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We obtain sharp decay estimates in time in the context of Sobolev spaces for smooth solutions to the one-dimensional Jin Xin model under the diffusion scaling, which are uniform with respect to the singular parameter of the scaling. This provides the convergence to the limit nonlinear parabolic… |
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In this paper, we review recent progress in relativistic lattice kinetic theory and its applications to relativistic hydrodynamics. Two methods for constructing the discretised distribution function, moment matching and projection onto orthogonal polynomials, are described. Extensions to ultra-high… |
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Barenblatt e. a. introduced a fluid model for groundwater flow in fissurised porous media. The system consists of two diffusion equations for the groundwater levels in, respectively, the porous bulk and the system of cracks. The equations are coupled by a fluid exchange term. Numerical evidence… |
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Systems medicine (SM) has emerged as a powerful tool for studying the human body at the systems level with the aim of improving our understanding, prevention and treatment of complex diseases. Being able to automatically extract relevant features needed for a given task from high-dimensional,… |
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Tumor resistance to chemotherapy represents an important challenge in modern oncology. Although platinum (Pt)-based drugs have demonstrated excellent therapeutic potential, their effectiveness in a wide range of tumors is limited by the development of resistance mechanisms. One of these mechanisms… |
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We consider a class of integral equations of Volterra type with constant coefficients containing a
logarithmic difference kernel. This class coincides for a=0 with the Symm's euqtion. We can transform the general integral
equation into an equivalent singular equation of Cauchy type which allows us… |
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The parametrization of small-scale turbulent fluctuations in convective systems and in the presence of strong stratification is a key issue for many applied problems in oceanography, atmospheric science, and planetology. In the presence of stratification, one needs to cope with bulk turbulent… |
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Global mean sea level rise associated with global warming has a major impact on coastal areas and represents one of the significant natural hazards. The Asia-Pacific region, which has the highest concentration of human population in the world, represents one of the larger areas on Earth being… |
