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1.
In this paper we consider minimizers of the functionalmin{λ1(Ω)++λk(Ω)+Λ|Ω|,:ΩD open} where DRd is a bounded open set and where 0<λ1(Ω)λk(Ω) are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets Ω have finite perimeter and that their free boundary ΩD is composed of a regular part, which is locally the graph of a C1,α-regular function, and a singular part, which is empty if d<d, discrete if d=d and of Hausdorff dimension at most dd if d>d, for some d{5,6,7}.  相似文献   
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3.
Secondary structures tend to be recognizable because they have repeating structural motifs, but mimicry of these does not have to follow such well-defined patterns. Bioinformatics studies to match side-chain orientations of a novel hydantoin triazole chemotype ( 1 ) to protein-protein interfaces revealed it tends to align well across parallel and antiparallel sheets, like rungs on a ladder. One set of these overlays was observed for the protein-protein interaction uPA⋅uPAR. Consequently, chemotype 1 was made with appropriate side-chains to mimic uPA at this interface. Biophysical assays indicate these compounds did in fact bind uPAR, and elicit cellular responses that affected invasion, migration, and wound healing.  相似文献   
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This mini-review highlights key structural features that should be taken into account when creating ambipolar redox-active closed-shell metal-free molecules. This type of compound is strongly required for the fabrication of all-organic ‘poleless’ batteries and semiconductors. The suggested strategies aimed at stabilization of both oxidized (cationic) and reduced (anionic) redox-states are based on the comprehensive analysis of the most successful structures taken from the recent publications.  相似文献   
6.
利用分子筛择形特点,对煤直接液化油中的混合酚实施高效分离。本研究选取间甲酚和对甲酚作为分离煤直接液化油馏分段混合酚的模型化合物,采用化学液相沉积法对HZSM-5吸附剂的孔口结构进行改变,分析分子筛硅铝比及颗粒粒径对模型化合物间甲酚和对甲酚吸附分离性能的影响,以获得高性能固相吸附剂,并将其应用于180-190℃馏分段混合酚分离。结果表明,当分子筛硅铝比为25、粒径为3-5 μm时,分子筛的孔口结构调节效果最优;当正硅酸乙酯的最小用量为0.2 mL/g时,固相吸附剂的吸附量为0.03 g/g,对甲酚选择性高于95%。由于外表面沉积物对吸附剂的孔口结构变化,导致对甲酚选择性的提高。进一步采用HZSM-5(1)吸附剂对真实煤直接液化油混合酚的分离中发现,苯酚和对甲酚的选择性均达到100%。  相似文献   
7.
The satisfiability (SAT) problem is a core problem in computer science. Existing studies have shown that most industrial SAT instances can be effectively solved by modern SAT solvers while random SAT instances cannot. It is believed that the structural characteristics of different SAT formula classes are the reasons behind this difference. In this paper, we study the structural properties of propositional formulas in conjunctive normal form (CNF) by the principle of structural entropy of formulas. First, we used structural entropy to measure the complex structure of a formula and found that the difficulty solving the formula is related to the structural entropy of the formula. The smaller the compressing information of a formula, the more difficult it is to solve the formula. Secondly, we proposed a λ-approximation strategy to approximate the structural entropy of large formulas. The experimental results showed that the proposed strategy can effectively approximate the structural entropy of the original formula and that the approximation ratio is more than 92%. Finally, we analyzed the structural properties of a formula in the solution process and found that a local search solver tends to select variables in different communities to perform the next round of searches during a search and that the structural entropy of a variable affects the probability of the variable being flipped. By using these conclusions, we also proposed an initial candidate solution generation strategy for a local search for SAT, and the experimental results showed that this strategy effectively improves the performance of the solvers CCAsat and Sparrow2011 when incorporated into these two solvers.  相似文献   
8.
This article explores the questions of long time orbital stability in high order Sobolev norms of plane wave solutions to the NLSE in the defocusing case.  相似文献   
9.
Doxorubicin (DOX), a recognized anticancer drug, forms stable associations with carbon nanotubes (CNTs). CNTs when properly functionalized have the ability to anchor directly in cancerous tumors where the release of the drug occurs thanks to the tumor slightly acidic pH. Herein, we study the armchair and zigzag CNTs with Stone–Wales (SW) defects to rank their ability to encapsulate DOX by determining the DOX-CNT binding free energies using the MM/PBSA and MM/GBSA methods implemented in AMBER16. We investigate also the chiral CNTs with haeckelite defects. Each haeckelite defect consists of a pair of square and octagonal rings. The armchair and zigzag CNT with SW defects and chiral nanotubes with haeckelite defects predict DOX-CNT interactions that depend on the length of the nanotube, the number of present defects and nitrogen doping. Chiral nanotubes having two haeckelite defects reveal a clear dependence on the nitrogen content with DOX-CNT interaction forces decreasing in the order 0N > 4N > 8N. These results contribute to a further understanding of drug-nanotube interactions and to the design of new drug delivery systems based on CNTs.  相似文献   
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