Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ 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 ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.     

Visible light-driven acridone catalysis for atom transfer radical polymerization

Acridone as a new kind of visible light photocatalyst has been developed to catalyze metal free atom transfer radical polymerization (ATRP). The photocatalyst possess low excited state potential as can undergo an oxidative quenching pathway to initiate ATRP of vinyl monomers. Kinetic study and light on/off reaction demonstrate the “living”/controlled nature of the polymerization by light. Block copolymers can be achieved by using PMMA as macroinitiator to reinitiate polymerization of other vinyl monomers, which shows highly preserved Br chain-end functionality in the synthesized polymers. Moreover, the polymerization can be conducted under air atmosphere as most photocatalysts need anaerobic condition, which may give inspiration of further application of this kind of photocatalyst.     

对自由落体的诺维科夫时间与牛顿绝对时间关系讨论

文章首先将史瓦西黑洞场中自由下落质点的固有时(诺维科夫坐标时)公式,由自然单位制化成了国际单位制中的形式.然后,根据牛顿第二定律和万有引力定律,推导出了自由下落质点经历的绝对时间公式,进而证明了广义相对论中自由落体经历的固有时,恰好等于牛顿力学给出的绝对时间.最后,对自由下落质点在黑洞内外经历的时间进行了特例计算.     

Chain transfer to solvent in BN 2-vinylnaphthalene radical polymerization

The synthesis of vinyl alcohol copolymers is limited due to the poor radical reactivity of vinyl acetate (VAc), the traditional precursor to polyvinyl alcohol (PVA). Main group monomers such as BN 2-vinylnaphthalene (BN2VN) have attracted attention as alternatives to VAc to form side chain hydroxyls via oxidation, but outstanding questions of molecular weight control remain. Herein we report systematic investigation of solvent, temperature, and initiator concentration as factors influencing BN2VN degree of polymerization. We find increased chain transfer to toluene, hypothesized to arise from differences in radical stabilization and reactivity by aromatic and BN aromatic rings. As a result of these combined efforts, high molecular weight (M_w ~ 10⁵ g mol⁻¹) BN2VN homopolymers and BN2VN-styrene copolymers were obtained.     

小孔流速实验中的排水时间和流量系数的研究

本文以水作为理想流体,考虑到水头损失和孔口缩流效应,对小孔流速实验涉及的容器排水问题进行了系统的理论和实验研究.从理论上推导得出了圆柱形容器排水时间的解析解,分析了排水时间和自由液面速度、流量系数之间的规律,提出了排水时间的等效性.实验上,加工了底部开有不同小孔的大型圆柱形容器,测量了容器排水时间随液面高度的变化关系,借助实验结果计算了流量系数值,验证了容器排水时间的等效性关系,实验结果与理论计算符合较好.     

New Phenomena in Organometallic‐Mediated Radical Polymerization (OMRP) and Perspectives for Control of Less Active Monomers

The impact of reversible bond formation between a growing radical chain and a metal complex (organometallic‐mediated radical polymerization (OMRP) equilibrium) to generate an organometallic intermediate/dormant species is analyzed with emphasis on the interplay between this and other one‐electron processes involving the metal complex, which include halogen transfer in atom transfer radical polymerization (ATRP), hydrogen‐atom transfer in catalytic chain transfer (CCT), and catalytic radical termination (CRT). The challenges facing the controlled polymerization of “less active monomers” (LAMs) are outlined and, after reviewing the recent achievements of OMRP in this area, the perspectives of this technique are analyzed.     

Doxorubicin Encapsulation in Carbon Nanotubes Having Haeckelite or Stone–Wales Defects as Drug Carriers: A Molecular Dynamics Approach

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.     

Naphthalimide‐phthalimide derivative based photoinitiating systems for polymerization reactions under blue lights

Naphthalimide‐phthalimide derivatives (NDPDs) have been synthesized and combined with an iodonium salt, N‐vinylcarbazole, amine or 2,4,6‐tris(trichloromethyl)‐1,3,5‐triazine to produce reactive species (i.e., radicals and cations). These generated reactive species are capable of initiating the cationic polymerization of epoxides and/or the radical polymerization of acrylates upon exposure to very soft polychromatic visible lights or blue lights. Compared with the well‐known camphorquinone based systems used as references, the novel NDPD based combinations employed here demonstrate clearly higher efficiencies for the cationic polymerization of epoxides under air as well as the radical polymerization of acrylates. Remarkably, one of the NDPDs (i.e., NDPD2) based systems is characterized by an outstanding reactivity. The structure/reactivity/efficiency relationships of the investigated NDPDs were studied by fluorescence, cyclic voltammetry, laser flash photolysis, electron spin resonance spin trapping, and steady state photolysis techniques. The key parameters for their reactivity are provided. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 665–674     

Physical aging in amorphous poly(ethylene furanoate): Enthalpic recovery,density, and oxygen transport considerations

The current work utilizes three separate techniques to study the physical aging process in amorphous poly(ethylene furanoate) (PEF), which is a recently introduced engineering thermoplastic with enhanced properties compared to petroleum‐sourced poly(ethylene terephthalate). Differential scanning calorimetry aging experiments were conducted at multiple aging temperatures and times, and the resultant enthalpic recovery values compared to the theoretical maximum enthalpy loss evaluated from calculations involving extrapolation of the equilibrium liquid line. Density measurements reveal densification of the matrix for the aged versus unaged samples, and provide an estimate for the reduction in free volume for the aged samples. Complementary oxygen permeation and pressure‐decay sorption experiments provide independent verification of the free volume reduction mechanism for physical aging in glassy polymers. The current work provides the first detailed aging study for PEF. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 389–399