Open Access Short Research Article

Rootless B-Fredholm Operators

Gabriel Kantun-Montiel

Journal of Advances in Mathematics and Computer Science, Page 1-6
DOI: 10.9734/BJMCS/2017/30520

Let T be a B-Fredholm operator on a Banach space X. We say that T is rootless if there is no bounded linear operator S and no positive integer n ≥ 2 such that T = Sn. In this note, some properties of the uniform topological descent are used to give some sucient conditions for B-Fredholm operators to be rootless.

Open Access Short Research Article

Time Series Analysis for Modeling and Forecasting International Tourist Arrivals in Sri Lanka

D. K. Ishara, P. Wijekoon

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2017/31726

Tourism is one of the income generating industries in a developing country which directly contribute to the economy. Therefore, forecasting tourist arrivals is important for making policy decisions to improve facilities and other related factors in this industry. In this paper, an attempt has been made to forecast tourists’ arrivals using time series modelling. The time span used for the study is from January 2000 to February 2016. In the modelling exercise, data has been analyzed based on the two sets of data; long-term (2000-2016), and post-war (2010-2016). This categorization was due to the significant change in the industry after the end of the civil war in 2009 in Sri Lanka. An Auto-Regressive Integrated Moving Average (ARIMA) method and Multiplicative Decomposition approach (MDA) were employed to model the data. When the forecasts from these models were validated, post-war data has more accurate results having low Mean absolute percentage error (MAPE) for MDA than the ARIMA approach. The comparison of actual data with the predicted values also confirmed that the MDA model obtained from the post-war series has high predictive ability.

Open Access Original Research Article

The Mathematical Proof for the Beal Conjecture

Oluwatobiloba Solomon Olanrewaju, Kehinde Kazeem Kanmodi

Journal of Advances in Mathematics and Computer Science, Page 1-6
DOI: 10.9734/BJMCS/2017/29996

The Beal conjecture is a number theory formulated in 1993 by the billionaire banker, Mr Andrew Beal. Mr Beal, very recently, declared a one-million-dollar award for the proof of this number theory. As at present, no proof of this conjecture has been generally found. In this article, we provided the proof for Beal conjecture in a crystal-clear systematic approach.

Open Access Original Research Article

Computational Model of Prime Numbers by the Modified Chi-square Function

Daniele Lattanzi

Journal of Advances in Mathematics and Computer Science, Page 1-19
DOI: 10.9734/BJMCS/2017/31589

An innovative approach that treats prime numbers as raw experimental data and as elements of larger and larger finite sequences {Pm}≡{P(mp)} is shown in the present report. The modified chi-square function Xk2(A,mp/xo) with its three parameters A, k and xo=xo(k) is the best-fit function of the finite sequences {ρm}≡{lgPm/lgmp} from the analytical viewpoint thus showing that the property of scale invariance does not hold for the finite sequences of this prime variable and so for primes themselves. In addition an injective map can be set between these {ρm} sequences and the {mα} progressions with domain N and co-domain R+ being α∈(–1,0)⊂R through the parameter k=2+2α of their common fit function Xk2(A,mp/xo). All that leads to induction algorithms and to relationships of the kind Pm≈P(mp), though within the precisions of the calculations and holding locally.

Open Access Original Research Article

Conflict Resolution for Sacramento-San-Joaquin Delta with Stability and Sensitivity Analyses Using the Graph Model

Ahmed E. Al-Juaidi, Tarek Hegazy

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2017/31225

The goal of this paper is to resolve the strategic long-term dispute for the Sacramento-San Joaquin Delta California using the Graph Model approach for conflict resolution. To facilitate the analysis, a Decision Support System (DSS) has been developed, incorporating multiple-criteria decision analysis, stability and equilibrium analysis, and uncertainty analysis using the info-gap technique. The DSS has been used on the Sacramento-San Joaquin Delta conflict. After specifying the stakeholders with their preferences and possible decisions, the DSS identified the most robust solution, considering the possible actions and counteractions of all stakeholders. Solution robustness was then tested under the uncertainty associated with stakeholders’ perspectives, and under cooperative and non-cooperative attitudes. The model results suggest the following: (1) with cooperation between the decision makers, building the tunnel is the most likely solution to replace the existing water export; (2) the second reliable solution is to have a dual conveyance "tunnel"; (3) when decision makers do not cooperate, no-export water is the best solution. Furthermore, no-export solution is impossible and unlikely for this problem since the agriculture production in the Sacramento-San Joaquin Delta is a multi-billion industry.

Open Access Original Research Article

A New Decision Making Method on Interval Valued Fuzzy Soft Matrix (IVFSM)

M. Zulqarnain, M. Saeed

Journal of Advances in Mathematics and Computer Science, Page 1-17
DOI: 10.9734/BJMCS/2017/31243

Interval valued fuzzy soft set and IVFSM are those mathematical tools which deal with problems involving uncertainties and imprecise or incomplete data. IVFSM may be useful for functions whose membership values vary. In this paper, we study basic definitions of IVFSM with some properties and prove commutative laws, associative laws and De-Morgan laws by using And-Operation and Or-Operation on IVFSM. We propose a new decision making method on IVFSM named as “interval valued fuzzy soft max-min decision making method” (IVFSMmDM) with the help of interval valued fuzzy soft max-min decision making function. Finally, we apply IVFSMmDM method for decision making to solve those problems which involving uncertainties by using data from [19].

Open Access Original Research Article

ms*-Modules

Ayşe Tuǧba Güroǧlu

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2017/31394

Let R be a ring and M a left R-module. A module M is called ms*-module if each maximal submodule is β* equivalent to a supplement in M. In this work, we focus on ms*-module and study various properties of this module.