World Academy of Science, Engineering and Technology

Authors: Qingqing Wang, Shouming Zhong

Abstract:

This paper is concerned with the stability problem with two additive time-varying delay components. By choosing one augmented Lyapunov-Krasovskii functional, using some new zero equalities, and combining linear matrix inequalities (LMI) techniques, two new sufficient criteria ensuring the global stability asymptotic stability of DNNs is obtained. These stability criteria are present in terms of linear matrix inequalities and can be easily checked. Finally, some examples are showed to demonstrate the effectiveness and less conservatism of the proposed method.

Keywords: Neural networks, Globally asymptotic stability, LMI approach, Additive time-varying delays.

Authors: N. Bachok, N. L. Aleng, N. M. Arifin, A. Ishak, N. Senu

Abstract:

The problem of laminar fluid flow which results from the shrinking of a permeable surface in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the mass suction parameter S, Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. It was found that the reduced Nusselt number is decreasing function of each dimensionless number.

Keywords: Boundary layer, Nanofluid, Shrinking sheet, Brownian motion, Thermophoresis, Similarity solution.

Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.

Authors: Zainab Yasir Al-Rekaby, Abdul Jalil M. Khalaf

Abstract:

Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W12 is chromatically unique.

Keywords: Chromatic Polynomial, Chromatically Equivalent, Chromatically Unique, Wheel.

Authors: Mahmoud Zarrini, Sanaz Torkaman

Abstract:

In this paper, we have proposed a numerical method for solving fuzzy Fredholm integral equation of the second kind. In this method a combination of orthonormal Bernstein and Block-Pulse functions are used. In most cases, the proposed method leads to the exact solution. The advantages of this method are shown by an example and calculate the error analysis.

Keywords: Fuzzy Fredholm Integral Equation, Bernstein, Block-Pulse, Orthonormal.

Authors: Biao Qin, Jin Huang, Jiaojiao Ren, Wei Kang

Abstract:

This paper deals with the problem of passivity analysis for stochastic neural networks with leakage, discrete and distributed delays. By using delay partitioning technique, free weighting matrix method and stochastic analysis technique, several sufficient conditions for the passivity of the addressed neural networks are established in terms of linear matrix inequalities (LMIs), in which both the time-delay and its time derivative can be fully considered. A numerical example is given to show the usefulness and effectiveness of the obtained results.

Keywords: Passivity, Stochastic neural networks, Multiple time delays, Linear matrix inequalities (LMIs).

Authors: Malika Yaici, Kamel Hariche, Tim Clarke

Abstract:

The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state space forms and moving on to any general state space form, we develop the identities that relate eigenvectors and latent vectors in either direction. Numerical examples illustrate this result. A brief discussion of the potential of these identities in linear control system design follows. Additionally, we present a consequent result: a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials.

Keywords: Eigenvalues/Eigenvectors, Latent values/vectors, Matrix fraction description, State space description.

Authors: D. Hilton

Abstract:

An analysis of the Australian Diabetes Screening Study estimated undiagnosed diabetes mellitus [DM] prevalence in a high risk general practice based cohort. DM prevalence varied from 9.4% to 18.1% depending upon the diagnostic criteria utilised with age being a highly significant risk factor. Utilising the gold standard oral glucose tolerance test, the prevalence of DM was 22-23% in those aged >= 70 years and <15% in those aged 40-59 years. Opportunistic screening in Australian general practice potentially can identify many persons with undiagnosed type 2 DM. An Australian Bureau of Statistics document published three years ago, reported the highest rate of DM in men aged 65-74 years [19%] whereas the rate for women was highest in those over 75 years [13%]. If you consider that the Australian Bureau of Statistics report in 2007 found that 13% of the population was over 65 years of age and that this will increase to 23-25% by 2056 with a further projected increase to 25-28% by 2101, obviously this information has to be factored into the equation when age related diabetes prevalence predictions are calculated. This 10-15% proportional increase of elderly persons within the population demographics has dramatic implications for the estimated number of elderly persons with DM in these age groupings. Computational methodology showing the age related demographic changes reported in these official statistical documents will be done showing estimates for 2056 and 2101 for different age groups. This has relevance for future diabetes prevalence rates and shows that along with many countries worldwide Australia is facing an increasing pandemic. In contrast Japan is expected to have a decrease in the next twenty years in the number of persons with diabetes.

Keywords: Epidemiological methods, aging, prevalence.

Authors: Anuar Ishak

Abstract:

The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Dual solutions, heat transfer, mixed convection, stability analysis.

Authors: Dibyendu Ghoshal, Pinaki Pratim Acharjya

Abstract:

Image segmentation process based on mathematical morphology has been studied in the paper. It has been established from the first principles of the morphological process, the entire segmentation is although a nonlinear signal processing task, the constituent wise, the intermediate steps are linear, bilinear and conformal transformation and they give rise to a non linear affect in a cumulative manner.

Keywords: Image segmentation, linear transform, bilinear transform, conformal transform, mathematical morphology.

Authors: Qingqing Wang, Shouming Zhong

Abstract:

In this paper, delay-dependent stability analysis for neutral type neural networks with uncertain paramters and time-varying delay is studied. By constructing new Lyapunov-Krasovskii functional and dividing the delay interval into multiple segments, a novel sufficient condition is established to guarantee the globally asymptotically stability of the considered system. Finally, a numerical example is provided to illustrate the usefulness of the proposed main results.

Keywords: Neutral type neural networks, Time-varying delay, Stability, Linear matrix inequality(LMI).

Authors: Liyuan Wang, Shouming Zhong

Abstract:

In this paper, the design problem of state estimator for neural networks with the mixed time-varying delays are investigated by constructing appropriate Lyapunov-Krasovskii functionals and using some effective mathematical techniques. In order to derive several conditions to guarantee the estimation error systems to be globally exponential stable, we transform the considered systems into the neural-type time-delay systems. Then with a set of linear inequalities(LMIs), we can obtain the stable criteria. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed criterion.

Keywords: State estimator, Neural networks, Globally exponential stability.

Authors: Yong Li

Abstract:

The paper is concerned with the existence of solution of nonlinear second order neutral stochastic differential inclusions with infinite delay in a Hilbert Space. Sufficient conditions for the existence are obtained by using a fixed point theorem for condensing maps.

Keywords: Mild solution, Convex multivalued map, Neutral stochastic differential inclusions.

Authors: M. Palanivel, R. Uthayakumar

Abstract:

In this paper, Economic Order Quantity (EOQ) based model for non-instantaneous Weibull distribution deteriorating items with power demand pattern is presented. In this model, the holding cost per unit of the item per unit time is assumed to be an increasing linear function of time spent in storage. Here the retailer is allowed a trade-credit offer by the supplier to buy more items. Also in this model, shortages are allowed and partially backlogged. The backlogging rate is dependent on the waiting time for the next replenishment. This model aids in minimizing the total inventory cost by finding the optimal time interval and finding the optimal order quantity. The optimal solution of the model is illustrated with the help of numerical examples. Finally sensitivity analysis and graphical representations are given to demonstrate the model.

Keywords: Power demand pattern, Partial backlogging, Time dependent holding cost, Trade credit, Weibull deterioration.

Authors: Gaurav Kumar, Rakesh Kumar Bajaj

Abstract:

The applicability of Net Present Value (NPV) in an investment project is becoming more and more popular in the field of engineering economics. The classical NPV methodology involves only the precise and accurate data of the investment project. In the present communication, we give a new mathematical model for NPV which uses the concept of intuitionistic fuzzy set theory. The proposed model is based on triangular intuitionistic fuzzy number, which may be known as Intuitionistic Fuzzy Net Present Value (IFNPV). The model has been applied to an example and the results are presented.

Keywords: Net Present Value, Intuitionistic Fuzzy Set, Investment Projects.

Authors: Navid Javidtash, Abdolmohamad Davodi, Mojtaba Hakimzadeh, Abdolreza Roozbeh

Abstract:

Economic dispatch (ED) is considered to be one of the key functions in electric power system operation. This paper presents a new hybrid approach based genetic algorithm (GA) to economic dispatch problems. GA is most commonly used optimizing algorithm predicated on principal of natural evolution. Utilization of chaotic queue with GA generates several neighborhoods of near optimal solutions to keep solution variation. It could avoid the search process from becoming pre-mature. For the objective of chaotic queue generation, utilization of tent equation as opposed to logistic equation results in improvement of iterative speed. The results of the proposed approach were compared in terms of fuel cost, with existing differential evolution and other methods in literature.

Keywords: Economic Dispatch(ED), Optimization, Fuel Cost, Genetic Algorithm (GA).

Authors: Yu Lou, Chunming Tang, Yanfeng Qi, Maozhi Xu

Abstract:

This paper considers the bent and hyper-bent properties of a class of Boolean functions. For one case, we present a detailed description for them to be hyper-bent functions, and give a necessary condition for them to be bent functions for another case.

Keywords: Boolean functions, bent functions, hyper-bent functions, character sums.

Authors: Mimi Hafizah Abdullah, Hanani Farhah Harun, Nik Ruzni Nik Idris

Abstract:

With the implied volatility as an important factor in financial decision-making, in particular in option pricing valuation, and also the given fact that the pricing biases of Leland option pricing models and the implied volatility structure for the options are related, this study considers examining the implied adjusted volatility smile patterns and term structures in the S&P/ASX 200 index options using the different Leland option pricing models. The examination of the implied adjusted volatility smiles and term structures in the Australian index options market covers the global financial crisis in the mid-2007. The implied adjusted volatility was found to escalate approximately triple the rate prior the crisis.

Keywords: Implied adjusted volatility, Financial crisis, Leland option pricing models.

Authors: Shuguo Yang, Xiaoyan Yang

Abstract:

It is practically significant to research the traffic flow of intersection because the capacity of intersection affects the efficiency of highway network directly. This paper analyzes the traffic conditions of an intersection in certain urban by the methods of queuing theory and statistical experiment, sets up a corresponding mathematical model and compares it with the actual values. The result shows that queuing theory is applied in the study of intersection traffic flow and it can provide references for the other similar designs.

Keywords: Intersection, Queuing theory, Statistical experiment, System metrics.

Authors: Ehsan Mahdavi

Abstract:

In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. Exp-function method is easy, succinct and powerful to implement to nonlinear partial differential equations arising in mathematical physics. We mainly try to present an application of Exp-function method and offer solutions for common errors wich occur during some of the recent works.

Keywords: Exp-function method, Rosenau Kawahara equation, Rosenau Korteweg-de Vries equation, nonlinear partial differential equation.

Authors: M. Ghorbany

Abstract:

A square matrix over the complex field with non- negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful representation of G by quasi-permutation matrices over the rationals and the complex numbers are denoted by q(G) and c(G) respectively. Finally r (G) denotes the minimal degree of a faithful rational valued complex character of C. The purpose of this paper is to calculate q(G), c(G) and r(G) for the group S L(2, q) when extended by a certain group of order two.

Keywords: General linear group, Quasi-permutation

Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

Abstract:

The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler Plate Equation, Numerical Simulations, Stability, Energy Decay, Finite Difference Method.

Authors: Vladimir S. Timofeev

Abstract:

In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: Characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation.

Authors: Youssef Khmou, Said Safi

Abstract:

In this paper, we investigated the effect of real valued transformation of the spectral matrix of the received data for Angles Of Arrival estimation problem.  Indeed, the unitary transformation of Partial Propagator (UPP) for narrowband sources is proposed and applied on Uniform Linear Array (ULA).

Monte Carlo simulations proved the performance of the UPP spectrum comparatively with Forward Backward Partial Propagator (FBPP) and Unitary Propagator (UP). The results demonstrates that when some of the sources are fully correlated and closer than the Rayleigh angular limit resolution of the broadside array, the UPP method outperforms the FBPP in both of spatial resolution and complexity.

Keywords: DOA, Uniform Linear Array, Narrowband, Propagator, Real valued transformation, Subspace, Unitary Operator.

Authors: Youssef Khmou, Said Safi

Abstract:

In this paper, a fifth order propagator operators are proposed for estimating the Angles Of Arrival (AOA) of narrowband electromagnetic waves impinging on antenna array when its number of sensors is larger than the number of radiating sources.

The array response matrix is partitioned into five linearly dependent phases to construct the noise projector using five different propagators from non diagonal blocks of the spectral matrice of the received data; hence, five different estimators are proposed to estimate the angles of the sources. The simulation results proved the performance of the proposed estimators in the presence of white noise comparatively to high resolution eigen based spectra.

Keywords: DOA, narrowband, antenna, propagator, high resolution. Array, operator, angular, spectrum, goniometry.

Authors: Shams-Ul-Islam, Hamid Rahman, Waqas Sarwar Abbasi

Abstract:

Numerical calculations of flow around a square cylinder are presented using the multi-relaxation-time lattice Boltzmann method at Reynolds number 150. The effects of upstream locations, downstream locations and blockage are investigated systematically. A detail analysis are given in terms of time-trace analysis of drag and lift coefficients, power spectra analysis of lift coefficient, vorticity contours visualizations and phase diagrams. A number of physical quantities mean drag coefficient, drag coefficient, Strouhal number and root-mean-square values of drag and lift coefficients are calculated and compared with the well resolved experimental data and numerical results available in open literature. The results had shown that the upstream, downstream and height of the computational domain are at least 7.5, 37.5 and 12 diameters of the cylinder, respectively.

Keywords: Grid independence, Multi-relaxation-time lattice Boltzmann method, Physical quantities, Square cylinder, Vorticity contours visualizations.

Authors: Qingqing Wang, Shouming Zhong

Abstract:

This paper deals with the problem of delay-dependent stability for neural networks with distributed delays. Some new sufficient condition are derived by constructing a novel Lyapunov-Krasovskii functional approach. The criteria are formulated in terms of a set of linear matrix inequalities, this is convenient for numerically checking the system stability using the powerful MATLAB LMI Toolbox. Moreover, in order to show the stability condition in this paper gives much less conservative results than those in the literature, numerical examples are considered.

Keywords: Neural networks, Globally asymptotic stability , LMI approach, Distributed delays.

Authors: N. R. N. Idris, S. Baharom

Abstract:

A meta-analysis may be performed using aggregate data (AD) or an individual patient data (IPD). In practice, studies may be available at both IPD and AD level. In this situation, both the IPD and AD should be utilised in order to maximize the available information. Statistical advantages of combining the studies from different level have not been fully explored. This study aims to quantify the statistical benefits of including available IPD when conducting a conventional summary-level meta-analysis. Simulated meta-analysis were used to assess the influence of the levels of data on overall meta-analysis estimates based on IPD-only, AD-only and the combination of IPD and AD (mixed data, MD), under different study scenario. The percentage relative bias (PRB), root mean-square-error (RMSE) and coverage probability were used to assess the efficiency of the overall estimates. The results demonstrate that available IPD should always be included in a conventional meta-analysis using summary level data as they would significantly increased the accuracy of the estimates.On the other hand, if more than 80% of the available data are at IPD level, including the AD does not provide significant differences in terms of accuracy of the estimates. Additionally, combining the IPD and AD has moderating effects on the biasness of the estimates of the treatment effects as the IPD tends to overestimate the treatment effects, while the AD has the tendency to produce underestimated effect estimates. These results may provide some guide in deciding if significant benefit is gained by pooling the two levels of data when conducting meta-analysis.

Keywords: Aggregate data, combined-level data, Individual patient data, meta analysis.

Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

Abstract:

In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results is in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes.

Keywords: Semi-Lagrangian method, Iteration free method, Nonlinear advection-diffusion equation.

Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

Abstract:

In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: Embedded Runge-Kutta-Fehlberg method, Initial value problem.