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20112026
most citedA Survey of Knowledge Tracing: Models, Variants, and Applications

168 citations

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7 papers · 1 filter

math-ph2014★ 28 cited

Rotational and Self-similar Solutions for the Compressible Euler Equations in R^3

Manwai Yuen

In this paper, we present rotational and self-similar solutions for the compressible Euler equations in R^3 using the separation method. These solutions partly complement Yuen's ir…

math-ph2014★ 18 cited

Periodic Solutions of 2D Isothermal Euler-Poisson Equations with Possible Applications to Spiral and Disk-like Galaxies

Man Kam Kwong, Manwai Yuen

Compressible Euler-Poisson equations are the standard self-gravitating models for stellar dynamics in classical astrophysics. In this article, we construct periodic solutions to th…

math-ph2014★ 2 cited

Blowup for Solutions of the N-dimensional Euler-Poisson Equations in Newtonian Cosmology

Manwai Yuen

Pressureless Euler-Poisson equations with attractive forces are standard models in Newtonian cosmology. In this article, we further develop the spectral dynamics method and apply a…

math-ph2014★ 18 cited

Similarity reductions and new nonlinear exact solutions for the 2D incompressible Euler equations

Engui Fan, Manwai Yuen

For the 2D and 3D Euler equations, their existing exact solutions are often in linear form with respect to variables x,y,z. In this paper, the Clarkson-Kruskal reduction method is…

math-ph2013★ 33 cited

Vortical and Self-similar Flows of 2D Compressible Euler Equations

Manwai Yuen

This paper presents the vortical and self-similar solutions for 2D compressible Euler equations using the separation method. These solutions complement Makino's solutions in radial…

math-ph2011★ 6 cited

Drifting Solutions with Elliptic Symmetry for the Compressible Navier-Stokes Equations with Density-dependent Viscosity

Hongli An, Manwai Yuen

In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successf…

math-ph2011★ 35 cited

Self-Similar Solutions with Elliptic Symmetry for the Compressible Euler and Navier-Stokes Equations in R^{N}

Manwai Yuen

Based on Makino's solutions with radially symmetry, we extend the corresponding ones with elliptic symmetry for the compressible Euler and Navier-Stokes equations in R^{N} (N\geq2)…