25,965 research outputs found
On continuity of Guo Wuwen function
We show that the functions g and gs introduced by Guo Wuwen in [4] are
continuous and semialgebraic. We use this fact to prove that the set Nn of
ordered n-tuples of real numbers, realizable by nonnegative matrices, is a
closed set
Comparison Between Simulated and Observational Results of Galaxy Formation for Large Scale Structures
The Millennium simulation is the largest numerical simulation of how minor fluctuations in the density of the universe’s dark matter distribution are amplified by gravity to develop into the large scale structures(LSS) and galaxy clusters seen today(Springel et al. 2005). Although the simulations have been compared with the astronomical observations of the local universe, the simulations have not been widely compared with high redshift, early universe observations. In our study we compare the simulation data(Wang et al. 2008; Guo et al. 2008(in preparation)) for the first time with observations from the COSMOS survey(Scoville et al. 2006). Three quantities are proposed to characterize the structures and the structures distribution, namely the percent area occupied by LSS at each redshift, the average area of LSS and the shapes as characterized by the square root of the area divided by the circumference. We calculate these quantities for both the observations and the simulations, and quantify discrepancies between the existing simulations and observations. In particular, the simulations exhibit earlier development of dense structures than is seen in the observational data
On 2-adic orders of some binomial sums
We prove that for any nonnegative integers and the binomial sum is divisible by
, where denotes the number of
1's in the binary expansion of . This confirms a recent conjecture of Guo
and Zeng.Comment: 6 page
The Eulerian distribution on the involutions of the hyperoctahedral group is unimodal
The Eulerian distribution on the involutions of the symmetric group is
unimodal, as shown by Guo and Zeng. In this paper we prove that the Eulerian
distribution on the involutions of the hyperoctahedral group, when viewed as a
colored permutation group, is unimodal in a similar way and we compute its
generating function, using signed quasisymmetric functions.Comment: 11 pages, zero figure
On spectrum of irrationality exponents of Mahler numbers
We consider Mahler functions which solve the functional equation where and
is integer. We prove that for any integer with either
is rational or its irrationality exponent is rational. We also compute
the exact value of the irrationality exponent for as soon as the
continued fraction for the corresponding Mahler function is known. This
improves the result of Bugeaud, Han, Wei and Yao where only an upper bound for
the irrationality exponent was provided
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