On the Hecke Eigenvalues of Maass Forms

Let $\phi$ denote a primitive Hecke-Maass cusp form for $\Gamma_o(N)$ with the Laplacian eigenvalue $\lambda_\phi=1/4+t_{\phi}^2$. In this work we show that there exists a prime $p$ such that $p\nmid N$, $|\alpha_{p}|=|\beta_{p}| = 1$, and $p\ll(N(1+|t_{\phi}|))^c$, where $\alpha _{p},\;\beta _{p}$ are the Satake parameters of $\phi$ at $p$, and $c$ is an absolute constant with $0<c<1$. In fact, $c$ can be taken as $0.27332$. In addition, we prove that the natural density of such primes $p$ ($p\nmid N$ and $|\alpha_{p}|=|\beta_{p}| = 1$) is at least $34/35$.Comment: Version 2: typos corrected and a new section on natural density adde

An Indoor Microwave Radiometer for Measurement of Tropospheric Water

This article presents the first detailed description of the innovative measurement setup of an indoor tropospheric microwave radiometer [TROpospheric WAter RAdiometer (TROWARA)] that avoids water films on radome. We discuss the performance of a commercial outdoor microwave radiometer [Humidity And Temperature PROfiler radiometer (HATPRO)] for measuring tropospheric water parameters in Bern, Switzerland. The HATPRO is less than 20 m from the TROWARA and has different instrument characteristics. Brightness temperatures measured by HATPRO are analyzed by comparing them with coincident measurements from TROWARA and Radiative Transfer Simulations based on the [European Centre for Medium-Range Weather Forecasts (ECMWF)] operational analysis data (denoted as RTSE). To find the source of brightness temperature bias, a gradient boosting decision tree is used to analyze the sensitivity of eight feature factors to bias. Data processing routines of the two radiometers use different algorithms to retrieve integrated water vapor (IWV) and integrated cloud liquid water (ILW), whereas the same physical algorithms based on the radiative transfer equation are applied to obtain the opacity and rain rate. Using 62 days of data with varied weather conditions, it was found that TROWARA brightness temperatures are in good agreement with RTSE. HATPRO brightness temperatures are significantly overestimated by about 5 K at 22 GHz, compared to TROWARA and RTSE. HATPRO brightness temperatures at 31 GHz agree well with TROWARA and RTSE (within about ±1 K). The overestimated brightness temperatures in the K-band and the HATPRO retrieval algorithm lead to an overestimation of IWV and ILW by HATPRO. The opacities at 31 GHz match very well for TROWARA and HATPRO during no rain with a verified R2of 0.96. However, liquid water floating or remaining water films on the radome of the outdoor HATPRO radiometer induce an overestimation of the rain rate. The physical reason for the overestimated 22-GHz brightness temperatures of the HATPRO is mainly the result of the combined effect of instrument calibration, the surrounding environment of the instrument, and the Sun elevation angle. This can be a problem with the Generation 2 HATPRO radiometer and this problem was resolved in the Generation 5 HATPRO radiometer

Engineering Properties of Sweet Potato Starch for Industrial Applications by Biotechnological Techniques Including Genome Editing

Sweet potato (Ipomoea batatas) is one of the largest food crops in the world. Due to its abundance of starch, sweet potato is a valuable ingredient in food derivatives, dietary supplements, and industrial raw materials. In addition, due to its ability to adapt to a wide range of harsh climate and soil conditions, sweet potato is a crop that copes well with the environmental stresses caused by climate change. However, due to the complexity of the sweet potato genome and the long breeding cycle, our ability to modify sweet potato starch is limited. In this review, we cover the recent development in sweet potato breeding, understanding of starch properties, and the progress in sweet potato genomics. We describe the applicational values of sweet potato starch in food, industrial products, and biofuel, in addition to the effects of starch properties in different industrial applications. We also explore the possibility of manipulating starch properties through biotechnological means, such as the CRISPR/Cas-based genome editing. The ability to target the genome with precision provides new opportunities for reducing breeding time, increasing yield, and optimizing the starch properties of sweet potatoes

Well-dispersed Pd–Sn nanocatalyst anchored on TiO 2 nanosheets with enhanced activity and durability for ethanol electarooxidation

Abstract(#br)Novel Pd 1 -Sn x /TiO 2 nanosheets catalyst with higher activity and durability for ethanol oxidation (EOR) was obtained by NaBH 4 co-reduction method in direct ethanol fuel cells (DEFCs). The electrochemical performance tested under alkaline conditions illustrates that the prepared Pd 1 –Sn 0.6 /TiO 2 NSs catalyst presents outstanding activity (3381 mA mg Pd − 1 ) and excellent CO anti-poisoning ability for EOR. Meanwhile, the residual current density of Pd 1 –Sn 0.6 /TiO 2 NSs nanocatalyst (1207 mA mg Pd − 1 ) is 8.5 times of the Pd/C (JM) catalyst (142 mA mg Pd − 1 ) after the durability test of 5000 s for EOR. Additionally, the Pd 1 -Sn x /TiO 2 nanosheets show prominent electrocatalytic activity in EOR comparison with Pd/TiO 2 nanosheets and Pd–Sn nanocatalysts. Thus, Pd and Sn doped in TiO 2 nanosheets not only display excellent electrocatalytic, but also reduce the cost of Pd, which have some reference value for DEFCs