Earthline Journal of Mathematical Sciences

On Quasi-Generalized ϕ-recurrent Para-Kenmotsu Manifolds

2026-07-23T16:12:18+00:00

The object of this paper is to study and reveal the various geometric properties of quasi-generalized $\phi-$recurrent (briefly, $\mathcal{QG}(\phi \mathcal{K}_{2n+1})$) para-Kenmotsu manifold. Among the results established here it is shown that a $\mathcal{QG}(\phi \mathcal{K}_{2n+1})$ para-Kenmotsu manifold is an Einstein manifold. Moreover, we prove that a Ricci soliton in a $\mathcal{QG}(\phi \mathcal{K}_{2n+1})$ para-Kenmotsu manifold is an expanding. Further, we study quasi-generalized $\mathcal{T}-\phi-$recurrent para-Kenmotsu manifold and obtain the results which reveal the nature of its associated 1-forms.

An Exponential-logarithmic Maximum Hardy-Hilbert-type Integral Inequality

2026-07-24T02:28:40+00:00

This paper introduces a new variant of the Hardy-Hilbert integral inequality, referred to as an exponential-logarithmic maximum Hardy-Hilbert-type integral inequality. Using this result, we establish an additional related inequality. For completeness and accessibility, the paper is self-contained, and all proofs are provided in detail.

Geometric Quantization of Coadjoint Superorbits and Schrödinger-Fock Representations of the Heisenberg Supergroup

2026-07-24T15:13:58+00:00

In the framework of Kirillov's orbit method for nilpotent supergroups, coadjoint superorbits of the Heisenberg supergroup naturally carry supersymplectic structures arising from the Kirillov-Kostant-Souriau form. Their geometric quantizationprovides a geometric realization of the irreducible unitary representations of the Heisenberg supergroup. In particular, after choosing an appropriate polarization, the resulting quantumstate space is identified with $L^2(\mathbb R^m)\otimes \Lambda^\bullet(\mathbb C^n),$ combining the bosonic Schrödinger representation with the fermionic Fock representation. Thus $\mathfrak h^{m|n}$ provides the simplest geometric model combining bosonic and fermionic quantization. The bosonic sector reproduces the canonical commutation relations, while the fermionic sector generates a Clifford algebra through anticommutation relations. This construction shows that Schrödinger-Fock representations arise naturally as the geometric quantization of coadjoint superorbits, thereby providing a deep connection between supergeometry, supersymplectic structures, and the representation theory of nilpotent supergroup. We begin by explicit calculations for the case $m=n=1$ and generalize to the arbitrary values of $m$ and $n$.

Some New Young-type Integral Inequalities

2026-07-27T16:52:01+00:00

In this article, we present new forms of Young-type integral inequalities. Some of these extend the classical Young integral inequality by including a function and its inverse, while others introduce a function and its ratio transformation or derivative. The proofs of the main results are based on the standard Young product inequality and well-calibrated analytical tools, such as the Chasles integral formula and the Cauchy-Schwarz integral inequality, as well as changes of variables. Several inequalities also address the case where the main function is decreasing, thus expanding the traditional framework, which assumes an increasing function. In particular, the decreasing case leads to elegant formulations. Some theoretical aspects are illustrated with examples.

Geometric Attributes of Normalized Seven-Parameters Mittag-Leffler Function in the Unit Disk

2026-07-28T15:20:53+00:00

This paper dedicated to suggest a normalization of the seven-parameter Mittag-Leffler function, then assume sufficient conditions to investigates certain essential geometric properties, such as starlikness, convexity and closed-to-convexity on the unit disk. In addition, it constructs specific relations involving that normalization to look into how it belong to a developed class of normalized univalent function.

Almost Polynomial Contraction Mapping Theorem in Metric Spaces

2026-08-02T06:58:32+00:00

In this paper, we introduce the notion of an almost polynomial type contraction mapping operator and obtain a fixed point theorem for such mappings in the setting of metric spaces. Some consequences of the main result and a conjecture are stated. We show that the conjecture may be true by illustrating it with an example.

On Rational Contractions and Fixed Points in m-Hemi-Metric Spaces

2026-08-03T02:16:47+00:00

In this paper, we investigate rational contraction mappings in the setting of m-hemi-metric spaces. Unlike the classical rational contractions formulated in metric, G-metric, and b-metric spaces, the proposed contractive condition is established directly within the framework of m-hemi-metrics by exploiting their multi-point distance structure. Under this nonlinear rational contractive condition, we prove an existence and uniqueness theorem for fixed points in h-complete m-hemi-metric spaces. Several examples are presented to illustrate the applicability of the proposed contraction. As an application, we establish the existence and uniqueness of continuous solutions for a class of nonlinear Fredholm integral equations by means of the obtained fixed point theorem. The results extend Banach-type fixed point theory to the setting of m-hemi-metric spaces and contribute to the study of nonlinear problems in generalized distance spaces.

Adaptive and Fault-Tolerant RNS-AEAD Cryptosystem with Optimized CRT Reconstruction Using ChaCha20-Poly1305 for High-Performance Secure Communication

2026-08-03T13:45:45+00:00

In the cloud computing, Internet of Things (IoT), and edge computing scenarios, modern cryptographic systems need to meet four conflicting requirements: Robust security assurances, Low compute latency, Built-in data parallelism, and Fault tolerance. This paper proposes an Adaptive Fault-Tolerant RNS-AEAD cryptosystem that meets all four requirements. The proposed framework combines an adaptive coprime modulus set $ M = \{2^k, 2^k - 1, 2^k + 1, p_r\} $, RRNS-based fault detection and correction, efficient CRT reconstruction using precomputed constants, and ChaCha20-Poly1305 AEAD encryption to achieve secure, reliable, and computationally efficient residue-domain processing. Encryption time: 0.042--0.050 ms (4–15 ASCII char plaintexts, 100 iterations, IQR filtered). Decryption time: 0.057--0.068 ms (4–15 ASCII char plaintexts, 100 iterations, IQR filtered). Experimental evaluation shows significant improvement in performance over the prevailing hybrid and conventional cryptographic approaches. The average entropy of the ciphertext is 4.985 bits/byte (62.3\% of the maximum of 8 bits/byte), uniqueness of nonces and authentication-tags are 100\%, fault-detection rate of the RRNS layer is 99.63\% (P(\text{miss}) = 1/269), and chi-square randomness testing passes at the 95\% confidence level. The IND-CPA and INT-CTXT guarantees are proven in a formal way, assuming standard conditions. The results show the proposed framework to be a practical, scalable, and theoretically sound solution for latency-critical secure communication in next-generation distributed environments.

On Some New Inequalities for a Specific Class of Functions

2026-08-07T16:23:36+00:00

This paper introduces a new class of functions motivated by a symmetry-type inequality satisfied by convex functions. By incorporating a real parameter, this class extends traditional convexity to accommodate more general functional behaviors while preserving useful structural properties. Several propositions are established, including new functional and integral inequalities inspired by classical results, such as the Hermite-Hadamard and Fejér integral inequalities. The paper concludes with perspectives for future research.

A Relationship Between the Ahmed Integral and the Lee Integral

2026-08-07T15:40:39+00:00

This note clearly establishes the relationship between two challenging integrals: the Ahmed integral and the Lee integral. We thus contribute to a deeper understanding of complex integral situations.

Almost Path-Averaged Polynomial Contractions: A New Generalization of Almost Polynomial Contractions, Almost Contractions, and Almost Path-Averaged Contractions

2026-08-07T15:59:10+00:00

In this paper, we combine the notions of polynomial contractions [3], path-averaged contractions which appeared in [5] for metric spaces, in [6, 7] for b-metric spaces, in [8] in suprametric spaces, while their combined notion appeared in [9], and almost contractions [2], to introduce almost path-averaged polynomial contractions. We obtain a fixed point theorem for such contractions in the setting of metric spaces. Finally, we give an example showing that almost path-averaged polynomial contractions are not Banach contractions.

Parameter Dependent Refinements for the Sinc Hyperbolic Function and Applications

2026-08-10T17:18:13+00:00

In this paper, we prove for \ $x \in (0,\infty)$ the double inequality for the Sinc hyperbolic function
$$\left( -2\, \left( {\frac {\tanh x }{x}} \right) ^{-\frac{ r}{2}}+3\, \left( \cosh x \right) ^{\frac{ r}{3}} \right) ^{\frac{1}{r}}
< \ {\frac {\sinh x }{x}}\ <\ \cosh x \left( \frac{2}{3} \left( {\frac {\tanh x }{x}} \right) ^{\frac{3}{2}
\,r}+\frac{1}{3} \right) ^{\frac{1}{r}}.$$ Both bounds converge to \ ${\frac {\sinh x }{x}}$ \ as $r$ approaches zero from the right.

Similar double inequalities are provided for the Huygens and the Wilker functions as well as for the Lazarewi\'c function.

A Semi-Markov Model for the Analysis of Crude Oil Spills in Niger Delta Region, Nigeria

2026-08-11T16:50:50+00:00

This paper developed a three-state Semi-Markov model with Weibull waiting time distribution to analyse crude oil spill occurrences in the Niger Delta region of Nigeria. Oil spills were categorized into minor, medium, and major categories based on the volume of spill. An empirical data from the National Oil Spill Detection and Response Agency (NOSDRA), Nigeria from January, 2006 to March, 2020 with particular consideration of crude oil spill incidences due to CHEVRON Nigeria Ltd and Nigeria Agip Oil Company (NAOC) was used in the analysis. In the case of NAOC, the stationary distribution of the Semi-Markov process was obtained as 0.6954, 0.2461 and 0.0585 for minor, medium and major oil spills respectively, with corresponding mean waiting times before transition of 2.5438, 2.7429 and 3.6204 days. For CHEVRON Nigeria Ltd, the stationary distribution of the Semi-Markov process was found to be 0.9373, 0.0393 and 0.0234 for minor, medium and major oil spills respectively with corresponding mean waiting times of 6.4609, 6.0408 and 8.7861 days. Further results reveal that crude oil spills due to NAOC occurred once in every 3 days while that of CHEVRON Nigeria Ltd was once in every 6 days. The study recommends further investigation on the associated risk factors to oil spills of all categories in the Niger Delta region.