Abstract: In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.
Abstract: In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.
Abstract: The author previously proposed an extension of differential evolution. The proposed method extends the processes of DE to handle interval numbers as genotype values so that DE can be applied to interval-valued optimization problems. The interval DE can employ either of two interval models, the lower and upper model or the center and width model, for specifying genotype values. Ability of the interval DE in searching for solutions may depend on the model. In this paper, the author compares the two models to investigate which model contributes better for the interval DE to find better solutions. Application of the interval DE is evolutionary training of interval-valued neural networks. A result of preliminary study indicates that the CW model is better than the LU model: the interval DE with the CW model could evolve better neural networks.
Abstract: Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.
Abstract: As p-Laplacian equations have been widely applied in field of the fluid mechanics and nonlinear elastic mechanics, it is necessary to investigate the periodic solutions of functional differential equations involving the scalar p-Laplacian. By using Mawhin’s continuation theorem, we study the existence of periodic solutions for p-Laplacian neutral Rayleigh equation (ϕp(x(t)−c(t)x(t − r))) + f(x(t)) + g1(x(t − τ1(t, |x|∞))) + β(t)g2(x(t − τ2(t, |x|∞))) = e(t), It is meaningful that the functions c(t) and β(t) are allowed to change
signs in this paper, which are different from the corresponding ones of known literature.
Abstract: By using the estimation of the Cauchy matrix of linear impulsive differential equations and Banach fixed point theorem as well as Gronwall-Bellman’s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic
solution for an impulsive neural networks with distributed delays. An example is presented to illustrate the feasibility and effectiveness of the results.
Abstract: In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.
Abstract: We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.
Abstract: In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.
Abstract: LuGre friction model is an ordinary differential equation that is widely used in describing the friction phenomenon
for mechanical systems. The importance of this model comes from the fact that it captures most of the friction behavior that has been observed including hysteresis. In this paper, we study some aspects related to the hysteresis behavior induced by the LuGre friction model.
Abstract: A mathematical model is proposed considering the forest biomass density B(t), density of wood based industries W(t) and density of synthetic industries S(t). It is assumed that the forest biomass grows logistically in the absence of wood based industries, but depletion of forestry biomass is due to presence of wood based industries. The growth of wood based industries depends on B(t), while S(t) grows at a constant rate, independent of B(t). Further there is a competition between W(t) and S(t) according to market demand. The proposed model has four ecologically feasible steady states, namely, E1: forest biomass free and wood industries free equilibrium; E2: wood industries free equilibrium and two coexisting equilibria E∗1 , E∗2 . Behavior of the system near all feasible equilibria is analyzed using the stability theory of differential equations. In the proposed model, the natural depletion rate h1 is a crucial parameter and system exhibits Hopf-bifurcation about the non-trivial equilibrium with respect to h1. The analytical results are verified using numerical simulation.
Abstract: In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.
Abstract: In this paper we propose a necessary condition for the existence of chaos in delay differential equations of fractional order. To explain the proposed theory, we discuss fractional order Liu system and financial system involving delay.
Abstract: We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.
Abstract: This paper presents a 14-bit cyclic-pipelined Analog to digital converter (ADC) running at 1 MS/s. The architecture is based on a 1.5-bit per stage structure utilizing digital correction for each stage. The ADC consists of two 1.5-bit stages, one shift register delay line, and digital error correction logic. Inside each 1.5-bit stage, there is one gain-boosting op-amp and two comparators. The ADC was implemented in 0.18µm CMOS process and the design has an area of approximately 0.2 mm2. The ADC has a differential input range of 1.2 Vpp. The circuit has an average power consumption of 3.5mA with 10MHz sampling clocks. The post-layout simulations of the design satisfy 12-bit SNDR with a full-scale sinusoid input.
Abstract: According to synthetic plastics obtained from petroleum cause some environmental problems. Therefore, degradable plastics become widely used and studied for replacing the synthetic plastic waste. A biopolymer of poly hydroxybutyrate-co-hydroxyvalerate (PHBV) is subgroups of a main kind of polyhydroxyalkanoates (PHAs). Naturally, PHBV is hard, brittle and low flexible while natural rubber (NR) is high elastic latex. Then, they are blended and the biodegradation of the blended PHBV and NR films were examined in soil environment. The results showed that the degradation occurs predominantly in the bulk of the samples. The order of biodegradability was shown as follows: PHBV> PHBV/NR> NR. After biodegradation, the blended films were characterized by appearance analysis such as Scanning Electron Microscope (SEM), Fourier transform infrared spectroscopy (FTIR) and Differential Scanning Calorimetry (DSC). It was found that the biodegradation mainly occurred at the polymer surface.
Abstract: This paper presents a customized deformable model
for the segmentation of abdominal and thoracic aortic aneurysms in
CTA datasets. An important challenge in reliably detecting aortic
aneurysm is the need to overcome problems associated with intensity
inhomogeneities and image noise. 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 Gaussian
kernel function in the level set formulation, which extracts the local
intensity information, 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. The results indicate the method is more effective than other
approaches in coping with intensity inhomogeneities.
Abstract: Heterogeneous repolarization causes dispersion of the T-wave and has been linked to arrhythmogenesis. Such heterogeneities appear due to differential expression of ionic currents in different regions of the heart, both in healthy and diseased animals and humans. Mice are important animals for the study of heart diseases because of the ability to create transgenic animals. We used our previously reported model of mouse ventricular myocytes to develop 2D mouse ventricular tissue model consisting of 14,000 cells (apical or septal ventricular myocytes) and to study the stability of action potential propagation and Ca2+ dynamics. The 2D tissue model was implemented as a FORTRAN program code for highperformance multiprocessor computers that runs on 36 processors. Our tissue model is able to simulate heterogeneities not only in action potential repolarization, but also heterogeneities in intracellular Ca2+ transients. The multicellular model reproduced experimentally observed velocities of action potential propagation and demonstrated the importance of incorporation of realistic Ca2+ dynamics for action potential propagation. The simulations show that relatively sharp gradients of repolarization are predicted to exist in 2D mouse tissue models, and they are primarily determined by the cellular properties of ventricular myocytes. Abrupt local gradients of channel expression can cause alternans at longer pacing basic cycle lengths than gradual changes, and development of alternans depends on the site of stimulation.
Abstract: This paper presents an effective technique for harmonic current mitigation using an adaptive notch filter (ANF) to estimate current harmonics. The proposed filter consists of multiple units of ANF connected in parallel structure; each unit is governed by two ordinary differential equations. The frequency estimation is carried out based on the output of these units. The simulation and experimental results show the ability of the proposed tracking scheme to accurately estimate harmonics. The proposed filter was implemented digitally in TMS320F2808 and used in the control of hybrid active power filter (HAPF). The theoretical expectations are verified and demonstrated experimentally.
Abstract: One of the main objectives of order reduction is to
design a controller of lower order which can effectively control the
original high order system so that the overall system is of lower
order and easy to understand. In this paper, a simple method is
presented for controller design of a higher order discrete system.
First the original higher order discrete system in reduced to a lower
order model. Then a Proportional Integral Derivative (PID)
controller is designed for lower order model. An error minimization
technique is employed for both order reduction and controller
design. For the error minimization purpose, Differential Evolution
(DE) optimization algorithm has been employed. DE method is
based on the minimization of the Integral Squared Error (ISE)
between the desired response and actual response pertaining to a
unit step input. Finally the designed PID controller is connected to
the original higher order discrete system to get the desired
specification. The validity of the proposed method is illustrated
through a numerical example.