The properties (a) and (b) state that assuming the linear model (Eq. (3)), the solution (Eq. (5)) is, in fact from a theoretical point of view, the best possible one. It often occurs that the model (Eq. (3)) contains many variables. Interpretation of the estimation results (Eq...
The proof of the main proposition 2 is based on considering all possible relationships between the assumed integer solution of the equation f(k, p 1) = 0 and the number ( -m) corresponding to this solution k. The proof was carried out using the mathematical ...
Mathematics and Mathematical Physics, 1968, 8(2): 63-87.The error principle in the solution of operational equations by the regularization method. Morozov V A. USSR Comput.Math.Math.Phys . 1968Morozov, V.A.: The error principle in the solution of operational equations by the regularization ...
In the 1980s, the intersection of complex analysis and nonlinear science injected an unprecedented new impetus into the solution of many important classical problems. The complex dynamic system has achieved groundbreaking development, giving birth to the 1994 Fields Award winner Yococoz and the 1998 ...
n. 1. A principle holding that two or more solutions to a linear equation or set of linear equations can be added together so that their sum is also a solution. 2. A principle holding that two or more states of a physical system can be added together to create an additional state. ...
Using a basis property of the sequence (tn:n∈N) (Lemma 1), we prove that if T is a continuous and restrictive Lipschitz mapping of a complete metrically convex space (X,d) into a metric space (Y,ρ), then T is Lipschitz continuous with the constant L, that is ...
This paper classifies the set of supersolutions of a general class of periodic-parabolic problems in the presence of a positive supersolution. From this result we characterize the positivity of the underlying resolvent operator through the positivity of the associated principal eigenvalue and the exist...
The use of the least action principle for the construction of discrete mathematical models in magnetohydrodynamics. Data Envelopment Analysis (DEA) is a non-parametric methodology for estimating technical efficiency of a set of Decision Making Units (DMUs) from a dataset... VM Goloviznin,AA Samarsk...
THEORY OF VIBRATION | Superposition M.G. Prasad, in Encyclopedia of Vibration, 2001 Modal Superposition In dealing with the linear vibrations of a continuous system, the superposition principle is very useful in evaluating the response of the system. The general solution of a wave equation is obta...
Similar plots, with the eigenvectors in the same quadrants, could be obtained for other values of α, hence the time-optimal control with a reactivity constraint for t0 < t < tf. That this process requires no switching on (t0,f) can also be shown by the solution to the adjoint system ...