Abstract: The goal of option pricing theory is to help the investors
to manage their money, enhance returns and control their financial
future by theoretically valuing their options. However, most of the
option pricing models have no analytical solution. Furthermore,
not all the numerical methods are efficient to solve these models
because they have nonsmoothing payoffs or discontinuous derivatives
at the exercise price. In this paper, we solve the American option
under jump diffusion models by using efficient time-dependent
numerical methods. several techniques are integrated to reduced
the overcome the computational complexity. Fast Fourier Transform
(FFT) algorithm is used as a matrix-vector multiplication solver,
which reduces the complexity from O(M2) into O(M logM).
Partial fraction decomposition technique is applied to rational
approximation schemes to overcome the complexity of inverting
polynomial of matrices. The proposed method is easy to implement
on serial or parallel versions. Numerical results are presented to prove
the accuracy and efficiency of the proposed method.
Abstract: Unsteady effects of MHD free convection flow past in an infinite vertical plate with heat source in presence of radiation with reference to all critical parameters that appear in field equations are studied in this paper. The governing equations are developed by usual Boussinesq’s approximation. The problem is solved by using perturbation technique. The results are obtained for velocity, temperature, Nusselt number and skin-friction. The effects of magnetic parameter, prandtl number, Grashof number, permeability parameter, heat source/sink parameter and radiation parameter are discussed on flow characteristics and shown by means of graphs and tables.
Abstract: The radial form of nuclear matter distribution, charge and the shape of nuclei are essential properties of nuclei, and hence, are of great attention for several areas of research in nuclear physics. More than last three decades have witnessed a range of experimental means employing leptonic probes (such as muons, electrons etc.) for exploring nuclear charge distributions, whereas the hadronic probes (for example alpha particles, protons, etc.) have been used to investigate the nuclear matter distributions. In this paper, p-9,11Li elastic scattering differential cross sections in the energy range to MeV have been studied by means of Coulomb modified Glauber scattering formalism. By applying the semi-phenomenological Bhagwat-Gambhir-Patil [BGP] nuclear density for loosely bound neutron rich 11Li nucleus, the estimated matter radius is found to be 3.446 fm which is quite large as compared to so known experimental value 3.12 fm. The results of microscopic optical model based calculation by applying Bethe-Brueckner–Hartree–Fock formalism (BHF) have also been compared. It should be noted that in most of phenomenological density model used to reproduce the p-11Li differential elastic scattering cross sections data, the calculated matter radius lies between 2.964 and 3.55 fm. The calculated results with phenomenological BGP model density and with nucleon density calculated in the relativistic mean-field (RMF) reproduces p-9Li and p-11Li experimental data quite nicely as compared to Gaussian- Gaussian or Gaussian-Oscillator densities at all energies under consideration. In the approach described here, no free/adjustable parameter has been employed to reproduce the elastic scattering data as against the well-known optical model based studies that involve at least four to six adjustable parameters to match the experimental data. Calculated reaction cross sections σR for p-11Li at these energies are quite large as compared to estimated values reported by earlier works though so far no experimental studies have been performed to measure it.
Abstract: Passenger comfort has been paramount in the design of suspension systems of high speed cars. To analyze the effect of vibration on vehicle ride quality, a vertical model of a six degree of freedom railway passenger vehicle, with front and rear suspension, is built. It includes car body flexible effects and vertical rigid modes. A second order linear shaping filter is constructed to model Gaussian white noise into random rail excitation. The temporal correlation between the front and rear wheels is given by a second order Pade approximation. The complete track and the vehicle model are then designed. An active secondary suspension system based on a Linear Quadratic Gaussian (LQG) optimal control method is designed. The results show that the LQG control method reduces the vertical acceleration, pitching acceleration and vertical bending vibration of the car body as compared to the passive system.
Abstract: The earliest theories of sloshing waves and solitary waves based on potential theory idealisations and irrotational flow have been extended to be applicable to more realistic domains. To this end, the computational fluid dynamics (CFD) methods are widely used. Three-dimensional CFD methods such as Navier-Stokes solvers with volume of fluid treatment of the free surface and Navier-Stokes solvers with mappings of the free surface inherently impose high computational expense; therefore, considerable effort has gone into developing depth-averaged approaches. Examples of such approaches include Green–Naghdi (GN) equations. In Cartesian system, GN velocity profile depends on horizontal directions, x-direction and y-direction. The effect of vertical direction (z-direction) is also taken into consideration by applying weighting function in approximation. GN theory considers the effect of vertical acceleration and the consequent non-hydrostatic pressure. Moreover, in GN theory, the flow is rotational. The present study illustrates the application of GN equations to propagation of sloshing waves and solitary waves. For this purpose, GN equations solver is verified for the benchmark tests of Gaussian hump sloshing and solitary wave propagation in shallow basins. Analysis of the free surface sloshing of even harmonic components of an initial Gaussian hump demonstrates that the GN model gives predictions in satisfactory agreement with the linear analytical solutions. Discrepancies between the GN predictions and the linear analytical solutions arise from the effect of wave nonlinearities arising from the wave amplitude itself and wave-wave interactions. Numerically predicted solitary wave propagation indicates that the GN model produces simulations in good agreement with the analytical solution of the linearised wave theory. Comparison between the GN model numerical prediction and the result from perturbation analysis confirms that nonlinear interaction between solitary wave and a solid wall is satisfactorilly modelled. Moreover, solitary wave propagation at an angle to the x-axis and the interaction of solitary waves with each other are conducted to validate the developed model.
Abstract: Conditions corresponding to the unconditional stability
of convection in a mechanically anisotropic fluid saturated porous
medium of infinite horizontal extent are determined. The medium
is heated from below and its bounding surfaces are subjected to
temperature modulation which consists of a steady part and a
time periodic oscillating part. The Brinkman model is employed
in the momentum equation with the Bousinessq approximation.
The stability region is found for arbitrary values of modulational
frequency and amplitude using the energy method. Higher order
numerical computations are carried out to find critical boundaries
and subcritical instability regions more accurately.
Abstract: A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.
Abstract: Modelling realized volatility with high-frequency returns is popular as it is an unbiased and efficient estimator of return volatility. A computationally simple model is fitting the logarithms of the realized volatilities with a fractionally integrated long-memory Gaussian process. The Gaussianity assumption simplifies the parameter estimation using the Whittle approximation. Nonetheless, this assumption may not be met in the finite samples and there may be a need to normalize the financial series. Based on the empirical indices S&P500 and DAX, this paper examines the performance of the linear volatility model pre-treated with normalization compared to its existing counterpart. The empirical results show that by including normalization as a pre-treatment procedure, the forecast performance outperforms the existing model in terms of statistical and economic evaluations.
Abstract: In this paper, the analytical tuning rules of IMC-PID controller are presented for the multivariable Smith predictor that involved the ideal decoupling. Accordingly, the decoupler is first introduced into the multivariable Smith predictor control system by a well-known approach of ideal decoupling, which is compactly extended for general nxn multivariable processes and the multivariable Smith predictor controller is then obtained in terms of the multiple single-loop Smith predictor controllers. The tuning rules of PID controller in series with filter are found by using Maclaurin approximation. Many multivariable industrial processes are employed to demonstrate the simplicity and effectiveness of the presented method. The simulation results show the superior performances of presented method in compared with the other methods.
Abstract: This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole
Abstract: Rough set theory is used to handle uncertainty and incomplete information by applying two accurate sets, Lower approximation and Upper approximation. In this paper, the rough clustering algorithms are improved by adopting the Similarity, Dissimilarity–Similarity and Entropy based initial centroids selection method on three different clustering algorithms namely Entropy based Rough K-Means (ERKM), Similarity based Rough K-Means (SRKM) and Dissimilarity-Similarity based Rough K-Means (DSRKM) were developed and executed by yeast dataset. The rough clustering algorithms are validated by cluster validity indexes namely Rand and Adjusted Rand indexes. An experimental result shows that the ERKM clustering algorithm perform effectively and delivers better results than other clustering methods. Outlier detection is an important task in data mining and very much different from the rest of the objects in the clusters. Entropy based Rough Outlier Factor (EROF) method is seemly to detect outlier effectively for yeast dataset. In rough K-Means method, by tuning the epsilon (ᶓ) value from 0.8 to 1.08 can detect outliers on boundary region and the RKM algorithm delivers better results, when choosing the value of epsilon (ᶓ) in the specified range. An experimental result shows that the EROF method on clustering algorithm performed very well and suitable for detecting outlier effectively for all datasets. Further, experimental readings show that the ERKM clustering method outperformed the other methods.
Abstract: Model updating is an inverse eigenvalue problem which
concerns the modification of an existing but inaccurate model with
measured modal data. In this paper, an efficient gradient based
iterative method for updating the mass, damping and stiffness
matrices simultaneously using a few of complex measured modal
data is developed. Convergence analysis indicates that the iterative
solutions always converge to the unique minimum Frobenius norm
symmetric solution of the model updating problem by choosing a
special kind of initial matrices.
Abstract: Digital images are widely used in computer
applications. To store or transmit the uncompressed images
requires considerable storage capacity and transmission bandwidth.
Image compression is a means to perform transmission or storage of
visual data in the most economical way. This paper explains about
how images can be encoded to be transmitted in a multiplexing
time-frequency domain channel. Multiplexing involves packing
signals together whose representations are compact in the working
domain. In order to optimize transmission resources each 4 × 4
pixel block of the image is transformed by a suitable polynomial
approximation, into a minimal number of coefficients. Less than
4 × 4 coefficients in one block spares a significant amount of
transmitted information, but some information is lost. Different
approximations for image transformation have been evaluated as
polynomial representation (Vandermonde matrix), least squares +
gradient descent, 1-D Chebyshev polynomials, 2-D Chebyshev
polynomials or singular value decomposition (SVD). Results have
been compared in terms of nominal compression rate (NCR),
compression ratio (CR) and peak signal-to-noise ratio (PSNR)
in order to minimize the error function defined as the difference
between the original pixel gray levels and the approximated
polynomial output. Polynomial coefficients have been later encoded
and handled for generating chirps in a target rate of about two
chirps per 4 × 4 pixel block and then submitted to a transmission
multiplexing operation in the time-frequency domain.
Abstract: In structures, stress concentration is a factor of fatigue
fracture. Basically, the stress concentration is a phenomenon that
should be avoided. However, it is difficult to avoid the stress
concentration. Therefore, relaxation of the stress concentration is
important. The stress concentration arises from notches and circular
holes. There is a relaxation method that a composite patch covers a
notch and a circular hole. This relaxation method is used to repair
aerial wings, but it is not systematized. Composites are more
expensive than single materials. Accordingly, we propose the
relaxation method that a single material patch covers a notch and a
circular hole, and aim to systematize this relaxation method.
We performed FEA (Finite Element Analysis) about an object by
using a three-dimensional FEA model. The object was that a patch
adheres to a plate with a circular hole. And, a uniaxial tensile load acts
on the patched plate with a circular hole. In the three-dimensional FEA
model, it is not easy to model the adhesion layer. Basically, the yield
stress of the adhesive is smaller than that of adherents. Accordingly,
the adhesion layer gets to plastic deformation earlier than the adherents
under the yield load of adherents. Therefore, we propose the
three-dimensional FEA model which is applied a nonlinear elastic
region to the adhesion layer. The nonlinear elastic region was
calculated by a bilinear approximation. We compared the analysis
results with the tensile test results to confirm whether the analysis
model has usefulness. As a result, the analysis results agreed with the
tensile test results. And, we confirmed that the analysis model has
usefulness.
As a result that the three-dimensional FEA model was used to the
analysis, it was confirmed that an out-of-plane deformation occurred
to the patched plate with a circular hole. The out-of-plane deformation
causes stress increase of the patched plate with a circular hole.
Therefore, we investigated that the out-of-plane deformation affects
relaxation of the stress concentration in the plate with a circular hole
on this relaxation method. As a result, it was confirmed that the
out-of-plane deformation inhibits relaxation of the stress concentration
on the plate with a circular hole.
Abstract: The main purpose of this paper is to consider the t-best co-approximation and t-best simultaneous co-approximation in fuzzy normed spaces. We develop the theory of t-best co-approximation and t-best simultaneous co-approximation in quotient spaces. This new concept is employed us to improve various characterisations of t-co-proximinal and t-co-Chebyshev sets.
Abstract: River flow prediction is an essential tool to ensure proper management of water resources and the optimal distribution of water to consumers. This study presents an analysis and prediction by using nonlinear prediction method with monthly river flow data for Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The reconstruction of phase space involves the reconstruction of one-dimension (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. The revenue of phase space reconstruction is used to predict the next 72 months. A comparison of prediction performance based on correlation coefficient (CC) and root mean square error (RMSE) was employed to compare prediction performance for the nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show that the prediction results using the nonlinear prediction method are better than ARIMA and SVM. Therefore, the results of this study could be used to develop an efficient water management system to optimize the allocation of water resources.
Abstract: The present study is carried out to investigate the magneto-viscous effects on incompressible ferrofluid flow over a porous rotating disc with suction or injection on the surface of the disc subjected to a magnetic field. The flow under consideration is axi-symmetric steady ferrofluid flow of electrically non-conducting fluid. Karman’s transformation is used to convert the governing boundary layer equations involved in the problem to a system of non linear coupled differential equations. The solution of this system is obtained by using power series approximation. The flow characteristics i.e. radial, tangential, axial velocities and boundary layer displacement thickness are calculated for various values of MFD (magnetic field dependent) viscosity and for different values of suction injection parameter. Besides this, skin friction coefficients are also calculated on the surface of the disk. The results thus obtained are presented numerically and graphically in the paper.
Abstract: Recent experimental evidences have shown that because
of a fast convergence and a nice accuracy, neural networks training
via extended kalman filter (EKF) method is widely applied. However,
as to an uncertainty of the system dynamics or modeling error, the
performance of the method is unreliable. In order to overcome this
problem in this paper, a new finite impulse response (FIR) filter based
learning algorithm is proposed to train radial basis function neural
networks (RBFN) for nonlinear function approximation. Compared
to the EKF training method, the proposed FIR filter training method
is more robust to those environmental conditions. Furthermore , the
number of centers will be considered since it affects the performance
of approximation.
Abstract: River flow prediction is an essential to ensure proper management of water resources can be optimally distribute water to consumers. This study presents an analysis and prediction by using nonlinear prediction method involving monthly river flow data in Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The phase space reconstruction involves the reconstruction of one-dimensional (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. Revenue of phase space reconstruction is used to predict the next 72 months. A comparison of prediction performance based on correlation coefficient (CC) and root mean square error (RMSE) have been employed to compare prediction performance for nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show the prediction results using nonlinear prediction method is better than ARIMA and SVM. Therefore, the result of this study could be used to develop an efficient water management system to optimize the allocation water resources.
Abstract: The ionization energy in semiconductor
systems in nano scale was investigated by using effective mass
approximation. By introducing the Hamiltonian of the system, the
variational technique was employed to calculate the ground state and
the ionization energy of a donor at the center and in the case that the
impurities are randomly distributed inside a cubic quantum well. The
numerical results for GaAs/GaAlAs show that the ionization energy
strongly depends on the well width for both cases and it decreases as
the well width increases. The ionization energy of a quantum wire
was also calculated and compared with the results for the well.