EXAMPLES OF LINEAR AND NONLINEAR DIFFERENTIAL EQUATIONS

The notions of equivalence and strict equivalence for order one differential
equations of the form f(y
0
, y,z) = 0 are introduced. The more explicit
notion of strict equivalence is applied to examples and questions concerning
autonomous equations and equations having the Painleve property. The ´
or[r]

For the first time, the finitetime stabilization with guaranteed cost control for linear
autonomous timevarying delay systems with bounded controls is studied in this paper.
Based on the Lyapunov functional method and a generalized Jensen integral inequality,
novel sufficient conditions for designin[r]

the advective-diffusive transport equation”, Numerical Methods for Partial DifferentialEquations, Vol. 5, pp. 203-26.Chen, C.J. and Chen, H.C. (1984), “Finite-analytic numerical method for unsteady two-dimensionalNavier-Stokes equations”, Journal of Computational Physics, Vol. 5[r]

4. Disk Method: The volume of a solid ofrevolution created by the curve .f(x) as itrevolves around an axis in the interval [a, b]is V= 7t f:[J(xW dx.J) [NOTICE: [f(x)P is the radius squared.];: = J(x)g(y) orJ(x)dx= g(ylv·VI. Chain Rule Equation: DJ(u) = D'/(u)DxU.VII. If F'(x) = J(x), then F([r]

Squeezing properties of the Hillery-type N-powered amplitude are investigated in the linear and nonlinear fan-state. For a given k, squeezing may appear to the even power N = 2k and the number of directions along which the Nth-powered amplitude is squeezed is exactly equal to N, in both linear (the[r]

... 3021 23 Chapter Graphene Oxide Induced Aggregation of Thiophene-Acrylonitrile-Carbazole Oligomer and Their Nonlinear Optical Limiting Properties 3.1 Introduction Nonlinear Optical limiting (NLO)... rational modification of both the electronic structure and conductivity of graphene sheets accompa[r]

This work is concerned with the Fredholm property of the second order differetial opertor associated
to a class of boundary conditions. Several sufficient conditions will be proved along with
constructing the generalized inverse for such operator. The result is a basic tool to analysis the
boundary[r]

Abstract—This paper discusses analysis and synthesis techniques
for robust pole placement in linear matrix inequality
(LMI) regions, a class of convex regions of the complex plane that
embraces most practically useful stability regions. The focus is on
linear systems with static uncertainty on the s[r]

as subscripthummation notation.Now imagine we want to write the simple vector relationshipThis equation is written in what we call vector notation. Notice how it does notdepend on a choice of coordinate system. In a particular coordinate system, we canwrite the relationship between these vect[r]

t. The stability analysis for linear implicit mth order difference equations is discussed.
We allow the leading coefficient coefficient to be singular, i.e., we include the situation that the system
does not generate an explicit recursion. A spectral condition for the characterization of asymptotic[r]

This paper deals with the problem of global exponential stabilization for a
class of nonautonomous cellular neural networks with timevarying delays. The system
under consideration is subject to timevarying coefficients and timevaying delays. Two
cases of timevarying delays are considered: (i) the de[r]

We consider a class of boundary value problem in a separable Banach space E, involving a nonlinear
differential inclusion of fractional order with integral bounday conditions, of the form



D
αu(t) ∈ F(t, u(t), D
α−1u (t)), a.e., t ∈ 0, 1,
I
β u(t)


t=0 = 0, u(1) = R
1
0
u (t) d t,
(1)
where[r]

This paper deals with the finitetime stability and H∞ control of linear discretetime
delay systems. The system under consideration is subject to interval timevarying
delay and normbounded disturbances. Linear matrix inequality approach is used to
solve the finitetime stability problem. First, new su[r]

ABSTRACT. We consider simultaneous solutions of operator Sylvester equations AiX −
XBi = Ci
, (1 ≤ i ≤ k), where (A1, ..., Ak) and (B1, ..., Bk) are commuting ktuples
of bounded linear operators on Banach spaces E and F, respectively, and (C1, ..., Ck)
is a (compatible) ktuple of bounded linear oper[r]

We consider a class of stochastic functional differential equations with distributed delays
whose coefficients are superlinear growth and H¨older continuous with respect to the delay components.
We introduce an EulerMaruyama approximation scheme for these equations and study
their strong rate of con[r]

Lecture Physical modeling in MATLAB has contents: Variables and values, scripts, loops, vectors, functions, zerofinding, functions of vectors, ordinary differential equations, systems of ODEs, secondorder systems, optimization and interpolation,...and other contents.

assessment level; those who have successfullycompleted MATH 107 but need more review; orstudents who unsuccessfully attempted MATH 120 andneed review of intermediate algebra skills. Features acomputer program to refresh those concepts identifiedas needed for each student, plus weekly contact[r]

We study the strong rate of convergence of the tamed EulerMaruyama
approximation for onedimensional stochastic differential equations
with superlinearly growing drift and H¨older continuous diffusion coef
ficients.

4Thang Long University Libraty(20/5, 45/5) = (4, 9) = 1.nh lỦ 1.4. N u a, b, c sao cho a | bc và a, b nguyên t cùng nhau thì a | c.nh lỦ 1.5. Cho a, b, c  . Khi đó (a + cb, b) = (a, b).Ví d 1.7. Xét ba s : a = 110, b = 44, c = 22. Theonh lý 1.4, ta s có(110 + 22×44, 44) = (110, 44) hay (1078, 44)[r]