Annals of Communications in Mathematics

Abstract.  This paper studies integral inequalities involving a function and its derivative, aiming to establish sharp lower bounds under general assumptions. The analysis employs  elementary techniques, yielding clear and transparent results. Several examples illustrate the effectiveness of the inequalities, with particular attention to applications involving the sine integral.

Abstract.  In this paper we introduce a new orbit-based contractive framework in the setting of G-metric spaces, called (m, α) G-path-averaged (G-PA) contractions with m ≥2. This notion extends Fabiano’s path-averaged contractions to the triadic geometry of Mustafa–Sims G-metrics and is designed to avoid collapse to pointwise contractility. For a G-continuous self-map on a complete G-metric space, we establish existence and uniqueness of a fixed point and prove that the Picard iteration converges to it in the sense of G-convergence. Moreover, we derive explicit quantitative estimates, including a posteriori and a priori geometric error bounds for the iterates. We also relate the new class to the induced metric dG, showing that every G-PA contraction yields a path-averaged contraction on (X, dG), and we provide examples demonstrating that the G-PA class can be strictly larger than the Banach-type contraction class. Finally, we obtain multi-step (t-point) fixed point and convergence results by embedding the recursion into a shift map on the product space (Xt , Gt) and applying the single-valued theory.

Abstract.  In 1969, two missionary nurses died due to Lassa fever infection, which led to the identification of the Lassa virus (LASV) in Nigeria. Infections from the Lassa virus are about 80% asymptomatic, but severe cases normally result in multi-organ failure or death. This accounts for about 15% of the hospitalized cases. Different scientific strategies to eradicate the disease have yielded minimal results. In this study, a mathematical model to study the transmission dynamics of Lassa fever is formulated and analyzed. The model has five compartments. The human population is compartmentalized into three sub-populations, while the rodent population is compartmentalized into two sub-populations. The model has two equilibrium states, namely, the disease-free equilibrium (DFE) and the disease endemic equilibrium (DEE). The stability analysis of the DFE revealed that it is locally asymptotically stable when the basic reproduction number (R0) is less than one and unstable otherwise. The sensitivity analysis on the model reproduction number revealed that the infection transmission rates from human-to-human, rodent-to-human, and from human-to-rodent are the causes of the disease persistence in the human population. The Hopf-bifurcation analysis of the model using the transmission rate from both rodents and humans to humans as the bifurcation parameter shows the stability point of the model at αh = 0.025. The numerical analysis result perfectly aligns with the model’s qualitative results obtained.

Abstract.  An injective function f : V (G) → {l1, l2, . . . , ln}, where lj is the jth Lucas number (j = 1, 2, . . . , n) is said to be Lucas product cordial labeling if the induced function f∗ : E(G) → {0, 1} defined by f ∗(uv) = (f(u)f(v)) (mod 2) satisfies the condition |ef∗ (0) − ef∗ (1)| ≤ 1. A graph which admits Lucas product cordial labeling is called Lucas product cordial graph. In this paper, we determined the Lucas Product Cordial Labeling of Quadrilateral Snake Graph Qn, Cycle Quadrilateral Snake Graph CQn, and Alternate Triangular Snake Graph A(Tn).

Abstract.  Hop domination was introduced as a distance-two analogue of domination and has been studied extensively in recent years. A secure hop dominating set, recently introduced, models a single adversarial attack at an unoccupied vertex (a vertex not in the current guard set) that can be defended by relocating one guard at distance two while preserving hop domination. Motivated by finite-order (multi-step) protection in classical secure domination, we introduce t-secure hop dominating sets (t ∈ N0), in which an adversary may launch a sequence of at most t attacks, each at a currently unoccupied vertex, and the defender responds by sequentially relocating one guard at distance two after each attack while maintaining hop domination throughout. Our main contribution is an exact correspondence: t-secure hop domination in a graph G is equivalent to smart t-secure domination in the hop graph H(G). This yields structural properties (monotonicity and additivity over components) and exact values for several graph families, including complete multipartite graphs, stars, paths, and cycles. In particular, we obtain closed formulas for γsh,t(Pn) and γsh,t(Cn) for all t ∈ N0, with explicit small-n exceptions in the cycle case.

Abstract.  Let WM be the wheel graph on M ≥ 4 vertices and let Kn be the independent graph on n ≥ 1 vertices. We study the corona product WM ◦ Kn and obtain an explicit formula for its pendant domination polynomial. The computation starts from the domination polynomial and subtracts a correction term that counts dominating sets whose induced subgraph contains no vertex of degree 1. For the wheel, the correction term reduces to counting subsets of the rim cycle for which the selected rim vertices are not isolated on the rim. We also determine the pendant domination number for this family.

Abstract.  Let G be the a graph. An Edouard Product Cordial Labeling (EPCL) of a graph G with |V (G)| = n is an injective function f : V (G) → {E0, E1, E2, . . . , En−1} where Ei is the ith Edouard number (i = 0, 1, 2, 3, . . . , n) that induced a function f∗ defined by f∗(uv) = (f(u)f(v)) (mod 2) for all edge e = uv such that |e∗f(0) − e∗f(1)| ≤ 1 where e∗f(0) is the number of verticeslabeled with 0 and e∗f(1) is the number of vertices labeled with 1. The graph that satisfies the condition of a edouard product cordial labeling is called an edouard product cordial graph (EPCG).

ABSTRACT. In this paper, we analyze a vector-host epidemic model with a piecewise smooth treatment rate. The use of piecewise-smooth treatment depicts the limited medical resource situation in the community. The treatment increases linearly with infective population until the treatment capacity is reached, after which constant treatment(i.e maximum treatment) is applied. The analysis indicates that there exists a critical value Ich0 = bhμh for the infective human population level Ih0 at which the health care system reaches its capacity. We derive that when Ih0 → Ich0, the namics of the model is completely determined by the basic reproduction number R0. When Ih0 < Ich0, the model exhibits multiple endemic equilibria.

ABSTRACT. This study introduces a new probability distribution called the Cosine Exponential (CEX) Distribution, which combines the Cosine-G family of distributions with the Exponential distribution as the baseline model to create a more adaptable model. The aim is to improve modeling capabilities across various statistical applications. The paper presents expression of the density and distribution functions of the CEX model and investigates its key properties such as survival and hazard rate functions, reverse hazard function, cumulative hazard function, quantile function, moments, and moment generating function. It also outlines the methodology for estimating model parameters using maximum likelihood estimation. Through application to real datasets, the effectiveness of the proposed CEX distribution is demonstrated, showing significant enhancements over existing models.This paper highlights the potential of the CEX distribution as a robust tool for statistical modeling and analysis.