SYSTEM OF LINEAR FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

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.

Mathematics 381MathematicsEach year, the list of careers demanding familiaritywith basic mathematical skills grows. Environmentalsciences, architecture, business management, nursing,dentistry, computer programming, electronics, forestrymanagement, psychology and photography representonly a sm[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.

We investigate the rate of convergence of linear sampling numbers of the embedding
Hα,β(T
d
) ,→ Hγ
(T
d
). Here α governs the mixed smoothness and β the isotropic smoothness
in the space Hα,β(T
d
) of hybrid smoothness, whereas Hγ
(T
d
) denotes the isotropic
Sobolev space. If γ > β we obtain sharp[r]

This book is the result of a sequence of two courses given in the School of Appliedand Engineering Physics at Cornell University. The intent of these courses has beento cover a number of intermediate and advanced topics in applied mathematics thatare needed by scie[r]

Routh-Hurwitz (1)•! The system is unstable if–! any of the coefficients ai is zero or negativewhile at least one is positive–! There is at least one sign change in thefirst column of the matrix H•! The matrix H is given byIntroduction to AeroelasticityRouth-Hurwitz (2)•! The con[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]

A simulation is the imitation of the operation of a realworld process or system over time. Whether done by
hand or on a computer, simulation involves the generation of an artificial history of a system and the observation
of that artificial history to draw inferences concerning the operating charact[r]

The main objective of the present note is to study positive solutions of the
following interesting system of integral equations in Rn



u(x) = Z
Rn
|x − y|
p
v(y)
−q
dy,
v(x) = Z
Rn
|x − y|
pu(y)
−q
dy,
(0.1)
with p, q > 0 and n > 1. Under the nonnegative Lebesgue measurability condition for[r]

... Autonomous Agents For Intrusion Detection. 2 AAFID was the first architecture of using autonomous agents for intrusion detection The system is based on independent entities called autonomous agents. .. order to limit the possibilities of interaction between the agents themselves and a potential[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]

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]

A feedback control system usually implements active and semiactive control of seismically excited structures.
The objective of the control system is described by a performance index, including weighting matrix norms. The
choice of weighting matrices is usually based on engineering experience. A new[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 find upper bounds for the rate of convergence when the EulerMaruyama approximation
is used in order to compute the expectation of nonsmooth functionals of some stochastic
differential equations whose diffusion coefficient is constant, whereas the drift coefficient may
be very irregular. As a bypr[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]

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]

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]

The infinite system of differential equations for the nonequilibrium Green functions of electrons in a single-level quantum dot connected with two conducting leads is truncated by applying the mean-field approximation to the mean values of the products of four operators. As the result the system of[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]