Search results for: Uniform And Non-Uniform Variational Interactions

Authors: Surendra Mund

Abstract:

At the beginning, the physical entity force was defined mathematically by Sir Isaac Newton in his Principia Mathematica as F ⃗=(dp ⃗)/dt in form of his second law of motion. Newton also defines his Universal law of Gravitational force exist in same outstanding book, but at the end of 20th century and beginning of 21st century, we have tried a lot to specify and unify four or five Fundamental forces or Interaction exist in universe, but we failed every time. Usually, Gravity creates problems in this unification every single time, but in my previous papers and presentations, I defined and derived Field and force equations for Gravitational like Interactions for each and every kind of central systems. This force is named as Variational Force by me, and this force is generated by variation in the scalar field density around the body. In this particular paper, at first, I am specifying which type of Interactions are Fundamental in Universal sense (or in all type of central systems or bodies predicted by my N-time Inflationary Model of Universe) and then unify them in Universal framework (defined and derived by me as Universal Mechanics in a separate paper) as well. This will also be valid in Universal dynamical sense which includes inflations and deflations of universe, central system relativity, Universal relativity, ϕ-ψ transformation and transformation of spin, physical perception principle, Generalized Fundamental Dynamical Law and many other important Generalized Principles of Generalized Quantum Mechanics (GQM) and Central System Theory (CST). So, In this article, at first, I am Generalizing some Fundamental Principles, and then Unifying Variational Forces (General form of Gravitation like Interactions) and Flow Generated Force (General form of EM like Interactions), and then Unify all Fundamental Forces by specifying Weak and Strong Interactions in form of more basic terms - Variational, Flow Generated and Transformational Interactions.

Keywords: Central System Force, Disturbance Force, Flow Generated Forces, Generalized Nuclear Force, Generalized Weak Interactions, Generalized EM-Like Interactions, Imbalance Force, Spin Generated Forces, Transformation Generated Force, Unified Force, Universal Mechanics, Uniform And Non-Uniform Variational Interactions, Variational Interactions

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Authors: Abdulatif Abdusalam, Mohamed Shaban

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In this paper, we consider the nonlinear pulse propagation through a nonuniform birefringent fiber Bragg grating (FBG) whose index modulation depth varies along the propagation direction. Here, the pulse propagation is governed by the nonlinear birefringent coupled mode (NLBCM) equations. To form the Bragg soliton outside the photonic bandgap (PBG), the NLBCM equations are reduced to the well known NLS type equation by multiple scale analysis. As we consider the pulse propagation in a nonuniform FBG, the pulse propagation outside the PBG is governed by inhomogeneous NLS (INLS) rather than NLS. We, then, discuss the formation of soliton in the FBG known as Bragg soliton whose central frequency lies outside but close to the PBG of the grating structure. Further, we discuss Bragg soliton compression due to a delicate balance between the SPM and the varying grating induced dispersion. In addition, Bragg soliton collision, Bragg soliton switching and possible logic gates have also been discussed.

Keywords: Bragg grating, non uniform fiber, non linear pulse

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Authors: Renu Tomar, Hitendra K. Malik, Raj P. Dahiya

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Similar to the sound waves in air, plasmas support the propagation of ion waves, which evolve into the solitary structures when the effect of non linearity and dispersion are balanced. The ion acoustic solitary waves have been investigated in details in homogeneous plasmas, inhomogeneous plasmas, and magnetized plasmas. The ion acoustic solitary waves are also found to reflect from a density gradient or boundary present in the plasma after propagating. Another interesting feature of the solitary waves is their collision. In the present work, we carry out analytical calculations for the head-on collision of solitary waves in a magnetized plasma which has dust grains in addition to the ions and electrons. For this, we employ Poincar´e-Lighthill-Kuo (PLK) method. To lowest nonlinear order, the problem of colliding solitary waves leads to KdV (modified KdV) equations and also yields the phase shifts that occur in the interaction. These calculations are accomplished for the uniform and nonuniform plasmas, and the results on the soliton properties are discussed in detail.

Keywords: inhomogeneous magnetized plasma, dust charging, soliton collisions, magnetized plasma

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Authors: Athmane Bakhta, Sebastien Leclaire, David Vidal, Francois Bertrand, Mohamed Cheriet

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This work presents a new three-dimensional variational model proposed for the simulation of ink seepage into paper sheets at the fiber level. The model, inspired by the Hising model, takes into account a finite volume of ink and describes the system state through gravity, cohesion, and adhesion force interactions. At the mesoscopic scale, the paper substrate is modeled using a discretized fiber structure generated using a numerical deposition procedure. A modified Monte Carlo method is introduced for the simulation of the ink dynamics. Besides, a multiphase lattice Boltzmann method is suggested to fine-tune the mesoscopic variational model parameters, and it is shown that the ink seepage behaviors predicted by the proposed model can resemble those predicted by a method relying on first principles.

Keywords: fibrous media, lattice Boltzmann, modelling and simulation, Monte Carlo, variational model

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Authors: Alberto Hananel

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The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: approximation, evolutionary PDE, Finite Element Method, temporomandibular disorders, variational spline

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Authors: Ming Su, Ziqiang Mu

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This paper proposes a synthesis method for nonuniform linear antenna arrays that combine Gaussian process regression (GPR) and genetic algorithm (GA). In this method, the GPR model can be used to calculate the array radiation pattern in the presence of mutual coupling effects, and then the GA is used to optimize the excitations and locations of the elements so as to generate the desired radiation pattern. In this paper, taking a 9-element nonuniform linear array as an example and the desired radiation pattern corresponding to a Chebyshev distribution as the optimization objective, optimize the excitations and locations of the elements. Finally, the optimization results are verified by electromagnetic simulation software CST, which shows that the method is effective.

Keywords: nonuniform linear antenna arrays, GPR, GA, mutual coupling effects, active element pattern

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Authors: Nileshkumar Vishnav, Aditya Tatu

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A recent approach of representing graph signals and graph filters as polynomials is useful for graph signal processing. In this approach, the adjacency matrix plays pivotal role; instead of the more common approach involving graph-Laplacian. In this work, we follow the adjacency matrix based approach and corresponding algebraic signal model. We further expand the theory and introduce the concept of similarity of two graphs. The similarity of graphs is useful in that key properties (such as filter-response, algebra related to graph) get transferred from one graph to another. We demonstrate potential applications of the relation between two similar graphs, such as nonuniform filter design, DTMF detection and signal reconstruction.

Keywords: graph signal processing, algebraic signal processing, graph similarity, isospectral graphs, nonuniform signal processing

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Authors: Sen Yung Lee, Chih Cheng Huang, Te Wen Tu

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A solution methodology without using integral transformation is proposed to develop analytical solutions for transient heat conduction in nonuniform hollow cylinders with time-dependent boundary condition at the outer surface. It is shown that if the thermal conductivity and the specific heat of the medium are in arbitrary polynomial function forms, the closed solutions of the system can be developed. The influence of physical properties on the temperature distribution of the system is studied. A numerical example is given to illustrate the efficiency and the accuracy of the solution methodology.

Keywords: analytical solution, nonuniform hollow cylinder, time-dependent boundary condition, transient heat conduction

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Authors: C. Juntarasaid, T. Pulngern, S. Chucheepsakul

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A formulation of postbuckling analysis of end supported rods under self-weight has been presented by the variational method. The variational formulation involving the strain energy due to bending and the potential energy of the self-weight, are expressed in terms of the intrinsic coordinates. The variational formulation is accomplished by introducing the Lagrange multiplier technique to impose the boundary conditions. The finite element method is used to derive a system of nonlinear equations resulting from the stationary of the total potential energy and then Newton-Raphson iterative procedure is applied to solve this system of equations. The numerical results demonstrate the postbluckled configurations of end supported rods under self-weight. This finite element method based on variational formulation expressed in term of intrinsic coordinate is highly recommended for postbuckling analysis of end-supported rods under self-weight.

Keywords: postbuckling, finite element method, variational method, intrinsic coordinate

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Taweechai Nuntawisuttiwong, Natasha Dejdumrong

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Newton-Lagrange Interpolations are widely used in numerical analysis. However, it requires a quadratic computational time for their constructions. In computer aided geometric design (CAGD), there are some polynomial curves: Wang-Ball, DP and Dejdumrong curves, which have linear time complexity algorithms. Thus, the computational time for Newton-Lagrange Interpolations can be reduced by applying the algorithms of Wang-Ball, DP and Dejdumrong curves. In order to use Wang-Ball, DP and Dejdumrong algorithms, first, it is necessary to convert Newton-Lagrange polynomials into Wang-Ball, DP or Dejdumrong polynomials. In this work, the algorithms for converting from both uniform and non-uniform Newton-Lagrange polynomials into Wang-Ball, DP and Dejdumrong polynomials are investigated. Thus, the computational time for representing Newton-Lagrange polynomials can be reduced into linear complexity. In addition, the other utilizations of using CAGD curves to modify the Newton-Lagrange curves can be taken.

Keywords: Lagrange interpolation, linear complexity, monomial matrix, Newton interpolation

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Authors: Sandeep Kumar, Naveen Gupta

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The propagation of the Non-Gaussian laser beam results in strong self-focusing as compare to the Gaussian laser beam, which helps to achieve a prerequisite of the plasma-based electron, Terahertz generation, and higher harmonic generations. The theoretical investigation on the evolution of non-Gaussian laser beam through the collisional plasma with ramped density has been presented. The non-uniform irradiance over the cross-section of the laser beam results in redistribution of the carriers that modifies the optical response of the plasma in such a way that the plasma behaves like a converging lens to the laser beam. The formulation is based on finding a semi-analytical solution of the nonlinear Schrodinger wave equation (NLSE) with the help of variational theory. It has been observed that the decentred parameter ‘q’ of laser and wavenumber of ripples of medium contribute to providing the required conditions for the improvement of self-focusing.

Keywords: non-Gaussian beam, collisional plasma, variational theory, self-focusing

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Authors: Semih Erdogan

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In this paper, the normal and shear stress distributions in Vlasov beams are determined by two-dimensional triangular finite element formulations. The proposed formulations take into account the warping effects along the beam axis. The shape of the considered beam sections may be arbitrary and varied throughout its length. The stiffness matrices and force vectors are derived for transversal forces, uniform torsion, and nonuniform torsion. The proposed finite element algorithm is validated by comparing the analytical solutions, structural engineering books, and related articles. The numerical examples include beams with different cross-section types such as solid, thick-walled, closed-thin-walled, and open-thin-walled sections. Materials defined in the examples are homogeneous, isotropic, and linearly elastic. Through these examples, the study demonstrates the capability of the proposed method to address a wide range of practical engineering scenarios.

Keywords: Vlasov beams, warping function, nonuniform torsion, finite element method, normal and shear stresses, cross-section properties

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Authors: Mounir Belattar

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In this paper the Analysis of voltage waves that propagate along a lossless exponential nonuniform line is presented. For this analysis the parameters of this line are assumed to be varying function of the distance x along the line from the source end. The approach is based on the tow-port networks cascading presentation to derive the ABDC parameters of transmission using Picard-Carson Method which is a powerful method in getting a power series solution for distributed network because it is easy to calculate poles and zeros and solves differential equations such as telegrapher equations by an iterative sequence. So the impedance, admittance voltage and current along the line are expanded as a Taylor series in x/l where l is the total length of the line to obtain at the end, the main transmission line parameters such as voltage response and transmission and reflexion coefficients represented by scattering parameters in frequency domain.

Keywords: ABCD parameters, characteristic impedance exponential nonuniform transmission line, Picard-Carson's method, S parameters, Taylor's series

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Authors: Azeddine El-Hassouny, Chandrashekhar Meshram, Geraldin Nanfack

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In recent years, learning from data with noisy labels (Label Noise) has been a major concern in supervised learning. This problem has become even more worrying in Deep Learning, where the generalization capabilities have been questioned lately. Indeed, deep learning requires a large amount of data that is generally collected by search engines, which frequently return data with unreliable labels. In this paper, we investigate the Label Noise in Deep Learning using variational inference. Our contributions are : (1) exploiting Label Noise concept where the true labels are learnt using reparameterization variational inference, while observed labels are learnt discriminatively. (2) the noise transition matrix is learnt during the training without any particular process, neither heuristic nor preliminary phases. The theoretical results shows how true label distribution can be learned by variational inference in any discriminate neural network, and the effectiveness of our approach is proved in several target datasets, such as MNIST and CIFAR32.

Keywords: label noise, deep learning, discrete latent variable, variational inference, MNIST, CIFAR32

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: Olayiwola Moruf Oyedunsi

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This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed that the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t.

Keywords: modified variational iteration method, Burger’s equation, porous media, partial differential equation

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Authors: Gustavo Funes, Eduardo Peters, Jose Delpiano

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It is widely known that photovoltaic technology has been massively distributed over the last decade despite its low-efficiency ratio. Dust deposition reduces this efficiency even more, lowering the energy production and module lifespan. In this work, we developed an artificial vision algorithm based on CIELAB color space to identify dust over panels in an autonomous way. We performed several experiments photographing three different types of panels, 30W, 340W and 410W. Those panels were soiled artificially with uniform and non-uniform distributed dust. The algorithm proposed uses statistical tools to provide a simulation with a 100% soiled panel and then performs a comparison to get the percentage of dirt in the experimental data set. The simulation uses a seed that is obtained by taking a dust sample from the maximum amount of dust from the dataset. The final result is the dirt percentage and the possible distribution of dust over the panel. Dust deposition is a key factor for plant owners to determine cleaning cycles or identify nonuniform depositions that could lead to module failure and hot spots.

Keywords: dust detection, photovoltaic, artificial vision, soiling

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Authors: T. H. Young, S. J. Huang, Y. S. Chiu

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This paper investigates the parametric stability of an axially moving web subjected to nonuniform in-plane edge excitations on two opposite, simply-supported edges. The web is modeled as a viscoelastic plate whose constitutive relation obeys the Kelvin-Voigt model, and the in-plane edge excitations are expressed as the sum of a static tension and a periodical perturbation. Due to the in-plane edge excitations, the moving plate may bring about parametric instability under certain situations. First, the in-plane stresses of the plate due to the nonuniform edge excitations are determined by solving the in-plane forced vibration problem. Then, the dependence on the spatial coordinates in the equation of transverse motion is eliminated by the generalized Galerkin method, which results in a set of discretized system equations in time. Finally, the method of multiple scales is utilized to solve the set of system equations analytically if the periodical perturbation of the in-plane edge excitations is much smaller as compared with the static tension of the plate, from which the stability boundaries of the moving plate are obtained. Numerical results reveal that only combination resonances of the summed-type appear under the in-plane edge excitations considered in this work.

Keywords: axially moving viscoelastic plate, in-plane periodic excitation, nonuniformly distributed edge tension, dynamic stability

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Authors: Jiangyong Liu, Xiangxiang Xu, Bote Luo, Xiaoxue Luo, Jiang Zhu, Lingzhi Yi

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To address the problems of non-linearity and high randomness of the original power load sequence causing the degradation of power load forecasting accuracy, a short-term load forecasting method is proposed. The method is based on the Least Square Support Vector Machine optimized by an Improved Sparrow Search Algorithm combined with the Variational Mode Decomposition proposed in this paper. The application of the variational mode decomposition technique decomposes the raw power load data into a series of Intrinsic Mode Functions components, which can reduce the complexity and instability of the raw data while overcoming modal confounding; the proposed improved sparrow search algorithm can solve the problem of difficult selection of learning parameters in the least Square Support Vector Machine. Finally, through comparison experiments, the results show that the method can effectively improve prediction accuracy.

Keywords: load forecasting, variational mode decomposition, improved sparrow search algorithm, least square support vector machine

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

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In this paper, we present the human action recognition method using the variational Bayesian HMM with the Dirichlet process mixture (DPM) of the Gaussian-Wishart emission model (GWEM). First, we define the Bayesian HMM based on the Dirichlet process, which allows an infinite number of Gaussian-Wishart components to support continuous emission observations. Second, we have considered an efficient variational Bayesian inference method that can be applied to drive the posterior distribution of hidden variables and model parameters for the proposed model based on training data. And then we have derived the predictive distribution that may be used to classify new action. Third, the paper proposes a process of extracting appropriate spatial-temporal feature vectors that can be used to recognize a wide range of human behaviors from input video image. Finally, we have conducted experiments that can evaluate the performance of the proposed method. The experimental results show that the method presented is more efficient with human action recognition than existing methods.

Keywords: human action recognition, Bayesian HMM, Dirichlet process mixture model, Gaussian-Wishart emission model, Variational Bayesian inference, prior distribution and approximate posterior distribution, KTH dataset

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Authors: A. W. Gbolagade, M. O. Olayiwola, K. O. Kareem

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In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method.

Keywords: lagrange multiplier, non-homogeneous equations, advection equations, mathematics

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Authors: Desmond Adair, Kairat Ismailov, Martin Jaeger

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Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made.

Keywords: Timoshenko beam, variational iteration method, two-parameter elastic foundation model

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Authors: Harendra Singh, Rajesh Pandey

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The paper presents a numerical method based on operational matrix of integration and Ryleigh method for the solution of a class of non-linear fractional variational problems (NLFVPs). Chebyshev first kind polynomials are used for the construction of operational matrix. Using operational matrix and Ryleigh method the NLFVP is converted into a system of non-linear algebraic equations, and solving these equations we obtained approximate solution for NLFVPs. Convergence analysis of the proposed method is provided. Numerical experiment is done to show the applicability of the proposed numerical method. The obtained numerical results are compared with exact solution and solution obtained from Chebyshev third kind. Further the results are shown graphically for different fractional order involved in the problems.

Keywords: non-linear fractional variational problems, Rayleigh-Ritz method, convergence analysis, error analysis

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Authors: Leena-Maria Alyedreessy

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Self-esteem is thought to be determined by ones’ own feeling of being included, liked and accepted by others. This research explores whether this concept may also be applied in the virtual world and assesses whether there is any relationship between Twitter users' self-esteem and the amount of interactions they receive. 20 female Arab participants were given a survey asking them about their Twitter interactions and their feelings of having an imagined audience to fill out and a Rosenberg Self-Esteem Assessment to complete. After completion and statistical analysis, results showed a significant correlation between the feeling of being Twitter elite, the feeling of having a lot of people listening to your tweets and having a lot of interactions with high self-esteem. However, no correlations were detected for low-self-esteem and low interactions.

Keywords: twitter, social media, self-esteem, narcissism, interactions

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Authors: T. H. Young, Y. J. Tsai

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A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work.  The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.

Keywords: stress analysis, free vibration, plate buckling, nonuniform in-plane edge shear

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Authors: César Garza

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In supervised binary classification and regression problems, it is well-known that learnability is equivalent to a uniform convergence of the hypothesis class, and if a problem is learnable, it is learnable by empirical risk minimization. For the general learning setting of unsupervised learning tasks, there are non-trivial learning problems where uniform convergence does not hold. We present here the task of learning centers of mass with an extra feature that “activates” some of the coordinates over the unit ball in a Hilbert space. We show that the learning problem is learnable under a stable RLM rule. We introduce a family of distributions over the domain space with some mild restrictions for which the sample complexity of uniform convergence for these problems must grow logarithmically with the dimension of the Hilbert space. If we take this dimension to infinity, we obtain a learnable problem for which the uniform convergence property fails for a vast family of distributions.

Keywords: statistical learning theory, learnability, uniform convergence, stability, regularized loss minimization

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Authors: Mohamed K. Metwally, Sherif H. El-Gohary, Kyung Min Byun, Seung Moo Han, Soo Yeol Lee, Min Hyoung Cho, Gon Khang, Jinsung Cho, Tae-Seong Kim

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Photoacoustic imaging (PAI) is a non-invasive and non-ionizing imaging modality that combines the absorption contrast of light with ultrasound resolution. Laser is used to deposit optical energy into a target (i.e., optical fluence). Consequently, the target temperature rises, and then thermal expansion occurs that leads to generating a PA signal. In general, most image reconstruction algorithms for PAI assume uniform fluence within an imaging object. However, it is known that optical fluence distribution within the object is non-uniform. This could affect the reconstruction of PA images. In this study, we have investigated the influence of optical fluence distribution on PA back-propagation imaging using finite element method. The uniform fluence was simulated as a triangular waveform within the object of interest. The non-uniform fluence distribution was estimated by solving light propagation within a tissue model via Monte Carlo method. The results show that the PA signal in the case of non-uniform fluence is wider than the uniform case by 23%. The frequency spectrum of the PA signal due to the non-uniform fluence has missed some high frequency components in comparison to the uniform case. Consequently, the reconstructed image with the non-uniform fluence exhibits a strong smoothing effect.

Keywords: finite element method, fluence distribution, Monte Carlo method, photoacoustic imaging

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Authors: Pushpendra Kumar, Sanjeev Kumar, R. Balasubramanian

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Estimation of optical flow from a sequence of images using variational methods is one of the most successful approach. Discontinuity between different motions is one of the challenging problem in flow estimation. In this paper, we design a new anisotropic diffusion operator, which is able to provide smooth flow over a region and efficiently preserve discontinuity in optical flow. This operator is designed on the basis of intensity differences of the pixels and isotropic operator using exponential function. The combination of these are used to control the propagation of flow. Experimental results on the different datasets verify the robustness and accuracy of the algorithm and also validate the effect of anisotropic operator in the discontinuity preserving.

Keywords: optical flow, variational methods, computer vision, anisotropic operator

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Authors: Adetunji A. Adeyanju., Mathew O. Omeike, Johnson O. Adeniran, Biodun S. Badmus

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In this paper, we discuss certain conditions for uniform asymptotic stability and uniform ultimate boundedness of solutions to some systems of Aizermann-type of differential equations by means of second method of Lyapunov. In achieving our goal, some Lyapunov functions are constructed to serve as basic tools. The stability results in this paper, extend some stability results for some Aizermann-type of differential equations found in literature. Also, we prove some results on uniform boundedness and uniform ultimate boundedness of solutions of systems of equations study.

Keywords: Aizermann, boundedness, first order, Lyapunov function, stability

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