Journal of Applied Mathematics has recently been accepted into Web of Science.
Journal of Applied Mathematics publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.
Journal of Applied Mathematics maintains an Editorial Board of practicing researchers from around the world, to ensure manuscripts are handled by editors who are experts in the field of study.
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An Efficient Convolution Algorithm for the Non-Markovian Two-Node Cyclic Network
Consider a closed cyclic queueing model that consists of two nodes and a total of customers. Each node buffer can accommodate all customers. Node 1 has servers, each having an exponential service time with rate . The second node consists of a single server with a general service time distribution function . The well-known machine repair model with spares, where a set of identical machines, , is served by a single repair person, is a key application of this model. This model has several other applications in performance evaluation, manufacturing, computer networks, and in reliability studies as it can be easily used to compute system availability. In this article, we give an efficient algorithm to derive an exact solution for the steady state system size probabilities. Our approach is based on developing an efficient polynomial convolution method to compute the transition probabilities of a birth process over node 2 service times and solving an imbedded Markov chain at node 2 service completion epochs. This is a significant improvement over the exponential algorithm given in an earlier paper. Numerical examples are given to demonstrate the performance of our method.
Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis
This paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpopulation. A qualitative analysis was performed to examine the invariant regions, positivity of solutions, and disease equilibrium points together with their stabilities. The basic reproduction number, , is computed and used as a threshold value to determine the existence and stability of the equilibrium points. It is established that, under a specific condition, the disease-free equilibrium exists and there is a unique endemic equilibrium when . It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable provided , and the unique endemic equilibrium point is locally asymptotically stable whenever using the concept of the Center Manifold Theory. A numerical simulation carried out showed that at , the model exhibits a forward bifurcation which, thus, validates the analytic results. Numerical analyses of the control strategies were performed and discussed. Further, a sensitivity analysis of was carried out to determine the contribution of the main parameters towards the die out of the disease. Finally, the effects that these parameters have on the infected humans were numerically examined, and the results indicated that combined application of treatment and WASH will be effective in eradicating schistosomiasis.
Key -Gram Extractions and Analyses of Different Registers Based on Attention Network
Key-gram extraction can be seen as extracting -grams which can distinguish different registers. Keyword (as , 1-gram is the keyword) extraction models are generally carried out from two aspects, the feature extraction and the model design. By summarizing the advantages and disadvantages of existing models, we propose a novel key -gram extraction model “attentive -gram network” (ANN) based on the attention mechanism and multilayer perceptron, in which the attention mechanism scores each -gram in a sentence by mining the internal semantic relationship between words, and their importance is given by the scores. Experimental results on the real corpus show that the key -gram extracted from our model can distinguish a novel, news, and text book very well; the accuracy of our model is significantly higher than the baseline model. Also, we conduct experiments on key -grams extracted from these registers, which turned out to be well clustered. Furthermore, we make some statistical analyses of the results of key -gram extraction. We find that the key -grams extracted by our model are very explanatory in linguistics.
Relation between Borweins’ Cubic Theta Functions and Ramanujan’s Eisenstein Series
Two-dimensional theta functions were found by the Borwein brothers to work on Gauss and Legendre’s arithmetic-geometric mean iteration. In this paper, some new Eisenstein series identities are obtained by using (, )-parametrization in terms of Borweins’ theta functions.
Fast Mumford-Shah Two-Phase Image Segmentation Using Proximal Splitting Scheme
The Mumford-Shah model is extensively used in image segmentation. Its energy functional causes the content of the segments to remain homogeneous and the segment boundaries to become short. However, the problem is that optimization of the functional can be very slow. To attack this problem, we propose a reduced two-phase Mumford-Shah model to segment images having one prominent object. First, initial segmentation is obtained by the k-means clustering technique, further minimizing the Mumford-Shah functional by the Douglas-Rachford algorithm. Evaluation of segmentations with various error metrics shows that 70 percent of the segmentations keep the error values below 50%. Compared to the level set method to solve the Chan-Vese model, our algorithm is significantly faster. At the same time, it gives almost the same or better segmentation results. When compared to the recent k-means variant, it also gives much better segmentation with convex boundaries. The proposed algorithm balances well between time and quality of the segmentation. A crucial step in the design of machine vision systems is the extraction of discriminant features from the images, which is based on low-level segmentation which can be obtained by our approach.
Evaluation of the DWT-PCA/SVD Recognition Algorithm on Reconstructed Frontal Face Images
The face is the second most important biometric part of the human body, next to the finger print. Recognition of face image with partial occlusion (half image) is an intractable exercise as occlusions affect the performance of the recognition module. To this end, occluded images are sometimes reconstructed or completed with some imputation mechanism before recognition. This study assessed the performance of the principal component analysis and singular value decomposition algorithm using discrete wavelet transform (DWT-PCA/SVD) as preprocessing mechanism on the reconstructed face image database. The reconstruction of the half face images was done leveraging on the property of bilateral symmetry of frontal faces. Numerical assessment of the performance of the adopted recognition algorithm gave average recognition rates of 95% and 75% when left and right reconstructed face images were used for recognition, respectively. It was evident from the statistical assessment that the DWT-PCA/SVD algorithm gives relatively lower average recognition distance for the left reconstructed face images. DWT-PCA/SVD is therefore recommended as a suitable algorithm for recognizing face images under partial occlusion (half face images). The algorithm performs relatively better on left reconstructed face images.