Results 321 to 330 of about 2,088,895 (372)

Linear Partial Differential Equations

1957
Although we shall mainly be concerned in this Part with differential equations, the methods we use here for their discussion and solution are intimately connected with the geometry of the rest of the volume. In particular, the results obtained depend to a great extent on the theory of modules and the intersections of a set of algebraic varieties ...
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Linear Differential Equations

2001
Here we consider a so called (scalar) normal system of n ordinary linear differential equations which is a system of the form $$\left\{ {\begin{array}{*{20}{c}} {{{{x'}}_{1}} = {{a}_{{11}}}(t){{x}_{1}} + {{a}_{{12}}}(t){{x}_{2}} + ... + {{a}_{{1n}}}(t){{x}_{n}} + {{f}_{1}}(t),} \\ {{{{x'}}_{2}} = {{a}_{{21}}}(t){{x}_{1}} + {{a}_{{22}}}(t){{x}_{2}} +
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Linear Differential Equations

1967
In this section we consider the vector equation $$ \mathop x\limits^. {\rm{ }} = {\rm{ }}A(t){\rm{ }}. $$ (58.1) We assume that the elements a i k (t) of the matrix A are continuous functions of t defined for t ≥ t0. Equations with a constant A, treated in sec. 4, are special cases of (58.1). On the other hand, (58.1) is a special case of the
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Stability in p-th moment for uncertain differential equation

Journal of Intelligent & Fuzzy Systems, 2014
An canonical process is stationary independent increment uncertain process whose increments are normal uncertain variables. Uncertain differential equation is a type of differential equation driven by the canonical process. This paper will give a concept
Y. Sheng, Chongguo Wang
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Linear Differential Equations

1998
We denote ri x n matrices by uppercase italic letters, $$ A = \left( {\begin{array}{*{20}{c}} {{a_{11}} \ldots {a_{1n}}} \\ { \vdots \ddots \vdots } \\ {{a_{n1}} \cdots {a_{nn}}} \end{array}} \right) = ({a_{ij}}), $$ where aij E R or C. With the usual definitions of addition and scalar multiplication of matrices, $$ A + B = ({a_{ij}} + {b_ ...
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Second Order Linear Differential Equations

1975
A second-order differential equation is an equation of the form $$\frac{{{d^2}y}}{{d{t^2}}} = f\left( {t,y,\frac{{dy}}{{dt}}} \right)$$ (1) .
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Linear Partial Differential Equations

1997
Partial differential equations arise frequently in the formulation of fundamental laws of nature and in the mathematical analysis of a wide variety of problems in applied mathematics, mathematical physics, and engineering science. This subject plays a central role in modern mathematical sciences, especially in physics, geometry, and analysis.
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Search for Steady States of Piecewise-Linear Differential Equation Models of Genetic Regulatory Networks

IEEE/ACM Transactions on Computational Biology & Bioinformatics, 2008
H. Jong, M. Page
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On linear differential-algebraic equations and linearizations

2005
On the background of a careful analysis of linear DAEs, linearizations of nonlinear index-2 systems are considered. Finding appropriate function spaces and their topologies allows to apply the standard Implicit Function Theorem again. Both, solvability statements as well as the local convergence of the Newton-Kantorovich method (quasilinearization ...
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Third-order linear differential equation with three additional conditions and formula for Green’s function

, 2010
S. Roman, A. Štikonas
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