Open Access Short Research Article

Zhao Yu- Ping, Fu Hua

In this paper, we consider the following higher-order nonlinear neutral differential equations: dn dtn [x(t) + cx(t - τ)] + (-1)n+1[P(t)f1 (x(t - σ)) - Q(t)f2 (x(t - δ))] = 0; t ≥ t0 where τ; σ; δ ∈ R+, c ∈ R; c ̸= ±1, and P(t); Q(t) ∈ C([t0; ∞); R+), fi(u) ∈ C(R; R), ufi(u) > 0. we obtain the results which are some sufficient conditions for existence of nonoscillation solutions, special case of the equation has also been studied.

Open Access Original Research Article

Gianni Bosi, Chiaramaria Panozzo, Magal`ı Ernestine Zuanon

We characterize the fuzzy T0 - Alexandrov topologies on a crisp set X, which are associated to fuzzy interval orders R on X. In this way, we generalize a well known result by Rabinovitch (1978), according to which a crisp partial order is a crisp interval order if and only if the family of all the strict upper sections of the partial order is nested.

Open Access Original Research Article

Abikesh Prasada Kumar Mahapatra, Anita Nanda, Bibhuti Bhusan Mohapatra, Archana Kumari Padhy, Indira Padhy

Collection of data and to check its suitability is the first step in any statistical data analysis. In such analyses, the presence of outliers appears as an unavoidable important problem. Outliers are unexpected random values in dataset, and they can alter the statistical conclusion and also affect their assumptions. Thus, in order to manage the data properly, outliers must be defined and treated. So all statisticians have to confront the analysis and forced to take a decision. There is only being one of the two extreme choices left for the researcher or statistician during the analysis of outliers. First, either to reject the outlier with the risk of loss of genuine information and the second one is to include them with the risk of error in drawing conclusion. The study therefore summarize the various potential causes of extreme scores in a data set (e.g., data recording or entry errors, sampling errors, and legitimate sampling), how to detect them, and whether they should be removed or not. Another objective of this study was to explore how significantly a small proportion of outliers can affect even simple analyses. The study was explored with citing suitable examples including outlier value and also excluding the outlier data. The examples show a strong beneficial effect of repetition of the study based on extreme of scores. One way ANOVA test was performed and the significance of extreme outlier was described.

Open Access Original Research Article

Y¨uksel Soykan

In this paper, we define the binomial transform of the generalized Tribonacci sequence and as special cases, the binomial transform of the Tribonacci, Tribonacci-Lucas, Tribonacci-Perrin, modified Tribonacci, modified Tribonacci-Lucas and adjusted Tribonacci-Lucas sequences will be introduced. We investigate their properties in details. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these binomial transforms. Moreover, we give some identities and matrices related with these binomial transforms.

Open Access Original Research Article

Jenica Cringanu

The purpose of this paper is to show the existence results for the following abstract equation Jpu = Nfu,

where Jp is the duality application on a real reflexive and smooth X Banach space, that corresponds to the gauge function φ(t) = tp-1, 1 < p < ∞. We assume that X is compactly imbedded in Lq(Ω), where Ω is a bounded domain in RN, N ≥ 2, 1 < q < p∗, p∗ is the Sobolev conjugate exponent.

Nf : Lq(Ω) → Lq′(Ω), 1/q + 1/q′ = 1, is the Nemytskii operator that Caratheodory function generated by a f : Ω × R → R which satisfies some growth conditions. We use topological methods (via Leray-Schauder degree), critical points methods (the Mountain Pass theorem) and a direct variational method to prove the existence of the solutions for the equation Jpu = Nfu.

Open Access Original Research Article

Devendra Kumar, B. Satyanarayana, Rajesh Kumar, Bholey Singh, R. K. Shrivastava

The present study deals with two layered MHD immiscible fluid flow through porous medium in presence of heat transfer through parallel plate channel. The fluids are incompressible, and flow is fully developed. The fluids are of different viscosities and thermal conductivities so flowing without mixing each other. Two different phases are accounted for study and are electrically conducting. Temperature of the walls of parallel plate channel is constant. Rheological properties of the immiscible fluids are constant in nature. The flow is governed by coupled partial differential equations which are converted to ordinary differential equations and exact solutions are obtained. The velocity profile and temperature distribution are evaluated and solved numerically for different heights and viscosity ratios for the two immiscible fluids. The effect of magnetic field parameter *M* and porosity parameter *K* is discussed for velocity profile and temperature distribution. Combined effects of porous medium and magnetic fields are accelerating the flow which, can be helpful in draining oil from oil wells.

Open Access Original Research Article

Wekesa Waswa Simon, Winifred Nduku Mutuku

Heat transfer fluids play a vital role in many engineering and industrial sectors such as power generation, chemical production, air-conditioning, transportation and microelectronics.

**Aim: **To numerically investigate the effect of double stratification on magneto-hydrodynamic boundary layer flow and heat transfer of an Eyring-Powell fluid.

**Study Design:** Eyring-Powell fluid is one of the non-Newtonian fluid that possess different characteristics thus different mathematical models have been formulated to describe such fluids by appropriate substitution into Navier-Stoke’s equations. The challenging complexity and the nature of the resultant equations are of great interest hence attract many investigations.

**Place and Duration of Study:** Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya between December 2019 and October 2020.

**Methodology: **The resultant nonlinear equations are transformed to linear differential equations by introducing appropriate similarity transformations. The resulting equations are solved numerically by simulating the predictor-corrector (P-C) method in matlab ode113. The results are graphically depicted and analysed to illustrate the effects of magnetic field, thermophoresis, thermal stratification, solutal stratification, material fluid parameters and Grashoff number on the fluid velocity, temperature, concentration, local Sherwood number and local Nusselt number.

**Results: **The results show that increasing the magnetic field strength, thermophoresis, thermal stratification and solutal stratification lead to a decrease in the fluid velocity, temperature, Sherwood number, Nusselt number and skin friction while an increase in the magnetic field strength, thermal stratification, solutal stratification, and thermophoresis increases the fluid concentration.

**Conclusion: **The parameters in this study can be varied to enhance heat ejection of Eyring-Powell fluid and applied in industries as a coolant or heat transfer fluid.

Open Access Original Research Article

Y¨uksel Soykan

In this paper, closed forms of the sum formulas ∑n k=0 xkWk2 for the squares of generalized Tetranacci numbers are presented. We also present the sum formulas ∑n k=0 xkWk+1Wk; ∑n k=0 xkWk+2Wk; and ∑n k=0 xkWk+3Wk: As special cases, we give summation formulas of the of Tetranacci, Tetranacci-Lucas and some other fourth order linear recurrance sequences.

Open Access Original Research Article

E. A. Adwan

** Aims/ Objectives: **In this paper, making use the Hadamard product , we introduce drive several interesting subordination results for a new class of analytic function. Furthermore, we mention some known and new results, which follow as special cases of our results.

Open Access Original Research Article

W. V. Nishadi, A. A. I. Perera

Graph factorization plays a major role in graph theory and it shares common ideas in important problems such as edge coloring and Hamiltonian cycles. A factor of a graph is a spanning subgraph of which is not totally disconnected. An - factor is an - regular spanning subgraph of and is -factorable if there are edge-disjoint -factors such that . We shall refer as an -*factorization *of a graph *.* In this research we consider -factorization of complete graph. A graph with vertices is called a complete graph if every pair of distinct vertices is joined by an edge and it is denoted by . We look into the possibility of factorizing with added limitations coming in relation to the rows of generalized Hadamard matrix over a cyclic group. Over a cyclic group of prime order , a square matrix of order all of whose elements are the root of unity is called a generalized Hadamard matrix if , where is the conjugate transpose of matrix and is the identity matrix of order . In the present work, generalized Hadamard matrices over a cyclic group have been considered. We prove that the factorization is possible for in the case of the limitation 1, namely, If an edge belongs to the factor , then the and entries of the corresponding generalized Hadamard matrix should be different in the row. In Particular, number of rows in the generalized Hadamard matrices is used to form -factorization of complete graphs. We discuss some illustrative examples that might be used for studying the factorization of complete graphs.