We prove a uniform bound on the topological Turán number of an arbitrary two-dimensional simplicial complex S: any n vertices with at least CSn3−1/5 facets contains homeomorph S, where CS > 0 is constant depending S alone. This result, analogue classical one-dimensonal result Mader, sheds some light old problem Linial from 2006.

Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $exp(G)$ and let $m=lfloorlog_pk floor$. We show that $exp(M^{(c)}(G))$ divides $exp(G)p^{m(k-1)}$, for all $cgeq1$, where $M^{(c)}(G)$ denotes the c-nilpotent multiplier of $G$. This implies that $exp( M(G))$ divides $exp(G)$, for all finite $p$-groups of class at most $p-1$. Moreover, we show that our result is an improvement...

Full simulations of homogeneous isotropic turbulence containing a homogeneous passive scalar were made at low Reynolds numbers and various Prandtl numbers. The results show that the spectral behavior of the two fields are quite similar; both fields decay as power-law functions of time. However. the decay exponent is quite dependent on both the Reynolds and Prandtl numbers. The decay exponent of...

Many experimental studies, over the past two decades, have constantly reported a critical behavior for the transition from the smectic- A phase of liquid crystals to the hexatic- B phase with non- XY critical exponents. However, according to symmetry arguments this transition must belong to the XY universality class. Using an optimized Monte Carlo simulation technique based on the multihistogra...