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The quest for innovative talent is more than an academic pursuit; it’s a strategic imperative for nations aiming to enhance their core competitiveness. Central to this quest is the early development of students’ scientific literacy, a focus grounded in cognitive behavior theory and enriched by the concept of ternary reciprocity. Our study introduces a novel approach to understanding and cultivating innovative talents, integrating a cognitive behavior system model to identify key influencing factors. Employing a fuzzy comprehensive evaluation method, we developed and tested an innovative talent cultivation strategy, yielding significant results: strategy effectiveness scores range from 2.1 to 2.3 for primary indicators and 1.8 to 2.3 for secondary indicators, with all indices showing statistically significant improvements (p < 0.05) when our strategies are applied. This research not only evidences the potency of our approach but also contributes actionable insights and methodologies for future innovative talent development.

For any $\\alpha \\in \\mathbb {R},$ we consider the weighted Taylor shift operators $T_{\\alpha }$ acting on the space of analytic functions in the unit disc given by $T_{\\alpha }:H(\\mathbb {D})\\rightarrow H(\\mathbb {D}),$ $$ \\begin{align*}f(z)=\\sum_{k\\geq 0}a_{k}z^{k}\\mapsto T_{\\alpha}(f)(z)=a_1+\\sum_{k\\geq 1}\\Big(1+\\frac{1}{k}\\Big)^{\\alpha}a_{k+1}z^{k}.\\end{align*}$$ We establish the optimal growth of frequently hypercyclic functions for $T_\\alpha $ in terms of $L^p$ averages, $1\\leq p\\leq +\\infty $ . This allows us to highlight a critical exponent.

We examine the boundary behaviour of the generic power series f with coefficients chosen from a fixed bounded set Λ in the sense of Baire category. Notably, we prove that for any open subset U of the unit disk D with a nonreal boundary point on the unit circle, f(U) is a dense set of ℂ. As it is demonstrated, this conclusion does not necessarily hold for arbitrary open sets accumulating to the unit circle. To complement these results, a characterization of coefficient sets having this property is given.

Series defined by means of the three-parametric Mittag-Leffler functions, called also the Prabhakar functions, are considered in this paper. Their behaviour is investigated on the boundaries of the convergence domains. Necessary and sufficient conditions for their overconvergence are proposed. The corresponding results for series in Mittag-Leffler functions are discussed as a particular case. Such kind of results are motivated by the fact that the solutions of some fractional order differential and integral equations can be written in terms of series (or series of integrals) of Mittag-Leffler type functions.

Functions in backward shift invariant subspaces have nice analytic continuation properties outside the spectrum of the inner function defining the space. Inside the spectrum of the inner function, Ahern and Clark showed that under some distribution condition on the zeros and the singular measure of the inner function, it is possible to obtain non-tangential boundary values of every function in the backward shift invariant subspace as well as for their derivatives up to a certain order. Here we will investigate, at least when the inner function is a Blaschke product, the non-tangential boundary values of the functions of the backward shift invariant subspace after having applied a co-analytic (truncated) Toeplitz operator. There appears to be a smoothing effect.

Universal Taylor series are defined on simply connected domains, but they do not exist on an annulus. Instead we introduce universal Laurent or Laurent–Faber series on finitely connected domains in $\\mathbb{C}$. These are generic universalities. Furthermore, we study some properties of universal Laurent series on an annulus.

We study some properties of the solutions of a class of functional equations. For example, we prove that if w(z) is a function analytic in the closed unit disc {z | |z| ≤ 1} such that w(0) = 0, 0 < ϵ < 1, and |w′(z)|+ϵ|w(z)| = 1, |z| = 1, then w(z) ≠ 0 if |z| = 1.