Poisson Centralizer of the Trace

The Poisson centralizer of the trace element is determined in the coordinate ring of SL_n endowed with the Poisson structure obtained as the semiclassical limit of its quantized coordinate ring. It turns out that this maximal Poisson-commutative subalgebra coincides with the subalgebra of invariants with respect to the adjoint action

Generalized solution for the Herman Protocol Conjecture

We have a cycle of $N$ nodes and there is a token on an odd number of nodes. At each step, each token independently moves to its clockwise neighbor or stays at its position with probability $\frac{1}{2}$. If two tokens arrive to the same node, then we remove both of them. The process ends when only one token remains. The question is that for a fixed $N$, which is the initial configuration that maximizes the expected number of steps $E(T)$. The Herman Protocol Conjecture says that the $3$-token configuration with distances $\lfloor\frac{N}{3}\rfloor$ and $\lceil\frac{N}{3}\rceil$ maximizes $E(T)$. We present a proof of this conjecture not only for $E(T)$ but also for $E\big(f(T)\big)$ for some function $f:\mathbb{N}\rightarrow\mathbb{R}^{+}$ which method applies for different generalizations of the problem

The Minimal Degree Standard Identity on MnE2M_nE^2 and MnE3M_nE^3

We prove an Amitsur--Levitzki-type theorem for Grassmann algebras, stating that the minimal degree of a standard identity that is a polynomial identity of the ring of $n \times n$ matrices over the $m$-generated Grassmann algebra is at least $2\left\lfloor\frac{m}{2}\right\rfloor+4n-4$ for all $n,m\geq 2$ and this bound is sharp for $m=2,3$ and any $n\geq 2$. The arguments are purely combinatorial, based on computing sums of signs corresponding to Eulerian trails in directed graphs.Comment: 22 pages, 7 figures, since version1 the statement of the lower bound got extended and a conjecture has been adde

Cocommutative elements form a maximal commutative subalgebra in quantum matrices

In this paper, we prove that the subalgebras of cocommutative elements in the quantized coordinate rings of Mn, GLn and SLn are the centralizers of the trace x1,1 + ⋯ + xn,n in each algebra, for q ∈ℂ × being not a root of unity. In particular, it is not only a commutative subalgebra as it was known before, but it is a maximal one. © 2018 World Scientific Publishing Company

THE SDSS-III APOGEE SPECTRAL LINE LIST FOR H-BAND SPECTROSCOPY

We present the H-band spectral line lists adopted by the Apache Point Observatory Galactic Evolution Experiment (APOGEE). The APOGEE line lists comprise astrophysical, theoretical, and laboratory sources from the literature, as well as newly evaluated astrophysical oscillator strengths and damping parameters. We discuss the construction of the APOGEE line list, which is one of the critical inputs for the APOGEE Stellar Parameters and Chemical Abundances Pipeline, and present three different versions that have been used at various stages of the project. The methodology for the newly calculated astrophysical line lists is reviewed. The largest of these three line lists contains 134,457 molecular and atomic transitions. In addition to the format adopted to store the data, the line lists are available in MOOG, Synspec, and Turbospectrum formats. The limitations of the line lists along with guidance for its use on different spectral types are discussed. We also present a list of H-band spectral features that are either poorly represented or completely missing in our line list. This list is based on the average of a large number of spectral fit residuals for APOGEE observations spanning a wide range of stellar parameters