f(T)f(T) Theories and Varying Fine Structure Constant

In analogy to $f(R)$ theory, recently a new modified gravity theory, namely the so-called $f(T)$ theory, has been proposed to drive the current accelerated expansion without invoking dark energy. In the present work, by extending Bisabr's idea, we try to constrain $f(T)$ theories with the varying fine structure "constant", $\alpha\equiv e^2/\hbar c$. We find that the constraints on $f(T)$ theories from the observational $\Delta\alpha/\alpha$ data are very severe. In fact, they make $f(T)$ theories almost indistinguishable from $\Lambda$CDM model.Comment: 12 pages, 4 figures, 1 table, revtex4; v2: discussions added, Phys. Lett. B in press; v3: published versio

On Frankl and Furedi's conjecture for 3-uniform hypergraphs

The Lagrangian of a hypergraph has been a useful tool in hypergraph extremal problems. In most applications, we need an upper bound for the Lagrangian of a hypergraph. Frankl and Furedi in \cite{FF} conjectured that the $r$-graph with $m$ edges formed by taking the first $m$ sets in the colex ordering of ${\mathbb N}^{(r)}$ has the largest Lagrangian of all $r$-graphs with $m$ edges. In this paper, we give some partial results for this conjecture.Comment: 19 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1211.650