Generating Functions of Binary Products of Tribonacci and Tribonacci Lucas Polynomials and Special Numbers

In this paper, we introduce a new operator defined in this paper, we give some new generating functions of binary products of Tribonacci and Tribonacci Lucas polynomials and special numbers.

Hankel Determinant Problem for q-strongly Close-to-Convex Functions

In this paper, we introduce a new class $K_{q}(\alpha), \quad 0<\alpha \leq1, \quad 0<q<1, $ of normalized analytic functions $f $ such that $\big|\arg\frac{D_qf(z)}{D_qg(z)}\big| \leq \alpha \frac{\pi}{2},$ where $g$ is convex univalent in $E= \{z: |z|<1\} $ and $D_qf $ is the $q$-derivative of $f $ defined as: $$D_qf(z)= \frac{f(z)-f(qz)}{(1-q)z}, \quad z\neq0\quad D_qf(0)= f^{\prime}(0). $$ The problem of growth of the Hankel determinant $H_n(k) $ for the class $K_q(\alpha) $ is investigated. Some known interesting results are pointed out as applications of the main results.

Strong Differential Sandwich Results for Bazilevic-Sakaguchi Type Functions Associated with Admissible Functions

In the present article, we define a new family for holomorphic functions (so-called Bazilevic-Sakaguchi type functions) and determinate strong differential subordination and superordination results for these new functions by investigating certain suitable classes of admissible functions. These results are applied to obtain strong differential sandwich results.

On Characterization of Optimal Control Model of Whooping Cough

Whooping cough is a vaccine avoidable public health problem which is caused by bacterium Bordetella Pertussis and it is a highly contagious disease of the respiratory system. In this paper, an SIR epidemiological model of whooping cough with optimal control strategy was formulated to control the transmission. The model was characterized to obtain the disease free and the endemic equilibrium points. Finally, the simulation was carried out using the Forward-backward sweep method by incorporating the Runge Kutta method to check the validity and the result obtained was an improvement over the existing results.

Bayesian Estimation of Weighted Inverse Maxwell Distribution under Different Loss Functions

In this study, the shape parameter of the weighted Inverse Maxwell distribution is estimated by employing Bayesian techniques. To produce posterior distributions, the extended Jeffery's prior and the Erlang prior are utilised. The estimators are derived from the squared error loss function, the entropy loss function, the precautionary loss function, and the Linex loss function. Furthermore, an actual data set is studied to assess the effectiveness of various estimators under distinct loss functions.

Classifying Features Persuading the Use of Long Lasting Insecticide Treated Nets (LLINs) and Its Implications in Exterminating the Incidence of Malaria-Death in Ghana

This is a cross-sectional quantitative study purported to identify features deemed to persuade the usage of LLINs in exterminating incidences of malaria-death in Ghana. The population consisted of mothers and caregivers of children under five in Asamankese a district in the Eastern region of Ghana. Questionnaires were developed based on the profile and the set of study objectives, it sought information on socio-economic variables, knowledge level on LLINs, and influence of climatic and environmental factors on LLINs usage. Data were coded and keyed into SPSS version 20. Frequencies, percentages, means, standard deviations, graphs and tables were used to explore the data. Chi-square test was used to do further investigation. It was revealed that LLINs usage was influenced by a group of features including: background characteristics of household; socio-economic variables, environmental variables and knowledge on importance of LLINs. There was an association between LLINs usage and monthly income of caregivers (p<0.05). Furthermore, there was a significant relationship (p<0.05) between environmental features and LLINs usage. There was a relationship (p<0.05) between one’s knowledge and use of LLINs. In addition, there was a relationship between usage and the number of times per month visits were made to the hospitals for health care. Environmental factors permitted the use of LLINs, Eighty-six (86%) of the respondents who used LLINs did use it because the weather aided them. It is recommended that behavior change education be intensified in the region so that more people can accept and adopt a lifestyle that will protect them from the deadly malaria diseases. Efforts must be made by the major players in the health sector to make the net readily available in the communities at low prices to enable the ordinary Ghanaian to purchase it.

Absolute Value Variational Inclusions

In this paper, we consider a new system of absolute value variational inclusions. Some interesting and extensively problems such as absolute value equations, difference of monotone operators, absolute value complementarity problem and hemivariational inequalities as special case. It is shown that variational inclusions are equivalent to the fixed point problems. This alternative formulation is used to study the existence of a solution of the system of absolute value inclusions. New iterative methods are suggested and investigated using the resolvent equations, dynamical system and nonexpansive mappings techniques. Convergence analysis of these methods is investigated under monotonicity. Some special cases are discussed as applications of the main results.

An Enhanced Clustering Method for Extending Sensing Lifetime of Wireless Sensor Network

Extending the lifetime of a wireless sensor network is vital in ensuring continuous monitoring functions in a target environment. Many techniques have appeared that seek to achieve such prolonged sensing gains. Clustering and improved selection of cluster heads play essential roles in the performance of sensor network functions. Cluster head in a hierarchical arrangement is responsible for transmitting aggregated data from member nodes to a base station for further user-specific data processing and analysis. Minimising the quick dissipation of cluster heads energy requires a careful choice of network factors when selecting a cluster head to prolong the lifetime of a wireless sensor network. In this work, we propose a multi-criteria cluster head selection technique to extend the sensing lifetime of a heterogeneous wireless sensor network. The proposed protocol incorporates residual energy, distance, and node density in selecting a cluster head. Each factor is assigned a weight using the Rank Order Centroid based on its relative importance. Several simulation tests using MATLAB 7.5.0 (R2007b) reveal improved network lifetime and other network performance indicators, including stability and throughput, compared with popular protocols such as LEACH and the SEP. The proposed scheme will be beneficial in applications requiring reliable and stable data sensing and transmission functions.

On Generalized p-Mersenne Numbers

In this paper, we introduce the generalized p-Mersenne sequence and deal with, in detail, two special cases, namely, p-Mersenne and p-Mersenne-Lucas-sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

Solution of Linear Fuzzy Fractional Differential Equations Using Fuzzy Natural Transform

The purpose of this paper is to apply the fuzzy natural transform (FNT) for solving linear fuzzy fractional ordinary differential equations (FFODEs) involving fuzzy Caputo’s H-difference with Mittag-Leffler laws. It is followed by proposing new results on the property of FNT for fuzzy Caputo’s H-difference. An algorithm was then applied to find the solutions of linear FFODEs as fuzzy real functions. More specifically, we first obtained four forms of solutions when the FFODEs is of order α∈(0,1], then eight systems of solutions when the FFODEs is of order α∈(1,2] and finally, all of these solutions are plotted using MATLAB. In fact, the proposed approach is an effective and practical to solve a wide range of fractional models.