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Trace formula for the Sturm-Liouville eigenvalue problem with its applications to n-body problem
Sturm-Liouville eigenvalue applications n-body problem
2015/3/18
Trace formula for the Sturm-Liouville eigenvalue problem with its applications to n-body problem.
Combinatorial Proof of the Inversion Formula on the Kazhdan-Lusztig R-Polynomials
Kazhdan-Lusztig R-polynomial inversion formula Bruhat order
2014/6/3
In this paper, we present a combinatorial proof of the inversion formula on the Kazhdan-Lusztig R-polynomials. This problem was raised by Brenti. As a consequence, we obtain a combinatorial interpreta...
A Note On the Accuracy of Ramanujan's Approximative Formula for the Perimeter of an Ellipse
Ramanujan's approximative formula Best constants Elliptic functions and integrals
2008/7/3
We present a detailed error analysis, with best possible constants, of Ramanujan's most accurate approximation to the perimeter of an ellipse.
Generalizations of the Trapezoid Inequalities Based on a New Mean Value Theorem for the Remainder in Taylor's Formula
Classical trapezoid inequality Perturbed trapezoid inequality Mean value theorem Generalizations
2008/7/1
Generalizations of the classical and perturbed trapezoid inequalities are developed using a new mean value theorem for the remainder in Taylor's formula. The resulting inequalities for N-times differe...
On an Integration-by-parts Formula for Measures
Integration-by-parts formula Harmonic sequences Inequalities
2008/6/30
An integration-by-parts formula, involving finite Borel measures supported by intervals on real line, is proved. Some applications to Ostrowski-type and Grüss-type inequalities are presented.
Ostrowski Type Inequalities Over Balls and Shells via a Taylor-Widder Formula
Ostrowski inequality multivariate inequality ball and shell Taylor-Widder formula extended complete Tschebyshev system
2008/6/27
The classical Ostrowski inequality for functions on intervals estimates the value of the function minus its average in terms of the maximum of its first derivative. This result is extended to higher o...
A formula for energy functionals of a Markov process and its subprocess will be given in this paper. This generalizes a formula in [1]. We also use this formula to get some important consequences.
Let $k$ be a field of characteristic zero, $\g$ a $k$-Lie algebra, $e:S\g@>>>U\g$ the symmetrization map. The PBW quantization is the one parameter family of associative products: $$ x\star_t y=\sum_{...