Search results for: differential motion.

Authors: Mahmoud Elmezain, Ayoub Al-Hamadi, Jörg Appenrodt, Bernd Michaelis

Abstract:

Gesture recognition is a challenging task for extracting meaningful gesture from continuous hand motion. In this paper, we propose an automatic system that recognizes isolated gesture, in addition meaningful gesture from continuous hand motion for Arabic numbers from 0 to 9 in real-time based on Hidden Markov Models (HMM). In order to handle isolated gesture, HMM using Ergodic, Left-Right (LR) and Left-Right Banded (LRB) topologies is applied over the discrete vector feature that is extracted from stereo color image sequences. These topologies are considered to different number of states ranging from 3 to 10. A new system is developed to recognize the meaningful gesture based on zero-codeword detection with static velocity motion for continuous gesture. Therefore, the LRB topology in conjunction with Baum-Welch (BW) algorithm for training and forward algorithm with Viterbi path for testing presents the best performance. Experimental results show that the proposed system can successfully recognize isolated and meaningful gesture and achieve average rate recognition 98.6% and 94.29% respectively.

Keywords: Computer Vision & Image Processing, Gesture Recognition, Pattern Recognition, Application

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Authors: Edikan E. Akpanibah, Ogunmodimu Dupe Catherine

Abstract:

The relevance of geometric Brownian motion (GBM) in modelling the behaviour of stock market prices (SMP) cannot be over emphasized taking into consideration the volatility of the SMP. Consequently, there is need to investigate how GBM models are being estimated and used in financial market to predict SMP. To achieve this, the GBM estimation and its application to the SMP of some selected companies are studied. The normal and log-normal distributions were used to determine the expected value, variance and co-variance. Furthermore, the GBM model was used to predict the SMP of some selected companies over a period of time and the mean absolute percentage error (MAPE) were calculated and used to determine the accuracy of the GBM model in predicting the SMP of the four companies under consideration. It was observed that for all the four companies, their MAPE values were within the region of acceptance. Also, the MAPE values of our data were compared to an existing literature to test the accuracy of our prediction with respect to time of investment. Finally, some numerical simulations of the graphs of the SMP, expectations and variance of the four companies over a period of time were presented using MATLAB programming software.

Keywords: Stock Market, Geometric Brownian Motion, normal and log-normal distribution, mean absolute percentage error.

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Authors: Shuenn-Yih Chang, Chiu-Li Huang

Abstract:

Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods.

Keywords: Dynamic analysis, high frequency, integration method, overshoot, weak instability.

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Authors: Costa, E.S., Borges, E.N.M., Afonso, M.M.

Abstract:

The modeling of sound radiation is of fundamental importance for understanding the propagation of acoustic waves and, consequently, develop mechanisms for reducing acoustic noise. The propagation of acoustic waves, are involved in various phenomena such as radiation, absorption, transmission and reflection. The radiation is studied through the linear equation of the acoustic wave that is obtained through the equation for the Conservation of Momentum, equation of State and Continuity. From these equations, is the Helmholtz differential equation that describes the problem of acoustic radiation. In this paper we obtained the solution of the Helmholtz differential equation for an infinite cylinder in a pulsating through free and homogeneous. The analytical solution is implemented and the results are compared with the literature. A numerical formulation for this problem is obtained using the Boundary Element Method (BEM). This method has great power for solving certain acoustical problems in open field, compared to differential methods. BEM reduces the size of the problem, thereby simplifying the input data to be worked and reducing the computational time used.

Keywords: Acoustic radiation, boundary element

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Authors: Rehana Naz, D. P. Mason, Fazal Mahomed

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.

Keywords: Axisymmetric jet, liquid jet, free jet, wall jet, conservation laws, conserved quantity.

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Authors: Hongbin Gu, Dongsu Wu, Hui Liu

Abstract:

A novel low-cost flight simulator with the development goals cost effectiveness and high performance has been realized for meeting the huge pilot training needs of airlines. The simulator consists of an aircraft dynamics model, a sophisticated designed low-profile electrical driven motion system with a subsided cabin, a mixed reality based semi-virtual cockpit system, a control loading system and some other subsystems. It shows its advantages over traditional flight simulator by its features achieved with open architecture, software solutions and low-cost hardware.

Keywords: Flight simulator, mixed reality, motion system, control loading system.

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Authors: H. Taghvafard, G. H. Erjaee

Abstract:

A method for solving linear and non-linear Goursat problem is given by using the two-dimensional differential transform method. The approximate solution of this problem is calculated in the form of a series with easily computable terms and also the exact solutions can be achieved by the known forms of the series solutions. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Several examples are given to demonstrate the reliability and the performance of the presented method.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: Anuar Ishak

Abstract:

The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. 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 suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Dual solutions, heat transfer, shrinking sheet, stability analysis.

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Authors: Shun-Chang Chang

Abstract:

In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.

Keywords: bifurcation, Poincare map, Lyapunov exponent, chaotic motion.

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Authors: Mamidi Ramakrishna Rao

Abstract:

Doubly-fed induction generators (DFIG) due to their advantages like speed variation and four-quadrant operation, find its application in wind turbines. DFIG besides supplying power to the grid has to support reactive power (kvar) under grid voltage variations, should contribute minimum fault current during faults, have high efficiency, minimum weight, adequate rotor protection during crow-bar-operation from +20% to -20% of rated speed.  To achieve the optimum performance, a good electromagnetic design of DFIG is required. In this paper, a simple and heuristic global optimization – Differential Evolution has been used. Variables considered are lamination details such as slot dimensions, stack diameters, air gap length, and generator stator and rotor stack length. Two operating conditions have been considered - voltage and speed variations. Constraints included were reactive power supplied to the grid and limiting fault current and torque. The optimization has been executed separately for three objective functions - maximum efficiency, weight reduction, and grid fault stator currents. Subsequent calculations led to the conclusion that designs determined through differential evolution help in determining an optimum electrical design for each objective function.

Keywords: Design optimization, performance, doubly fed induction generators, DFIG, differential evolution.

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Authors: Alireza Fereidooni, Kamran Behdinan, Zouheir Fawaz

Abstract:

The integral form of equations of motion of composite beams subjected to varying time loads are discretized using a developed finite element model. The model consists of a straight five node twenty-two degrees of freedom beam element. The stability analysis of the beams is studied by solving the matrix form characteristic equations of the system. The principle of virtual work and the first order shear deformation theory are employed to analyze the beams with large deformation and small strains. The regions of dynamic instability of the beam are determined by solving the obtained Mathieu form of differential equations. The effects of nonconservative loads, shear stiffness, and damping parameters on stability and response of the beams are examined. Several numerical calculations are presented to compare the results with data reported by other researchers.

Keywords: Finite element beam model, Composite Beams, stability analysis

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Authors: Qazi Umer Jamil, Abubakr Siddique, Mubeen Ur Rehman, Nida Aziz, Mohsin I. Tiwana

Abstract:

This paper discusses a brain controlled robotic gait trainer for neurorehabilitation of Spinal Cord Injury (SCI) patients. Patients suffering from Spinal Cord Injuries (SCI) become unable to execute motion control of their lower proximities due to degeneration of spinal cord neurons. The presented approach can help SCI patients in neuro-rehabilitation training by directly translating patient motor imagery into walkers motion commands and thus bypassing spinal cord neurons completely. A non-invasive EEG based brain-computer interface is used for capturing patient neural activity. For signal processing and classification, an open source software (OpenVibe) is used. Classifiers categorize the patient motor imagery (MI) into a specific set of commands that are further translated into walker motion commands. The robotic walker also employs fall detection for ensuring safety of patient during gait training and can act as a support for SCI patients. The gait trainer is tested with subjects, and satisfactory results were achieved.

Keywords: Brain Computer Interface (BCI), gait trainer, Spinal Cord Injury (SCI), neurorehabilitation.

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Authors: B. Bagheri Nakhjavanlo, T. S. Ellis, P.Raoofi, Sh.ziari

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.

Keywords: Image segmentation, Level-sets, Local fitting binary, Thoracic aorta.

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Authors: Süha Yılmaz, Melih Turgut

Abstract:

The curves, of which the square of the distance between the two points equal to zero, are called minimal or isotropic curves [4]. In this work, first, necessary and sufficient conditions to be a Pseudo Helix, which is a special case of such curves, are presented. Thereafter, it is proven that an isotropic curve-s position vector and pseudo curvature satisfy a vector differential equation of fourth order. Additionally, In view of solution of mentioned equation, position vector of pseudo helices is obtained.

Keywords: Classical Differential Geometry, Euclidean space, Minimal Curves, Isotropic Curves, Pseudo Helix.

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Authors: J. Ranjbarn, A. Alibeigloo

Abstract:

In this paper, we present an analytical method for analysis of nano-scale spherical shell subjected to thermo-mechanical shocks based on nonlocal elasticity theory. Thermo-mechanical properties of nano shpere is assumed to be temperature dependent. Governing partial differential equation of motion is solved analytically by using Laplace transform for time domain and power series for spacial domain. The results in Laplace domain is transferred to time domain by employing the fast inverse Laplace transform (FLIT) method. Accuracy of present approach is assessed by comparing the the numerical results with the results of published work in literature. Furtheremore, the effects of non-local parameter and wall thickness on the dynamic characteristics of the nano-sphere are studied.

Keywords: Nano-scale spherical shell, nonlocal elasticity theory, thermomechanical shock.

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Authors: A. A. Sharma, B. J. N. Sharma

Abstract:

This paper deals with the study of reflection and transmission characteristics of acoustic waves at the interface of a semiconductor half-space and elastic solid. The amplitude ratios (reflection and transmission coefficients) of reflected and transmitted waves to that of incident wave varying with the incident angles have been examined for the case of quasi-longitudinal wave. The special cases of normal and grazing incidence have also been derived with the help of Gauss elimination method. The mathematical model consisting of governing partial differential equations of motion and charge carriers’ diffusion of n-type semiconductors and elastic solid has been solved both analytically and numerically in the study. The numerical computations of reflection and transmission coefficients has been carried out by using MATLAB programming software for silicon (Si) semiconductor and copper elastic solid. The computer simulated results have been plotted graphically for Si semiconductors. The study may be useful in semiconductors, geology, and seismology in addition to surface acoustic wave (SAW) devices.

Keywords: Quasilongitudinal, reflection and transmission, semiconductors, acoustics.

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Authors: S. Maheswari, P. Arockia Jansi Rani

Abstract:

Human action is recognized directly from the video sequences. The objective of this work is to recognize various human actions like run, jump, walk etc. Human action recognition requires some prior knowledge about actions namely, the motion estimation, foreground and background estimation. Region of interest (ROI) is extracted to identify the human in the frame. Then, optical flow technique is used to extract the motion vectors. Using the extracted features similarity measure based classification is done to recognize the action. From experimentations upon the Weizmann database, it is found that the proposed method offers a high accuracy.

Keywords: Background subtraction, human silhouette, optical flow, classification.

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Authors: O. Punjarat, S. Chucheepsakul, T. Phanyasahachart

Abstract:

This paper focuses on a variational formulation of large amplitude free vibration behavior of a very sag marine cable. In the static equilibrium state, the marine cable has a very large sag configuration. In the motion state, the marine cable is assumed to vibrate in in-plane motion with large amplitude from the static equilibrium position. The total virtual work-energy of the marine cable at the dynamic state is formulated which involves the virtual strain energy due to axial deformation, the virtual work done by effective weight, and the inertia forces. The equations of motion for the large amplitude free vibration of marine cable are obtained by taking into account the difference between the Euler’s equation in the static state and the displaced state. Based on the Galerkin finite element procedure, the linear and nonlinear stiffness matrices, and mass matrices of the marine cable are obtained and the eigenvalue problem is solved. The natural frequency spectrum and the large amplitude free vibration behavior of marine cable are presented.

Keywords: Axial deformation, free vibration, Galerkin Finite Element Method, large amplitude, variational method.

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Authors: Guosheng Wu, Luning Wang, Changyuan Fan, Xi Zhu

Abstract:

This paper provides a new approach to solve the motion planning problems of flying robots in uncertain 3D dynamic environments. The robots controlled by this method can adaptively choose the fast way to avoid collision without information about the shapes and trajectories of obstacles. Based on sphere coordinates the new method accomplishes collision avoidance of flying robots without any other auxiliary positioning systems. The Self-protection System gives robots self-protection abilities to work in uncertain 3D dynamic environments. Simulations illustrate the validity of the proposed method.

Keywords: Collision avoidance, Mobile robots, Motion-planning, Sphere coordinates, Self-protection.

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Authors: Zhoucheng Bao, Haiyan Zhu, Tingting Pang, Zuling Wang

Abstract:

This paper presents a multi population Differential Evolution (DE) with adaptive mutation and local search for global optimization, named AMMADE in order to better coordinate the cooperation between the populations and the rational use of resources. In AMMADE, the population is divided based on the Euclidean distance sorting method at each generation to appropriately coordinate the cooperation between subpopulations and the usage of resources, such that the best-performed subpopulation will get more computing resources in the next generation. Further, an adaptive local search strategy is employed on the best-performed subpopulation to achieve a balanced search. The proposed algorithm has been tested by solving optimization problems taken from CEC2014 benchmark problems. Experimental results show that our algorithm can achieve a competitive or better result than related methods. The results also confirm the significance of devised strategies in the proposed algorithm.

Keywords: Differential evolution, multi-mutation strategies, memetic algorithm, adaptive local search.

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Authors: B. Bagheri Nakhjavanlo, T. J. Ellis, P. Raoofi, J. Dehmeshki

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.

Keywords: Abdominal and thoracic aortic aneurysms, intensityinhomogeneity, level sets, local fitting binary.

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Authors: Mahmoud Saeidi, Ali Nazemipour

Abstract:

In this paper, we propose a novel adaptive spatiotemporal filter that utilizes image sequences in order to remove noise. The consecutive frames include: current, previous and next noisy frames. The filter proposed in this paper is based upon the weighted averaging pixels intensity and noise variance in image sequences. It utilizes the Appropriate Number of Consecutive Frames (ANCF) based on the noisy pixels intensity among the frames. The number of consecutive frames is adaptively calculated for each region in image and its value may change from one region to another region depending on the pixels intensity within the region. The weights are determined by a well-defined mathematical criterion, which is adaptive to the feature of spatiotemporal pixels of the consecutive frames. It is experimentally shown that the proposed filter can preserve image structures and edges under motion while suppressing noise, and thus can be effectively used in image sequences filtering. In addition, the AWA filter using ANCF is particularly well suited for filtering sequences that contain segments with abruptly changing scene content due to, for example, rapid zooming and changes in the view of the camera.

Keywords: Appropriate Number of Consecutive Frames, Adaptive Weighted Averaging, Motion Estimation, Noise Variance, Motion Compensation

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Authors: S. Sowmyayani, P. Arockia Jansi Rani

Abstract:

This paper integrates Octagon and Square Search pattern (OCTSS) motion estimation algorithm into H.264/AVC (Advanced Video Coding) video codec in Adaptive Group of Pictures (AGOP) mode. AGOP structure is computed based on scene change in the video sequence. Octagon and square search pattern block-based motion estimation method is implemented in inter-prediction process of H.264/AVC. Both these methods reduce bit rate and computational complexity while maintaining the quality of the video sequence respectively. Experiments are conducted for different types of video sequence. The results substantially proved that the bit rate, computation time and PSNR gain achieved by the proposed method is better than the existing H.264/AVC with fixed GOP and AGOP. With a marginal gain in quality of 0.28dB and average gain in bitrate of 132.87kbps, the proposed method reduces the average computation time by 27.31 minutes when compared to the existing state-of-art H.264/AVC video codec.

Keywords: Block Distortion Measure, Block Matching Algorithms, H.264/AVC, Motion estimation, Search patterns, Shot cut detection.

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Authors: Avinesh Prasad, Bibhya Sharma, Jito Vanualailai

Abstract:

This paper proposes a solution to the motion planning and control problem of a point-mass robot which is required to move safely to a designated target in a priori known workspace cluttered with fixed elliptical obstacles of arbitrary position and sizes. A tailored and unique algorithm for target convergence and obstacle avoidance is proposed that will work for any number of fixed obstacles. The control laws proposed in this paper also ensures that the equilibrium point of the given system is asymptotically stable. Computer simulations with the proposed technique and applications to a planar (RP) manipulator will be presented.

Keywords: Point-mass Robot, Asymptotic stability, Motionplanning, Planar Robot Arm.

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Authors: F.Ebrahimi, A.Rastgo

Abstract:

Analytical investigation of the free vibration behavior of circular functionally graded (FG) plates integrated with two uniformly distributed actuator layers made of piezoelectric (PZT4) material on the top and bottom surfaces of the circular FG plate based on the classical plate theory (CPT) is presented in this paper. The material properties of the functionally graded substrate plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents and the distribution of electric potential field along the thickness direction of piezoelectric layers is simulated by a quadratic function. The differential equations of motion are solved analytically for clamped edge boundary condition of the plate. The detailed mathematical derivations are presented and Numerical investigations are performed for FG plates with two surface-bonded piezoelectric layers. Emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. The results are verified by those obtained from threedimensional finite element analyses.

Keywords: Circular plate, CPT, Functionally graded, Piezoelectric.

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Authors: Hui-Jae You, Sun-Tae Chung, Souhwan Jung

Abstract:

SAD (Sum of Absolute Difference) algorithm is heavily used in motion estimation which is computationally highly demanding process in motion picture encoding. To enhance the performance of motion picture encoding on a VLIW processor, an efficient implementation of SAD algorithm on the VLIW processor is essential. SAD algorithm is programmed as a nested loop with a conditional branch. In VLIW processors, loop is usually optimized by software pipelining, but researches on optimal scheduling of software pipelining for nested loops, especially nested loops with conditional branches are rare. In this paper, we propose an optimal scheduling and implementation of SAD algorithm with conditional branch on a VLIW DSP processor. The proposed optimal scheduling first transforms the nested loop with conditional branch into a single loop with conditional branch with consideration of full utilization of ILP capability of the VLIW processor and realization of earlier escape from the loop. Next, the proposed optimal scheduling applies a modulo scheduling technique developed for single loop. Based on this optimal scheduling strategy, optimal implementation of SAD algorithm on TMS320C67x, a VLIW DSP is presented. Through experiments on TMS320C6713 DSK, it is shown that H.263 encoder with the proposed SAD implementation performs better than other H.263 encoder with other SAD implementations, and that the code size of the optimal SAD implementation is small enough to be appropriate for embedded environments.

Keywords: Optimal implementation, SAD algorithm, VLIW, TMS320C6713.

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Authors: A. Junaid, M. A. Z. Raja, I. M. Qureshi

Abstract:

An evolutionary computing technique for solving initial value problems in Ordinary Differential Equations is proposed in this paper. Neural network is used as a universal approximator while the adaptive parameters of neural networks are optimized by genetic algorithm. The solution is achieved on the continuous grid of time instead of discrete as in other numerical techniques. The comparison is carried out with classical numerical techniques and the solution is found with a uniform accuracy of MSE ≈ 10-9 .

Keywords: Neural networks, Unsupervised learning, Evolutionary computing, Numerical methods, Fitness evaluation function.

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Authors: M. A. Talha, M. Osman Gani, M. Ferdows

Abstract:

This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number P_r, magnetic field parameter M, Peclet number P_e, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.

Keywords: Convection flow, internal heat generation, similarity, spectral method, numerical analysis, Williamson nanofluid.

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Gronwall-Bellman-Type integral inequalities, integrodifferential equation, p-exponentially stable, mixed delays.

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Authors: Li Xiguang

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.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

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