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A recent question in generalized Ramsey theory is that for fixed positive integers $s\leq t$, at least how many vertices can be covered by the vertices of no more than $s$ monochromatic members of the...
Let A be the adjacency matrix of a graph $X$ and suppose U(t)=exp(itA). We view A as acting on $\cx^{V(X)}$ and take the standard basis of this space to be the vectors $e_u$ for $u$ in $V(X)$. Physici...
Blowup for the C^1 Solutions of the Euler-Poisson Equations of Gaseous Stars in R^N
C^1 Solutions Euler-Poisson Equations Gaseous Stars
2011/2/25
The Newtonian Euler-Poisson equations with attractive forces are the classical models for
the evolution of gaseous stars and galaxies in astrophysics. In this paper, we use the integration method to ...
Let Σ=Σ_{i=1}^{t}(n_i-1) and Λ=Σ_{j=1}^s(m_j-1). This paper considers the generalized Ramsey number R(K_{1,n_1},…, K_{1,n_t},m_1K_2,…, m_sK_2) for any Σ and Λ. And the authors get their exact values i...