Jordan Journal of Mathematics and Statistics

Solutions of the equation d (kn) = ϕ (ϕ (n))

Amroune Zahra — 2024-10-29

Let d(n) and ϕ (n) denote the number of positive integers dividing the positive integer n and the Euler’s phi function
representing the numbers less than and prime to n, respectively. In this paper, we determine all solutions of the equation d(n) = ϕ (ϕ (n))
and we prove that the equation d(kn) = ϕ (ϕ (n)) has a finite number of solutions for any k ≥ 1. Further, we characterize all solutions
of the last equation when k is prime.

Two-Parameter Exponential Distribution with Randomly Censored and Outlier Data

Parviz Nasiri — 2024-10-29

The two-parameter exponential distribution is an important statistical distribution, widely used in medicine, engineering,
economics, demography, and longevity data. In the present work, the two-parameter exponential distribution under random censoring
with the presence of outlier data is presented, and its parameters are estimated using the moment, maximum likelihood, and Bayesian
methods. In parameter estimation, using maximum likelihood estimators, asymptotic confidence intervals are determined; while, by
considering appropriate prior distributions, Bayesian estimation under squared error and LINEX loss functions is presented for the
parameters. Next, using simulation, the estimators are compared by using statistical measures. Finally, utilizing a real data set, the
suitability of the fitness of the model is evaluated according to different estimation methods.

Examination of the geodesic curvatures and geodesic torsions of the transversal intersection curve in E^n

Bedia Merih ¨ OZC¸ ETIN — 2024-10-29

This study aims to compute all geodesic curvatures and geodesic torsions of an implicit curve in Euclidean n-space. Since
an implicit curve is determined by the intersection of (n − 1) implicit hypersurfaces in E^n, the results obtained in this paper complete
the lacking curvatures for a transversal intersection curve. As a result, the approach proposed in the paper can be viewed as a partial
solution to the open problem that Goldman identified in 2005. An algorithm has been proposed to handle the difficulty of calculating
geodesic curvatures and geodesic torsions in spaces of higher dimensions. Then, an computational algorithms produced by MATLAB
are utilized to display the outcomes in the form of illustrative examples.

Explicit formulas for flux surfaces and scalar flux functions according to Killing magnetic vectors in SL(2, R)

Noria BEKKOUCHE — 2024-10-29

In this paper, we determine flux surfaces according to Killing magnetic vectors and its associate scalar flux functions in
3-dimensional Riemannian space SL(2, R). We give for each parametric flux surface an example and its graphical representations in
Euclidean 3-space.

Frames as Operator Orbits for Quaternionic Hilbert spaces

Ruchi Bhardwaj — 2024-10-29

In this paper, we study frames which can be expressed as operator orbits {T^n(φ )}n∈Zunder a single generator φ and an operator T on a right quaternionic Hilbert space H and prove a necessary and sufficient condition under which the sequence {hn}n∈Z is expressible as orbit of some operator T . Also, a necessary condition for a frame {hn}n∈Z to have an operator orbit representation
{hn}n∈Z = {T^n(h0)}n∈Z using a bounded operator T is given. Further, a characterization for the boundedness of the operator T ,
given that {hn}n∈Z = {T^n(h0)}n∈Z forms a frame is obtained. Moreover, it is proved that a redundant frame with finite excess can
never be expressed as an orbit of a bounded operator whereas for a Riesz sequence an operator orbit representation with a bounded
operator is always possible. Furthermore, we discuss the stability of frames that can be expressed as an orbit of some operator and
prove that it remains undisturbed under some perturbation conditions. Finally as an application, we approximate frames that cannot be expressed as operator orbit using the sub-orbit representation of hypercyclic operators.

Bijective Product and Product Square k-Cordial Labeling of Graphs

W.C. Shiu — 2024-10-29

In this paper, we introduce two new concepts namely bijective product k-cordial labeling and bijective product square kcordial labeling and show that some standard graphs admit bijective product k-cordial labeling, where k = 2, 3. Also, we establish that
the path, cycle, flower, helm and gear graphs are bijective product square 3-cordial graphs.

PERISTALSIS OF ELECTRO-OSMOTIC JEFFREY FLUID IN THE PRESENCE OF THERMAL RADIATION AND HEAT TRANSFER WITH THE PERMEABLE WALL

MAHADEV M CHANNAKOTE — 2024-10-29

The electro kinetic movement of fluids through microchannel and micro-peristaltic transport has raised concerns in the field
of improved medical technology and various areas of biomedical science. In light of this, the electro-osmotic impact on the peristaltic
flow of a Jeffrey fluid (ionic solution) in a microchannel with a permeable wall is investigated. To analytically solve the governing
equations of the modulated problem, we make the assumptions of a long wavelength (δ ≤ 0) and a low Reynolds number(Re → 0).
The modelling also includes an analysis of the impacts of thermal radiation and heat transfer. In order to investigate the electro-kinetic
mechanism, the Poisson-Boltzmann equation is analyzed, taking into account the zeta potential. The obtained set of dimensionless
expressions is solved using Mathematica software. The effects of various parameters on flow deliveries are confirmed through plots. The analysis presented here may be helpful in examining the features of bio fluids and can initiate their movement through the application of an external electric field. The main findings demonstrate that electro osmosis plays a key role in regulating heat transfer as well as flow. Furthermore, this study holds potential implications across various disciplines including design, hematology, electrophoresis, and the enhancement of bio-mimetic electro-osmotic pumps

Existence and Uniqueness of Weak Solutions and Error Analysis of the Galerkin Finite Element Method for Time-Dependent Convective Nanofluid Poiseuille Flow Problems

Andrew O. McCartney — 2024-10-29

A finite element analysis of the plane Poiseuille nanofluid flow and heat transfer based on the time-dependent Buongiorno
model equations is performed. A suitable weak formulation of the sequentially-linearized governing equations is first constructed.
Then, the spatial discretization of the weak form is done using the Galerkin finite element formulation, while a Backward-Euler finite
difference scheme is used for the temporal discretization. Existence, uniqueness, and stability of the weak, semi-discrete and fullydiscrete forms are discussed. Furthermore, L^2-error estimates for the semi-discrete and fully-discrete forms are obtained. Moreover,numerical computations are performed to verify the theoretical results and estimate the rate of convergence.

Applicability of Petryshyn’s Fixed Point Theorem on the Existence of a Solution to Weakly Singular Integral Equations

H. R. Sahebi — 2024-10-29

Various approach have been introduced for the existence of solutions for integral equations but, for the most part, researchers
have deal with the Darbo fixed point theorem as an extension of Schauder theorem. Under certain hypotheses, we establish the existenceof solution for weakly singular integral equations by employing the generalization of Darbos fixed point theorem and measures of noncompactness in Banach space. Finally, some examples are given and with the help of MATLAB R2018a parameters is finding.

Sine exponential pareto distribution: properties, estimation, and applications

Doaa abd Khalil ELhertaniy — 2024-10-29

The work of the Sine-G distribution family is extended in this paper. The applicability of the sine exponential Pareto distribution is highlighted via the goodness-of-fit approach to data. Various properties of the suggested distribution, including moments, quantiles, entropy, and order statistics are acquired. For model parameters estimation, the maximum likelihood technique is used. Four extensive data sets are empirically used to demonstrate the potential significance and applicability of the proposed distribution. The results of the investigation indicated that the Sine Exponential Pareto distribution was superior than numerous other competing distributions.

Variable Fluid Properties and Partial Slip Effect of MHD Flow of Nanofluids over a permeable Stretching Sheet with Heat Radiation and Viscous Dissipation

Khaled K. Jaber — 2024-10-29

The simultaneous effects of variable fluid properties and velocity slip on a nanofluid flow over a continuously stretching
semi-infinite horizontal sheet are investigated. The contribution of thermal radiation term is taken into account in the temperature
equation. Viscous dissipation, Brownian motion and thermophoresis effects are taking into account. The flow is subjected to a
transverse uniform magnetic field. Thermal conductivity and fluid viscosity are assumed to related linearly and inversely linear with
temperature, respectively. The system of equations governed the problem is transformed into a dimensionless system of ordinary
differential equations. This system is solved using shooting technique in conjunction with Rung-Kuta method. Convergence of the
obtained solutions is examined. It is found that the velocity improved due to increasing θr, whereas increasing tv yields to decrease the
velocity. Increasing volume fraction parameter ϕ and nanolayer thickness tv tend to reduce the temperature. We discuss in detail the
effect of involved parameters on the velocity, temperature, and concentration profiles. In addition, we provide discussions and
tabulated data on skin friction, Nusselt number, and Sherwood numbers.