Research Article
An Innovative Result on the Radius of Convexity and Uniform Convexity of Normalised Bessel Function
Natarajan Saraswathi*
,
Murugesan Kasthuri
Issue:
Volume 14, Issue 3, June 2026
Pages:
115-119
Received:
4 April 2026
Accepted:
20 April 2026
Published:
30 April 2026
Abstract: This paper investigates the geometric properties of normalised Bessel functions of the first kind, focusing on the radii of convexity and uniform convexity. Using analytic techniques such as logarithmic differentiation and properties of zeros of the Bessel function. Additionally, we provide new proofs related to the order convexity and compare our results with existing results to reveal interesting relationships, and we provide a graphical interpretation that supports the analytical findings.
Abstract: This paper investigates the geometric properties of normalised Bessel functions of the first kind, focusing on the radii of convexity and uniform convexity. Using analytic techniques such as logarithmic differentiation and properties of zeros of the Bessel function. Additionally, we provide new proofs related to the order convexity and compare our ...
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Research Article
Zia Theory of Temporal Reality (ZTTR): A Unified Deterministic–Probabilistic Model of Time and Reality
Md. Ziaur Rahman*
Issue:
Volume 14, Issue 3, June 2026
Pages:
120-128
Received:
18 April 2026
Accepted:
3 May 2026
Published:
18 May 2026
DOI:
10.11648/j.ajam.20261403.12
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Views:
Abstract: Time and reality are central concepts in both philosophy and physics. While classical mechanics describes the universe as deterministic, where the present emerges from past conditions, quantum theory introduces probabilistic interpretations suggesting inherent uncertainty at microscopic scales. These two perspectives have led to an ongoing debate regarding whether reality is fundamentally deterministic, probabilistic, or a combination of both. The Zia Theory of Temporal Reality (ZTTR) integrates these frameworks by proposing that the present state of reality is determined by accumulated past causes, while the future evolves probabilistically under uncertainty. To formalize this concept, the Zia Unified Continuity Equation (ZUCE) is expressed as a stochastic model where the state of reality represents a combination of initial conditions, integrated causal influences, and stochastic fluctuations represented by a Wiener process. To enhance generality and address limitations of fixed functional assumptions, the uncertainty term is further extended as a generalized function, allowing different forms such as diffusion-like, logarithmic, or nonlinear growth depending on system dynamics. In this framework, deterministic causal accumulation represents the structured continuity of past influences, while the stochastic component reflects uncertainty arising from complexity, interaction, and incomplete knowledge of system variables. This interpretation aligns with developments in statistical mechanics, information theory, and complex systems research. The applicability of the model is illustrated through conceptual and numerical examples drawn from physical processes, biological systems, and learning dynamics. These examples demonstrate that deterministic historical structures and stochastic variations can coexist within a single temporal framework. The Zia Theory of Temporal Reality thus provides a generalized and mathematically consistent perspective on temporal evolution and contributes to interdisciplinary research in physics, complexity science, and artificial intelligence.
Abstract: Time and reality are central concepts in both philosophy and physics. While classical mechanics describes the universe as deterministic, where the present emerges from past conditions, quantum theory introduces probabilistic interpretations suggesting inherent uncertainty at microscopic scales. These two perspectives have led to an ongoing debate r...
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