LpL^p integrability of functions with Fourier support on a smooth space curve

We prove that if $f\in L^p(\mathbb{R}^k)$ with $p<(k^2+k+2)/2$ satisfies that $\widehat{f}$ is supported on a small perturbation of the moment curve in $\mathbb{R}^k$, then $f$ is identically zero. This improves the more general result of Agranovsky and Narayanan, and the exponents are sharp in all dimensions. In the process, we develop a mechanism that should lead to further progress on related problems

Preparation of ordered TiO2 macroporous membrane using PBMA colloid crystal as template

Poly(butyl methacrylate) (PBMA) colloidal crystal templates were assembled orderly on the clean substrates of monocrystalline silicon by dip-drawing technique and titanium dioxide (TiO2) macroporous membranes were prepared by using sol-dipping template method to fill the interstices among the PBMA templates, followed by calcination to remove the templates at 550℃. Calcination of the PBMA templates was carried out according to the following procedure: the rate of rising temperature was 5℃/min from room temperature to 150℃, 2℃/min from 150℃ to 270℃, 1℃ /min from 270℃ to 430℃, 2℃/min from 430℃ to 550℃ and maintained it at 550℃ for 2h. X-ray diffraction (XRD) spectra indicated the macroporous materials were anatase structure. The polymerization mechanism of BMA with Fenton reagent as a new initiator was discussed, and the removal process of the PBMA templates and the formation of TiO2 pore size were investigated, respectively. The results showed that the new method of polymerization overcomes many problems associated with the conventional emulsion polymerization techniques such as long reaction time, necessary deoxygenation, and complicated operation

Mixed Eucalyptus plantations in subtropical China enhance phosphorus accumulation and transformation in soil aggregates

IntroductionThe production of Eucalyptus, a principal economic tree genus in China, is faced with challenges related to soil phosphorus (P) limitations. In this study, we explore variations in phosphorus content, storage, and transformation in Eucalyptus forests. We hypothesize that mixed forests augment soil aggregate stability and P content and that microaggregates are pivotal in determining P differences between mixed and pure forests. Additionally, we posit that mixed forests foster P transformation, enhancing its efficacy in the soil. Current research on the distribution and transformation of soil total P (TP) and P fractions at the soil aggregate level is limited.MethodsIn this study, we selected soil from a Eucalyptus-Mytilaria laosensis Lecomte mixed forest, Eucalyptus-Erythrophleum fordii Oliv mixed forest, and pure Eucalyptus forest in Chongzuo County, Guangxi, China, as the research objects. Using a dry-sieving method, we divided the soil collected in situ from the 0–40 cm layer into aggregates of &gt;2, 1–2, 0.25–1, and &lt;0.25 mm particle sizes, measured the TP and P fractions (resin-extractable inorganic P, bicarbonate-extractable inorganic P, bicarbonate-extractable organic P, sodium hydroxide-extractable inorganic P, sodium hydroxide-extractable organic P, dilute hydrochloric acid-extractable P, concentrated hydrochloric acid extractable inorganic P, concentrated hydrochloric acid-extractable organic P and residue-P) in different aggregates, and used redundancy analysis and PLS SEM to reveal key factors affecting soil P accumulation and transformation.ResultsThe results showed that compared to pure Eucalyptus forests, mixed Eucalyptus forests significantly enhanced the stability of soil aggregates and the content and storage of phosphorus, especially the Eucalyptus-Mytilaria laosensis mixed forest. The content of total soil phosphorus and its fractions decreased with increasing aggregate particle size, while the opposite trend was observed for stored P, with aggregates &lt;0.25 mm being the main fraction influencing soil phosphorus accumulation. The transformation process of P fractions was primarily constrained by dissolution rates, mineralization rates, biological activity, including the action of microbes, fungi, and plant–root interactions, and other factors.DiscussionMixed forests increased the transformation of phosphorus in soil aggregates, effectivel enhancing the availability of soil phosphorus. In summary, this study provides important evidence for the systematic management of subtropical artificia Eucalyptus forests and the sustainable utilization of soil resources

TiEV: The Tongji Intelligent Electric Vehicle in the Intelligent Vehicle Future Challenge of China

TiEV is an autonomous driving platform implemented by Tongji University of China. The vehicle is drive-by-wire and is fully powered by electricity. We devised the software system of TiEV from scratch, which is capable of driving the vehicle autonomously in urban paths as well as on fast express roads. We describe our whole system, especially novel modules of probabilistic perception fusion, incremental mapping, the 1st and the 2nd planning and the overall safety concern. TiEV finished 2016 and 2017 Intelligent Vehicle Future Challenge of China held at Changshu. We show our experiences on the development of autonomous vehicles and future trends

A practical overview of image classification with variational tensor-network quantum circuits

Circuit design for quantum machine learning remains a formidable challenge. Inspired by the applications of tensor networks across different fields and their novel presence in the classical machine learning context, one proposed method to design variational circuits is to base the circuit architecture on tensor networks. Here, we comprehensively describe tensor-network quantum circuits and how to implement them in simulations. This includes leveraging circuit cutting, a technique used to evaluate circuits with more qubits than those available on current quantum devices. We then illustrate the computational requirements and possible applications by simulating various tensor-network quantum circuits with PennyLane, an open-source python library for differential programming of quantum computers. Finally, we demonstrate how to apply these circuits to increasingly complex image processing tasks, completing this overview of a flexible method to design circuits that can be applied to industrially-relevant machine learning tasks

Tree–litter–soil system C:N:P stoichiometry and tree organ homeostasis in mixed and pure Chinese fir stands in south subtropical China

IntroductionCultivation of Chinese fir (Cunninghamia lanceolata) have alleviated timber shortages and mixed stands with Chinese fir and indigenous species represent a sustainable forestry model. Studying system nutrient balance and tree nutrient homeostasis can provide insights into the ecological advantages of Chinese fir mixed stands and guide the management of plantations.MethodsMixed Chinese fir plantations with two native broadleaf species (Michelia macclurei and Mytilaria laosensis) and pure Chinese fir stands were examined for our study. The responses in carbon (C), nitrogen (N), and phosphorus (P) distribution and their stoichiometric characterization in the tree–litter–soil system to stand changes were evaluated. In addition, the ecological stoichiometric homeostasis of leaves, branches, trunks, bark and roots was used to measure the trees’ adaptive capacity to stand changes.ResultsThe results showed that the mixed stands of Michelia macclurei and Chinese fir significantly increased soil OC, TN, and TP, and improved the carbon sequestration and nutrient storage functions of the plantations. The mixed stands improved the litter mass and C:N and C:P to different degrees. The soil N and P imbalance reduced the leaf N:P, resulting in N limitation of different trees, while the principal component analysis showed that the improvement of soil TN in the mixed plantation alleviated the N limitation. In addition, mixed stands reduced N, P, and N:P homeostasis in branch, trunk, and bark of some Chinese fir trees, whereas mixed species showed flexibility in leaf N:P homeostasis.DiscussionTherefore, the selection of mixed species for mixed forests is a critical factor to consider when creating mixed plantations. These results contribute to our understanding of the ecological stoichiometry of fir plantations and are of considerable importance for the sustainable development of plantations as well as for the response to global climate change