On the low regularity of the fifth order Kadomtsev-Petviashvili I equation

We consider the fifth order Kadomtsev-Petviashvili I (KP-I) equation as $\partial_tu+\alpha\partial_x^3u+\partial^5_xu+\partial_x^{-1}\partial_y^2u+uu_x=0,$ while $\alpha\in \mathbb{R}$. We introduce an interpolated energy space $E_s$ to consider the well-posedeness of the initial value problem (IVP) of the fifth order KP-I equation. We obtain the local well-posedness of IVP of the fifth order KP-I equation in $E_s$ for $0<s\leq1$. To obtain the local well-posedness, we present a bilinear estimate in the Bourgain space in the framework of the interpolated energy space. It crucially depends on the dyadic decomposed Strichartz estimate, the fifth order dispersive smoothing effect and maximal estimate. Key words: The fifth order KP-I equation, Bourgain space, Dyadic decomposed Strichartz estimate, Dispersive smoothing effect, Maximal estimate.Comment: 30page

Low regularity solutions of two fifth-order KdV type equations

The Kawahara and modified Kawahara equations are fifth-order KdV type equations and have been derived to model many physical phenomena such as gravity-capillary waves and magneto-sound propagation in plasmas. This paper establishes the local well-posedness of the initial-value problem for Kawahara equation in $H^s({\mathbf R})$ with $s>-\frac74$ and the local well-posedness for the modified Kawahara equation in $H^s({\mathbf R})$ with $s\ge-\frac14$. To prove these results, we derive a fundamental estimate on dyadic blocks for the Kawahara equation through the $[k; Z]$ multiplier norm method of Tao \cite{Tao2001} and use this to obtain new bilinear and trilinear estimates in suitable Bourgain spaces.Comment: 17page

Genetic mapping and functional analysis of a classical tassel branch number mutant Tp2 in maize

Tassel branch number is a key trait that contributes greatly to grain yield in maize (Zea mays). We obtained a classical mutant from maize genetics cooperation stock center, Teopod2 (Tp2), which exhibits severely decreased tassel branch. We conducted a comprehensive study, including phenotypic investigation, genetic mapping, transcriptome analysis, overexpression and CRISPR knock-out, and tsCUT&amp;Tag of Tp2 gene for the molecular dissection of Tp2 mutant. Phenotypic investigation showed that it is a pleiotropic dominant mutant, which is mapped to an interval of approximately 139-kb on Chromosome 10 harboring two genes Zm00001d025786 and zma-miR156h. Transcriptome analysis showed that the relative expression level of zma-miR156h was significantly increased in mutants. Meanwhile, overexpression of zma-miR156h and knockout materials of ZmSBP13 exhibited significantly decreased tassel branch number, a similar phenotype with Tp2 mutant, suggesting that zma-miR156h is the causal gene of Tp2 and targets ZmSBP13 gene. Besides, the potential downstream genes of ZmSBP13 were uncovered and showed that it may target multiple proteins to regulate inflorescence structure. Overall, we characterized and cloned Tp2 mutant, and proposed a zma-miR156h-ZmSBP13 model functioning in regulating tassel branch development in maize, which is an essential measure to satisfy the increasing demands of cereals

An improved positioning algorithm in a long-range asymmetric perimeter security system

In this paper, an improved positioning algorithm is proposed for a long-range asymmetric perimeter security system. This algorithm employs zero-crossing rate to detect the disturbance starting point, and then utilizes an improved empirical mode decomposition to obtain the effective time-frequency distribution of the extracted signal. In the end, a cross-correlation is used to estimate the time delay of the effective extracted signal. The scheme is also verified and analyzed experimentally. The field test results demonstrate that the proposed scheme can achieve a detection of 96.60% of positioning errors distributed within the range of 0-±20 m at the sensing length of 75 km, which significantly improves the positioning accuracy for the long-range asymmetric fence perimeter application

Transformation between phreatic water and soil water during freeze–thaw periods

During freeze–thaw periods, the exchange between shallow groundwater and soil water is unusually strong and bidirectional, which causes soil salinization and affects the accuracy of water resources assessment. The objectives of this study were to explore the laws of transformation between phreatic water and soil water through nine different groundwater table depths (GTDs) and three kinds of lithologies during three successive freeze–thaw periods using field lysimeters. The results showed that phreatic evaporation increased with smaller average soil particle sizes. The differences between phreatic evaporation and recharge to groundwater (DPR) and GTDs were well fitted by the semi-logarithmic model, and the regression coefficients A and B of the model were well fitted by the linear relationship with the average soil particle size. With the increase of soil particle size, the change of DPR decreased with the change rate of soil particle size. The extent of transformation between phreatic water and soil water decreased with the increase of soil particle size. During the whole freeze–thaw period, the negative value of DPR increased with an decrease in GTD. The groundwater depths of zero DPR (D-zero) of sandy loam, fine sand and sandy soil during the freeze–thaw periods were 2.79 m, 2.21 m and 2.12 m, respectively. This research is significant for the prevention of soil salinization disasters and the accurate assessment of water resources

Tunable van Hove singularity without structural instability in Kagome metal CsTi3_3Bi5_5

In Kagome metal CsV$_3$Sb$_5$, multiple intertwined orders are accompanied by both electronic and structural instabilities. These exotic orders have attracted much recent attention, but their origins remain elusive. The newly discovered CsTi$_3$Bi$_5$ is a Ti-based Kagome metal to parallel CsV$_3$Sb$_5$. Here, we report angle-resolved photoemission experiments and first-principles calculations on pristine and Cs-doped CsTi$_3$Bi$_5$ samples. Our results reveal that the van Hove singularity (vHS) in CsTi$_3$Bi$_5$ can be tuned in a large energy range without structural instability, different from that in CsV$_3$Sb$_5$. As such, CsTi$_3$Bi$_5$ provides a complementary platform to disentangle and investigate the electronic instability with a tunable vHS in Kagome metals