Showing papers in "Applied mathematical sciences in 2013"
TL;DR: In this article, the Witt-type formula for Daehee numbrers and polynomials is considered and some properties of those numbers are investigated, in particular the relation between higher-order Bernoulli numbers and Bernoullis numbers of the second kind.
Abstract: We consider the Witt-type formula for Daehee numbrers and polynomials and investigate some properties of those numbers and polynomials. In particular, Daehee numbers are closely related to higher-order Bernoulli numbers and Bernoulli numbers of the second kind.
93 citations
TL;DR: An application of artificial neural networks to the real-world problem of predicting forest fires is presented and some examples of illustrating results that show the performance and the usefulness of the resulting neural system are discussed.
Abstract: In this paper, we present an application of artificial neural networks to the real-world problem of predicting forest fires. The neural network used for this application is a multilayer perceptron whose architectural parameters, i.e., the number of hidden layers and the number of neurons per layer were heuristically determined. The synaptic weights of this architecture were adjusted using the backpropagation learning algorithm and a large set of real data related to the studied problem. We also present and discuss some examples of illustrating results that show the performance and the usefulness of the resulting neural system. Mathematics Subject Classification: 68T05
65 citations
TL;DR: In this article, the authors conduct empirical analyses on detecting the existence of EKC using the five common pollutants emissions (i.e. CO2, SO2, BOD, SPM10, and GHG) as proxy for environmental quality.
Abstract: Previous studies show that the environmental quality and economic growth can be represented by the inverted U curve called Environmental Kuznets Curve (EKC). In this study, we conduct empirical analyses on detecting the existence of EKC using the five common pollutants emissions (i.e. CO2, SO2, BOD, SPM10, and GHG) as proxy for environmental quality. The data spanning from year 1961 to 2009 and cover 40 countries. We seek to investigate if the EKC hypothesis holds in two groups of economies, i.e. developed versus developing economies. Applying panel data approach, our results show that the EKC does not hold in all countries. We also detect the existence of U shape and increasing trend in other cases. The results reveal that CO2 and SPM10 are good data to proxy for environmental pollutant and they can be explained well by GDP. Also, it is observed that the developed countries have higher turning points than the developing countries. Higher economic growth may lead to different impacts on environmental quality in different economies.
61 citations
TL;DR: In this article, a new class of Log-Logistic distribution using MarshallOlkin transformation is introduced and its characterization and statistical properties are obtained, and using the proposed model, an autoregressive model and its minification structure are investigated.
Abstract: In this paper, a new class of Log-Logistic distribution using MarshallOlkin transformation is introduced. Its characterization and statistical properties are obtained. The proposed model extends the Log-Logistic distribution and is more flexible. Using the proposed model, we construct an autoregressive model and investigate its minification structure. Mathematics Subject Classification: 60E05, 62F10
45 citations
TL;DR: This model describes cancer growth on a cell population level with combination immunotherapy and chemotherapy treatments, and shows that for parameter set patient 9 and patient 10, the biochemotherapy more effective than the immunotherapy, chemotherapy and chemotherapy.
Abstract: In this paper, mathematical model of cancer treatments have been presented and analyzed using coupled ordinary differential equations (ODEs). This model describes cancer growth on a cell population level with combination immunotherapy and chemotherapy treatments are often called biochemotherapy. This model also describes the effect of tumor infiltrating lymphocytes (TIL), interleukin-2 (IL-2) and interferon alpha (INF-α) on dynamics of tumor cells under the influence of immunotherapy, chemotherapy and biochemotherapy. Through this mathematical model, numerical simulations of immunotherapy, chemotherapy and biochemotherapy for some cases such as variation of tumor size and variation of parameter among patient 9 and patient 10 were presented. Our result shown that for parameter set patient 9 and patient 10, the biochemotherapy more effective than the immunotherapy and chemotherapy.
44 citations
TL;DR: In this paper, the rotations of a microcopter are parametrized in terms of quaternions, taking into account the linearity of the quaternion formulation, their stability and eciency.
Abstract: The purpose of this paper is to present the basic mathematical modeling of microcopters, which could be used to develop proper methods for stabilization and trajectory control. The microcopter taken into account consists of six rotors, with three pairs of counter-rotating xedpitch blades. The microcopter is controlled by adjusting the angular velocities of the rotors which are spun by electric motors. It is assumed as a rigid body, so the dierential equations of the microcopter dynamics can be derived from both the Newton-Euler and Euler-Lagrange equations. Euler-angle parametrization of three-dimensional rotations contains singular points in the coordinate space that can cause failure of both dynamical model and control. In order to avoid singularities, the rotations of the microcopter are parametrized in terms of quaternions. This choice has been made taking into consideration the linearity of quaternion formulation, their stability and eciency.
39 citations
TL;DR: The concept of generalized interval-valued vague soft set is introduced along with its operations of intersection and union and an application in decision making with respect to degree of preference is illustrated.
Abstract: The concept of generalized interval-valued vague soft set is introduced along with its operations of intersection and union. An application of generalized interval-valued vague soft sets in decision making with respect to degree of preference is illustrated.
39 citations
TL;DR: In this article, the Binet's formula for k-Pell-Lucas numbers was obtained and some properties of the binet formula were obtained for the k-pell-laas numbers.
Abstract: We obtain the Binet’s formula for k-Pell-Lucas numbers and as a consequence we obtain some properties for k-Pell-Lucas numbers. Also we give the generating function for the k-Pell-Lucas sequences and another expression for the general term of the sequence, using the ordinary generating function, is provided. Mathematics Subject Classification: 11B37, 05A15, 11B83.
37 citations
TL;DR: Two methods of image classification are compared, i.e. ML (Maximum Likelihood), a supervised method, and ISODATA (Iterative Self- Organizing Data Analysis Technique), an unsupervised method, which can classify land covers with a higher accuracy and therefore is more widely used.
Abstract: The aim of this study is to compare two methods of image classification, i.e. ML (Maximum Likelihood), a supervised method, and ISODATA (Iterative Self-
Organizing Data Analysis Technique), an unsupervised method. The former is knowledge-driven, while the latter is data-driven. The former needs a priori knowledge about the study area but the latter does not. In practice, the former can classify land covers with a higher accuracy and therefore is more widely used but there have been very few attempts to investigate this. Here we use both methods
in our study area, Selangor, Malaysia and compare the outcomes by means of qualitative and quantitative analyses to have a better understanding of the underlying reasons that drive the performance of both methods.
36 citations
TL;DR: In this paper, the negative binomial-generalized exponential (NB-GE) distribution is proposed for counting data with a large number of zeros and overdispersion in Poisson distribution.
Abstract: This paper introduced a new mixed distribution, namely the negative binomial-generalized exponential (NB-GE) distribution, which it obtained by mixing the negative binomial (NB) distribution with a generalized exponential (GE) distribution. The NB-GE distribution offers the advantage of being able to handle this kind of data sets, while still maintaining similar characteristics as the traditional negative binomial. The closed form and the factorial moment of the NB-GE distribution are derived. The NB-GE distribution appropriate when we find the one related to count data which have a large number of zeros and overdispersion in Poisson distribution. In addition, we present the basic properties of the new distribution such as mean, variance, skewness and kurtosis. Including, the negative binomial-exponential distributions are presented as special cases of this NB-GE distribution. Parameters estimation is also implemented using maximum likelihood method and the usefulness of the NB-GE distribution is illustrated by real data set. When using a goodness of fit test, the results show that the NB-GE distribution can provide a better fit than the NB distribution and Poisson distribution for count data that contain a large number of zeros.
35 citations
TL;DR: The concept of possibility interval-valued vague soft set is introduced along with its operations of subset, intersection and union and an application in decision making with respect to degree of preference is illustrated.
Abstract: The concept of possibility interval-valued vague soft set is introduced along with its operations of subset, intersection and union. An application of possibility interval-valued vague soft sets in decision making with respect to degree of preference is then illustrated.
TL;DR: A large number of experimental results show that the algorithm can enhance the image contrast and get high definition images, and outperforms in visual quality and effectively preserves texture and detail information of original images.
Abstract: Because of light scattered by the suspended particles in the atmosphere, photographs taken in the foggy day look gray and lack of visibility. In order to unveil the clear image’s structures and colors, we propose a image defogging algorithm of single color image based on wavelet transform and histogram equalization. Firstly, using histogram equalization to enhancement image, then to nonlinear enhancement the approximate coefficients of wavelet transform, and to distribution more uniform gray of image. A large number of experimental results show that the algorithm can enhance the image contrast and get high definition images, and outperforms in visual quality and effectively preserves texture and detail information of original images.
TL;DR: In this paper, the notion of balanced intuitionistic fuzzy graphs was introduced and some properties of balanced fuzzy graphs were presented, and it was shown that G1 � G2 is balanced if and only if D(G1 )= D(g2 )=D(G2 ) = D (G 1 � G 2 ).
Abstract: In this paper, we introduce the notion of balanced intuitionistic fuzzy graphs and present some of their properties. We also prove that G1 � G2 is balanced if and only if D(G1 )= D(G2 )= D(G1 � G2).
TL;DR: FPGA (Field Programmable Gate Array) technology is applied to obtain chaotic sequence in this paper, the Xilinx system generator technology was used for the conception of Lorenz chaotic system and this code is used again to configuring the FPGA.
Abstract: Taking the Lorenz chaotic system as an example, FPGA (Field Programmable Gate Array) technology is applied to obtain chaotic sequence in this paper, the Xilinx system generator technology was used for the conception of Lorenz chaotic system and generating the VHDL code. This code is used again to configuring the FPGA. Experiment shows the output sequence of the designed system has a good result. The generated chaotic sequence may be used for information security in the modern communication field.
TL;DR: In this paper, the steady two-dimensional laminar flow of a viscous incompressible electrically conducting fluid over an exponentially stretching sheet in the presence of a uniform transverse magnetic field with viscous dissipation and radiative heat flux is studied.
Abstract: The steady two-dimensional laminar flow of a viscous incompressible electrically conducting fluid over an exponentially stretching sheet in the presence of a uniform transverse magnetic field with viscous dissipation and radiative heat flux is studied. By suitable similarity transformations, the governing boundary layer equations are transformed to ordinary differential equations and solved numerically by standard techniques. The effects of various parameters like, Magnetic and Radiation parameters, Prandtl number and Eckert number for velocity and temperature distributions have been discussed in detail with graphical representation.
TL;DR: This paper presents a fitting way to generate a strong pseudo random number sequence (PRNS) that satisfy the cryptography requirements from the chaotic system of Chua’s circuit.
Abstract: Due to its attractive proprieties for data encryption; chaotic systems becomes an active research area in this last dedicate. Applying chaos proprieties in cryptography has taken many ways and approaches, using chaotic systems as pseudo random number generators is the most known technic. In this paper we present a fitting way to generate a strong pseudo random number sequence (PRNS) that satisfy the cryptography requirements from the chaotic system of Chua’s circuit. The PRNS randomness then evaluated using the NIST-800-22 statistical tests, and used to encrypt an image. A hardware implementation of the chaotic system was done using a FPGA.
TL;DR: It is shown how the convergence rate and the performance of the solver are strictly linked to the discretized grid resolution and to the Laplace coefficients of the oceanic model.
Abstract: In this paper, the preconditioning technique of an elliptic Laplace problem in a global circulation ocean model is analyzed. We suggest an inverse preconditioning technique in order to efficiently compute the numerical solution of the elliptic kernel. Moreover, we show how the convergence rate and the performance of the solver are strictly linked to the discretized grid resolution and to the Laplace coefficients of the oceanic model. Finally, we present an easy-toimplement version of the solver on the Graphics Processing Units (GPUs). Mathematics Subject Classification: 65Y05; 65Y10; 65F08; 65F35; 37N10
TL;DR: This work discusses a naive and two optimised CUDA algorithms for the two kernel density estimation methods: univariate and multivariate, based on the use of shared memory tiles and loop unrolling techniques.
Abstract: The main problem of the kernel density estimation methods is the huge computational requirements, especially for large data sets. One way for accelerating these methods is to use the parallel processing. Recent advances in parallel processing have focused on the use Graphics Processing Units (GPUs) using Compute Unied Device Architecture (CUDA) programming model. In this work we discuss a naive and two optimised CUDA algorithms for the two kernel estimation methods: univariate and multivariate. These optimised algorithms are based on the use of shared memory tiles and loop unrolling techniques. We also present exploratory experimental results of the proposed CUDA algorithms according to the several values of parameters such as number of threads per block, tile size, loop unroll level, number of variables and data (sample) size. The experimental results show signicant performance gains of all proposed CUDA algorithms over serial CPU version and small performance speed-ups of the two optimised CUDA algorithms over naive GPU algorithms. Finally, based on extended performance results are obtained general conclusions of all proposed CUDA algorithms for some parameters.
TL;DR: A wavelet based hybrid method is employed to provide the quick and accurate solutions of fractional Black-Scholes equation with boundary condition for a European option pricing (EOP) problem.
Abstract: In this paper, a wavelet based hybrid method is employed to provide the quick and accurate solutions of fractional Black-Scholes equation with boundary condition for a European option pricing (EOP) problem. The fractional Black-Scholes is used as a model for valuing European or American call and put options on a non-dividend paying stock. To the best of our knowledge, until now there is no rigorous Legendre wavelet solutions have been reported for the fractional Black-Scholes
TL;DR: Detailed overview of intra compression data-flow in HEVC and VP9 is get into, common and unique stages of both standards are described, and the efficiency of both codecs, the corresponding standards and their intra compression algorithms are discussed.
Abstract: The amount of video data stored on local devices or transmitted over the networks is permanently increased. The emerging of a more efficient next generation video coding standard is of a high demand at the moment. There seem to be two main contenders for the position of the next state-of-the-art video compression standard: JCT-VC H.265/HEVC and Google VP9. The announced aim of HEVC is to achieve twice more efficient compression compared to H.264/AVC, and VP9 was developed to get half the bit-rate of VP8 with royalty-free video 6804 M.P. Sharabayko, O.G. Ponomarev and R.I. Chernyak codec. Intra compression is one of the main features that determines the compression efficiency of the whole codec. In this paper we get into detailed overview of intra compression data-flow in HEVC and VP9. We describe common and unique stages of both standards. Then we carry out experiments with JCT-VC HM and WebM VP9 encoders on intra compression efficiency. We also turn some of the HEVC features off to get its dataflow as close to VP9 as possible. Finally we get into discussion of the efficiency of both codecs, the corresponding standards and their intra compression algorithms. Mathematics Subject Classification: 94A08
TL;DR: In this paper, some properties of (m, n)-ideals in LA-semigroups and in locally associative LA-Semigroups have been provided. But the purpose of this paper is not to study the properties of these properties.
Abstract: The purpose of this paper is to study (m,n)-ideals in LA-semigroups. Some properties of (m,n)-ideals in LA-semigroups and in locally associative LA-semigroups has been provided. Mathematics Subject Classification: 20M10, 20N99
TL;DR: In this paper, the authors used kernel smoothing in multi-response nonparametric regression model and applied it for estimating children up to five years old growth, where the model consists of three response variables i.e. weight, height and head circumference, and age as a predictor variable.
Abstract: Physical children growth is measured by using anthropometric measures i.e. weight, height and head circumference. The children around two years old grow rapidly, and than decrease slowly along with increasing of children age. It means that locally model approach is more appropriate to the data. Kernel smoothing is one of estimation methods in nonparametric regression. In this paper, we study about Kernel smoothing in multi-response nonparametric regression model and apply it for estimating children up to five years old growth. The model consists of three response variables i.e. weight, height and head circumference, and age as a predictor variable. For determining optimal bandwidth for each response variable, we use cross-validation method. Based on children data in Surabaya 2010, and the 50 th percentiles estimation of weight, height and head circumference versus age, we obtain the mean squared error value is 0.05583 and coefficient of determination is 99.99%. The estimation model of children growth curve based on multi-respon kernel smoothing shows fluctuation of the curve and gives mean squared error value tends to zero and coefficient of determination tends to one. These facts mean that the estimation has satisfied goodness of fit criterion.
TL;DR: The Padovan and Perrin numbers have the matrix formula, Qn ⎡ ⎣ 0 3 0 0 0 1 2 ⎤ ⎦ = as discussed by the authors.
Abstract: The Padovan and Perrin numbers have the matrix formula, Qn ⎡ ⎣ 0 3 0 0 1 2 ⎤ ⎦ = ⎡ ⎣ 0 1 0 0 0 1 1 1 0 ⎤ ⎦ n ⎡ ⎣ 0 3 0 0 1 2 ⎤ ⎦ . The matrix product is a 3× 2 matrix that when raised to the nth power give a matrix product whose entries are Padovan and Perrin numbers. For which we established by mathematical induction such that, Q ⎡ ⎣ 0 3 0 0 1 2 ⎤ ⎦ = ⎡ ⎣ 0 1 0 0 0 1 1 1 0 ⎤ ⎦ n ⎡ ⎣ 0 3 0 0 1 2 ⎤ ⎦ = ⎡ ⎣ Pn Pn Pn+1 Pn+1 Pn+2 Pn+2 ⎤ ⎦ , where Pn and Pn are the Padovan and Perrin sequences, respectively. Mathematics Subject Classification: 11B39, 11B99
TL;DR: It is proved that the optimal value for a fuzzy transportation problem, when solved using octagonal fuzzy number gives a much more optimal value than when it is solved using trapezoidal fuzzy number as done by Basirzadeh [3].
Abstract: In this paper, a general fuzzy transportation problem model is discussed. There are several approaches by different authors to solve such a problem viz., [1,2,3,6,7,8]. We introduce octagonal fuzzy numbers using which we develop a new model to solve the problem. By defining a ranking to the octagonal fuzzy numbers, it is possible to compare them and using this we convert the fuzzy valued transportation problem (cost, supply and demand appearing as octagonal fuzzy numbers) to a crisp valued transportation problem, which then can be solved using the MODI Method. We have proved that the optimal value for a fuzzy transportation problem, when solved using octagonal fuzzy number gives a much more optimal value than when it is solved using trapezoidal fuzzy number as done by Basirzadeh [3] which is illustrated through a numerical example. Mathematics Subject Classification: 03B52, 68T27, 68T37, 94D05
TL;DR: The order relations of comparative sets and an application to emission influences on sets of urban building conflict situations are investigated with non-ordered as-built properties and their effects on the property market.
Abstract: The order relations of comparative sets and an application to emission influences on sets of urban building conflict situations are investigated with non-ordered as-built properties and their effects on the property market. Sets of points, independent of convexity properties and varying according to the consideration of socio-economic properties, are comparatively examined, concerning minima and maxima.
TL;DR: In this article, the authors present results of a numerical study using finite-difference methods of non-stationary heat transfer processes in permafrost from heat sources generated by various technical systems (production wells) as well as from cold sources used for thermal stabilization of the soil, for example, seasonal cooling devices.
Abstract: This paper presents results of a numerical study using finite-difference methods of non-stationary heat transfer processes in permafrost from heat sources generated by various technical systems (production wells) as well as from cold sources used for thermal stabilization of the soil, for example, seasonal cooling devices. In the simulation a number of climatic factors (monthly average temperature variation and power of solar radiation which are characteristic of a considered geographic place), thermal parameters and lithology of the soil, as well as the technical features of considered engineering facilities are taken into account. Mathematics Subject Classification: 35Q79, 35K61, 65N06
TL;DR: In this paper, the twisted tangent numbers Tn,w and polynomials Tnw,w(x) are introduced and some interesting results and relationships are obtained.
Abstract: In this paper we introduce the twisted tangent numbers Tn,w and polynomials Tn,w(x). Some interesting results and relationships are obtained.
TL;DR: In this paper, Bayes and classical estimators have been obtained for two parameters exponentiated inverted Weibull distribution when sample is available from complete and type II censoring scheme.
Abstract: The exponentiated inverted Weibull distribution is a generalization of the exponentiated inverted exponential distribution as well as the inverted Weibull distribution. In this paper, Bayes and classical estimators have been obtained for two parameters exponentiated inverted Weibull distribution when sample is available from complete and type II censoring scheme. Several Bayesian estimates are obtained against different symmetric and asymmetric loss functions such as squared error and LINEX. This was done with respect to the conjugate priors for two shape parameters. As expected, when the shape parameters are unknown, the closed-form expressions of the Bayes estimators cannot be obtained. We used an approximation based on the Lindley and Markov chain Monte Carlo method (MCMC) methods for obtaining Bayes estimates under these loss functions. All Bayesian estimates are compared with the corresponding maximum likelihood estimates numerically in terms of their mean square error values. Finally, real data sets are analyzed for the purpose of illustration.
TL;DR: In this paper, the authors used Akaike's information criterion (AIC) as the goodness of fit measure and mean absolute percentage error (MAPE) as forecasting performance measure, and concluded that GARCH is a more appropriate model.
Abstract: The purpose of the current study is to forecast the prices of Kijang Emas, the official Malaysian gold bullion. Two methods are considered, which are Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH). Using Akaike's information criterion (AIC) as the goodness of fit measure and mean absolute percentage error (MAPE) as the forecasting performance measure, the study concludes that GARCH is a more appropriate model. Analysis are carried out by using the E-views software.
TL;DR: New algorithms in classical and linear programming for fuzzy assignment problem with fuzzy cost based on the ranking method are presented and generalized fuzzy numbers are used for solving real life problems.
Abstract: In this paper, we present new algorithms in classical and linear programming for fuzzy assignment problem with fuzzy cost based on the ranking method. The fuzzy cost is measured as generalized fuzzy number. We developed the classical algorithm using fundamental theorems of fuzzy assignment problem to obtain minimum fuzzy cost and also for the variations in the fuzzy assignment problem. Proposed algorithms are illustrated with an example. The proposed algorithms are easy to understand and apply to find the optimal fuzzy cost occurring in the real life situations. There are several papers in the literature in which generalized fuzzy numbers are used for solving real life problems but to the best of our knowledge, till now no one has used generalized fuzzy numbers for solving the assignment problems.