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Bayer Noise symmetric functions and some combinatorial algebraic structures

Abdulwahid Adnan Hashim, Elamami Elgaddafi

Journal of Mathematics and Applications

2023

Vol. 46

115--148

Symmetric functions play a crucial role in classifying representations of symmetric groups, and they are largely involved with combinatorial algebras and graph theory. Bayer filter technique is largely applied in most of the professional digital cameras due to the fact that it is a low-cost, and it allows photosensors not only to capture the intensity of light, but also to record the wavelength of light as well. Using Bayer Pattern, we introduce the Bayer Noise symmetric functions and the Bayer Noise Schur functions, and we study some combinatorial structures on the Bayer Noise modules. We study the connection between Bayer Noise symmetric functions and other bases for the algebra of symmetric functions, and we explicitly calculate special cases over a fixed commutative ring k. We also study the compatibility of such algebraic and coalgebraic structures.

Analytic, symmetric functions that omit zero

Śladkowska Janina

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2004

z. 27 [212]

69-81

Let Fo] (b), b is an element of R denote the class of functions of the form f{z) = b+b1z+..., analytic in the unit disk U and such that 0 [...] and let Fo(b) be the set of functions of the class Fo(b) such that f(z) €is an element of R iff z (-1,1). The functions from the class ^{b) are closely related to the typically-real functions, namely for each f is an element of Fo(b) there exist two typically-real functions T1 and T2 such that f = bT1/T2. So it is possible to treat Fo (b) as a subclass of the class[...] of all the functions of the form bT1/T2, where T1,T2 are arbitrary typically-real functions. It is easy to obtain the variational formulas in the class [...] (b) by utilizing the known formulas obtained in the class of typically-real functions [1]. Certain extremal problems in the class FoR(b) and also in the class Fo(b), for example estimation from below of the second coefficient, were solved with the aid of these formulas.

Univalence problems for classes of functions preserving sectors

Koczan Leopold

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2002

z. 26 [199]

89-95

Let A be the set of all functions that are analytic in the disk delta = [z is an element of C : \z\ < 1} and normalized by f(O) = f'(O) - 1 = 0. Abu-Muhanna and MacGregor discussed in the paper [1] different classes of functions which preserved some sectors. For k > 2 they used notation: [...].