Tìm thấy 20+ kết quả cho từ khóa "Differential equations"
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On the asymptotic behavior of delay differential equations and its relationship with C 0 - semigoup. In this paper, we study the asymptotic behavior of linear differential equations under nonlinear perturbation. Let’s consider the delay differential equations:. We will give some sufficient conditions for uniformly stable and asymptotic equivalence of above equations..
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Ordinary differential and differential-algebraic equations. Difference equations. Partial differential equations. Stochastic differential equations. On data-dependence of exponential stability and stability radii for linear time-varying differential-algebraic systems Vu Hoang Linh (Vietnam National University, Hanoi):. Stability radii for linear time-varying differential-algebraic equations with respect to dynamic perturbations.
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Ugail, “Shape morphing of complex geometries using partial differential equations”, Journal of Multimedia 2 (6) pages . You, “Fast surfaces modelling using a 6th order PDE”, Computer Graphics Forum 23 (3) pages . Wilson, “Interactive design using higher order PDEs”, The Visual Computer 20 (10) pages . Qin, “Direct manipulation and interactive sculpting of PDE surfaces”, Computer Graphics Forum 9 (3) pages . [65] Differential Equations. ACM Transactions on Graphics
000000105368-TT.pdf.pdf
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In addition, it introduces Differential Transformation Method (DTM) and their characteristics with my demonstrations or provements. Chapter 2: In this chapter, it formulated differential equations of bending vibrations for three kinds of beams which are mentioned in the first chapter. Chapter 3: Applying the differential transformation method to calculate free vibration frequencies of Euler – Bernoulli beams.
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Nguyen Minh Tuan, Nguyen Thi Thu Huyen, The solvability and explicit solutions of two integral equations via generalized convolutions, J. Appl., vol. Nguyen Minh Tuan and Nguyen Thi Thanh Lan, On solutions of a system of hereditary and self-referred partial-differential equations, Numerical Algorithms, vol. Bui Thi Giang and Nguyen Minh Tuan, Generalized convolutions and the integral equations of the convolution type, Complex Var. Elliptic Equ., vol.
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Nguyen Minh Tuan, Nguyen Thi Thu Huyen, The solvability and explicit solutions of two integral equations via generalized convolutions, J. Appl., vol. Nguyen Minh Tuan and Nguyen Thi Thanh Lan, On solutions of a system of hereditary and self-referred partial-differential equations, Numerical Algorithms, vol. Bui Thi Giang and Nguyen Minh Tuan, Generalized convolutions and the integral equations of the convolution type, Complex Var. Elliptic Equ., vol.
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For example, the Sturm–Liouville problem arises in the study of the harmonics of waves in a violin string or a drum, and is a central problem in ordinary differential equations. [29] The problem is a differential equation of the form. The problem only has solutions for certain values of λ, called eigenvalues of the system,. and this is a consequence of the spectral theorem for compact operators applied to the integral operator defined by the Green's function for the system.
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000000296205.pdf
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Sau khi rời rạc hóa hệ phương trình PDEs trong không gian, ta sẽ thu được một hệ phương trình vi phân thường (ODEs: Ordinary Differential Equations) có dạng như sau. Trong đó : ω là các biến của hệ phương trình PDEs, F là hàm thu được từ bước rời rạc hóa theo không gian, t là biến thời gian. Có nhiều phương pháp để giải hệ phương trình vi phân thường ODEs, trong luận văn này chúng tôi sẽ sử dụng phương pháp Euler thuận (Forward Euler).
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Valls Stable manifolds for nonautonomous equations with- out exponential dichotomy", J. Valls Smooth center manifolds for nonuniformly partially hyperbolic trajectories", J. Jones Invariant manifolds for semilinear partial differential equations", Dyn. Rezounenko Inertial manifolds for retarded semilinear prabolic equations", Nonlinear Anal., 34, pp. Temam Inertial manifolds for nonlinear evolution- ary equations", J.
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This is followed by an outline of the correspondence principle. 4.7 Determination of the State of a System. 5.2 Nonuniqueness of the Commutation Relations. 8.4 Determination of the Eigenvalues by Factorization Method. 9.2 Determination of the Angular Momentum Eigenvalues. 10.6 Integration of the Operator Differential Equations. 10.8 Another Numerical Method for the Integration of the Equations of Motion. 12.2 Approximate Determination of the Eigenvalues for Nonpolynomial Potentials. 14.6 Analytical
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This is followed by an outline of the correspondence principle. 4.7 Determination of the State of a System. 5.2 Nonuniqueness of the Commutation Relations. 8.4 Determination of the Eigenvalues by Factorization Method. 9.2 Determination of the Angular Momentum Eigenvalues. 10.6 Integration of the Operator Differential Equations. 10.8 Another Numerical Method for the Integration of the Equations of Motion. 12.2 Approximate Determination of the Eigenvalues for Nonpolynomial Potentials. 14.6 Analytical
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Qian and J.Weiss, `Wavelet-Galerkin Solutions for One Dimensional Partial Di_erential Equations', Int. Qian and J.Weiss, `Wavelets and the Numerical Solution of Partial Differential Equations', J
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On the other hand, there are many unsolved models of differential equations even in the classical physics. Newton succeed in solving two body problems in gravitational fields, however, he were faced the difficulty in solving many body problems in the same framework. Differential equations know the motion of the Sun and the Earth interacting by gravitation, they cannot provide the clear solution with fundamental functions to the problem of the motion of the Sun, the Earth and the Moon exactly.
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We’ll just invoke here the result from the theory of differential equations that says that in this special case, the other solution is of the form te −γt. Our solution is therefore of the form. This is true because in the underdamped case (γ <. ω), the envelope of the oscillatory motion goes like e −γt , which goes to zero slower than e −ωt , because γ <. And in the overdamped case (γ >. How can we solve something of the form. (3.20), let’s guess a solution of the form x(t.
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On stability of Lyapunov exponents. stability of Lyapunov exponents of linear differential equations in R n . Sufficient conditions for the upper - stability of maximal exponent of linear systems under linear perturbations are given. stability, maximal exponent.. It is well known that the above assumption guarantees the boundesness of the Lyapunov exponents of system (1). Denote by. λ n ) the Lyapunov exponents of system (1)..
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However, this model is not used to solve the analysis and synthesise problem of systems and we have to transform this model into the form of sets of state equations (sets of Cauchy differential equations) or transfer function form. There is a close, easy to exchange relation between set of state equations and transfer function. The transfer function's model of controlled object is often in the following form:. 0 - the dead time delay.
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(i) Derive the differential equations of motion (for small oscillations) of the bobs.. where E is the total energy of the system. where k is the spring constant of the spring.. Find the amplitude of the resultant motion.. Here ν is the frequency of the damped oscillatory motion.. The equation of motion of the particle is. is the undamped frequency of the simple pendulum. Determine the equilibrium extension of the spring. Total energy of the system is given by E = 1.
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Because of this, we will also perform a simple qualitative analysis of (3.8) so that we may later on, compare, the qualitative behaviours of the radial equations in black-hole and flat spacetimes.. It turns out that the second-order differential equations that we seek are of the form,. 0, some rearrangement of the equation is needed in order to make an identification with. Notice that we have included the r sin 1/2 θ factor on account of the factorisation ansatz.
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, Fuzzy Sets and Systems 156, pp. (1957), Random fixed point theorems, Trans. (1977), A random fixed point theorem for a multivalued con- traction mapping, Pacific J. (1979), Random fixed-point theorems with an application to random differential equations in Banach spacess, J. (2008), Coincidence and fixed point results for non-commuting maps, Tamkang J. (1988), Random approximations and random fixed point theorems for non-self-maps, Proc. (1977), Fixed point theorems for mappings with a con- tractive