Mathematical and Computational Applications

722 KiB

Open AccessArticle

Finite Convergence for Feasible Solution Sequence of Variational Inequality Problems

by Wenling Zhao, Ruyu Wang and Hongxiang Zhang

Math. Comput. Appl. 2017, 22(2), 36; https://doi.org/10.3390/mca22020036 - 20 Jun 2017

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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, [...] Read more.

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

1038 KiB

Open AccessArticle

3-Homogeneous Groups and Block-Transitive 7–(v, k, 3) Designs

by Xiaolian Liao, Guohua Chen and Shangzhao Li

Math. Comput. Appl. 2017, 22(2), 35; https://doi.org/10.3390/mca22020035 - 15 Jun 2017

Viewed by 2562

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 [...] Read more.

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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3161 KiB

Open AccessArticle

Image Interpolation via Scanning Line Algorithm and Discontinuous B-Spline

by Cheng-ming Liu, Ze-kun Wang, Hai-bo Pang and Jun-xiao Xue

Math. Comput. Appl. 2017, 22(2), 34; https://doi.org/10.3390/mca22020034 - 31 May 2017

Cited by 2 | Viewed by 3038

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 [...] Read more.

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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2933 KiB

Open AccessArticle

Surface Roughness Modeling Using Q-Sequence

by A.M.M. Sharif Ullah

Math. Comput. Appl. 2017, 22(2), 33; https://doi.org/10.3390/mca22020033 - 06 May 2017

Cited by 11 | Viewed by 4432

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(n − Q(n − 1)) [...] Read more.

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(n − Q(n − 1)) + Q(n − Q(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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234 KiB

Open AccessArticle

Topology on Soft Continuous Function Spaces

by Taha Yasin Öztürk and Sadi Bayramov

Math. Comput. Appl. 2017, 22(2), 32; https://doi.org/10.3390/mca22020032 - 27 Apr 2017

Cited by 9 | Viewed by 3543

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 [...] Read more.

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

777 KiB

Open AccessArticle

A New Smoothing Nonlinear Penalty Function for Constrained Optimization

by Touna Yang, Nguyen Thanh Binh, Tran Manh Thang and Duong Thi Hoa

Math. Comput. Appl. 2017, 22(2), 31; https://doi.org/10.3390/mca22020031 - 12 Apr 2017

Cited by 3 | Viewed by 3459

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 [...] Read more.

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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5897 KiB

Open AccessArticle

Broken Bar Diagnosis for Squirrel Cage Induction Motors Using Frequency Analysis Based on MCSA and Continuous Wavelet Transform

by Danilo Granda ,, Wilbert G. Aguilar, Diego Arcos-Aviles and Danny Sotomayor

Math. Comput. Appl. 2017, 22(2), 30; https://doi.org/10.3390/mca22020030 - 11 Apr 2017

Cited by 22 | Viewed by 5320

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 [...] Read more.

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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735 KiB

Open AccessArticle

Analysis of a Hand-Foot-Mouth Disease Model with Standard Incidence Rate and Estimation for Basic Reproduction Number

by Chunqing Wu

Math. Comput. Appl. 2017, 22(2), 29; https://doi.org/10.3390/mca22020029 - 08 Apr 2017

Cited by 2 | Viewed by 4039

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 [...] Read more.

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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327 KiB

Open AccessArticle

An Algorithm Based on GSVD for Image Encryption

by Mohammed Abdul Hameed Jassim Al-Kufi, Hayder Raheem Hashim, Ameer Mohammed Hussein and Hind Rustum Mohammed

Math. Comput. Appl. 2017, 22(2), 28; https://doi.org/10.3390/mca22020028 - 28 Mar 2017

Cited by 1 | Viewed by 3059

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 [...] Read more.

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

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Math. Comput. Appl., Volume 22, Issue 2 (June 2017) – 9 articles

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