Abstract: In this paper we define generalized differential operators from some well-known operators on the class A of analytic functions in the unit disk U = {z ∈ C : |z| < 1}. New classes containing these operators are investigated. Also univalence of integral operator is considered.
Abstract: Based on a theoretical erbium-doped fiber amplifier
(EDFA) model, we have proposed an application of disturbance
observer(DOB) with proportional/integral/differential(PID) controller
to EDFA for minimizing gain-transient time of wavelength
-division-multiplexing (WDM) multi channels in optical amplifier in
channel add/drop networks. We have dramatically reduced the
gain-transient time to less than 30μsec by applying DOB with PID
controller to the control of amplifier gain. The proposed DOB-based
gain control algorithm for EDFA was implemented as a digital control
system using TI's DSP(TMS320C28346) chip and experimental
results of the system verify the excellent performance of the proposed
gain control methodology.
Abstract: In this paper, Differential Evolution (DE) algorithm, a new promising evolutionary algorithm, is proposed to train Radial Basis Function (RBF) network related to automatic configuration of network architecture. Classification tasks on data sets: Iris, Wine, New-thyroid, and Glass are conducted to measure the performance of neural networks. Compared with a standard RBF training algorithm in Matlab neural network toolbox, DE achieves more rational architecture for RBF networks. The resulting networks hence obtain strong generalization abilities.
Abstract: This paper investigates the solutions of two-point fuzzy boundary value problems as the form x = f(t, x(t)), x(0) = A and x(l) = B, where A and B are fuzzy numbers. There are four different solutions for the problems when the lateral type of H-derivative is employed to solve the problems. As f(t, x) is a monotone function of x, these four solutions are reduced to two different solutions. As f(t, x(t)) = λx(t) or f(t, x(t)) = -λx(t), solutions and several comparison results are presented to indicate advantages of each solution.
Abstract: Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.
Abstract: Kernel function, which allows the formulation of nonlinear variants of any algorithm that can be cast in terms of dot products, makes the Support Vector Machines (SVM) have been successfully applied in many fields, e.g. classification and regression. The importance of kernel has motivated many studies on its composition. It-s well-known that reproducing kernel (R.K) is a useful kernel function which possesses many properties, e.g. positive definiteness, reproducing property and composing complex R.K by simple operation. There are two popular ways to compute the R.K with explicit form. One is to construct and solve a specific differential equation with boundary value whose handicap is incapable of obtaining a unified form of R.K. The other is using a piecewise integral of the Green function associated with a differential operator L. The latter benefits the computation of a R.K with a unified explicit form and theoretical analysis, whereas there are relatively later studies and fewer practical computations. In this paper, a new algorithm for computing a R.K is presented. It can obtain the unified explicit form of R.K in general reproducing kernel Hilbert space. It avoids constructing and solving the complex differential equations manually and benefits an automatic, flexible and rigorous computation for more general RKHS. In order to validate that the R.K computed by the algorithm can be used in SVM well, some illustrative examples and a comparison between R.K and Gaussian kernel (RBF) in support vector regression are presented. The result shows that the performance of R.K is close or slightly superior to that of RBF.
Abstract: In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.
Abstract: We propose a reduced-ordermodel for the instantaneous
hydrodynamic force on a cylinder. The model consists of a system of
two ordinary differential equations (ODEs), which can be integrated
in time to yield very accurate histories of the resultant force and
its direction. In contrast to several existing models, the proposed
model considers the actual (total) hydrodynamic force rather than its
perpendicular or parallel projection (the lift and drag), and captures
the complete force rather than the oscillatory part only. We study
and provide descriptions of the relationship between the model
parameters, evaluated utilizing results from numerical simulations,
and the Reynolds number so that the model can be used at any
arbitrary value within the considered range of 100 to 500 to provide
accurate representation of the force without the need to perform timeconsuming
simulations and solving the partial differential equations
(PDEs) governing the flow field.
Abstract: The present paper represents a methodology for
investigating flow characteristics near orifice plate by using a
commercial computational fluid dynamics code. The flow
characteristics near orifice plate which is located in the auxiliary
feedwater system were modeled via three different levels of grid and
four different types of Reynolds Averaged Navier-Stokes (RANS)
equations with proper near-wall treatment. The results from CFD code
were compared with experimental data in terms of differential pressure
through the orifice plate. In this preliminary study, the Realizable k-ε
and the Reynolds stress models with enhanced wall treatment were
suitable to analyze flow characteristics near orifice plate, and the
results had a good agreement with experimental data.
Abstract: In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.
Abstract: Reactiondiffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear parabolic partial differential equations, whose general form is ÔêétX(x, t) = DΔX(x, t), where X(x, t) is the state vector, D is the matrix of the diffusion coefficients and Δ is the Laplace operator. If the solute move in an homogeneous system in thermal equilibrium, the diffusion coefficients are constants that do not depend on the local concentration of solvent and of solutes and on local temperature of the medium. In this paper a new stochastic reaction-diffusion model in which the diffusion coefficients are function of the local concentration, viscosity and frictional forces of solvent and solute is presented. Such a model provides a more realistic description of the molecular kinetics in non-homogenoeus and highly structured media as the intra- and inter-cellular spaces. The movement of a molecule A from a region i to a region j of the space is described as a first order reaction Ai k- → Aj , where the rate constant k depends on the diffusion coefficient. Representing the diffusional motion as a chemical reaction allows to assimilate a reaction-diffusion system to a pure reaction system and to simulate it with Gillespie-inspired stochastic simulation algorithms. The stochastic time evolution of the system is given by the occurrence of diffusion events and chemical reaction events. At each time step an event (reaction or diffusion) is selected from a probability distribution of waiting times determined by the specific speed of reaction and diffusion events. Redi is the software tool, developed to implement the model of reaction-diffusion kinetics and dynamics. It is a free software, that can be downloaded from http://www.cosbi.eu. To demonstrate the validity of the new reaction-diffusion model, the simulation results of the chaperone-assisted protein folding in cytoplasm obtained with Redi are reported. This case study is redrawing the attention of the scientific community due to current interests on protein aggregation as a potential cause for neurodegenerative diseases.
Abstract: The aim of this work was to study the in vitro effects
of δ-lactam 1 and its 4-chlorophenyl derivative 2, on the proliferative
responses of human lymphocytes and Th1 and Th2 cytokine
secretion. The possible protective role of vitamin E on intracellular
stress oxidative induced by these compounds was also investigated.
Peripheral blood lymphocytes were isolated using differential
centrifugation on a density gradient of Histopaque. They were
cultured with mitogen concanavalin A, vitamin E (10 μM) and with
different concentrations of the compounds 1 and 2 (0.1 to 10 μM).
Proliferation (MTT assay), IL-2, INFγ and IL-4 (Elisa kits),
intracellular superoxide anion were determined. 1 and 2 were
immunostimulant and increased cytokine secretion with a shift away
from Th1 response to Th2. These properties were however
accompanied by an increase in intracellular oxidative stress. The
presence of vitamin E exhibited protective effects by reducing δ-
lactam-induced superoxide anion generation in lymphocytes.
Abstract: A systematic way to derive the conserved quantities for the axisymmetric liquid jet, free jet and wall jet using conservation laws is presented. The flow in axisymmetric jets is governed by Prandtl-s momentum boundary layer equation and the continuity equation. The multiplier approach is used to construct a basis of conserved vectors for the system of two partial differential equations for the two velocity components. The basis consists of two conserved vectors. By integrating the corresponding conservation laws across the jet and imposing the boundary conditions, conserved quantities are derived for the axisymmetric liquid and free jet. The multiplier approach applied to the third-order partial differential equation for the stream function yields two local conserved vectors one of which is a non-local conserved vector for the system. One of the conserved vectors gives the conserved quantity for the axisymmetric free jet but the conserved quantity for the wall jet is not obtained from the second conserved vector. The conserved quantity for the axisymmetric wall jet is derived from a non-local conserved vector of the third-order partial differential equation for the stream function. This non-local conserved vector for the third-order partial differential equation for the stream function is obtained by using the stream function as multiplier.
Abstract: A series of microarray experiments produces observations
of differential expression for thousands of genes across multiple
conditions.
Principal component analysis(PCA) has been widely used in
multivariate data analysis to reduce the dimensionality of the data in
order to simplify subsequent analysis and allow for summarization of
the data in a parsimonious manner. PCA, which can be implemented
via a singular value decomposition(SVD), is useful for analysis of
microarray data.
For application of PCA using SVD we use the DNA microarray
data for the small round blue cell tumors(SRBCT) of childhood
by Khan et al.(2001). To decide the number of components which
account for sufficient amount of information we draw scree plot.
Biplot, a graphic display associated with PCA, reveals important
features that exhibit relationship between variables and also the
relationship of variables with observations.
Abstract: This paper presents an application of level sets for the segmentation of abdominal and thoracic aortic aneurysms in CTA
datasets. An important challenge in reliably detecting aortic is the
need to overcome problems associated with intensity
inhomogeneities. Level sets are part of an important class of methods
that utilize partial differential equations (PDEs) and have been extensively applied in image segmentation. A kernel function in the
level set formulation aids the suppression of noise in the extracted
regions of interest and then guides the motion of the evolving contour
for the detection of weak boundaries. The speed of curve evolution
has been significantly improved with a resulting decrease in segmentation time compared with previous implementations of level
sets, and are shown to be more effective than other approaches in
coping with intensity inhomogeneities. We have applied the Courant
Friedrichs Levy (CFL) condition as stability criterion for our algorithm.
Abstract: The deviation between the target state variable and the
practical state variable should be used to form the state tending factor
of complex systems, which can reflect the process for the complex
system to tend rationalization. Relating to the system of basic
equations of complete factor synergetics consisting of twenty
nonlinear stochastic differential equations, the two new models are
considered to set, which should be called respectively the
rationalizing tendency model and the non- rationalizing tendency
model. Therefore we can extend the theory of programming with the
objective function & constraint condition suitable only for the realm
of man-s activities into the new analysis with the tendency function &
constraint condition suitable for all the field of complex system.
Abstract: In this paper, we explore the applicability of the Sinc-
Collocation method to a three-dimensional (3D) oceanography model.
The model describes a wind-driven current with depth-dependent
eddy viscosity in the complex-velocity system. In general, the
Sinc-based methods excel over other traditional numerical methods
due to their exponentially decaying errors, rapid convergence and
handling problems in the presence of singularities in end-points.
Together with these advantages, the Sinc-Collocation approach that
we utilize exploits first derivative interpolation, whose integration
is much less sensitive to numerical errors. We bring up several
model problems to prove the accuracy, stability, and computational
efficiency of the method. The approximate solutions determined by
the Sinc-Collocation technique are compared to exact solutions and
those obtained by the Sinc-Galerkin approach in earlier studies. Our
findings indicate that the Sinc-Collocation method outperforms other
Sinc-based methods in past studies.
Abstract: Fluid flow and heat transfer of vertical full cone
embedded in porous media is studied in this paper. Nonlinear
differential equation arising from similarity solution of inverted cone
(subjected to wall temperature boundary conditions) embedded in
porous medium is solved using a hybrid neural network- particle
swarm optimization method.
To aim this purpose, a trial solution of the differential equation is
defined as sum of two parts. The first part satisfies the initial/
boundary conditions and does contain an adjustable parameter and
the second part which is constructed so as not to affect the
initial/boundary conditions and involves adjustable parameters (the
weights and biases) for a multi-layer perceptron neural network.
Particle swarm optimization (PSO) is applied to find adjustable
parameters of trial solution (in first and second part). The obtained
solution in comparison with the numerical ones represents a
remarkable accuracy.
Abstract: In the present study, a procedure was developed to
determine the optimum reaction rate constants in generalized
Arrhenius form and optimized through the Nelder-Mead method. For
this purpose, a comprehensive mathematical model of a fixed bed
reactor for dehydrogenation of heavy paraffins over Pt–Sn/Al2O3
catalyst was developed. Utilizing appropriate kinetic rate expressions
for the main dehydrogenation reaction as well as side reactions and
catalyst deactivation, a detailed model for the radial flow reactor was
obtained. The reactor model composed of a set of partial differential
equations (PDE), ordinary differential equations (ODE) as well as
algebraic equations all of which were solved numerically to
determine variations in components- concentrations in term of mole
percents as a function of time and reactor radius. It was demonstrated
that most significant variations observed at the entrance of the bed
and the initial olefin production obtained was rather high. The
aforementioned method utilized a direct-search optimization
algorithm along with the numerical solution of the governing
differential equations. The usefulness and validity of the method was
demonstrated by comparing the predicted values of the kinetic
constants using the proposed method with a series of experimental
values reported in the literature for different systems.
Abstract: This paper evaluate the multilevel modulation for
different techniques such as amplitude shift keying (M-ASK), MASK,
differential phase shift keying (M-ASK-Bipolar), Quaternary
Amplitude Shift Keying (QASK) and Quaternary Polarization-ASK
(QPol-ASK) at a total bit rate of 107 Gbps. The aim is to find a costeffective
very high speed transport solution. Numerical investigation
was performed using Monte Carlo simulations. The obtained results
indicate that some modulation formats can be operated at 100Gbps
in optical communication systems with low implementation effort
and high spectral efficiency.