SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS MATHEMATICA

Abstract. This paper studies both nonautonomous stochastic differential
equations and stochastic differential delay equations with Markovian
switching. A new result on almost sure stability of stochastic
differential equations is given. Moreover, we provide new conditions for
tightness and almost su[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]

Abstract. For given ktuples of commuting matrices (A1, ..., Ak) and (B1, ..., Bk)
of dimensions m × m and n × n, respectively, we prove that the system of Sylvester
equations AiX − XBi = Ci (i = 1, ..., k) has a simultaneous solution X such that

I X
O O 
double commutes with 
Ai Ci
O Bi

(for e[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]

The goal of these notes is to explain recent results in the theory of complex varieties,
mainly projective algebraic ones, through a few geometric questions pertaining to hyperbolicity
in the sense of Kobayashi. A complex space X is said to be hyperbolic if analytic disks
f : D → X through a given p[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]

equations, it is not true that any solution willdo; only one particular solution also satisfiessome given initial conditions.D. Thus, in addition to the differential equation,specific numbers, a and e, might be given,such that the differential problemy' = J(x),with y = e when x[r]

COMPUTATIONALBUSINESS ANALYTICSK14110_FM.indd 111/19/13 6:40 PMChapman & Hall/CRCData Mining and Knowledge Discovery SeriesSERIES EDITORVipin KumarUniversity of MinnesotaDepartment of Computer Science and EngineeringMinneapolis, Minnesota, U.S.A.AIMS AND SCOPEThis series aims t[r]

Mô tả khái quát hoặc trừu tượng hóa của một thực thể
(simplified description or abstraction of a reality).
 Modeling: Quá trình tạo ra một mô hình.
 Mathematical modeling: Description of a system using mathematical
concepts and language
 Linear vs. nonlinear; deterministic vs. probabilistic; stat[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]

The remarkable feature of sliding mode control (SMC) is the stability robustness against disturbances and variations of the system. However to design SMC, the exact model of the plant has to be known. Moreover the large gain of an SMC may intensify the chattering on the sliding surface. To cope with[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]

... 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]

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.

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 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.

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]

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]

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]

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]