Annals of Communications in Mathematics

AbstractWith the advancement of scientific studies, problems involving uncertainty have emerged. Classical mathematics needed to be more robust to model or make sense of these uncertain problems. Due to this insufficiency, scientists have put forward new theories. One of them is the soft set theory, which Molodtsov first studied. Then, many researchers have done various studies in different fields using soft sets. In this study, bipolar soft ideals of a gamma near-ring were defined. Some basic properties of this algebraic structure have been analyzed. The bipolar soft coset set was determined with the help of bipolar soft ideals, and this set was shown to be a gamma near-ring. Finally, a function was defined with the help of bipolar soft ideals of a gamma near-ring, and this study concluded by showing that this function is a gamma near-ring epimorphism.

Abstractn this article, we revisit a well-known result from the literature that can be considered a variant of the Hardy integral inequality. First, we present a counterexample to demonstrate the invalidity of the current formulation. We then revise the result by identifying and addressing a gap in the original proof. Finally, as an additional contribution, we derive a new integral inequality.

Abstractn this article, we revisit a well-known result from the literature that can be considered a variant of the Hardy integral inequality. First, we present a counterexample to demonstrate the invalidity of the current formulation. We then revise the result by identifying and addressing a gap in the original proof. Finally, as an additional contribution, we derive a new integral inequality.

AbstractIn this paper, we introduce the notion of a fuzzy weak interior ideal as a generalization of a fuzzy ideal of a semiring. We characterize the regular semiring in terms of fuzzy weak interior ideals of a semiring.

AbstractThe notion of AB-algebras was introduced in 2017 by Hameed and Abbas. Subsequently, this class of algebras was the subject of study by several authors. In this paper, in addition to giving an overview of some of the results and assertions about this class of logical algebras, we comment on a significant number of demonstrations of these assertions, and also state several new assertions and demonstrate their proofs.

AbstractThis paper establishes a k-analogue of the lambda gamma function and in troduces a k-Riemann zeta function and a k-lambda Riemann zeta function. In addition, the paper establishes a relationship between the k-analogue of the lambda gamma function, the k-Riemann zeta function and the k-lambda Riemann zeta function. Finally, the paper establishes some properties of the k-analogue of the lambda gamma function similar to existing properties satisfied by the classical gamma function, the k-analogue of the gamma function and the lambda gamma function.

AbstractIn this paper, we define α-Product Soft Matrices which generalize the Product Soft Matrices. Further, we also provide a decision theory using these α-Product Soft Matrices. As a practical application, we formulate a novel approach to environmental toxicology by modeling multi-layered chemical interactions in aquatic ecosystems.

AbstractIn this work are studied in detail the multivariate symmetrized and perturbed hyperbolic tangent activated convolution type operators of three kinds. Here this is done with the method of positive linear operators. Their alternative approximation properties are established by the quantitative convergence to the unit operator using the modulus of continuity. It is also studied the related multivariate simultaneous approximation, as well as the multivariate iterated approximation.

AbstractHardy-Hilbert-type integral inequalities lie at the heart of mathematical analysis. They have been the subject of much research. In this article, we make a contribution to the field by examining two new two-parameter modifications of the classical Hardy-Hilbert integral inequality. We derive the closed-form expression of the optimal constant for each modification. We also present supplementary results, including one-function and primitive variants. All proofs are provided in full, with each step justified, to ensure the article is self-contained.

AbstractProbability distributions are essential for modeling and analyzing complex datasets across various scientific disciplines. However, classical distributions often fail to capture intricate features such as skewness, heavy tails, or high variability observed in real-world data. To address these limitations, this study proposes the Sine Type II Topp-Leone Gompertz (STIITLG) distribution, a novel extension of the Gompertz model based on the sine type II Topp-Leone family. The proposed model enhances the flexibility of the classical Gompertz distribution by incorporating an additional shape parameter, enabling it to better accommodate diverse data behaviors. Several key properties of the model, including moments, inverse moment, mean residual life function, entropy, and order statistics, were derived to establish its theoretical foundation. The model parameters were estimated using the maximum likelihood estimation method, and a comprehensive simulation study confirmed the consistency of these estimators. The practical utility of the model was demonstrated by applying it to two real-life datasets, where it outperformed several existing models based on goodness-of-fit criteria. These findings underscore the potential of the proposed distribution as a robust tool for modeling complex phenomena in diverse fields.

AbstractThis short communication proposes a novel Iterated Function System (IFS) to construct the Jerusalem square fractal, a two-dimensional projection of the Jerusalem cube, characterized by its cross-like self-similar structure. We provide a step-by-step con- struction, a proof of its fractal nature, and Python code for visualization. Properties such as self-similarity, fractal dimension, and connectivity are analyzed with formal proofs. The IFS offers a new perspective on Jerusalem square fractal generation. Results demonstrate the fractal’s intricate geometry, with applications in computer graphics and geometric mod- eling.

AbstractWe provide a proof of the theorem that, assuming Zorn’s lemma, two Hamel bases of a vector space have equal cardinality.

AbstractIn this paper, we obtain some results on infinite products in bi-complex space, and the exact order of simultaneous results with quantitative estimate for the bi- complex gamma functions and bi-complex Beta functions. Finally using the specific re- sults of complex gamma operator and complex beta operator we introduce the bi-complex gamma functions and bi-complex beta operators and obtain some results.

AbstractThis study presents two mathematical models to improve understanding of cytokine-mediated effects on abortive HIV-1 infection. The models describe interactions among healthy CD4+ T cells, abortively and actively HIV-1-infected CD4+ T cells, in- flammatory cytokines, and free HIV-1 particles. In the second model, four types of dis- tributed time delays are incorporated. The biological feasibility of the models is established by demonstrating the non-negativity and boundedness of solutions. Two equilibrium points are identified, and their existence and stability are characterized in terms of the basic repro- duction number ℜ0. The global stability of the equilibria is analyzed using the Lyapunov method. Numerical simulations support the analytical results. Sensitivity analysis is con- ducted to identify key parameters influencing ℜ0. The impact of time delays on HIV-1 progression is also examined. The findings suggest that longer delays can significantly reduce ℜ0, potentially suppressing HIV-1 replication.