# Journal of Mathematical Sciences & Computational Mathematics (JMSCM)(ISSN Number (Online) - 2644-3368) (ISSN Number (Print) - 2688-8300)

## Volume3 Issue1:

### SOLUTION OF AN INTEGRO-DIFFERENTIAL EQUATION WITH DIRICHLET CONDITIONS USING TECHNIQUES OF THE INVERSE MOMENTS PROBLEM

#### María B. Pintarelli1,2

##### 2Departmento de Ciencias Basicas de la Facultad de Ingenieria Universidad Nacional de La Plata -1900. Argentina Email: [email protected]
###### Page Number: 1-12

It will be shown that finding solutions from some integro-differential equation under Dirichlet conditions is equivalent to solving an integral equation, which can be treated as a generalized two-dimensional moment problem over a domain
`𝐸 = {(𝑥,𝑡), 0 < 𝑥 < 𝐿; 𝑡 > 0}`
We will see that an approximate solution of the equation integro-differential can be found using the techniques of generalized inverse moments problem and bounds for the error of the estimated solution. First the problem is reduced to solving a hyperbolic or parabolic partial derivative equation considering the unknown source. The method consists of two steps. In each one an integral equation is solved numerically using the two-dimensional inverse moment problem techniques. We illustrate the different cases with examples

Keywords:
Integro-differential equation, integral equations, generalized moment problem.

### APPLICATION OF BOX-JENKINS MODELS TO THE TOURIST INFLOW IN BHUTAN

#### Dorji Om, ChompunoochThamanukornsri, kado & MontipTiensuwan

##### Email: [email protected]; [email protected]; [email protected]; [email protected]
###### Page Number: 13-25

Bhutan has now increasingly become a popular destination for many international tourists. Tourism in Bhutan is considered as one of the largest foreign earning industries. The number of tourist inflow in the country is increasing year by year. Forecasting is very necessary for administration and tourist agent for creating awareness and planning for the future development. It can also predict the future trends as accurately as possible and helps in staying one step ahead of the competition. This study aims to apply mathematical model for forecasting monthly tourist inflow from Malaysia, Singapore, China, USA, England, France, Germany, Thailand, Australia and Japan to Bhutan. The Box-Jenkins model is used to identify the parameters of Autoregressive integrated moving average (ARIMA) model of monthly tourist visited data of above mentioned countries in the period 2011-2015 obtained from Tourism Council of Bhutan. An Akaike’s Information Criterion, Schwartz’s Bayesian Criterion and estimate variance of white noise are used throughout to test for the identification of best fit model. Further, the periodogram analysis was used to confirm the seasonal period of the model. The results showed ARIMA model for Thai, Chinese, Malaysian and Japanese, while seasonal ARIMA for American, Australian, British, French, Singaporean and German. Further, seasonal ARIMA model was obtained as the best fit model for the overall data. These models are illustrated and could possibly forecast the monthly tourist inflow of one year ahead with acceptable accuracy.

Keywords:
Akaike’s information criterion, Box-Jenkins model, Schwartz’s Bayesian criterion, variance of white noise.

### INJECTIVE EDGE COLORING OF CUBIC GRAPHS

#### J. Naveen

##### Email: [email protected]
###### Page Number: 26-49

Three edges 𝑒1, 𝑒2 and 𝑒3 in a graph 𝐺 are consecutive if they form a cycle of length 3 or a path in this order. A 𝑘-injective edge-coloring of a graph 𝐺 is an edge-coloring of 𝐺, (not necessarily proper), such that if edges 𝑒1, 𝑒2, 𝑒3 are consecutive, then 𝑒1 and 𝑒3 receive distinct colors. The minimum 𝑘 for which 𝐺 has a 𝑘-injective edge-coloring is called the injective edge-coloring number, denoted by 𝜒𝑖 ′ (𝐺). In this paper, injective edge-coloring numbers of 𝐻- graph and generalized 𝐻-graph are determined.

Keywords:
Edge-coloring; k-injective edge-coloring; injective edge-coloring number; 𝐻-graph and generalized 𝐻-graph.

### MULTIVARIATE ANALYSIS AND MODELING THE EFFECT OF THE GDP OF NIGERIA ON THE PETROLEUM PRODUCT PRICES (1987- 2018)

#### 1Elekanachi, Maraizu Stella, 2Wonu, Nduka & 3Onu, Obineke Henry

##### Corresponding Author Email: [email protected]
###### Page Number: 50-65

The study presented multivariate analysis and modeling of the effect of the GDP of Nigeria on the Nigerian petroleum product prices from 1987 to 2018. The petroleum products considered as the response variables were the Premium Motor Spirit (PMS(Y1), Automotive Gas Oil (AGO(Y2)) and Dual Purpose Kerosene (DPK(Y3)) while the predictors were GDP(Z1), Total Reserve(Z2), External Debt(Z3), Gross National Expenditure(Z4) and GDP/Capita(Z5). These predictors were studied in pairs on the responses and also studied jointly with all the five predictors on the responses. Comparisons were made among the pairs, also, each pair was compared with the joint analysis. SPSS software was used in the analysis in which Pillai’s Trace, Wilks’ Lambda, F-value, P-value, coefficient of determination and sum of square errors were applied to determine the contributions of each predictor variable in the models built, to the petroleum product prices. Correlation and covariance analysis were also applied to know the joint effects of the variables. It was observed that PMS was greatly affected by the economic policies of Nigeria, same to the AGO and then DPK. PMS is insignificantly impacted in an economy with two indicators where GNE is involved. PMS and AGO proved better than DPK in the economy of Nigeria. The relationship between GDP on Total reserve or External debt is positive. That is to say, any increase in these variables will result to an increase in the petroleum product prices. Correlation and Covariance analysis revealed that the analysis between GNE and External debt proved to be the worst pair. The analysis on all the five predictors, GNE and External Debt, Total Reserve and External Debt, Total Reserve and GNE and Total Reserve and GDP had no negative correlation, while GDP and GNE had negative correlations between AGO and DPK and AGO and PMS, also, GDP and GDP/Capita and GDP and Total Reserve recorded negative correlation respectively between PMS and AGO and AGO and PMS

Keywords:
Petroleum products prices, GDP, GNE, Total Reserve, External Debt, economy.

### SOLVING SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS USING A NEW HYBRID SEMI-ANALYTICAL METHOD

#### 1George Albert Toma & 1Shaza Alturky

##### Email: [email protected], [email protected]
###### Page Number: 66-77

This paper presents a new hybrid method that combines Kharrat-Toma transform technique with the homotopy perturbation method for the solutions of linear and nonlinear initial value problems represented by integro-differential equations systems with initial conditions. Where, the advantages of this hybrid approach are rapid convergence to an approximate or exact solution, reduces the computational steps and integrals which making it a highly efficient and applicable method compared with the classical methods. Therefore, this proposed new hybrid approach (Kharrat-Toma transform and homotopy perturbation method) can be apply to find the analytical solutions of integro-differential equations systems arising in many applications. To show the accuracy and effectiveness of the presented technique several examples are introduced

Keywords:
Homotopy perturbation method, Kharrat-Toma transform, System of Integro-differential equations.

### A NEW APPROACH TO CONSTRUCT (K, N) THRESHOLD SECRET SHARING SCHEMES BASED ON FINITE FIELD EXTENSION

#### 1Vanashree Gupta & 2Smita Bedekar

##### Email: 1[email protected] ,2[email protected]
###### Page Number: 78-87

With increase in use of internet there is need to keep passwords, secret keys, important information secret. One way to do this is encryption. But it also need key which should be kept secure. Sometimes key is secure. But what will happens if the key is lost, forgotten etc. This problem can be solved using secret sharing. Instead of sharing whole secret, it is divided into pieces and distributed to finite set of pieces and some subset of pieces called access structure of scheme, which can recover secret. Here we propose a new way to construct threshold secret sharing schemes based on finite field extension using Blakley’s secret sharing as a base. It is useful in many cryptographic applications and security. Because of finite fields the size of numbers stays within a specified range, doesn’t matter how many operations we apply on number.

Keywords:
Finite Field extension, Secret Sharing Scheme, Blakley’s secret sharing, Access structure, Security.

### DATA AGGREGATION IN WIRELESS SENSOR NETWORKS: EMERGING RESEARCH AREAS

#### Ajobiewe, Damilola Nnamaka

##### Email: [email protected]
###### Page Number: 88-101

Wireless Sensor Networks (WSNs) generate an immense measure of explicit data usage. Such data, which is an exorbitant issue, should be prepared and then transmitted to the base station. Efficient data handling and energy monitoring are primary challenges. since WSN hubs are asset-compelled. The point of wireless sensor networks is not confined to data collection in the present climate. Yet the retrieval of beneficial data still depends on it. The term used for the retrieval of beneficial data is data aggregation. In social affairs, data aggregation helps to collect data in energy-efficient ways to elongate the network's duration. The majority of the detected data by the sensors were seen to be excessive. On the off chance that data repetition can be reduced, it will prompt the organization's extended lifetime and decreased inertness at that point. This paper explains a wide methodological analysis of literature on data aggregation in WSNs. Review of various strategies to reduce data repetition, and specifically through aggregation, as well as scientific categorization of data aggregation, challenges, and brokendown aggregation methods proposed over the last ten (10) years, are discussed.

Keywords:
Data Aggregation, Wireless Sensor Network, Security, Network Lifespan, Energy Efficiency.

### FIXED POINT THEOREMS IN REVISED FUZZY METRIC SPACES

#### 1Dr. A. Muraliraj & 2R. Thangathamizh

##### Email: [email protected]
###### Page Number: 102-109

In this paper, we examine the existence of fixed point results for Banach and Edelstein contraction theorems in Revised fuzzy metric spaces with the assistance of Grabiec. Thus, we create a new path in Revised fuzzy theory to obtain fixed point results. We hope that this paper creates a new way to come up with several fixed point results in the Revised fuzzy metric spaces.

Keywords:
Revised fuzzy metric space, continuous t-conorm, banach contraction, Edelstein contraction, fixed point

### THERMAL RADIATION EFFECTS ON MHD UNSTEADY COUETTE FLOW HEAT AND MASS TRANSFER FREE CONVECTIVE IN VERTICAL CHANNELS DUE TO RAMPED AND ISOTHERMAL TEMPERATURE

#### F. Abdullahi, M.A Sani, D.A. Sani, M.M. Sani, M. Ibrahim, F. Abubakar & I.M. Garba

##### Email: [email protected]
###### Page Number: 110-126

Numerical investigations were carried out to study thermal radiation effects on magneto-hydrodynamics (MHD) unsteady Couette flow heat mass transfer free-convective in vertical channels due to ramped and isothermal temperature. The governing coupled non-linear partial differential equations of the flow were transformed into non-dimensional form using suitable dimensional quantities. Finite element method (FEM) was employed to find numerical solution of the dimensionless governing coupled boundary layer partial differential equations. The expressions of velocity, temperature, concentration, skin friction, Nusselt number as well as Sherwood number have been obtained and discussed using line graph. From the outcome of the result it was revealed that, increase of porosity parameter K, ratio of mass transfer parameter N, Time parameter t, Eckert number Ec enhances the velocity and temperature while reverse is the case with the with increase of Magnetic parameter M, Radiation parameter tern R and Prandtl number Pr. At y = 0, the fluid skin friction gets enlarged with increase in porosity parameter K, Nusselt number gets increased with increase of Prandtl number Pr and Sherwood number gets boosted with increase of Eckert number Ec . Similarly, at y = 1 skin friction gets enhanced with increase of porosity parameter K, Nusselt number diminishes with increase of Prandtl number Pr and Sherwood number gets enlarged with increase of Eckert number Ec.

Keywords:
MHD, thermal radiation effects, isothermal temperature, ramped temperature.

### THE ASSESSMENT OF CARBON DIOXIDE (CO2) ADSORPTION AND SPATIAL BIOMASS DISTRIBUTION MAPPING IN THE RESERVOIR OF HINBOUN HYDROPOWER PROJECT

#### S.Phoummixay1,*, Biswadip Basu Mallik2 , T.Khampasith1 , V.Somchay1 , K.Phouphavanh1 ,P.Sengkeo1, S.Sivakone1

##### *Corresponding Author Email: [email protected]
###### Page Number: 127-133

Geographical Information System (GIS) is an excellent tool to be employed with computer control system and play very significant role for database management, storing, capture, mapping and data analysis which includes vector and raster data. This study is mainly to focus on: (i) to study on the tree volumes, carbon storages and analyze the adsorption of carbon dioxide (CO2), (ii) to estimate the existing biomass within the reservoir and (iii) to create the spatial biomass distribution maps. Consequently, the distribution maps are described and indicated in low to high biomass density within the study area. Hence, this study has found that: there are 10,365.3 m3 of the total volume, 421.423 kg of total Carbone storage, 1,542.41kg of total CO2 absorption and 36,346.48 tons of total Biomass within the study area.

Keywords:
GIS, Biomass, Carbon Dioxide, Adsorption, Dam.

### APPLICATION OF ZZ-TRANSFORM WITH HOMOTOPY PERTURBATION METHOD FOR SOLVING HIGHER-ORDER BOUNDARY VALUE PROBLEMS

#### George Albert Toma

##### Email: [email protected]
###### Page Number: 134-141

In this paper, a new hybrid scheme for solving the higher-order boundary value problems is introduced. the presented approach is based on combination of the ZZ-transform method with the homotopy perturbation method to find the solutions of boundary value problems. To show the power of the proposed technique, several examples are tested and the comparison results are tabulated.

Keywords:
ZZ-transform method, homotopy perturbation method, hybrid scheme, higher-order, boundary value problems.