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1.
Steven Heilman 《Random Structures and Algorithms》2020,56(1):154-168
We prove the endpoint case of a conjecture of Khot and Moshkovitz related to the unique games conjecture, less a small error. Let n ≥ 2. Suppose a subset Ω of n‐dimensional Euclidean space satisfies ?Ω = Ωc and Ω + v = Ωc (up to measure zero sets) for every standard basis vector . For any and for any q ≥ 1, let and let . For any x ∈ ?Ω, let N(x) denote the exterior normal vector at x such that ‖N(x)‖2 = 1. Let . Our main result shows that B has the smallest Gaussian surface area among all such subsets Ω, less a small error: In particular, Standard arguments extend these results to a corresponding weak inequality for noise stability. Removing the factor 6 × 10?9 would prove the endpoint case of the Khot‐Moshkovitz conjecture. Lastly, we prove a Euclidean analogue of the Khot and Moshkovitz conjecture. The full conjecture of Khot and Moshkovitz provides strong evidence for the truth of the unique games conjecture, a central conjecture in theoretical computer science that is closely related to the P versus NP problem. So, our results also provide evidence for the truth of the unique games conjecture. Nevertheless, this paper does not prove any case of the unique games conjecture. 相似文献
2.
In this study, nanocrystalline cellulose (NCC) prepared from microcrystalline cellulose using high‐intensity ultrasonication as mechanical method without any chemical treatment. The obtained NCC with around 30–50 nm diameters, utilized as support, reducing and stabilizing agent for in‐situ green and eco‐friendly synthesis of silver nanoparticles (Ag NPs). The catalytic activity of composite was examined for degradation of environmental pollutants. The structure of as‐synthesized composite (Ag@NCC) was characterized by ultraviolet–visible spectroscopy (UV–vis), field emission scanning electron microscopy (FE‐SEM); Transmission electron microscopy (TEM); Energy dispersive spectroscopy (EDS), Fourier transform infrared spectroscopy (FT‐IR), X‐ray diffraction (XRD) and thermogravimetric analysis (TGA). The results of the catalytic reaction experiments showed that spherically shaped silver nanoparticles of around 20 nm distributed on the surface of nanocellulose demonstrated high catalytic efficiency towards the removal of methyl orange (MO) and 4‐nitrophenol (4‐NP). 相似文献
3.
《Physics letters. A》2019,383(19):2290-2295
Cooling rate is critical in synthesizing nanoparticles (NPs), which determines the microstructure and the corresponding mechanical, thermal and electrical properties. This research, as the most initiative one, studies microstructure formation of three different sized high entropy alloy (HEA) NPs under three different cooling rates, employing molecular dynamics (MD). Through analysis of potential energy, “common neighbor analysis”, radial distribution function, and also the mean square displacement, it is found that phase transition temperature is independent of HEA NP size, and as cooling rate decrease, more amorphous atoms transform to fcc and hcp orders, which can alternate the mechanical and thermodynamic properties of the final structure. The Cr atoms are found to aggregate into one cluster inside the NP and also try to migrate to the surface of the HEA NP, due to the large diffusivity. This research provides new insights in the size dependency of the nanoparticles, which may motivate more applications in which the strong size dependency is not desirable. 相似文献
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The ability to separate enzymes, nucleic acids, cells, and viruses is an important asset in life sciences. This can be realised by using their spontaneous asymmetric partitioning over two macromolecular aqueous phases in equilibrium with one another. Such phases can already form while mixing two different types of macromolecules in water. We investigate the effect of polydispersity of the macromolecules on the two-phase formation. We study theoretically the phase behavior of a model polydisperse system: an asymmetric binary mixture of hard spheres, of which the smaller component is monodisperse and the larger component is polydisperse. The interactions are modelled in terms of the second virial coefficient and are assumed to be additive hard sphere interactions. The polydisperse component is subdivided into sub-components and has an average size ten times the size of the monodisperse component. We calculate the theoretical liquid–liquid phase separation boundary (the binodal), the critical point, and the spinodal. We vary the distribution of the polydisperse component in terms of skewness, modality, polydispersity, and number of sub-components. We compare the phase behavior of the polydisperse mixtures with their concomittant monodisperse mixtures. We find that the largest species in the larger (polydisperse) component causes the largest shift in the position of the phase boundary, critical point, and spinodal compared to the binary monodisperse binary mixtures. The polydisperse component also shows fractionation. The smaller species of the polydisperse component favor the phase enriched in the smaller component. This phase also has a higher-volume fraction compared to the monodisperse mixture. 相似文献
6.
Chiral Separations in Normal‐phase Liquid Chromatography: Updating a Screening Strategy with a Chlorine‐containing Polysaccharide‐based Selector 下载免费PDF全文
Jie Zhou Shanshan Chen Pei Luo Chong Sun Lingchang Meng Qiuzheng Du Fang Sun 《中国化学会会志》2015,62(12):1059-1067
The screening conditions of an existing column and mobile phase selection strategy for chiral compounds in normal‐phase high performance liquid chromatography (NP‐HPLC) were tested for their applicability on Chiralpak IC, which is a chiral stationary phase (CSP) made by immobilising cellulosic tris (3,5‐dichlorophenyl‐carbamate) on silica gel. In this study, the applicability of the optimization steps of the existing separation strategy was examined using 36 compounds representing the three possible resolution situations that occur after screening. The cumulative number of separated compounds is 27 (75.0 %), and the cumulative number of baseline separated compounds is 19 (52.8 %). 相似文献
7.
A heavy and hard peak-shaped inclusion in an elastic body provokes to concentration of eigenvalues in the low-frequency range of the spectrum and localization of the corresponding eigenmodes near the peak tip. To cite this article: S.A. Nazarov, C. R. Mecanique 335 (2007). 相似文献
8.
RENÉ A. SALINAS WILLIAM H. STIVER JOSEPH L. CORN SUZANNE LENHART CHARLES COLLINS MARGUERITE MADDEN KURT C. VERCAUTEREN BRANDON B. SCHMIT ELLEN KASARI AGRICOLA ODOI GRAHAM HICKLING HAMISH MCCALLUM 《Natural Resource Modeling》2015,28(1):18-36
The expansion of feral hog (Sus scrofa) populations in the United States has resulted in increased efforts to develop and implement control strategies designed to minimize the impacts done by this invasive species. We describe an individual‐based model for feral hogs in Great Smoky Mountains National Park (GSMNP). The objectives of the model are to provide an understanding of the population dynamics of this feral hog population and to determine the efficacy of the annual harvest as a population control method. Results suggest that the dynamics of the population are driven by fall hard mast production and the GSMNP harvests currently limit growth of the population, but these control efforts have not reduced the population. 相似文献
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10.
在工程应用的很多摩擦对偶中,往往有一方是锐形的,因此,研究锐形滑块的滚动与滑动具有重要的实用意义。以锐缘硬质轮在挤压铝和软钢两种平面试样表面的滚动和滑动为研究对象,考察了两种摩擦过程中材料的受力状况和变形状况,结果表明,要在同种金属试样表面造成相同宽度的槽痕,滚动法所需要的垂直负荷比滑动法所需要的大,然而滚动法所需要的切向牵引力却比滑动法所需要的小.对两种摩擦过程中界面上的应力与材料的强度性能之关系的分析讨论指出,滚动试验中接触界面上的正应力相应于变形材料的屈服应力,因而滚动试验可以作为材料硬度的一种测量方法;滑动试验中接触界面上的剪应力相应于变形材料的流动剪应力;但滚动试验中界面剪应力与材料的流动剪应力之间,以及滑动试验中界面正应力与材料的屈服应力之间却都没有直线关系. 相似文献