Quadratic ideals and Rogers-Ramanujan recursions

We give an explicit recursive description of the Hilbert series and Gr\"obner bases for the family of quadratic ideals defining the jet schemes of a double point. We relate these recursions to the Rogers-Ramanujan identity and prove a conjecture of the second author, Oblomkov and Rasmussen.Comment: 17 page

On Cohomology of The Space of Linear Generic Points in Three Dimensional Projective Space

In this paper, we first introduce a type of generalized configuration spaces $C_n^m$ and \p C_n^m, namely, it consists the $n$-tuples in affine or projective $m$ spaces where any $m+1$ points are not contained in a hyperplane. The spaces can be considered as complements of affine and projective algebraic sets respectively and hence are quasi-projective varieties. There is a free action of AGL_{m+1}(\C) and PGL_{m+1}(\C) on $C_n^m$ and \p C_n^m respectively, which gives the spaces a structure as trivial bundles. Also, similar to the classic configuration spaces, there is a natural $S_n$ action on these spaces and that puts an induced $S_n$-represnetation structure on the cohomology.Based on these structures, there are a few result in fundamental group and cohomology group of these spaces studied by other mathematicians. We will introduce some of the results and focus on the cohomology of \p C_n^m. To go one more step further, let $X_n^m$ be the quotient of \p C_n^m by PGL_{m+1}(\C), we will study the cohomology of $X_n^3$ as a $S_n$ representation for $n=6$ and $7$. In the case that $n=7$, our result is based on the assumption that the cohomology groups $H^k(X_n^m)$ are pure of Hodge-Tate type $(k,k)$. The calculation is done by the technique of twisted point counting introduced by \cite{Church_2014}. To utilize the point counting technique, we will discuss the background that makes it possible and introduce the Grothendiecck-Lefchetz formula which is the main foundation of the calculation

Performance Analysis of Restraint Grouting-Anchoring Lap Connection of Rebar in Prefabricated Shear Walls

This study aims to obtain the key engineering parameters for the reliability performance of restraint grouting-anchoring lap connection of rebar, so as to achieve the promotion of prefabricated building. To study the performance of restraint grouting-anchoring lap connection of rebar in prefabricated shear walls, four parameters rebar diameter, lap length, bellows diameter and concrete strength were selected as the main subjects of the test. Specimens were prepared according to four important parameters. The test results show that the connection performance is reliable in the specimen of restraint grouting-anchoring lap connection of rebar for pre-drilled bellows. Through theoretical analysis, a force model was proposed to provide a quantitative analysis method for the theoretical calculation of the mechanical properties of restraint grouting-anchoring lap connection of rebar. As the diameter of the rebar increases, the spread of concrete stresses in the specimens becomes more pronounced; as the diameter of the rebar increases, the spread of concrete stresses in the specimens becomes more pronounced; the shorter the lap length, the higher the bond stress between the rebar and the concrete interface in the specimen, the damage of the specimen is from mild to severe; as the strength of the concrete increases, a larger diameter of rebar and a shorter lap length are required to achieve the same damage pattern in the specimen

Genome-wide identification and expression analysis of the U-box E3 ubiquitin ligase gene family related to salt tolerance in sorghum (Sorghum bicolor L.)

Plant U-box (PUB) E3 ubiquitin ligases play essential roles in many biological processes and stress responses, but little is known about their functions in sorghum (Sorghum bicolor L.). In the present study, 59 SbPUB genes were identified in the sorghum genome. Based on the phylogenetic analysis, the 59 SbPUB genes were clustered into five groups, which were also supported by the conserved motifs and structures of these genes. SbPUB genes were found to be unevenly distributed on the 10 chromosomes of sorghum. Most PUB genes (16) were found on chromosome 4, but there were no PUB genes on chromosome 5. Analysis of cis-acting elements showed that SbPUB genes were involved in many important biological processes, particularly in response to salt stress. From proteomic and transcriptomic data, we found that several SbPUB genes had diverse expressions under different salt treatments. To verify the expression of SbPUBs, qRT-PCR analyses also were conducted under salt stress, and the result was consistent with the expression analysis. Furthermore, 12 SbPUB genes were found to contain MYB-related elements, which are important regulators of flavonoid biosynthesis. These results, which were consistent with our previous multi-omics analysis of sorghum salt stress, laid a solid foundation for further mechanistic study of salt tolerance in sorghum. Our study showed that PUB genes play a crucial role in regulating salt stress, and might serve as promising targets for the breeding of salt-tolerant sorghum in the future

A New Gate Driver for Suppressing Crosstalk of SiC MOSFET

High switching-speed Silicon Carbide Metal-Oxide-Semiconductor Field-Effect Transistor (SiC MOSFET) has serious crosstalk issues. During the turn-ON transition and turn-OFF transition of the active switch in a phase-leg configuration, the voltage drops across the common-source inductor and the displacement current of the gate-drain capacitor of the OFF-state switch induce a spurious pulse on its gate-source voltage. This paper proposes a new gate driver using two Bipolar Junction Transistors (BJTs) and one diode to connect the gate terminal of SiC MOSFET and the negative driver voltage, which provides a low impedance path to bypass the displacement current of the gate-drain capacitor when crosstalk issues occur. The simulation results prove the proposed driver is valid on suppressing the crosstalk issue. The comparisons between the prior drivers and the proposed driver show the superiority of the proposed driver. Finally, the proposed gate driver is successfully implemented and experimentally verified on a 1.1 kW synchronous buck prototype

Effect of dietary Bio-fermented selenium on growth performance, nonspecific immune enzyme, proximate composition and bioaccumulation of zebrafish (Danio rerio)

A four-weeks feeding trial was conducted to evaluate the effects of dietary Bio-fermented selenium (Bio-Se) on zebrafish (Danio rerio). Effects of three Se diets containing basal diet (1.63 mg Se/kg), L-Se diet (3 mg Se/kg), and H-Se diet (10 mg Se/kg) on growth performance, nonspecific immune enzyme activities, proximate composition, and selenium accumulation of zebrafish were tested. The results indicate that body weight gain (BWG), specific growth rate (SGR), and nonspecific immune enzyme [glutathione peroxidase (GPx), superoxide dismutase (SOD), and alkaline phosphatase (ALP)] activities of fish fed with L-Se diet were significantly highest among all the groups. However, increased H2O2 content and decreased SOD activity indicates oxidative stress when fish was fed with H-Se diet. Dietary Se did not affect the proximate composition of zebrafish. The Se concentration in muscle increased in a dose-dependent manner, and the highest Se concentration was recorded in H-Se diet. In summary, the growth performance and nonspecific immunity of zebrafish fed with L-Se diet improved, but exposure to higher concentrations of Bio-Se severely affects the health status of fish. Keywords: Bio-fermented selenium, Zebrafish, Growth performance, Nonspecific immune enzyme, Bioaccumulatio

The Effects of Ambient Temperature and Atmospheric Humidity on the Diffusion Dynamics of Hydrogen Fluoride Gas Leakage Based on the Computational Fluid Dynamics Method

In order to investigate the impact of environmental temperature and atmospheric humidity on the leakage and diffusion of hydrogen fluoride (HF) gas, this study focused on the real scenario of an HF chemical industrial park. Based on the actual dispersion scenario of HF gas, a proportionally scaled-down experimental platform for HF gas leakage was established to validate the accuracy and feasibility of numerical simulations under complex conditions. Using the validated model, the study calculated the complex scenarios of HF leakage and diffusion within the temperature range of 293 K to 313 K and the humidity range of 0% to 100%. The simulation results indicated that different environmental temperatures had a relatively small impact on the hazardous areas (the lethal area, severe injury area, light injury area, and maximum allowable concentration (MAC) area) formed by HF gas leakage. At 600 s of dispersion, the fluctuation range of hazardous area sizes under different temperature conditions was between 3.11% and 13.07%. In contrast to environmental temperature, atmospheric relative humidity had a more significant impact on the dispersion trend of HF leakage. Different relative humidity levels mainly affected the areas of the lethal zone, light injury zone, and MAC zone. When HF continued to leak and disperse for 600 s, compared to 0% relative humidity, 100% relative humidity reduced the lethal area by 35.7%, while increasing the light injury area and MAC area by 27.26% and 111.6%, respectively. The impact on the severe injury area was relatively small, decreasing by 1.68%. The results of this study are crucial for understanding the dispersion patterns of HF gas under different temperature and humidity conditions