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This paper concerns a fractional function of the form x^Ta/sqrt{x^TBx}, where B is positive definite. We consider the game of choosing x from a convex set, to maximize the function, and choosing (a,B)...
Early in 1904, Hadamard [1] showed the scale implicit function theorem of finite dimensions. Then it was generalized to infinite dimensions. In this paper a new proof of this theorem is given and the ...
Let G be a 2-connected simple graph of order n. In this paper we prove the following generalization of Ore's theorem: If G is a 2-connected graph such that |N(u) \cup N(v)|+|N(u) \cup N(w)| ≥ n for ev...
A method for mechanical geometry theorem proving is presented. By using this method, if the ascending chains derived via Wu-Ritt's well ordering algorithm satisfy a condition, all the irreducible char...
l. By c(G) we denote the length of the longest cycle in G; in particular, G is called a Hamiltonian graph if c(G)=n. H.A. Jung proved that every 1-tough graph with order n≥11 and σ2≥n-4 is Hamiltonian...

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