Numerical methods of calculating water flow in soils usually rely on solving Richards' equation, which is obtained by combining the equation of continuity with Darcy's law for water fluxes. In this study, the one-dimensional equation of continuity was solved using tables of precomputed steady-...
Obviously, [Math Processing Error]u(x) solves (1.1) iff [Math Processing Error]ψ(x,t) solves the above equation with [Math Processing Error]V(x)=W(x)−E. Additionally, it is easy to see that problem (1.1) has nonlocal characteristics in the nonlinearity due to the effect of the ...
changes in pregnancy can lead to increased mitral and aortic valve gradients on TTE, leading to overestimation of the severity of the valve lesion,22 and so stenosis should be quantified by valve area assessed using planimetry, or by pressure half-time for MS or by the continuity equation ...
regularity of the optimal controldegeneracy phenomenonLIPSCHITZ CONTINUITYIn this paper a class of optimal control problems with state constraints involving a dynamic equation and an integral cost which are respectively affine and quadratic in the control variable is considered. Conditions may be imposed ...
The dynamic performance analysis was decomposed into three modules: mooring system, the floating structure, and the wind turbine, with the characteristics of each discipline assembled into one equation of motion based on a linear spring–mass–damper system in the frequency-domain (as presented in ...
A different (and stronger) way of saying that r1 is more disordered than r2 is given by the following equation: Xk lrj 1 j¼1 Xk lrj 2 ; j¼1 8k ! 1; ð1Þ where the vectors kr1 and kr2 consist of the eigenvalues of the respective states arranged in decreasing order. If...
Comparing with the continuity equation ∂tρ + ∂xj = 0, we recognize the terms within the large brackets in the second line as the probability flux. If c = 0 (i.e. the Hamiltonian is only quadratic in ), the flux is the real part of so that for a Hamiltonian quadratic in , ...
Steps in the equation for each DV B Improvement Model Nagel-kerke χ2 df P χ2 df P R2 Maternal iteractive styles DV popular (1) Aggression −.308 6.043 1 .014 6.043 1 .014 .218 (2) Control Patterns −1.101 5.133 1 .023 11.176 2 .004 .375 DV rejected (1) Disconfirming 1.74...
Prussian blue analogues (PBAs) are archetypes of microporous coordination polymers/metal–organic frameworks whose versatile composition allows for diverse functionalities. However, developments in PBAs have centred solely on their crystalline state, and
Indeed, it can 9 be shown that, for a given sampling period T > 0, the matrix differential equation (7) may admit a solution even when A is not Hurwitz stable [30]. We are now in position to solve the TBVP introduced in Theorem 1. First of all, remember that, if a solution to...