International Journal of Mathematical Sciences and Computing @ijmsc
Статьи журнала - International Journal of Mathematical Sciences and Computing
Все статьи: 258
Статья научная
In this paper, we studied to obtain numerical solutions of partial differential equations with fractional variable coefficient by MAPLE 18 software algorithm on New Iterative Method. We examined and investigated behaviours of the fractional variable coefficients (Even and Odd) on first order partial differential equation; we obtain numerical solution and plot 2D/3D graphs representation of eight (8) cases for the study of the sequential trend of the fractional coefficients. The simplicity and the accuracy of the proposed numerical scheme are verified. More numerical examples will be used in the future for further testing the ability of the proposed scheme for solving some classical problems in engineering sciences.
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On E–Optimality Design for Quadratic Response Surface Model
Статья научная
In response surface methodology, optimality criteria is a major tools used to measure the goodness of a design. Optimal experimental designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. E – Optimality criterion is one of the traditional alphabetical criterion used to explore the right choice of a design in both linear and quadratic response surface models. In this paper, we investigated E – optimal experimental designs for a quadratic response surface model with two factor predictors. We developed an algorithm and a flowchart in line with a program to obtain E – optimal design and compare the result with an existing method. Two designs were formulated each with six points to illustrate the usefulness of the new method. The result revealed that the new technique outperformed better than the existing method. The significance of the later to the former technique is that, it minimizes error due to approximation and also make the computation of the aforementioned optimality easier. We, therefore recommended this method to be used at all length of points when E – optimality is to be evaluated.
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Статья научная
This paper aims at providing in-depth refinement to switching time-variant autoregressive processes via the mode as a stable location parameter in adopted noisy Fisher’s z-distribution that was impelled in a Bayesian setting. Explicitly, a four-parameter Fisher’s z-distribution of Bayesian Mixture Autoregressive (FZBMAR) process was proposed to congruous k-mixture components of Fisher’s z-switching mixture autoregressive processes that was based on shifting number of modes in the marginal density of any switching time-variant series of interest. The proposed FZBMAR process was not only used to seize what is term “most likely mode value” of the present conditional modal distribution given the immediate past but was also used to capture the conditional modal distribution of the observations given the immediate past that can either be perceived as an asymmetric or symmetric distributed varieties. The proposed FZBMAR process was compared with the existing Student-t Mixture Autoregressive (StMAR) and Gaussian Mixture Autoregressive (GMAR) processes with the demonstration of monthly average share prices (stock prices) of sixteen (16) swaying European economies. Based on the findings, the FZBMAR process outperformed the existing StMAR and GMAR processes in explaining the sixteen (16) swaying European economies share prices via a minimum Pareto-Smoothed Important Sampling Leave-One-Out Cross-Validation (PSIS-LOO) error process performance in comparison with AIC, HQIC by the latters. The same singly truncated student-t prior distribution was adopted for the noisy adoption of Fisher’s z hyper-parameters and the embedded autoregressive coefficients in the proposed FZBMAR process; such that their resulting posterior distributions gave the same singly truncated student-t distribution (conjugate) with an embedded Gamma variate.
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On the Relations between Lucas Sequence and Fibonacci-like Sequence by Matrix Methods
Статья научная
In the present paper first and foremost we introduce a generalization of a classical Fibonacci sequence which is called a Fibonacci-Like sequence and at hindmost we obtain some relationships between Lucas sequence and Fibonacci-Like sequence by using two cross two matrix representation to the Fibonacci-Like sequence. The most worth noticing cause of this article is our proof method, since all the identities are proved by using matrix methods.
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On the number of Perfect Matchings of Tubular Fullerene Graphs
Статья научная
The perfect matchings counting problem of graphs has important applications in combinatorial optimization, statistical physics, quantum chemistry and other fields. A perfect matching of a graph G is a set of non-adjacent edges that covers all vertices of G . The number of perfect matchings of a graph is closely related to its number of vertices. A fullerene graph is a 3-connected cubic planar graphs all of whose faces are pentagons and hexagons. Došlić obtained that a fullerene graph with P vertices has at least P/2+1 perfect matchings, Zhang et al. proved a better lower bound 3(p+2)/4 of the number of perfect matchings of a fullerene graph. We have known that the fullerene graph has a nontrivial cyclic 5-edge-cut if and only if it is isomorphic to the graph Tn for some integer n >=1, where Tn is the tubular fullerene graph Tn comprised of two caps formed of six pentagons joined by n concentric layers of hexagons. In this paper, the perfect matchings of the graph Tn is classified by matching a certain vertex, and recursive relations of a set of perfect matching numbers are obtained. Then the calculation formula of the number of perfect matchings of the graph Tn is given by recursive relationships. Finally, we get the number of perfect matchings of Tn with P vertices.
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Статья научная
It has been of concern for the most appropriate control mechanism associated with the growing complexity of dual HIV-HBV infectivity. Moreso, the scientific ineptitude towards an articulated mathematical model for co-infection dynamics and accompanying methodological application of desired chemotherapies inform this present investigation. Therefore, the uniqueness of this present study is not only ascribed by the quantitative maximization of susceptible state components but opined to an insight into the epidemiological identifiability of dual HIV-HBV infection transmission routes and the methodological application of triple-dual control functions. Using ODEs, the model was formulated as a penultimate 7-Dimensional mathematical dynamic HIV-HBV model, which was then transformed to an optimal control problem, following the introduction of multi-therapies in the presence of dual adaptive immune system and time delay lags. Applying classical Pontryagin’s maximum principle, the system was analyzed, leading to the derivation of the model optimality system and uniqueness of the system. Specifically, following the dual role of the adaptive immune system, which culminated into triple-dual application of multi-therapies, the investigation was characterized by dual delayed HIV-HBV virions decays from infected double-lymphocytes in a biphasic manner, accompanied by more complex decay profiles of infectious dual HIV-HBV virions. The result further led to significant triphasic maximization of susceptible double-lymphocytes and dual adaptive immune system (cytotoxic T-lymphocytes and humeral immune response) achieved under minimal systemic cost. Therefore, the model is comparatively a monumental and intellectual accomplishment, worthy of emulation for related and future dual infectivity.
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Статья научная
An innovative and creative docking technique known as cross- docking (CD) strategy was initiated in 1930s to make supply chain fast and productive. However, it only became popular from 1980s. Vehicle routing between suppliers/customers to CD terminal (CDT) is one of operational level problems at CDT. Moreover, moving unloaded products from indoors to outdoors of CDT is one of the internal operations inside a CDT. The main difference between this study and the existing studies which find in the literature is that to consider the activities inside CDT. Also, loading or unloading shipments at all the nodes including CDT are taken into account. Moreover, homogenous fleets of vehicles within pickup or delivery process are assumed, but heterogeneous fleets of vehicles between pickup and delivery processes are assumed in this study. A mixed integer non-linear programming model is developed to address this problem. In our proposed model, costs of transportation between nodes, service at nodes including CDT, moving shipments inside CDT and vehicle operation are considered as the contributors to the total cost. The proposed model was tested for fifteen randomly generated small scale problems using Branch and Bound algorithm and the algorithm was run using LINGO (version 18) optimization software. The average computational time to reach the optimal solution is estimated. The study revealed that for small scale problems, the convergence rate of the problems rises to polynomial with degree 6. Also, the study shows that for moderately large and large scale problems the computational time to reach the optimal solution is exponential. Therefore, this study recommends using a suitable evolutionary algorithm to reach a near optimal solution for moderately large and large scale problems. It further recommends that, this model can be used for last time planning for similar small scale problems.
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Optimal bounding function for GNR-enumeration
Статья научная
The proposed pruning technique by Gama-Nguyen-Regev for enumeration function makes this pruned enumeration (GNR-enumeration) as a claimant practical solver for SVP. The total cost of GNR-enumeration over a specific input lattice block with pre-defined enumeration radius and success probability would be minimized, just if this enumeration uses an optimal bounding function for pruning. Unfortunately, the running time of the original proposed algorithm of searching optimal bounding function by the work of Chen-Nguyen (in 2011) is not analyzed at all, so our work in this paper tries to introduce some efficient searching algorithms with exact analysis of their time/space complexity. In fact, this paper proposes a global search algorithm to generate the optimal bounding function by a greedy idea. Then, by using our greedy strategy and defining the searching steps based on success probability, a practical search algorithm is introduced, while it’s time-complexity can be determined accurately. Main superiorities of our algorithm include: complexity analysis, using high-performance version of each sub-function in designing search algorithm, jumping from local optimums, simple heuristics to guide the search, trade-off between quality of output and running time by tuning parameters. Also by using the building blocks in our practical search algorithm, a high-quality and fast algorithm is designed to approximate the optimal bounding function.
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Optimal control dynamics: control interventions for eradication of ebola virus infection
Статья научная
In affirmation of the existence of control interventions for the eradication of Ebola virus infection as a remedy to complete lack of outright medical cure, the present study seek and formulated using continuous ordinary differential equations an extended BEB-SEIR 4-Dimensional mathematical Ebola dynamic model vested with the scope of establishing the epidemiological impact of identified structured Ebola control measures. Derived model was presented as an optimal control problem subjected to structured dual treatment functions. Moreso, following the validity of model state components as representatives of living organisms and the establishment of existence of boundedness of solutions; we performed our analysis using classical Pontryagin’s maximum principle with which the optimality system of the model was established. Numerical simulations of derived model via Runge-Kutter of order 4 in a Mathcad surface were conducted. Result clearly indicated enhanced impact of intermediary and secondary control interventions as Ebola virus treatment functions with high significant maximization of susceptible population devoid of Ebola infection. Both the exposed and infectious classes were maximally reduced to near zero with possibilities of achieving complete eradication if time interval could be extended exceeding the of Ebola life-cycle. Furthermore, recovery rate of removed class justified the formulation and application of the model. The study therefore suggests further articulation of the model to account for possible intracellular delay in the biological mechanism.
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Outlier Detection Algorithm Based on Fuzzy C-Means and Self-organizing Maps Clustering Methods
Статья научная
Data mining and machine learning methods are important areas where studies have increased in recent years. Data is critical for these areas focus on inferring meaningful conclusions from the data collected. The preparation of the data is very important for the studies to be carried out and the algorithms to be applied. One of the most critical steps in data preparation is outlier detection. Because these observations, which have different characteristics from the observations in the data, affect the results of the algorithms to be applied and may cause erroneous results. New methods have been developed for outlier detection and machine learning and data mining algorithms have been provided with successful results with these methods. Algorithms such as Fuzzy C Means (FCM) and Self Organization Maps (SOM) have given successful results for outlier detection in this area. However, there is no outlier detection method in which these two powerful clustering methods are used together. This study proposes a new outlier detection algorithm using these two powerful clustering methods. In this study, a new outlier detection algorithm (FUSOMOUT) was developed by using SOM and FCM clustering methods together. With this algorithm, it is aimed to increase the success of both clustering and classification algorithms. The proposed algorithm was applied to four different datasets with different characteristics (Wisconsin breast cancer dataset (WDBC), Wine, Diabetes and Kddcup99) and it was shown to significantly increase the classification accuracy with the Silhouette, Calinski-Harabasz and Davies-Bouldin indexes as clustering success indexes.
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Статья научная
One distress of network and data security professionals and advisers globally is about the abilities of infectious malicious agents (Malware) to invade the entire network terminals to wreak havoc extending from identity theft, financial fraud to systemic digital assault on critical national resources. This work studies the behavioural dynamics of the susceptible, infected, the recovered terminals on the mobile wireless network and the effective use of antivirus security signature as countermeasure. Solving for stability state, we found out that its Eigen value gives a positive value which means that the stability is at an unstable state. Using Homotopy perturbation to calculate the approximate solution of the system. The expression derived was simulated using a mathematical tool (mat lab).
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Performance Evaluation of Industrial and Commercial bank of China based on DuPont Analysis
Статья научная
With the reform of Chinese economic system, the development of enterprises is facing many risks and challenges. In order to understand the state of operation of enterprises, it is necessary to apply relevant methods to evaluate the enterprise performance. Taking Industrial and Commercial Bank of China as an example, this paper selects its financial data from 2018 to 2021. Firstly, DuPont analysis is applied to decompose the return on equity into the product of profit margin on sales, total assets turnover ratio and equity multiplier. Then analyzes the effect of the changes of these three factors on the return on equity respectively by using the Chain substitution method. The results show that the effect of profit margin on sales on return on equity decreases year by year and tends to be positive from negative. The effect of total assets turnover ratio on return on equity changes from positive to negative and then to positive, while the effect of equity multiplier is opposite. These results provide a direction for the adjustment of the return on equity of Industrial and Commercial Bank of China. Finally, according to the results, some suggestions are put forward for the development of Industrial and Commercial Bank of China.
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Periodic pattern formation analysis numerically in a chemical reaction-diffusion system
Статья научная
In this paper, we analyze the pattern formation in a chemical reaction-diffusion Brusselator model. Two-component Brusselator model in two spatial dimensions is studied numerically through direct partial differential equation simulation and we find a periodic pattern. In order to understand the periodic pattern, it is important to investigate our model in one-dimensional space. However, direct partial differential equation simulation in one dimension of the model is performed and we get periodic traveling wave solutions of the model. Then, the local dynamics of the model is investigated to show the existence of the limit cycle solutions. After that, we establish the existence of periodic traveling wave solutions of the model through the continuation method and finally, we get a good consistency among the results.
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Prediction of Rainfall Using Unsupervised Model based Approach Using K-Means Algorithm
Статья научная
Prediction of rainfall has gained a significant importance because of many associated factors like cultivating, aqua-culture and other indirect parameters allied with the rainfall like global heat. Therefore it is necessary to predict the rainfall from the satellite images effectively. In this article, a segmentation algorithm is developed based on Gaussian mixture models. The initial parameters are estimated using k-means algorithm. The process is presented by using an 2-fold architecture, where in the first stage database creation is considered and the second stage talks about the prediction. The performance analysis is carried out using metrics like PSNR, IF and MSE. The developed model analyzes the satellite images and predicts the Rainfall efficiently.
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Predictive Analytics of Employee Attrition using K-Fold Methodologies
Статья научная
Currently, every company is concerned about the retention of their staff. They are nevertheless unable to recognize the genuine reasons for their job resignations due to various circumstances. Each business has its approach to treating employees and ensuring their pleasure. As a result, many employees abruptly terminate their employment for no apparent reason. Machine learning (ML) approaches have grown in popularity among researchers in recent decades. It is capable of proposing answers to a wide range of issues. Then, using machine learning, you may generate predictions about staff attrition. In this research, distinct methods are compared to identify which workers are most likely to leave their organization. It uses two approaches to divide the dataset into train and test data: the 70 percent train, the 30 percent test split, and the K-Fold approaches. Cat Boost, LightGBM Boost, and XGBoost are three methods employed for accuracy comparison. These three approaches are accurately generated by using Gradient Boosting Algorithms.
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Статья научная
Objective: The COVID-19 pandemic situation has deeply affected students' psychological, financial, and career problems. The objective of our study is to find out the prevalence and identify significant risk factors of psychological, financial and career effects among the students in the pandemic. Methods: The cross-sectional survey was performed online via multiple social media sites such as Facebook, Email, WhatsApp, and the survey included 723 individuals. Chi-square analysis was performed to show the association between different selected factors and psychological, financial and career problems. Risk factors were obtained by logistics regression on the basis of p-value (p-value<0.05). Findings: Our findings illustrate that 68.11% of students suffer from depression, 60.86% from anxiety, 61.98% from a mood disorder, and 63.23% from financial difficulties, such as being unable to afford the cost of education, working frustrated all the time, and losing interest in many things. Binary logistic regression demonstrated that student’s gender, feeling helpless, worried, lost interest, educational expenses, and opinion of solve the problems and problems for prolonging education system were the risk factors of career effects. On the other hand, student’s gender, marital status, feeling bad about yourself, symptoms of corona virus, feeling nervous, short term memory loss, mood change, communicating problem, lost interest, feeling helpless, continue of income, study interrupt, irritable mood were associated factors of psychological problems. Family income status, feeling bad about yourself, lost interest, educational expenses, continue of income source, study interrupt, reason of study interrupt, were the factors associated with financial problems. Novelty: We have found many statistically significant risk factors of the psychological (depression, anxiety and mood disorder) as well as financial and career of the students in the pandemic situation, which have not been discussed in previous studies.
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Статья научная
One of the most important reasons for information systems failure is lack of quality. Information Systems Quality (ISQ) evaluation is important to prevent the lack of quality. ISQ evaluation is one of the most important Multi-Criteria Decision Making (MCDM) problems. The concept of Single Valued Triangular Neutrosophic Numbers (SVTrN-numbers) is a generalization of fuzzy set and intuitionistic fuzzy set that make it is the best fit in representing indeterminacy and uncertainty in MCDM. This paper aims to introduce an ISQ evaluation model based on SVTrN- numbers with introducing two types of evaluating and ranking methods. The results indicated that the proposed model can handle ill-known quantities in evaluating ISQ. Also by analyzing and comparing results of ranking methods, the results indicated that each method has its own advantage that make the proposed model introduces more than one option for evaluating and ranking ISQ.
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Proving Riemann Hypothesis through the Derivative of Zeta Reflection
Статья научная
A novel proof is presented in this work indicating that all non-trivial zeros of the zeta function has a real part equal to ½. As no proof has been validated yet, this work was successful in introducing a proof through the use of elementary calculus theorems. A second version of the proof was also shown where a more advanced series analysis (e.g. Fourier series) is used.
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Pseudo-Complemented Semigroups
Статья научная
We shall introduce the notion of pseudo – complemented semigroup, which is a natural generalization of the notion of pseudo- complemented semi-lattices, and give certain properties of such semi-groups. We also introduced the notion of Baer- Stone semigroup, which is Pseudo complimented semigroup satisfy certain additional properties.
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Quantum Mechanics Analysis: Modeling and Simulation of some simple systems
Статья научная
Quantum Mechanics is a radically new way of thinking about the Nature. It is used for explaining the behavior of an electron to the possible existence of parallel universes. Most of the times, it is just too difficult to get an intuitive grasp of Quantum Mechanics. Quantum Mechanics is a mathematical framework for describing atomic and subatomic systems. In this paper the basic principles of Quantum Mechanics have been presented. It has been shown that classical probabilities when added increase the overall probability while in quantum probabilities can cancel each other and hence lower the overall probability. A simple approach has been taken by modeling the systems as graphs. The states and dynamics of the systems have been modeled as matrices. The principle of Superposition and the phenomenon of Interference have been explained in a single simulation. Finally the BLAS functions of Julia programming language have been used for simulating the systems under study on a classical computer and a detailed discussion is presented to highlight the incapability of the classical explanation of quantum phenomenon.
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