Abstract: In this research, we are studying the possibility of contribution in solving the Vehicle Routing Problem With Time Windows (VRPWTW), that is one of the optimization problems of the NP-hard type. This problem has attracted a lot of attention at the present time because of its Real Life applications. However, there is still no algorithm that provides us with the perfect solution to this problem because of the complexity of polynomial time. This means that the time of the solution to the Vehicle Routing Problem With Time Windows is growing steadily with the increase in the number of nodes. All the used algorithms have given solutions that are close to the optimal one. We'll show in our search Improved Ant Colony System algorithm (IACS) that is capable of searching multiple search areas simultaneously in the solution space is good in diversification, and Simulated Annealing algorithm (SA) is a local search technique that has been successfully applied to many NP-hard problems. In this research, we will  present the In this research Hybrid algorithm (HA) Hybrid Algorithm provided (IACS-SA) that integrate between improved ant algorithm and Simulated Annealing algorithm . We will then compare the quality of the solution resulted from this hybrid approach with the results of well-known standard tests to determine the effectiveness of the presented approach.

Keywords: Vehicle Routing Problem With Time Windows, Simulated Annealing Algorithm, Improved Ant Colony System Algorithm, Hybrid Algorithm, 2-Opt Local Search, Nearest Neighbor Algorithm, Meta-Heuristics.
Title: An Integration between the Improved Ant Algorithm and the Simulated Annealing Algorithm to Contribute To Solve the Vehicle Routing Problem with Time Windows
Author: Dr. Mohammed Hassan Hassan, Dr. Laina Makdyssiian, Waseem Habib Bila
ISSN 2394-9651
International Journal of Novel Research in Physics Chemistry & Mathematics
Novelty Journals

Abstract: Forecasting plays a major role in tourism planning at all levels in both private and public sectors. Hence, finding appropriate forecasting techniques is essential. The current study was focused on modelling international tourist flows to Sri Lanka by considering the post-war period. Monthly arrival data from January 2010 to December 2014 was obtained from Sri Lanka Tourism Development Authority. Smoothing techniques were tested during the study. Model selection criteria were Mean Absolute Percentage Errors (MAPE's). According to descriptive statistics, mean arrivals were 88217.The distribution of the tourist arrivals is normally distributed. Winter’s three parameter multiplicative model;   length 4, α = 0.9,   β = 0.1, γ = 0.1 and additive model; length 4, α = 0.9, β = 0.2 and γ = 0.5 have least MAPE (13%). Residuals of all the models were normally distributed. Mean Absolute Deviation and Mean Squared Deviation also agreed with MAPE’s. It was concluded that Holt’s Winter’s three parameter model is the suitable model for forecasting international tourist arrivals to Sri Lanka. It is recommended to test Decomposition techniques, Box-Jenkins ARIMA model, GARCH and ARCH models etc, for better forecasting. 

Keywords:  Forecasting, Smoothing techniques, Tourist arrivals, Post-war.
Title: Forecasting Tourist Arrivals to Sri Lanka: Post-War Period
Author: K.M.U.B Konarasinghe
ISSN 2394-9651
International Journal of Novel Research in Physics Chemistry & Mathematics
Novelty Journals

Abstract: Forecasting is essential for a healthy stock market. Mathematical and statistical modeling plays a vital role in forecasting share returns. A statistical model named as Capital Asset Pricing Model (CAPM) is the mostly used model for the purpose all over the world. Literature gives enough evidence for the inefficiency of CAPM in forecasting returns. Yet, Sri Lankan stock market depends on CAPM for forecasting risk and returns of securities. Literature revealed that the Sri Lankan share market returns follow wave like patterns with no trend. This study tested a new forecasting model for forecasting individual company returns. The model, which is named as “Circular Model”, is based on Fourier transformation. 

Keywords: Mathematical models, Statistical models, Fourier transformation, Circular Model.
Title: Circular Model on Forecasting Returns of Sri Lankan Share Market
Author: W.G. S. Konarasinghe, N. R. Abeynayake, L.H.P.Gunaratne
ISSN 2394-9651
International Journal of Novel Research in Physics Chemistry & Mathematics
Novelty Journals

Abstract: In this paper, Bessel’s differential equation and Bessel functions were used via the cylindrical coordinates of Laplace equation and the method of Frobenius, the solutions of Schrödinger equation applied to Neumann and Hankel functions were obtained by the application of undetermined coefficients.

Keywords: Bessel differential equation, Bessel functions, Hankel functions, Neumann functions and Schrödinger equation.
Title: Bessel’s Equation and Bessel Functions Solution to Schrödinger Equation in a Neumann and Hankel Functions
Author: SALIHU SABIU MUSA, ASSOC. PROF. DR. EVREN HINCAL
ISSN 2394-9651
International Journal of Novel Research in Physics Chemistry & Mathematics
Novelty Journals

Abstract: Here we define ‘addition’ and ‘multiplication’ on the set  M(F) of all matrices over a field  F as an extension of traditional matrix addition and multiplication respectively and study about the algebraic structure (M(F),+,.).
Again, since a matrix can be thought as a linear transformation from a vector space to a vector space over a given field F, we shall have a kind of extension of all linear spaces of linear transformations over the field F.

Keywords: addition of matrices, extension of linear spaces, extension of matrix algebra, multiplication of matrices, weak hemi-ring, weak hemi-vector space.
Title: Extension of Matrix Algebra and Linear spaces of Linear Transformations
Author: Jayanta Biswas
ISSN 2394-9651
International Journal of Novel Research in Physics Chemistry & Mathematics
Novelty Journals

Abstract: Atmospheric parameters that affect ground reaching UV-B irradiance include ozone, solar zenith angle, earth–sun distance, clouds, aerosols, etc. It is a known fact that total column ozone and ground reaching UV-B irradiance are inversely related   The aim of this paper is to estimate  the variation of the biologically effective UV-B irradiance with variation in ozone at a coastal urban location Visakhapatnam for the year  2012 with the help of a regression model that was developed with measurements made by a UV-B Photometer operated at Visakhapatnam in 1990 (Krishna et al., 2005) long back. This now reused to estimate the incoming UV-B irradiance by inputting TOMS ozone for the year 2012. An attempt was made to compare both measurements which are reported in this paper.  For the analyzed period (January 2012 – December 2012), variation of estimated UV-B irradiance with ozone for different wavelengths is found for 12.50 solar zenith angle. These results indicate the efficiency of the regression model developed for this station.

Keywords: UV-B irradiance, Regression, Ozone.
Title: Regression Technique That Relate UV-B and Ozone at Visakhapatnam
Author: N.V. Krishna Prasad, M.S.S.R.K. Sarma, N. Madhavi
ISSN 2394-9651
International Journal of Novel Research in Physics Chemistry & Mathematics
Novelty Journals

Abstract: In this paper, we determine the various causes of floods, where the floods in Tamil Nadu (Chennai & Cuddalore). There are numerous factors which affects the people who are living in Chennai and Cuddalore and affect the standard of living. We analyze some of the main areas of problems due to heavy rain. The data given in this paper are based on the several reports; articles come up in magazines .The data reapplied in Markovian process, which is one of the circumstances of random process. The impact of flood in Chennai and Cuddalore were analyzed in this paper using Markovian process.

Keywords:  Living Standard, floods, Markovian, Chennai & Cuddalore.
Title: TAMILNADU (CHENNAI&CUDDALORE) HAD SEEN ITS WORST FLOODS
Author: C.JESURAJ, G.MURUGAN, M.ANANDHKUMAR
ISSN 2394-9651
International Journal of Novel Research in Physics Chemistry & Mathematics
Novelty Journals

Abstract: The kinetics of the oxidation of disodium 3,3’-dioxobi-indolin-2,2’- ylidene-5,5’ disulphonate (I.C) by quinolinium dichromate(QDC) in aqueous acid medium has been studied at 30±10C. The reaction is first order in [IC],[monomeric QDC] and [acid].A stoichiometric mole ratio of IC : QDC is 3:2. Variations in ionic strength did not affect the rate of reaction. The mechanism involved the attack of protonated monomeric QDC (QMC) on the substrate in the rate determining step. The effect of anionic micelle (SDS) and neutral micelle (TX-100) on the system was studied using Berezin’s kinetic model and the binding constant for both the reactants with the micelle have been computed. The thermodynamic parameters like enthalpy, entropy, and Gibbs free energy are determined. A mechanism confirming to the kinetic observations is suggested.

Keywords: Indigo Carmine, QDC, protonated QMC, SDS, TX-100, binding constant.
Title: Mechanistic Investigation of Micelle Effects on the Oxidation of Indigo Carmine by Quinolinium Dichromate in Perchloric Acid Media: A Kinetic Approach
Author: D.Suryakala, Md.Asif, K.Rama Krishna, P.V.Subba Rao
ISSN 2394-9651
International Journal of Novel Research in Physics Chemistry & Mathematics
Novelty Journals

Abstract: In this paper, I will discuss the Runge Kutta method of solving simple linear differential equations. I start by starting why the Runge Kutta method is idea for solving simple linear differential equations numerically in comparison to move elementary methods. I will then proceed to explain what steps the method actually carries out in solving the differential equation along with the high level programming language code, I used to write a simple Runge Kutta solver and the output of the code, given some basic differential equations. I will then end by discussing the method is used to some examples to illustrate the accuracy and the implementation of the method.

Keywords: Euler, Improved Euler, Runge -Kutta.
Title: A Study on Numerical Exact Solution of Euler, Improved Euler and Runge - Kutta Method
Author: Mrs. P. Sampoornam
ISSN 2394-9651
International Journal of Novel Research in Physics Chemistry & Mathematics
Novelty Journals