ‘Karl Kraus’ (1931), since Benjamin detected in the anarchic, destructive, and technologically driven figure of the early Mickey Mouse a similar project to overcome bourgeois civilization and, especially, the individual subjectivity upon which humanism was based. The chapter also draws on some references to Disney films as dream images in the Arcades Project (1928–1940).

In search of a pristine signal for (scale-)chiral symmetry in nuclei

I describe the long-standing search for a “smoking-gun” signal for the manifestation of (scale-)chiral symmetry in nuclear interactions. It is prompted by Gerry Brown’s last unpublished note, reproduced verbatim below, on the preeminent role of pions and vector ([Formula: see text]) mesons in providing a simple and elegant description of strongly correlated nuclear interactions. In this note written in tribute to Gerry Brown, I first describe a case of an unambiguous signal in axial-charge transitions in nuclei and then combine his ideas with the more recent development on the role of hidden symmetries in nuclear physics. What transpires is the surprising conclusion that the Landau–Migdal fixed point interaction [Formula: see text], the nuclear tensor forces and Brown–Rho scaling, all encoded in scale-invariant hidden local symmetry, as Gerry put, “run the show and make all forces equal.”

ON THE NON-TRIVIALITY OF THE λφ4 MODEL

The λφ4 model is conventionally used to explain the origin of mass of elementary particles through the Spontaneous Symmetry Breaking (SSB) phenomena. The triviality status of the λφ4 model in 4-dimensional spacetime remains an open question despite attempts by several authors. This study establishes a new approach to determine the triviality status of the λφ4 model based on an unpublished note by Professor Bryce DeWitt. We adopted the DeWitt's Ansatz for the 2-point connected correlation function on the lattice [Formula: see text] where α is a parameter that measures the departure from triviality. Calling α's continuum counterpart as β, then a non-zero value of β signifies non-triviality of the λφ4 model. The 2-point connected correlation function, given in terms of an Euclidean functional integral, is computed numerically via Monte Carlo methods. Our analysis, based on β, is different from the traditional analysis based on the renormalized coupling constant λR. To test the new approach, we performed the simulation in 2 dimensions and obtained results that are consistent with previous findings: 2-dimensional λφ4 model is non-trivial. Finally, for the case in 4 dimensions, our results show that the model is non-trivial.

A Matrix Dynamics Approach to Golomb's Recursion

In an unpublished note Golomb proposed a family of "strange" recursions of metafibonacci type, parametrized by $k$. Previously we showed that contrary to Golomb's conjecture, for each $k$ there are many increasing solutions, and an explicit construction for multiple solutions was displayed. By reformulating our solution approach using matrix dynamics, we extend these results to a characterization of the asymptotic behaviour of all solutions of the Golomb recursion. This matrix dynamics perspective is also used to construct what we believe is the first example of a "nontrivial" nonincreasing solution, that is, one that is not eventually increasing.