Sampling expansions associated with quaternion difference equations

Starting with a quaternion difference equation with boundary conditions, a parameterized sequence which is complete in finite dimensional quaternion Hilbert space is derived. By employing the parameterized sequence as the kernel of discrete transform, we form a quaternion function space whose elements have sampling expansions. Moreover, through formulating boundary-value problems, we make a connection between a class of tridiagonal quaternion matrices and polynomials with quaternion coefficients. We show that for a tridiagonal symmetric quaternion matrix, one can always associate a quaternion characteristic polynomial whose roots are eigenvalues of the matrix. Several examples are given to illustrate the results

MS imaging of small metabolites in fruits

MS Imaging of large molecules, e.g. proteins and lipids, have been reported with MALDI. On the other hand, few works have been done on mapping the small molecules by MALDI imaging. This is mainly due to the high chemical noise background interference in the low mass region caused by chemical matrices. DESI Imaging, however, could be complementary to MALDI in that sample can be analyzed directly without matrices. A large group of small metabolites are of considerable physiological and morphological importance in plants, e.g. flavonols involve in plant defense against environmental stresses and organic acids are one of important factors for fruit quality, but knowledge of their precise functions is limited due to insufficient characterization of their spatial responses. In this communication we will discuss methodological details about MS imaging of small metabolites in apple and grape in terms of sample preparation, imaging methods, and other experimental concerns by using MALDI [1] and DESI source coupled with a high resolution/accurate LTQ-Orbitrap mass spectrometer. Finally, we will describe the spatial distributions of flavonols and organic acids in apple and grape, respectively

LAMOST observations in the Kepler field. Analysis of the stellar parameters measured with the LASP based on the low-resolution spectra

All of the 14 subfields of the Kepler field have been observed at least once with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST, Xinglong Observatory, China) during the 2012-2014 observation seasons. There are 88,628 reduced spectra with SNR$_g$ (signal-to-noise ratio in g band) $\geq$ 6 after the first round (2012-2014) of observations for the LAMOST-Kepler project (LK-project). By adopting the upgraded version of the LAMOST Stellar Parameter pipeline (LASP), we have determined the atmospheric parameters ($T_{\rm eff}$ , $\log g$, and $\rm [Fe/H]$) and heliocentric radial velocity $v_{\rm rad}$ for 51,406 stars with 61,226 spectra. Compared with atmospheric parameters derived from both high-resolution spectroscopy and asteroseismology method for common stars in Huber et al. (2014), an external calibration of LASP atmospheric parameters was made, leading to the determination of external errors for the giants and dwarfs, respectively. Multiple spectroscopic observations for the same objects of the LK-project were used to estimate the internal uncertainties of the atmospheric parameters as a function of SNR$_g$ with the unbiased estimation method. The LASP atmospheric parameters were calibrated based on both the external and internal uncertainties for the giants and dwarfs, respectively. A general statistical analysis of the stellar parameters leads to discovery of 106 candidate metal-poor stars, 9 candidate very metal-poor stars, and 18 candidate high-velocity stars. Fitting formulae were obtained segmentally for both the calibrated atmospheric parameters of the LK-project and the KIC parameters with the common stars. The calibrated atmospheric parameters and radial velocities of the LK-project will be useful for studying stars in the Kepler field.Comment: 53 pages, 21 figures, 5 tables, Accepted for publication by ApJ