Dinesh Kumar

activity

20212026

collaborators

11 papers

math.CO2026

Structural Classification of a Graph with Independence Number Five

Manisha Kumari, Dinesh Kumar

The independence polynomial of a simple graph $G$ is given by $ I_G(z) = i_0 + i_1 z + i_2 z^2 + \cdots + i_αz^α$, where $ i_α$ denotes the size of a maximum independent set, a…

math.DS2026

A survey on permutable transcendental entire functions and their dynamics

Dinesh Kumar

In this paper, we survey important results on the dynamics of permutable transcendental entire functions from 1958 to 2025. We have discussed the forms of transcendental entire fun…

math.DS2026

Results on the postsingular set of compositions of transcendental entire functions

Manisha Kumari, Dinesh Kumar

In this paper, we study the dynamics of commuting transcendental entire functions $f$ and $g$ , where $g = a f^{p} + b$ with $a, b \in C$ , $p \in N$ , and $a \neq = 0, 1$ . We exami…

cs.LG2026

Holomorphic Neural ODEs with Kolmogorov-Arnold Networks for Interpretable Discovery of Complex Dynamics

Bhaskar Ranjan Karn, Dinesh Kumar

Complex dynamical systems governed by holomorphic maps such as $z^{2} + c$ exhibit fractal boundaries with extreme sensitivity to initial conditions. Accurately modelling these struc…

math.DS2026

Equality of the dynamical sets of two commuting transcendental entire functions

Manisha Kumari, Dinesh Kumar

In this paper, we study the dynamics of commuting transcendental entire functions $f$ and $g$ , where $g$ is of the form $a f^{p} + b$ with $a,b \in \C$, $p \in N$ , and $a \neq = 0, 1$ .…

math.NT2026

Inverses of six classes of permutation polynomials of the form $x + γ Tr_{q}^{q^{2}} (h (x))$ over finite fields of even characteristic

Rajesh P. Singh, Dinesh Kumar, Jitendra Prakash

Recently, Jiang et al. \cite{JIANG2025102522} obtained several classes of Permutation Polynomial of the form $x + γ Tr_{q}^{q^{2}} (h (x))$ over finite fields $\mathbb{F}_{q^…

math.DS2025

On Dynamics of the Bungee set and the Filled Julia set of a Transcendental Semigroup

Manisha Kumari, Dinesh Kumar

We have introduced the notion of the bungee set and the filled Julia set of a transcendental semigroup using Fatou-Julia theory. Numerous results of the bungee set of a single tran…

hep-th2025

Effect of Non-Extensive Parameter on Page Curve

Ankit Anand, Dinesh Kumar, Aditya Singh

This work employs the quantum extremal surface framework to compute the Page curve for black holes corrected by non-extensive entropy. The entropy of Hawking radiation increases li…

math.CA2024

Study of dynamical symmetrietry algebra of $Ψ_{2}$ -Humbert function

Ayman Shehata, Dinesh Kumar

The study is devoted to the construction of dynamical symmetry algebra of confluent hypergeometric function $_{1} F_{1}$ and $Ψ_{2}$ -Humbert function and to derive some generating relatio…

math.DS2024

Results on Dynamics of Bungee set of Composite Entire Functions in the Eremenko-Lyubich Class

Dinesh Kumar, Soumyajeet Das

In this paper, we have discussed the dynamics of composite entire functions in terms of relationship between bungee set, escaping set and filled-in Julia set. We have established s…

math.CA2021

On extension of the $_{r} R_{s, q} (α, β, z)$ function and their $q$ -calculus

Ayman Shehata, Dinesh Kumar

In this article, we investigate and establish some properties including analytic properties, contiguous relations, differential properties, differential operators, an expansion for…

Structural Classification of a Graph with Independence Number Five

A survey on permutable transcendental entire functions and their dynamics

Results on the postsingular set of compositions of transcendental entire functions

Holomorphic Neural ODEs with Kolmogorov-Arnold Networks for Interpretable Discovery of Complex Dynamics

Equality of the dynamical sets of two commuting transcendental entire functions

Inverses of six classes of permutation polynomials of the form x+γTrqq2​(h(x)) over finite fields of even characteristic

On Dynamics of the Bungee set and the Filled Julia set of a Transcendental Semigroup

Effect of Non-Extensive Parameter on Page Curve

Study of dynamical symmetrietry algebra of Ψ2​-Humbert function

Results on Dynamics of Bungee set of Composite Entire Functions in the Eremenko-Lyubich Class

On extension of the r​Rs,q​(α,β,z) function and their q-calculus

Inverses of six classes of permutation polynomials of the form $x + γ Tr_{q}^{q^{2}} (h (x))$ over finite fields of even characteristic

Study of dynamical symmetrietry algebra of $Ψ_{2}$ -Humbert function

On extension of the $_{r} R_{s, q} (α, β, z)$ function and their $q$ -calculus