Isoparametric foliation and Yau conjecture on the first eigenvalue

A well known conjecture of Yau states that the first eigenvalue of every closed minimal hypersurface $M^n$ in the unit sphere $S^{n+1}(1)$ is just its dimension $n$. The present paper shows that Yau conjecture is true for minimal isoparametric hypersurfaces. Moreover, the more fascinating result of this paper is that the first eigenvalues of the focal submanifolds are equal to their dimensions in the non-stable range.Comment: to appear in J.Diff.Geo

Isoparametric functions and exotic spheres

The first part of the paper is to improve the fundamental theory of isoparametric functions on general Riemannian manifolds. Next we focus our attention on exotic spheres, especially on "exotic" 4-spheres (if exist) and the Gromoll-Meyer sphere. In particular, as one of main results we prove: there exists no properly transnormal function on any exotic 4-sphere if it exists. Furthermore, by projecting an $S^3$-invariant isoparametric function on $Sp(2)$, we construct a properly transnormal but not an isoparametric function on the Gromoll-Meyer sphere with two points as the focal varieties.Comment: 21 pages, to appear in Journal f\"ur die reine und angewandte Mathematik (Crelles Journal

Robust Adaptive Beamforming Based on a Convolutional Neural Network

To address the advancements in jamming technology, it is imperative to consider robust adaptive beamforming (RBF) methods with finite snapshots and gain/phase (G/P) errors. This paper introduces an end-to-end RBF approach that utilizes a two-stage convolutional neural network. The first stage includes convolutional blocks and residual blocks without downsampling; the blocks assess the covariance matrix precisely using finite snapshots. The second stage maps the first stage’s output to an adaptive weight vector employing a similar structure to the first stage. The two stages are pre-trained with different datasets and fine-tuned as end-to-end networks, simplifying the network training process. The two-stage structure enables the network to possess practical physical meaning, allowing for satisfying performance even with a few snapshots in the presence of array G/P errors. We demonstrate the resulting beamformer’s performance with numerical examples and compare it to various other adaptive beamformers

Reduced Degrees of Freedom in Space-Time Adaptive Processing for Space-based Early Warning Radar

The clutter of space-based early warning radar exhibits tight coupling in the azimuth-elevation-Doppler domain due to the high speed of satellites and the Earth’s rotation. As a result, conventional Space-Time Adaptive Processing (STAP) suffers significant performance degradation when detecting slow moving targets. The azimuth-elevation-Doppler three-dimensional STAP method provides the ability to decouple clutter and thus can achieve sub-optimal performance for clutter suppression. However, in contrast to the situation in non-sidelooking airborne early warning radar, this method requires large system degrees of freedom when applied to space-based early warning radar. Therefore, in practice, both the computational load and the sample requirement are too large to meet. In this study, the space-time signal model of the planar array for space-based early warning radar is first constructed. Then, the tight coupling characteristic of clutter in the azimuth-elevation-Doppler domain is analyzed in detail. On this basis, a novel three-dimensional STAP method with reduced degrees of freedom with factored structure is proposed. The sidelobe clutter is first suppressed via amplitude taper in azimuth, and the mainlobe clutter responding to each ambiguous range is further canceled by adaptive processing in the elevation-Doppler domain. The simulation results show that the proposed method can achieve sub-optimal performance under low computational load and limited sample conditions. Therefore, the proposed method is suitable for practical application in space-based early warning radar

Expression of Pinellia pedatisecta Agglutinin PPA Gene in Transgenic Sugarcane Led to Stomata Patterning Change and Resistance to Sugarcane Woolly Aphid, Ceratovacuna lanigera Zehntner

The sugarcane woolly aphid is one of the main pests of sugarcane worldwide. The Pinellia pedatisecta agglutinin (PPA) gene has been demonstrated to function towards aphid resistance in other crops. In our study, in order to investigate the PPA function towards aphid control in sugarcane and its underlying mechanism, the PPA gene was overexpressed in a sugarcane Zhongzhe 1 (ZZ1) cultivar in independent transgenic sugarcane lines. It was confirmed in this study that PPA transgenic sugarcane can resist aphids via detecting the aphids’ development and tracing the survival number on PPA−transgenic sugarcane lines as well as PPA negative control lines. The mechanism of PPA lectin−associated defense against aphids was preliminarily explored. Stomatal patterning differences of sugarcane leaves between PPA−transgenic sugarcane lines and negative control lines were found. PPA overexpression led to an increase in stomata number and a decrease in stomata size that might have changed the transpiration status, which is critical for aphids’ passive feeding. Moreover, the antioxidant enzyme, sugar, tannin and chlorophyll content in sugarcane leaves before and after aphid infestation was determined. The results indicated that PPA overexpression in sugarcane resulted in an increase in antioxidant enzyme activity and tannin content, as well as a reduction in the decline of certain sugars. These together may improve sugarcane resistance against the sugarcane woolly aphid

Forest Conversion and Soil Depth Can Modify the Contributions of Organic and Inorganic Colloids to the Stability of Soil Aggregates

The stability of soil aggregates is critical for maintaining soil structures and is positively correlated with soil resident organic and inorganic colloids. Forest conversion and soil depth affects the formation of soil aggregates; however, the detailed mechanisms involved in their stabilization have not been well investigated. Therefore, to explore the main factors that influence the stability of soil aggregates for different forest types and soil depths, twelve soil samples were collected from four types of forests (native, mixed, Chinese fir, and bamboo forest) and three soil depths (0–10 cm, 10–20 cm, and 20–30 cm) in subtropical forests. The results revealed that the distributions and mean weight diameters (MWDs) of large macroaggregates in the bamboo forest were significantly lower than those in the other forest types at all soil depths (p < 0.05). Organic and inorganic colloids (organically-complexed Fe oxide and fulvic acid) in the soil directly impacted the stability of soil aggregates, while soil properties (e.g., pH and bulk density) indirectly promoted soil aggregate stability through the modification of colloids. In both native and bamboo forests, organic colloids contributed most to the stability of soil aggregates, reaching 80.31% and 61.37%, respectively. The contributions of organic colloids were found to decrease with soil depth, which was primarily due to changes in the organic matter caused by the decomposition of litter. Elucidating and promoting the specific contributions of organic and inorganic colloids on the stability of soil aggregates will be increasingly important for the optimal management of different forest types

Tripsazea, a Novel Trihybrid of Zea mays, Tripsacum dactyloides, and Zea perennis

A trispecific hybrid, MTP (hereafter called tripsazea), was developed from intergeneric crosses involving tetraploid Zea mays (2n = 4x = 40, genome: MMMM), tetraploid Tripsacum dactyloides (2n = 4x = 72, TTTT), and tetraploid Z. perennis (2n = 4x = 40, PPPP). On crossing maize-Tripsacum (2n = 4x = 56, MMTT) with Z. perennis, 37 progenies with varying chromosome numbers (36-74) were obtained, and a special one (i.e., tripsazea) possessing 2n = 74 chromosomes was generated. Tripsazea is perennial and expresses phenotypic characteristics affected by its progenitor parent. Flow cytometry analysis of tripsazea and its parents showed that tripsazea underwent DNA sequence elimination during allohexaploidization. Of all the chromosomes in diakinesis I, 18.42% participated in heterogenetic pairing, including 16.43% between the M- and P-genomes, 1.59% between the M- and T-genomes, and 0.39% in T- and P-genome pairing. Tripsazea is male sterile and partly female fertile. In comparison with previously synthesized trihybrids containing maize, Tripsacum and teosinte, tripsazea has a higher chromosome number, higher seed setting rate, and vegetative propagation ability of stand and stem. However, few trihybrids possess these valuable traits at the same time. The potential of tripsazea is discussed with respect to the deployment of the genetic bridge for maize improvement and forage breeding