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Solution of a Weakly Delayed Difference System
Šafařík, Jan
The paper solves a weakly delayed difference systém x(k+1) = Ax(k)+Bx(k-1) where k = 0;1; : : : , A = (ai j)3 i; j=1, B = (bi j)3i ; j=1 are constant matrices. An explicit solution is given with a discussion on the number of independent initial data.
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Weakly Delayed Systems In ℝ3
Šafařík, Jan
The paper is concerned with a linear discrete system with delay x(k+1) = Ax(k)+Bx(k-m); k = 0,1,…, in R3. It is assumed that the system is weakly delayed. For one of the possible Jordan forms solution of an arbitrary initial problem is given.
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Solution of a Weakly Delayed Difference System
Šafařík, Jan
The paper solves a weakly delayed difference systém x(k+1) = Ax(k)+Bx(k-1) where k = 0;1; : : : , A = (ai j)3 i; j=1, B = (bi j)3i ; j=1 are constant matrices. An explicit solution is given with a discussion on the number of independent initial data.
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Periodic solutions of damped oscillations
HOLUB, Miroslav
The main topic of the Thesis is qualitative analysis of linear differential equations of second order. The Thesis is divided into five parts. At the first part there are explained basic type of oscillators (mathematical pendulum and spring). The second part is devoted to definitions and theorems, which are necessary in the study of differential equations. The third part shows the model of linear differential equation of second order. The solution of this equation depending on various parameters is indicated in the fourth part. Some open questions are formulated in the last part.
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