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Weighted quasisymmetric enumerator for generalized permutohedra
(Springer, 2020)
We introduce a weighted quasisymmetric enumerator function associated to generalized permutohedra. It refines the Billera, Jia and Reiner quasisymmetric function which also includes the Stanley chromatic symmetric function. ...
Geometrical, Fresnel, and Fraunhofer Regimes of Single-Slit Diffraction
(American Association of Physics Teachers - AAPT.org, 2019)
Recently, Panuski and Mungan presented the results of their study of light diffraction from a variable-width single slit by observing and measuring the diffraction pattern on an observation screen placed at a fixed distance. ...
On the Generalized Strongly Nil - Clean Property of the Matrix Rings
(World Scientific Publishing Company, 2021)
Let R be an associative unital ring and not necessarily commutative. We
analyzes conditions under which every n×n matrix A over R is expressible as a sum
A = E1 + ... +Es +N of (commuting) idempotent matrices Ei and a ...
On the influence of resonance photon scattering on atom interference
(Physica Scripta, 2010)
Here, the influence of resonance photon-atom scattering on the atom interference pattern at the exit of a three-grating Mach-Zehnder interferometer is studied. It is assumed that the scattering process does not destroy the ...
Chebyshev polynomials and r-circulant matrices
(Applied Mathematics and Computation, 2022)
This paper connects two attractive topics in applied mathematics, r-circulant matrices and the
Chebyshev polynomials. The r-circulant matrices whose entries are the Chebyshev polynomials
of the first or second kind are ...
On the extension of the Erdös-Mordell type inequalities
(Mathematical Inequalities & Applications, 2014)
We discuss the extension of inequality R_A >= c/a * r_b + b/a * r_c to the plane of triangle ABC. Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdos-Mordell ...
Trajectory-Based Interpretation of Laser Light Diffraction by a Sharp Edge
(Springer, 2018)
In the diffraction pattern produced by a half-plane sharp edge when it obstructs the passage of a laser beam, two characteristic regions are noticeable. There is a central region, where the diffraction of laser light appears ...