Lindgren, F., Rue, H., Lindström, J.: An explicit link between Gaussian fields and Gaussian Markov random fields: The stochastic partial differential equation approach. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 73(4), 423–498 (2011) Article MathSciNet MATH Google Scholar Luengo,...
The corresponding-states principle of the equation of state is here introduced as, (2.12)pVRT=F(VVc,TTc)=F(Vr,Tr) The modern theories of the equation of state investigate the virial coefficients of the series expansion in the universal form of the corresponding-states principle, (2.13)pVRT=...
[10] first proved the well-posedness of the associated systems of master equation of MFGs in short time under weaker assumptions. Ambrose et al. [3] studied the well-posedness of short time classical solutions for a class of master equations involving non-separable local Hamiltonians in the ...
Step-by-Step Text Solution:1. Definition of Continuity of State: The term 'continuity of state' refers to the ability to transition between different states of matter, specifically between liquids and gases. Th
hence has a soliton-like behavior. Obviously,u(x)solves (1.1) iffψ(x,t)solves the above equation withV(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 convolution part, which is different from...
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 ...
In this study, the one-dimensional equation of continuity was solved using tables of precomputed steady-state fluxes read from disk. This results in simpler and faster code for applications such as field water balance models, which may use relatively large depth spacings and many repeated ...
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The key insight is that we can circumvent the master equation and reduce the mean field equilibrium to a system of forward-backward systems of (random) ordinary differential equations by conditioning on common noise events. In the absence of common noise, our setup reduces to that of Gomes, ...
We study evolution of primordial black holes (PBH) in thef(Q) modified gravity for matter accretion from the cosmic fluid surrounding the PBH. For matter described by non-linear equation of statep=f(ρ), the accretion of matter in PBH is probed. Two different branches of non-linear EoS ...