# Mathematics articles list

## Comparative growth of jipe tilapia, oreochromis jipe and nile tilapia, oreochromis niloticus using regression modeling

Regression modeling analyses the relationship between two or more variables and can be used to predict the response variable from one or more independent variables. The present study uses linear regression analysis to evaluate the growth in the two fish species of genus Oreochromis, Nile tilapia and Jipe tilapia, under aquaculture conditions. The models were fitted using a collection of functions in the R-software library. The final models were selected using the goodness of fit criteria based on the coefficient of differentiation, the model p- values and Akaike information criteria. The significance of the linear relationship between predictor variables and the mean response was tested by comparing the computed standardized parameter estimates, whereas the confidence intervals were constructed to assess the uncertainty of predicting the response variable and determine outliers in the model. Generally, both species exhibited good condition during growth and all the measured water quality variables significantly afffected growth (p<0.05). However, only temperature and dissolved oxygen produced the most important linear relationship with fish weight. The study recommends that data from a controlled experiment should be used the determine the interactions between the two growth variables.

## Determination of the rich structural wave dynamic solutions to the caudrey–dodd–gibbon equation and the lax equation

This article addresses the implementation of the new generalized (G'∕G)-expansion method to the Caudrey–Dodd–Gibbon (CDG) equation and the Lax equation which are associated with the fifth-order KdV (fKdV) equation. The method works well to derive a variety of standard and functional closed-form wave solutions with distinct physical structures, such as, soliton, kink, periodic soliton, and bell-shaped soliton solutions. The solutions obtained using this method are useful and adequate than other methods. In order to understand the physical aspects and importance of the method, the attained solutions have been simulated graphically. The extracted results definitely establish that the new generalized(G'∕G)-expansion method is an effective mathematical tool to work out new solutions to different types of local nonlinear evolution equations emerging in applied science and engineering, but this method is not effective in solving nonlocal equations.

## Kink and periodic solutions to the jimbo-miwa equation and the calogero-bogoyavlenskii-schiff equation

In this article, we form the exact wave solutions of the Jimbo-Miwa equation and the Calogero-Bogoyavlenskii-Schiff equation by applying the new generalized (G'/G)-expansion method. We explained the new generalized (G'/G)-expansion method to look for more general traveling wave solutions of the above mentioned equations. The traveling wave solutions attained by this method are in terms of hyperbolic, trigonometric and rational functions. The graphical representation of the obtained solutions is kink soliton, singular kink soliton, singular soliton and singular periodic solution. This method is very significant for extracting exact solutions of NLEEs which habitually occur in mathematical physics, engineering sciences and applied mathematics.

## Abundant wave solutions of the boussinesq equation and the (2+ 1)-dimensional extended shallow water wave equation

In this article, we establish the exact wave solutions of the Boussinesq equation and the (2 + 1)-dimensional extended shallow water wave equation by applying the new generalized (G'/G)-expansion method. When the condition of the fluid is such that the horizontal length scale is much greater than the vertical length scale, the shallow water equations are mostly suitable. In Ocean engineering, Boussinesq-type equations are commonly used in computer simulations for the model of water waves in shallow seas and harbors. We explained the new generalized (G'/G)-expansion method to seek further general traveling wave solutions of the above mentioned equations. The traveling wave solutions attained by this method are exposed in terms of hyperbolic, trigonometric and rational functions. The shape of the obtained solutions are bell shaped soliton, kink soliton, singular kink soliton, singular soliton, singular periodic solution and compaction. This method is very influential mathematical tool for extracting exact solutions of NLEEs which frequently arise in mathematical physics, engineering sciences and many scientific real world application fields.

## A linear programming integer model for cellular manufacturing layout design with machine flexibility and dynamic criteria

The Cellular Manufacturing is adopted in batch type manufacturing industries nowadays for their production with increased productivity, less cost and time with effective control. The proposed optimization model is used to determine the cost of machine cells, i.e., machine duplication, part subcontract, inter intra cellular movements cost and cost of production associated with machine cell, such as machine reconfiguration and part inventory considering machine flexibility for various time periods. Initially, mathematical model is proposed to calculate machine cell cost with and without considering machine flexibility and then another lpp integer model is proposed to calculate the machine cell production and associated cost for the changes in time period, part type and volume considering machine flexibility. The manufacturing data in the incidence matrix and machine cell, part family data in the block diagonal form are given as input to the optimization programming language Cplex and the output are given for the two mathematical models. The data related to machine duplication, part subcontract, inter intra cellular movement; machine reconfiguration and part inventory are given. Two dimensional shop floor layouts are presented in rectilinear coordinates for all the problems for easy analysis of material movement length and shop floor area

## Primes of form 6^n+1

We pose various congruences on the integers of form 6^n+1,n∈Z_+, which may encourage younger number theorists to research number theory and settle new dimensions in this field. We observed that there are only three prime numbers, namely 7,37, and 1297 of form 6^n+1,n∈Z_+, and no one Fermat numbers attains this form. Moreover, these integers end with 7, like Fermat numbers F_n,n≥2. Also, we discussed some congruences with number theoretic functions σ,φ and Möbious function μ.

Ncism

## Dr T Premalatha

Assistant Professor

## Olukayode Apata

Texas A&m University

Department Of Microbiology, North Tehran Branch, Islamic Azad University

M Pharmacy

## Mangala Dhotre

Assistant Professor