Journal of Informatics and Mathematical Sciences

Dynamic Epidemiological Models for HIV/AIDS Associated TB Transmission: A Review

Maitri R. Raval — 2025-09-16

An extensive literature review suggests a significant link between HIV/AIDS and other diseases such as Pneumocystis pneumonia (PCP), Candidiasis, Cryptococcal meningitis, Toxoplasmosis, and Tuberculosis (TB). Here, our emphasis is on the HIV/AIDS associated Tuberculosis (TB) transmission dynamics. Since the last decade, due to the advancement in machine languages and neural networking, researchers have developed mathematical models to predict and investigate the dynamics of transmission of HIV/AIDS linked Tuberculosis (TB) globally. It includes the therapeutic aspects, like antiretroviral drug screening and treatment factors, in the study. We aim to cover the diversity of developed models to address the numerous key issues of the infection dynamics and provide the status of current and developed models to the global scientific community. Hence, it would help to build highly accurate future models to track the actual dynamics of the concerned disease. In this paper, we discussed deterministic modeling for the HIV/AIDS mediated Tuberculosis (TB) infection dynamics. Additionally, the threshold behaviour and the extended effect of mediations have been discussed. We conclude with an outline of the utilizations and accomplishments of HIV/AIDS-TB modeling and some proposed future directions.

Three New Min-Max Variations of the Hardy-Hilbert Integral Inequality

Christophe Chesneau — 2025-09-16

Building on the work of Li and He in 2007, this article presents three new variations of the Hardy-Hilbert integral inequality using minimum and maximum kernel functions. Detailed proofs are provided.

The Ideal Structure of the Minimal Tensor Product of Ternary Rings of Operators

Arpit Kansal — 2025-09-16

Let \(V\) be a ternary ring of operator, and let \(B\) be a \(C^*\)-algebra. We study the structure of the ideal space of the operator space injective tensor product \(V \otimes^{\mathrm{tmin}} B\) via two maps:
\begin{align*}
\Phi(I, J) = \ker(q_I \otimes^{\mathrm{tmin}} q_J) \quad \text{and} \quad \Delta(I, J) = I \otimes^{\mathrm{tmin}} B + V \otimes^{\mathrm{tmin}} J.
\end{align*}
We prove that \(\Phi\) is continuous with respect to the hull-kernel topology, and that its restriction to primitive and prime ideals defines a homeomorphism onto dense subsets of the respective ideal spaces of \(V \otimes^{\mathrm{tmin}} B\). We prove that if \(\Phi = \Delta\), then \(\Phi\) induces a homeomorphism between the space of minimal primal ideals of \(V \otimes^{\mathrm{tmin}} B\) and the product of the spaces of minimal primal ideals of \(V \) and \(B\).

Mean Inequalities for Derivatives of the Generalised Exponential Integral Function

Rahamatu Iddi — 2025-09-16

In this paper, among other things, we establish arithmetic, geometric and harmonic mean inequalities for derivatives of the generalised exponential integral function. The methods of proof rely heavily on monotonicity properties of certain functions associated with the generalised exponential integral function. The results obtained generalise some existing results in the literature.

Analogies of Coding Systems of DNA and Elementary Particles

Ani Girgvliani — 2025-09-16

We suggest that physical reality can be described in the language of division algebras, which dictates that their symmetries must be manifested in the coding systems of different structures of nature. We compare the structures of DNA and fundamental fermions. In both cases we observe (3+4)-element divisions which may arise from the symmetries of the 8-dimensional normed split-algebra. The analogies between the genetic code (given by codons that contain three nucleotide bases) and the properties of the structures of all possible baryons (quark triplets) are discussed. In the genetic code we have the degeneracy of codons built by four standard nucleotides that specify 21 amino acids in humans. Similarly, there are 21 major types of baryons built by four lightest quarks with the degeneration of their spin values. These analogies can help to address some unsolved problems in genetics and physics, like the origin of codon degeneracy, the fermion generation problem and structure of atomic nuclei.

Common Fixed Points of Generalized Interpolative Kannan-Meir-Keeler Pair Contraction

Rohit Kumar Verma — 2025-09-16

In this paper, we introduce a generalized version of Meir-Keeler type contraction by incorporating interpolative conditions for a pair of mappings in metric spaces. We establish new common fixed point theorems that extend as well as unify several well-known results in the literature. Our findings generalize and enhance the recent results of Noorwali et al. [10].

Nazarov Uncertainty Principle for Certain Lie Groups

Piyush Bansal — 2025-09-16

Nazarov uncertainty principle is established for the Fourier transform and the continuous modulated shearlet transform on the groups of the form \(\mathbb{R}^n \times K\), where \(K\) is a locally compact group. As special cases, Nazarov uncertainty principle follows for the Gabor transform, the shearlet transform and the wavelet transform on these groups.