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Vapor pressure measurements were performed for solutions of poly(methyl methacrylate-ran-tert-butyl methacrylate) with different weight fractions of tert-butyl methacrylate units, and their parental homopolymers in chloroform at 323 K, over a large domain of concentrations. The Flory-Huggins interaction parameters obtained from these experimental investigations show complex dependences of the Flory-Huggins interaction parameter on concentration and
Read moreThe q-binomial coefficients are specializations of the elementary symmetric functions. In this paper, we use this fact to give a new expression for the generating function of the number of divisors. As corollaries, we obtained new connections between partitions and divisors.
Read moreThe r-Whitney numbers of both kinds are specializations of complete and elementary symmetric functions. In this paper, we use this fact to express a finite discrete convolution involving r-Whitney numbers of both kinds in terms of Bernoulli polynomials.
Read moreThe complete and elementary symmetric functions are special cases of Schur functions. It is well-known that the Schur functions can be expressed in terms of complete or elementary symmetric functions using two determinant formulas: Jacobi–Trudi identity and Nägelsbach–Kostka identity. In this paper, we study new connections between complete and elementary symmetric functions.
Read moreBinomial coefficients can be expressed in terms of multinomial coefficients as sums over integer partitions. This approach allows us to introduce new upper bounds for the number of partitions into a given number of parts.
Read moreA very special case of a Ramus’s identity is used in this note to derive an infinite family of inequalities involving finite sums with cosecant function. As a corollary of this result, we obtain the Wallis's formula.
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