Orthogonal array Latin hypercube designs have become popular in practice among strategies used for developing computer experiments. Hadamard matrices have been used to construct orthogonal arrays based on the connection between Hadamard matrices and orthogonal arrays (OAs). A Hadamard matrix is a square matrix of +1 and -1 whose rows are orthogonal. This study aimed at proposing an enhanced algorithm that employed the maximin criterion in the k-Nearest Neighbour with Euclidean distance for constructing optimal space-filling design called Orthogonal Array Latin Hypercube Design (OALHD). Orthogonal arrays (OAs) were constructed from Hadamard matrices of orders 4λ and 8λ which are subsequently used to construct the desired OALHD. The Orthogonal array (n, k) Latin hypercube designs were constructed at parameter values of OA (n, k, s, t, λ) = (8, 7, 2, 2, 2) and (16, 8, 2, 3, 2). The OA (8, 7) LHD and OA (16,8) LHD constructed have better space-filling properties and they achieve uniformity in each dimension. MATLAB 2015 computer package was used for the development of the algorithm that constructs the OALHDs.

Computer experiments, Hadamard matrices, Latin hypercube designs, Orthogonal array, Space-filling designs.

In teaching mathematics at high schools, the mathematics competency of teacher is an important procedure in teaching process. This paper, I pointed out some application of complex numbers in mathematics. And i hope it will help the teachers to develop high school their mathematics competency in Vietnam.

Teachers’ mathematics competency, complex numbers, teaching methods.

Teaching through the application of mathematical modelling has been concerned in recent years in Vietnam high schools. In which it clearly shows the application of the mathematical modelling with parts of life. This paper mentions to teaching and learning the AM-GM inequality and its application from theory and practice.

Mathematical modelling, mathematics teaching methods, the AM-GM Inequality, theoretical and practical.

The paper examines contemporary issues with cognitive radio networks as it relates to spectrum scarcity and the demand of users. With recent advancement in technology and increase in the need for wireless communication systems, this has given rise to search for desirable spectrum bands for transmission. Cognitive Radios renders an answer to the trouble by sensing the idle (licensed) bands and allowing (secondary) users to broadcast and transmit in these idle spaces. Spectrum sensing forms the main block of cognition cycle. However research has shown by previous researchers that radio spectrums are being under- utilized in most cases. This paper attempts to profound a solution to efficient and effective spectrum utilization has identified the current challenges and issues faced by spectrum sensing for cognitive networks. The principal issues with cognitive radios are that it should not interfere with the primary users and should vacate the band when it is required. For this sole reason, energy detector system model was used in this paper and performance evaluation was calculated. The performance evaluation is done for cooperative spectrum sensing schemes under non fading environment This paper provides a clear understanding of cognitive radio technology, and its role in national development. Then several challenges and security issues are discussed.

Cognitive Radio; Spectrum Sensing; Primary Users; Secondary Users; Wireless Communication; Spectrum Hole; Cognitive Cycle; Cognitive Capabilities.

Man communicates with man by natural language, sign language, or/and gesture but communicates with machine via electromechanical devices such as mouse, and keyboard. The media of effecting machine to man be enhanced using language technology. This paper proposed a man to machine communication through Text-To-Speech system for Yoruba language. The process used involves text analysis, natural language processing and digital signal processing. The developed system shows an exhaustive representation of Yoruba language through concatenation of possible syllables in the language. The proposed model was evaluated using mean opinion score. Results showed a significant performance with an average of 92% for similarity and naturalness in the samples.

Tex-To-Speech, Yoruba Language, Syllable Structure, Similarity, Naturalness, Communication.

Number theory has turned out to be one of the useful when it comes to computer security. For instance, number theory helps to protect sensitive data such as credit card numbers when you shop online, when online transactions is performed. The prime application of it’s is in the RSA cryptosystem. Rivest Shamir Adleman (RSA) algorithm is known to be a slower algorithm. The modular arithmetic in RSA is computationally expensive. In view of this, it has become a major challenge to implement RSA decryption in a faster manner. In this paper, we proposed an efficient method to implement RSA decryption based on Chinese Remainder Theorem and Strong prime. Three different operations, primitive traditional method, Chinese Remainder Theorem method and Chinese Remainder Theorem and strong prime criterion were used for comparisons. Our proposal achieves about 60% computational cost reduction of traditional method using Chinese Remainder method. More interesting, if the method based on Chinese Remainder Theorem and strong prime is implemented, about 84% computational cost can be reduced. Also, comparing to the Chinese Remainder method, the method based on Chinese Remainder Theorem and strong prime of RSA criterion takes about 37% of computational cost, almost 3.2 times faster than the Chinese Remainder Theorem based method. Theoretically, it was observed that our scheme is faster and it is also cheaper.

RSA, RSA-CRT, Number theory, computational cost, CRT-strong prime criterion.

This paper considers three different approaches of handling multicollinearity in regression analysis using economic data. These techniques were applied to study determinants of money supply of the sector of the economy. The goal is to determine which of the economic variables included in the factors that influence money supply (either in the broad ‘M1’ or the narrow ‘M2’sense) is not actually contributing to the effect of money supply by monetary authority of the sector of the economy. A comparative analysis of the three methods using the adjusted R2 , Mean Square Error and Root Mean Error, as the statistics criteria, revealed that the result obtained from the Ridge Regression gave the outstanding performance as compared with the other two techniques. On the overall, it was found that the Ridge Regression performed best, followed by Principal Component Regression, while Latent Root Regression performed least.

Multicollinearity, Ordinary Least Squares, Principal Component Regression, Latent Root Regression and Ridge Regression

Many authors have applied Two-Phase Sampling for Stratification (TFSS) to different areas of specialization. It was observed that such application is yet to be extended to the software industry. This research applied TFSS to the comparison of the two software types, Free and Open Source Software (FOSS) and Proprietary Software (PS). The estimated FOSS mean (4.5749) compared to PS mean (3.6390) revealed that FOSS is more rated than PS. The minimum estimated variance in FOSS (0.0046) over PS (0.0484) showed that FOSS is efficient than PS. The relative efficiency further confirmed that FOSS is 1052.17% efficient over PS. FOSS user rating has higher precision with Coefficient of Variation (CV) of 0.0148 as against PS user rating CV of 0.0605. It was, finally, concluded that FOSS is efficiently rated than PS by the software users.

Two-phase Sampling for Stratification, User rating, Free-and-Open-Source Software, Proprietary Software

Speech Recognition is a vital part of different computer-based applications in communication and security systems. However, there has been very little research in the aspect of speech Human Computer Interaction system for African languages such as Hausa, hence, the need to extend the research in order to bring in, the different systems based on speech recognition. Also, Hausa is an important ethnic tribe of lingua franca in both west and central Africa countries. Isolated word recognition is an easy speech type because it demands the user to pause between each word. In this study, the two algorithms that were used to implement a system of Recognition of Hausa isolated digits are Dynamic Time Warping and Hidden Markov Model. To perform the recognition efficiently, speech endpoint, framing blocking, speech normalization, vector quantization and Mel Frequency Cepstral Coefficient techniques were used to process the speech. The accuracy of about 94% was obtained for recognition with HMM-based system. In a very noisy environment, the performance of the two techniques is bad but the pattern matching using HMM is better than the pattern matching using DTW.

DTW, Hausa Language, HMM, Speech Recognition, MFCC.

Lassa fever is an acute viral haemorrhagic fever caused by the Lassa virus and first discovered in 1969 in Lassa, a town in Borno State, Nigeria though it has been in existence since 1950s. Lassa virus belong to a member of the Arenaviridae family, a single stranded Ribonucleic Acid virus (RNA), has characteristic similar to Ebola virus. Lassa fever has killed thousands of people in West Africa, most especially in Nigeria, many of whose lives could have been saved if rapid diagnostic test was available; people who could have received treatment early and also who could have been isolated early enough to reduce spread of Lassa fever. Recently many people have died in the rural areas due to late detection or delay access to proper medical attention. This is due to the fact that most medical centres equipped with handling Lassa fever cases are situated far away from the rural communities. Hence, it would be of great necessity to provide a computerized system that will provide a complementary medical service where the experts are not sufficient. Therefore, in this paper, a rule-based medical expert system is developed and tested to address the various challenges of the traditional method of diagnosing Lassa fever. This research work tried to replace the manual method of diagnosing the Lassa fever by Medical Expert, with an Expert System (ES) which is capable of correcting all the limitations associated with the manual method.

Expert System, Artificial Intelligence, Lassa Fever, Rule Based Expert System, Medical Expert System, Viral Hemorrhagic Fever.

Let Σ be an alphabet. A subset X of the free monoid Σ* is a code over Σ if for all m, n ≥ 1 and x1, ..., xn, y1, ...ym ∈ X, the condition: x1 ... xn = y1 ... ym implies n = m and xi = yi for i=1, ...,n. In other words, a set X is a code if any word in X+ can be written uniquely as a product of words in X. It is not always easy to verify a given set of words is a code. In this paper, we give the construction and representation by deterministic finite automata of some variable length codes.

Words and languages, the free monoid and relatives, morphisme of monoids, deterministic finite automata.

This study seeks to elucidate of structures of unknown Guaiane sesquiterpenes from their 13C chemical shift values using Generalized Regression Neural Network (GRNN) and scatter plot methods. The 13C values for each of the fifteen (15) positions of the skeletons of the Guaiane sesquiterpenes were predicted using GRNN. From these predicted values, the substituents attached to each of the positions were predicted using GRNN and Scatter Plot methods. In predicting the skeletal 13C values, the 13C data of 116 Guaiane sesquiterpenes were used as input to GRNN while their corresponding data were used as the target data. The network was trained and simulated using twenty-five (25) test compounds. The best results were obtained at a spread constant of 5.0. In predicting the substituents on each position on the skeleton using the GRNN approach, the predicted 13C skeletal values of the test compounds were simulated following training of the GRNN using skeletal data of the 116 compounds as input data and their corresponding substituents (given codes) as the target data. The best results were obtained at a spread constant of 5.0. In the Scatter Plots method, graphs of codes of substituents for the 116 guaiane sesquiterpenes were plotted against the corresponding 13C chemical shift values of the skeletal Carbon to which they were attached. This gave the range of values over which each substituent may be obtained. The most likely substituent(s) for each position were selected. The degree of recognition of the test compounds (from both methods) ranged between 46.67 and 100%. Both methods gave similar recognition rates for the test compounds. GRNN and Scatter plots demonstrated great potential for use in the structural elucidation of unknown compounds from 13C values.

GRNN, Scatter plots, structural elucidation, 13C, Guaiane sesquiterpenes.

A Mathematical Model of HIV/AIDS with mother – to – child transmission in the presence of treatment was examine in this paper, it ascertain the impact of treated individuals on the transmission dynamics of HIV/AIDS. Equilibrium points of the model system were found, stability analysis and numerical simulation was carried out. The result show that with treatment, the measure of the effect of health policies is realistic and control rate of mother – to – child is effective.

HIV Transmission, ARVs, Compartmental model, stability, equilibrium points and Treatment.

Oil and gas sector has been faced with huge losses in Nigeria as a result; insurance companies pay high premium due to these loses and Extreme Value Theory (EVT) is found to be suitable in modeling the extreme losses. Claims resulting from Nigeria Oil, and Gas insurance class of business for five insurance companies were modeled with EVT to estimate Value-at-Risk (VaR), where VaR measures the minimal anticipated loss over a period with a given probability and under exceptional market conditions. The mean excess plot was obtained which helps in determining the threshold value to be chosen and gives the shape of the distribution in the tail. Q-Q plot being linear and curved tail plots reveals that parametric model fits the data well. VaR based on EVT-Generalized Parameter (GPD) was carried using the chosen thresholds at 5% confidence interval. Results obtained were compared with VaR based on Historical and Gaussian method; it was established that Extreme VaR is most suitable to calculate VaR as against the Historical and Gaussian method.

Extreme Value Theory, Value-at-Risk, GPD model, Peak-Over-threshold, Insurance.

Generalization of distributions is usually motivated by limitations in characteristics of existing distributions so as to introduce more flexibility and improve goodness of fit. This is done by parameter induction into an existing distribution and therefore remains an approach to generalizing distributions. In this article, families of generalized distributions are generated by sequential application of methods in permutations of five distinct parameter induction methods: Lehmann Alternative 1 (LA1); Lehmann Alternative 2 (LA2); Marshal and Olkin Method (M-OM); α-Power Transformation (APT); and Power Transformation Method (PTM). This is done by taken two methods at a time. Sixteen distinct families of generalized distributions were generated. Some of the families of generalized distributions obtained are already in existence while several others are entirely new.

Generalized distributions; Lehmann Alternatives; α-Power Transformation Method; Power Transformation Method; Marshall and Olkin Method.

Given a permutation pattern say τ = τ₁ ... τ_k ∈ S_k and permutation ω = ω₁ ... ω_n ∈ S, we say that ω contains the pattern τ if there exist 1 ≤ i₁ < ... < i_k ≤ n such that red(ω_i1 ... ω_ik) = τ. Each subsequence in ω is known as an occurrence of the pattern ω. Conversely, if there exists no occurrence of τ in ω, then we say that the permutation ω avoids the pattern τ. The popularity of a pattern τ is the total number of copies of τ within all permutations of a set. In this work, we address popularity of length-3 patterns in Γ1 - non deranged permutations in two approaches; algebraically and algorithmically. We first establish algebraically that pattern τ₁ is the most popular and pattern τ₃, τ₄ and τ₅ are equipopular in G^Γ1_p. We further provide efficient algorithms that also report same results on popularity and equipopularity of patterns of length-3 in G^Γ1_p as obtained by the algebraic approach.

Permutation, Pattern, Popularity, Equipopularity, Sorting.

In this paper, efficiency of Audu & Adewara (2017) two-phase factor-type estimators with two auxiliary variables for estimating finite population mean were examined using simulation. These estimators were obtained by incorporating some known functions of auxiliary variables X and Z in some existing factor-type estimators. Bias and Mean square error (MSE) of these estimators, ӯ_FTAA^ß1(d) and ӯ_FTAA^ß2(d) were obtained using tailor’s series expansion. Audu & Adewara (2017) revealed that although ӯ_FTAA^ß1(d) and ӯ_FTAA^ß2(d), have minimum MSE and high PRE than all other related existing factor-type estimators considered using three life dataset but of these two, which is more efficient and most preferred. The simulation results obtained in this study revealed that ӯ_FTAA^ß2(d) is more efficient than ӯ_FTAA^ß1(d) and hence, most preferred.

Factor-type estimator, Two-phase sampling, Mean square error (MSE), Efficiency.Permutation, Pattern, Popularity, Equipopularity, Sorting.

Broyden-like methods (or hybrid Broyden methods) are one of the efficient modifications of the classical Broyden method proposed to solve nonlinear systems of equations and to overcome the deficiencies of the classical Newton method. In this work, a variant of the Broyden-like method is proposed using the weighted combination of the Trapezoidal, Simpson and Midpoint quadrature rules. Hence a new hybrid Broyden method known as TSMM has been created based on these rules. The numerical tests confirm that TSMM is promising when subjected to comparison with other Broyden-like methods.

Broyden method, quadrature formula, predictor corrector, nonlinear systems, convergence, numerical examples.

Modern economies are highly interconnected systems dominated by financial exchange. We propose a novel approach of analyzing the structure of the world financial markets by applying methodologies from the field of complex network analysis on a data set comprising he evolution of exchange rates on 23 major currencies over a time span of 14 years. Interesting economical insight is given based only on the topological properties of the correlation network which validate our methodology.

econometrics, graphs, scale free networks, currency, exchange rate, community structure, correlation.

In teaching mathematical in Vietnamese elementary schools, teachers must place emphasis on both the science and mathematical contents in the teaching and learning. This paper presents the importance of the integration of mathematics and science and describes what the integration of math and science at primary schools should be by providing some examples which illustrate.

Integration science, mathematics, teaching methods.

Job Shop Scheduling is an optimization problem and is considered to be one of the most daunting combinatorial problems. It can be used to maximize the productivity in many industries, particularly in the automobile industry. There are two finite sets involved in this problem, one for the number of machines and the other for the number of jobs which each machine has to do. The real challenge is to find out the most efficient way to complete these tasks. This problem remains one of the most discussed problems, with researchers from all over the world discovering new and different methods to solve it. A plethora of methods and algorithms, including different types of queuing algorithms and even some genetic algorithms have been used to solve this problem. The practicality of the problem further makes it interesting and the computer science community is motivated to make the solution even more efficient. In this paper, we have used Ant Colony Optimization and Particle Swarm Optimization, techniques which are probabilistic and iterative respectively to solve the problem. The tool used for this purpose is MATLAB. After tabulating and visualizing the results, it is found that the Particle Swarm Optimization is much more efficient than the Ant Colony Optimization method. The processing time of the Ant Colony Optimization is approximately four times more than that of the Particle Swarm Optimization.

Job Shop Scheduling, Automobile Industry, Ant Colony Optimization, Particle Swarm Optimization, MATLAB.

Individual or organizational sensitive data and information need to be prevented from unauthorized access. Several reports of middle man attacks and intrusion in form of hacking have been reported over the years when data are sent over wired or wireless media. One of the ways to prevent these is to either secure the medium through which information is being sent or to put measures in place to secure the actual information being sent. Though implementing both options could be expensive, however, implementing any of the option could still be effective. This could be achieved by making the data being sent meaningless to a third party but meaningful to the intending recipient. Cryptography is a proven way to achieve this. It entails using certain mathematical techniques to make a data unreadable and meaningless to any other person except the actual recipient who has the key needed to decrypt the encrypted data. Rijndael algorithm; which is the Advanced Encryption Standard (AES) for implementing cryptography is presented in this paper. It is a symmetric approach to implementing cryptography as it uses the same key for encryption and decryption. A detailed analysis of its implementation using its various 128, 192 and 256 bits key lengths is presented in this paper. The encryption and decryption process is made more secured by sending the encrypted text to the recipients email while the decryption key is sent to the recipient’s phone number. This is done to prevent instances where the recipients email is hacked.

Advanced Encryption Standard, Cryptography, Encryption, Decryption, Rijndael algorithm.

The study investigates the classification of learning algorithms in a bootstrap paradigm, the study examined features classification with binary class attributes in a bootstrap paradigm. Support Vector Machine, k-Nearest Neighbour, Random Forest, rpart, Artificial Neural Network and Naïve Bayes learning algorithms were compared. Accuracy, Prediction error, Sensitivity and Specificity were used as assessment criteria of the classifier after tuning to have minimum cost. The study therefore sample the training set and classifying each of the training set, the summary of the prediction error was obtained based on the testing dataset, the study showed that artificial neural network outperformed other learning algorithms with respect to accuracy criterion whereas the celebrated support vector machine performed poorly amongst the learning algorithms considered, the study depicted that artificial neural network outperformed other learning algorithms with the least misclassification error. The study depicted that K nearest neighbour outperformed other learning algorithms with highest sensitivity while ANN outperformed other learning algorithms with highest specificity. This study affirmed that there would be need to use more than a learning algorithm when there are irrelevant features in the data sets.

SVM, Naïve Bayes, Bootstrap, Classification and learning algorithms.

In this paper, we consider Internet models, which respond to a congestion signal from the network described by a stochastic differential equation. We consider Internet networks with one source and n access links, as well as with r sources and single access link. We analyze the conditions for the existence of a solution and the algorithms needed to determine the solution. We carry out numerical simulations for certain parameter values.

Systems with delay; Stochatic processes; Wiener processes.

After presenting a survey using the expert system implemented at the “Tibiscus” University of Timisoara, Romania, applied for at least five years to analyze the quality assessment of the educational process, compulsory made by the students at our university using an online web-based application and based on the requirements of the Romanian Agency for Quality Insurance in Higher Education (ARACIS), we’re now introducing the results of a survey upon the Computer Science master students. The results of the statistical analysis are used on departments to ensure the transparent policy of the educational high education evaluation. The application allows first the evaluation by students, then the interpretation of the results and finally the study of the evolution of the results. The mathematical apparatus we’re using are statistical indicators as the average, the mean squared deviations, the class values, the correlations and others. We continue to suggest that a widely implementation of our solution permits to have the same evaluation system in all universities and, by consequence, a unitary insight to the higher education level.

Fisher test, Student test, students' satisfaction, education assessment.

Patient registries are being developed worldwide in response to the increasing demands of healthcare providers, for both clinical and research benefits. We describe the development and operation of the first national registries implemented for patients with extracorporeal support of vital functions, by hemofiltration and artificial lung, respectively. The registry development was accomplished under the auspices of the Romanian Society of Anesthesia and Intensive Care (SRATI). The registries are currently in use, serving a multicentric network of hospitals in Romania. The National Artificial Lung Registry is available on the website novalung.srati.ro, while the Hemofiltration National Registry is available on the website hemofiltrare.srati.ro. The beneficiaries are the Intensive Care Units medical staff, researchers and patients themselves. This also results in improved healthcare services and allows translation towards larger scale registry networks, at national and international level, by implementing standards defined in CEN 13606 and HL7.

electronic patient registry, multicentric registry, hemofiltration, artificial lung, extracorporeal support, intensive care unit.