Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability

We consider concentrated vorticities for the Euler equation on a smooth domain $\mathrm{\Omega }?{\mathbf{R}}^2$ in the form of

$\omega =\sum _{j=1}^N{\omega }_j{\chi }_{{\mathrm{\Omega }}_j},|{\mathrm{\Omega }}_j|=\pi r_j^2,\underset{{\mathrm{\Omega }}_j}{\int }{\omega }_{j}d\mu ={\mu }_j\ne 0,$

supported on well-separated vortical domains ${\mathrm{\Omega }}_j$, $j=1,\dots ,N$, of small diameters $O(r_j)$. A conformal mapping framework is set up to study this free boundary problem with ${\mathrm{\Omega }}_j$ being part of unknowns. For any given vorticities ${\mu }_1,\dots ,{\mu }_N$ and small $r_1,\dots ,r_N\in {\mathbf{R}}^{+}$, through a perturbation approach, we obtain such piecewise constant steady vortex patches as well as piecewise smooth Lipschitz steady vorticities, both concentrated near non-degenerate critical configurations of the Kirchhoff–Routh Hamiltonian function. When vortex patch evolution is considered as the boundary dynamics of $?{\mathrm{\Omega }}_j$, through an invariant subspace decomposition, it is also proved that the spectral/linear stability of such steady vortex patches is largely determined by that of the 2N-dimensional linearized point vortex dynamics, while the motion is highly oscillatory in the 2N-codim directions corresponding to the vortical domain shapes.     

介绍一个与材料相关的研究型综合化学实验——壳聚糖的制备与表征

在中国科学技术大学夏季学期的研究型实验课程"化学科研基础训练"中开设"壳聚糖的制备与表征"综合实验,以龙虾壳为原料,通过除蛋白、脱盐、脱色、脱乙酰等一系列反应,制备得到目标产物壳聚糖。运用红外光谱、核磁共振仪、黏度法、滴定等对产品的结构及性能进行表征。     

Computational Design of Novel Allosteric Inhibitors for Plasmodium falciparum DegP

The serine protease, DegP exhibits proteolytic and chaperone activities, essential for cellular protein quality control and normal cell development in eukaryotes. The P. falciparum DegP is essential for the parasite survival and required to combat the oscillating thermal stress conditions during the infection, protein quality checks and protein homeostasis in the extra-cytoplasmic compartments, thereby establishing it as a potential target for drug development against malaria. Previous studies have shown that diisopropyl fluorophosphate (DFP) and the peptide SPMFKGV inhibit E. coli DegP protease activity. To identify novel potential inhibitors specific to PfDegP allosteric and the catalytic binding sites, we performed a high throughput in silico screening using Malaria Box, Pathogen Box, Maybridge library, ChEMBL library and the library of FDA approved compounds. The screening helped identify five best binders that showed high affinity to PfDegP allosteric (T0873, T2823, T2801, {"type":"entrez-protein","attrs":{"text":"RJC02337","term_id":"1480409465","term_text":"RJC02337"}}RJC02337, CD00811) and the catalytic binding site (T0078L, T1524, T2328, BTB11534 and 552691). Further, molecular dynamics simulation analysis revealed {"type":"entrez-protein","attrs":{"text":"RJC02337","term_id":"1480409465","term_text":"RJC02337"}}RJC02337, BTB11534 as the best hits forming a stable complex. WaterMap and electrostatic complementarity were used to evaluate the novel bio-isosteric chemotypes of {"type":"entrez-protein","attrs":{"text":"RJC02337","term_id":"1480409465","term_text":"RJC02337"}}RJC02337, that led to the identification of 231 chemotypes that exhibited better binding affinity. Further analysis of the top 5 chemotypes, based on better binding affinity, revealed that the addition of electron donors like nitrogen and sulphur to the side chains of butanoate group are more favoured than the backbone of butanoate group. In a nutshell, the present study helps identify novel, potent and Plasmodium specific inhibitors, using high throughput in silico screening and bio-isosteric replacement, which may be experimentally validated.     

ZnO nanowire lines and bundles: Template-deformation-guided alignment for patterned field-electron emitters

One-dimensional ZnO materials have been promising for field-emission (FE) application, but how to facially control the alignment of ZnO emitters is still a great challenge especially for patterned display application. Here, we report the fabrication of novel ZnO nanowire (NW) line and bundle arrays for patterned field-electron emitters. The effects of PS template size and heating time on the resulted ZnO nanoarrays were systematically studied. The deformation degree of PS templates was controlled and hence utilized to adjust the alignment of electrochemically deposited ZnO arrays. It was found that the length of NW lines and the density of NW bundles can effectively tuned by the PS template heating time. The optimal FE performance with turn-on electric field as low as of 4.4 V μm⁻¹ and the field-enhancement factor as high as of 1450 were achieved through decreasing the screening effect among the patterned field-electron emitters.     

Condensation of all-cis-tetraphenylcyclotetrasiloxanetetraol in ammonia: new method for preparation of ladder-like polyphenylsilsesquioxanes

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Path integral quantization corresponding to the deformed Heisenberg algebra

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.