Open Journal of Mathematical Sciences (OMS)

This article proposes a new unit distribution based on the power-logarithmic scheme. The corresponding cumulative distribution function is defined by a special ratio of power and logarithmic functions that is dependent on one parameter. We show that this function benefits from great flexibility characterized by a large selection of convex and concave shapes. The other key functions are determined and studied. In particular, we show that the probability density function may take on different decreasing or U shapes, and the hazard rate function has a wide panel of U shapes. These functional capabilities are rare for a one-parameter unit distribution. In addition, we prove certain stochastic order results, provide the expression of the quantile function via the Lambert function, some interesting distributional results, and give simple expressions for the ordinary moments, mean, variance, skewness, kurtosis, moment generating function and incomplete moments. Subsequently, a basic statistical approach is described, to show how the new distribution can be applied in a data analysis scenario. Finally, complementary mathematical findings are presented, yielding new integrals linked to the Euler constant via some well-known moments properties.

We determine a radius of convergence for an efficient iterative method with frozen derivatives to solve Banach space defined equations. Our convergence analysis use \(\omega-\) continuity conditions only on the first derivative. Earlier studies have used hypotheses up to the seventh derivative, limiting the applicability of the method. Numerical examples complete the article.

In this paper, we aim to introduce a new notion of convex functions namely the harmonic \(s\)-type convex functions. The refinements of Ostrowski type inequality are investigated which are the generalized and extended variants of the previously known results for harmonic convex functions.

The present study proposes a generalized mean estimator for a sensitive variable using a non-sensitive auxiliary variable in the presence of measurement errors based on the Randomized Response Technique (RRT). Expressions for the bias and mean squared error for the proposed estimator are correctly derived up to the first order of approximation. Furthermore, the optimum conditions and minimum mean squared error for the proposed estimator are determined. The efficiency of the proposed estimator is studied both theoretically and numerically using simulated and real data sets. The numerical study reveals that the use of the Randomized Response Technique (RRT) in a survey contaminated with measurement errors increases the variances and mean squared errors of estimators of the finite population mean.

The generalized inverse Gaussian distribution converges in law to the inverse gamma or the gamma distribution under certain conditions on the parameters. It is the same for the Kummer’s distribution to the gamma or beta distribution. We provide explicit upper bounds for the total variation distance between such generalized inverse Gaussian distribution and its gamma or inverse gamma limit laws, on the one hand, and between Kummer’s distribution and its gamma or beta limit laws on the other hand.

In this article, we continue our research on quasi-ordered residuated systems introduced in 2018 by S. Bonzio and I. Chajda and various types of filters in them. Some fundamental properties of strong quasi-ordered residuated systems are given in this article. In addition, the concepts of prime and irreducible filters in such systems are introduced and analyzed.

Each \(p\)-ring class field \(K_f\) modulo a \(p\)-admissible conductor \(f\) over a quadratic base field \(K\) with \(p\)-ring class rank \(\varrho_f\) mod \(f\) is classified according to Galois cohomology and differential principal factorization type of all members of its associated heterogeneous multiplet \(\mathbf{M}(K_f)=\lbrack(N_{c,i})_{1\le i\le m(c)}\rbrack_{c\mid f}\) of dihedral fields \(N_{c,i}\) with various conductors \(c\mid f\) having \(p\)-multiplicities \(m(c)\) over \(K\) such that \(\sum_{c\mid f}\,m(c)=\frac{p^{\varrho_f}-1}{p-1}\). The advanced viewpoint of classifying the entire collection \(\mathbf{M}(K_f)\), instead of its individual members separately, admits considerably deeper insight into the class field theoretic structure of ring class fields. The actual construction of the multiplet \(\mathbf{M}(K_f)\) is enabled by exploiting the routines for abelian extensions in the computational algebra system Magma.

In the present work, we study the effect of time varying delay damping on the stability of a one-dimensional porous-viscoelastic system. We also illustrate our findings with some examples. The present work improve and generalize existing results in the literature.

None can underestimate the importance of mathematical modelling for their role in clarifying dynamics of epidemic diseases. They can project the progress of the disease and demonstrate the result of the epidemic to public health in order to take precautions. HIV attracts global attention due to rising death rates and economic burdens and many other consequences that it leaves behind. Up to date, there is no medicine and vaccine of HIV/AIDS but still many researches are conducted in order to see how to mitigate this epidemic and reduce the death rate or increase the life expectancy of those who are infected. A delayed HIV/AIDS treatment and vertical transmission model has been investigated. The model took into account both infected people from the symptomatics group and asymptomatic group to join AIDS group. We considered that a child can be infected from the mother to an embryo, fetus or childbirth. Those who are infected, it will take them some time to get mature and spread the disease. By using mathematical model, reproduction number, positivity, boundedness, and stability analysis were determined. The results showed that the model is much productive if time delay is considered.

Let \((a, b, c)\) be a primitive Pythagorean triple parameterized as \(a=u^2-v^2,\ b=2uv,\ c=u^2+v^2\), where \(u>v>0\) are co-prime and not of the same parity. In 1956, L. Jeśmanowicz conjectured that for any positive integer \(n\), the Diophantine equation \((an)^x+(bn)^y=(cn)^z\) has only the positive integer solution \((x,y,z)=(2,2,2)\). In this connection we call a positive integer solution \((x,y,z)\ne (2,2,2)\) with \(n>1\) exceptional. In 1999 M.-H. Le gave necessary conditions for the existence of exceptional solutions which were refined recently by H. Yang and R.-Q. Fu. In this paper we give a unified simple proof of the theorem of Le-Yang-Fu. Next we give necessary conditions for the existence of exceptional solutions in the case \(v=2,\ u\) is an odd prime. As an application we show the truth of the Jeśmanowicz conjecture for all prime values \(u < 100\).