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Math. Comput. Appl., Volume 22, Issue 2 (June 2017)

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Research

Open AccessArticle An Algorithm Based on GSVD for Image Encryption
Math. Comput. Appl. 2017, 22(2), 28; doi:10.3390/mca22020028
Received: 28 January 2017 / Revised: 10 March 2017 / Accepted: 17 March 2017 / Published: 28 March 2017
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Abstract
This paper represents a new image encryption algorithm based on modifying generalized singular value decomposition (GSVD) by decomposing the plain-image into two segments using GSVD with an exchanged key-image to produce the cipher-image. The exchanged key-image is used as an encrypting and decrypting
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This paper represents a new image encryption algorithm based on modifying generalized singular value decomposition (GSVD) by decomposing the plain-image into two segments using GSVD with an exchanged key-image to produce the cipher-image. The exchanged key-image is used as an encrypting and decrypting image. Mathematically, this procedure is represented by transforming the plain-image’s matrix into two different matrices and applying the GSVD with the exchanged key-image’s matrix to obtain the cipher-image’s matrix. The two encoded segments can be kept in several places or assigned to a group of authorized persons. No one can obtain the information of the image easily without the knowledge of the decrypting key. This proposed algorithm is represented as one of the digital image encryption techniques used to enhance the security of images that have been sent between recipients. Full article
Open AccessArticle Analysis of a Hand-Foot-Mouth Disease Model with Standard Incidence Rate and Estimation for Basic Reproduction Number
Math. Comput. Appl. 2017, 22(2), 29; doi:10.3390/mca22020029
Received: 8 February 2017 / Revised: 2 April 2017 / Accepted: 4 April 2017 / Published: 8 April 2017
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Abstract
Firstly, an SEIR mathematical model with standard incidence rate is established to describe the transmission of Hand-Foot-Mouth disease (HFMD). The equilibrium of the nondimensionalized model is calculated and the basic reproduction number of the model is defined. In addition, the local stability of
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Firstly, an SEIR mathematical model with standard incidence rate is established to describe the transmission of Hand-Foot-Mouth disease (HFMD). The equilibrium of the nondimensionalized model is calculated and the basic reproduction number of the model is defined. In addition, the local stability of the equilibrium is analyzed via the characteristic roots of the Jacobian matrix at the equilibrium, respectively. Numerical simulations are given to confirm the theoretical results. Secondly, a formula aimed to estimate the basic reproduction number of the transmission of HFMD is deduced. As examples to make use of the formula, the basic reproduction number of the HFMD transmission of Singapore of years 2015 and 2016 is estimated based on the newly infected cases notified by the surveillance organizations, respectively. The formula can realize real time estimation for the basic reproduction number and does not need to estimate the transmission efficiency of HFMD between individuals. Full article
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Open AccessArticle Broken Bar Diagnosis for Squirrel Cage Induction Motors Using Frequency Analysis Based on MCSA and Continuous Wavelet Transform
Math. Comput. Appl. 2017, 22(2), 30; doi:10.3390/mca22020030
Received: 10 January 2017 / Revised: 5 April 2017 / Accepted: 7 April 2017 / Published: 11 April 2017
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Abstract
The importance of early fault detection in electric motors has attracted the attention of research groups, as the detection of incipient faults can prevent damage spreading and increase the lifetime of the motor. At present, studies have focused their attention on optimization procedures
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The importance of early fault detection in electric motors has attracted the attention of research groups, as the detection of incipient faults can prevent damage spreading and increase the lifetime of the motor. At present, studies have focused their attention on optimization procedures used for fault detection in induction machines to achieve a quick and easy-to-interpret assessment at an industrial level. This paper proposes an alternative approach based on the Continuous Wavelet Transform (CWT) for broken bar diagnosis in squirrel cage induction motors. This work uses the Motor Current Signature Analysis (MCSA) method to acquire the current signal of the induction motor. The novelty of this study lies in broken bar detection in electric machines operating at non-load by analyzing variations in the spectrum of the motor’s current signal. This way, the faults are presented as oscillations in the current signal spectrum. Additionally, a quantification of broken bars for the same type of motors operating at fullload is performed in this study. An experimental validation and the comparison with the Fast Fourier Transform (FFT) technique are provided to validate the proposed technique. Full article
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Open AccessArticle A New Smoothing Nonlinear Penalty Function for Constrained Optimization
Math. Comput. Appl. 2017, 22(2), 31; doi:10.3390/mca22020031
Received: 5 November 2016 / Revised: 29 March 2017 / Accepted: 4 April 2017 / Published: 12 April 2017
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Abstract
In this study, a new smoothing nonlinear penalty function for constrained optimization problems is presented. It is proved that the optimal solution of the smoothed penalty problem is an approximate optimal solution of the original problem. Based on the smoothed penalty function, we
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In this study, a new smoothing nonlinear penalty function for constrained optimization problems is presented. It is proved that the optimal solution of the smoothed penalty problem is an approximate optimal solution of the original problem. Based on the smoothed penalty function, we develop an algorithm for finding an optimal solution of the optimization problems with inequality constraints. We further discuss the convergence of this algorithm and test this algorithm with three numerical examples. The numerical examples show that the proposed algorithm is feasible and effective for solving some nonlinear constrained optimization problems. Full article
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Open AccessArticle Topology on Soft Continuous Function Spaces
Math. Comput. Appl. 2017, 22(2), 32; doi:10.3390/mca22020032
Received: 28 December 2016 / Revised: 25 March 2017 / Accepted: 3 April 2017 / Published: 27 April 2017
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Abstract
The concept of soft sets was initiated by Molodtsov. Then, some operations on soft sets were defined by Maji et al. Later on, the concept of soft topological space was introduced. In this paper, we introduce the concept of the pointwise topology of
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The concept of soft sets was initiated by Molodtsov. Then, some operations on soft sets were defined by Maji et al. Later on, the concept of soft topological space was introduced. In this paper, we introduce the concept of the pointwise topology of soft topological spaces. Finally, we investigate the properties of soft mapping spaces and the relationships between some soft mapping spaces. Full article
Open AccessArticle Surface Roughness Modeling Using Q-Sequence
Math. Comput. Appl. 2017, 22(2), 33; doi:10.3390/mca22020033
Received: 29 March 2017 / Revised: 1 May 2017 / Accepted: 2 May 2017 / Published: 6 May 2017
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Abstract
Dynamical systems play a vital role in studying highly non-linear phenomena. One of the families of the dynamical systems is integer sequences. There is an integer sequence called Q-sequence: Q(n) = Q(nQ(n − 1))
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Dynamical systems play a vital role in studying highly non-linear phenomena. One of the families of the dynamical systems is integer sequences. There is an integer sequence called Q-sequence: Q(n) = Q(nQ(n − 1)) + Q(nQ(n − 2)); for n = 3, 4, …; and Q(1) = Q(2) = 1. It exhibits a unique chaotic-order that might help develop approximate models of highly nonlinear phenomena. We explore this possibility and show how to modify a segment of the Q-sequence so that the modified segment becomes an approximate model of surface roughness (a highly non-linear phenomena that results from the material removal processes (e.g., turning, milling, grinding, and so on). The Q-sequence-based models of surface roughness can be used to recreate the surface heights whenever necessary. As such, it is a helpful means for developing simulation systems for virtual manufacturing. Full article
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Open AccessArticle Image Interpolation via Scanning Line Algorithm and Discontinuous B-Spline
Math. Comput. Appl. 2017, 22(2), 34; doi:10.3390/mca22020034
Received: 12 May 2017 / Revised: 23 May 2017 / Accepted: 23 May 2017 / Published: 31 May 2017
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Abstract
Image interpolation is a basic operation in image processing. Lots of methods have been proposed, including convolution-based methods, edge modeling methods, point spread function (PSF)-based methods or learning-based methods. Most of them, however, present a high computational complexity and are not suitable for
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Image interpolation is a basic operation in image processing. Lots of methods have been proposed, including convolution-based methods, edge modeling methods, point spread function (PSF)-based methods or learning-based methods. Most of them, however, present a high computational complexity and are not suitable for real time applications. However, fast methods are not able to provide artifacts-free images. In this paper we describe a new image interpolation method by using scanning line algorithm which can generate C - 1 curves or surfaces. The C - 1 interpolation can truncate the interpolation curve at big skipping; hence, the image edge can be kept. Numerical experiments illustrate the efficiency of the novel method. Full article
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Open AccessArticle 3-Homogeneous Groups and Block-Transitive 7–(v, k, 3) Designs
Math. Comput. Appl. 2017, 22(2), 35; doi:10.3390/mca22020035
Received: 25 November 2016 / Revised: 25 May 2017 / Accepted: 29 May 2017 / Published: 15 June 2017
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Abstract
The classification of a block-transitive designs is an important subject on algebraic combinatorics. With the aid of MATLAB software, using the classification theorem of 3-homogeneous permutation groups, we look at the classification problem of block-transitive 7–(v, k, 3) design and
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The classification of a block-transitive designs is an important subject on algebraic combinatorics. With the aid of MATLAB software, using the classification theorem of 3-homogeneous permutation groups, we look at the classification problem of block-transitive 7–(v, k, 3) design and prove our main theorem: If the automorphism group of a 7–(v, k, 3) design is block-transitive, then it is neither isomorphic to Affine Type Groups nor Almost Simple Type Groups. Full article
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Open AccessArticle Finite Convergence for Feasible Solution Sequence of Variational Inequality Problems
Math. Comput. Appl. 2017, 22(2), 36; doi:10.3390/mca22020036
Received: 19 April 2017 / Revised: 31 May 2017 / Accepted: 7 June 2017 / Published: 20 June 2017
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Abstract
We establish the notion of augmented weak sharpness of solution sets for the variational inequality problems which can be abbreviated to VIPs. This notion of augmented weak sharpness is an extension of the weak sharpness of the solution set of monotone variational inequality,
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We establish the notion of augmented weak sharpness of solution sets for the variational inequality problems which can be abbreviated to VIPs. This notion of augmented weak sharpness is an extension of the weak sharpness of the solution set of monotone variational inequality, and it overcomes the defect of the solution set not satisfying the weak sharpness in many cases. Under the condition of the solution set being augmented weak sharp, we present a necessary and sufficient condition for finite convergence for feasible solution sequence of VIP. The result is an extension of published results, and the augmented weak sharpness also provides weaker sufficient conditions for the finite convergence of many optimization algorithms. Full article
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