Mathematics Interdisciplinary Research
Volume:8 Issue: 4, Autumn 2023

‎A nonnegative square and real matrix $R$ is a row stochastic matrix if the sum of the entries of each row is equal to one‎. ‎Let $x$‎, ‎$y \in \mathbb{R}_{n}$‎. ‎The vector $x$ is said to be matrix majorized by $y$ and denoted by $ x\prec_{r} y$ if $x=yR$ for some row stochastic matrix $R$‎. ‎In the present paper‎, ‎we characterize the linear preservers of matrix majorization $T:\mathbb{R}_{m} \rightarrow \mathbb{R}_{n}$‎.

‎A new subclass of meromorphic univalent functions by using the q-hypergeometric and Hurwitz-Lerch Zeta functions is defined‎. ‎Also‎, ‎by applying the generalized Liu-Srivastava operator on meromorphic functions‎, ‎some geometric properties of the new defined subclass such as coefficient estimates‎, ‎extreme points‎, ‎convexity and connected set structure are investigated‎.

‎In the present paper it is shown that Bogomolov multipliers of isoclinic Lie rings are isomorphic‎. ‎Also‎, ‎we show that isoclinic finite Lie rings have isoclinic CP covers‎. ‎Finally‎, ‎it is proved that if $CE_1$ and $CE_2$ are central extensions which are isoclinic‎, ‎then $CE_2$ is a CP extension if $CE_1$ is so‎.

‎In this paper‎, ‎we extend the notion of approximate convexity to set-valued maps and obtain some relations between approximate convexity and approximate monotonicity of their normal subdifferential‎.

‎This paper presents the visualization process of finding the roots of a complex polynomial‎ - ‎which is called polynomiography‎ - ‎by the Caputo fractional derivative‎. ‎In this work‎, ‎we substitute the variable-order Caputo fractional derivative for classic derivative in Newton's iterative method‎. ‎To investigate the proposed root-finding method‎, ‎we apply it for two polynomials $p(z)=z^5-1$ and $ p(z)=-2z^4+z^3+z^2-2z-1 $ on the complex plane and compute the MNI and CAI parameters‎.‎Presented examples show that through the expressed process‎, ‎we can obtain very interesting fractal patterns‎. ‎The obtained patterns show that the proposed method has potential artistic application‎.

‎This paper presents a method for characteristic function assignment on rational functions by adding perturbation in systems with irrational characteristic functions‎. ‎Generally‎, ‎in systems with irrational characteristic loci‎, ‎commutative compensator designs are not possible‎. ‎Irrational characteristic functions have different forms‎. ‎In our previous work‎, ‎mentioned in the introduction section‎, ‎a form of these characteristic functions was presented‎. ‎Another form of irrational characteristic functions is considered in this paper‎. ‎This approach is not based on the transfer function inverting‎, ‎and characteristic loci are not used directly in the design process‎. ‎The efficacy of the proposed approach is investigated through two numerical examples‎.