Jones polynomial of knots formed by repeated tangle replacement operations

In this paper, we prove that the Jones polynomial of a link diagram obtained through repeated tangle replacement operations can be computed by a sequence of suitable variable substitutions in simpler polynomials. For the case that all the tangles involved in the construction of the link diagram have at most k crossings (where k is a constant independent of the total number n of crossings in the link diagram), we show that the computation time needed to calculate the Jones polynomial of the link diagram is bounded above by O(nk). In particular, we show that the Jones polynomial of any Conway algebraic link diagram with n crossings can be computed in O(n²) time. A consequence of this result is that the Jones polynomial of any Montesinos link and two bridge knot or link of n crossings can be computed in O(n²) time.     

The Path-Connectivity of s-Elementary Frame Wavelets with Frame MRA

MRA wavelets have been widely studied in recent years due to their applications in signal processing. In order to understand the properties of the various MRA wavelets, it makes sense to study the topological structure of the set of all MRA wavelets. In fact, it has been shown that the set of all MRA wavelets (in any given dimension with a fixed expansive dilation matrix) is path-connected. The current paper concerns a class of functions more general than the MRA wavelets, namely normalized tight frame wavelets with a frame MRA structure. More specifically, it focuses on the parallel question on the topology of the set of all such functions (in the given dimension with a fixed dilation matrix): is this set path-connected? While we are unable to settle this general path-connectivity problem for the set of all frame MRA normalized tight frame wavelets, we show that this holds for a subset of it. An s-elementary frame MRA normalized tight frame wavelets (associated with a given expansive matrix A as its dilation matrix) is a normalized tight frame wavelet whose Fourier transform is of the form $\frac{1}{\sqrt{2\pi}}\chi_{E}$ for some measurable set E?? ^d . In this paper, we show that for any given d×d expansive matrix A, the set of all (A-dilation) s-elementary normalized tight frame wavelets with a frame MRA structure is also path-connected.     

正仲氢催化转化性能低温测试装置设计

液氢在新能源、工业生产等领域有重要的用途.结合液氢生产中正仲氢转化的特点,提出了一种可实现多种转化方式的正仲氢催化转化性能低温测试装置设计.通过液氮预冷和G-M制冷机实现正仲氢转化温度可控、通过设置正仲氢预反应实现入口原料仲氢组分可控,并采用更换可拆卸转化器和热沉方式实现多种正仲氢转化方式.实现不同工况下(等温绝热、连...     

铯原子气室中相干布居俘获的参数依赖关系研究

基于铯原子基态6S_1/2的两个超精细能级（F=3与F=4）与激发态6P_3/2的超精细能级（F′=4）构成的Λ型三能级系统,采用室温下的未充缓冲气体和充有分压为266.6 Pa的氖气作为缓冲气体的铯原子气室对于相干布居俘获（CPT）的参数依赖关系进行了实验研究和理论分析.主要研究了CPT信号的半高全宽和幅度对于频率差为铯原子基态6S_1/2的超精细分裂（9.19263177 GHz）且位相锁定的两激光束的功率、光强比值、光斑直径、磁屏蔽之后的剩余磁场以及是否充缓冲气体等实验参数的依赖关系.在优化的实验参数条件下获得了约340 Hz的CPT信号半高全宽.     

Widely and continuously tunable optical parametric generator infrared laser

The experimental results of a high efficiency infrared laser are demonstrated on a quasi phase matched optical parametric generator in PPMgLN (5% MgO doping) pumped by a 1064 nm Nd:YAG laser. A broad continuous signal spectrum 1.56?C1.67 ??m are obtained by tuning the crystal temperature from 20°C to 200°C. When the average pump power is 1.82 W with about 70 ns pulse duration operating at a repetition rate of 10 kHz, the maximum total output power of the PPMgLN OPG is about 323.58 mW consisting of 210 mW of 1.639 ??m signal radiation and 113.58 mW of 3.02 ??m idler radiation.     

原位制备SrSb2O6/g-C3N4新型二维异质结用于可见光催化降解四环素的研究

本文采用高温固相原位制备新型二维SrSb2O6/g-C3N4异质结光催化复合材料,并将其用于可见光催化降解四环素.通过XRD和FT-IR谱对其结构进行表征.光催化降解实验表明,异质结复合材料较母体g-C3N4和SrSb2O6而言,光催化效率均得到了提升.其中,异质结样品SSO-CN-2对四环素溶液具有最优的光催化降解效...     

Isolation and Reactivity of Homoleptic Diphosphene Lead Complexes

Due to their limited capacity for π-backdonation, isolation of π-complexes of main-group elements remains a great challenge. We report herein the synthesis of a homoleptic diphosphene lead complex ( 2 ) from the degradation of P₄ with a bis(germylene)-stabilized Pb(0) complex. Structural and computational studies showed that 2 possesses significant π bonding interactions between Pb atom and diphosphene ligands, which is reminiscent of transition-metal diphosphene complexes. Consistent with its unique electronic structure, complex 2 can deliver Pb(0) atoms to perform redox reaction with an iminoquinone to produce a cyclic plumbylene ( 4 ) and perform 2,5-dimethyl-3,4-dimethylimidazol-1-ylidene (IMe₂Me₂) induced phosphorus cation abstraction to give an anionic PbP₃ complex ( 6 ).     

ZnF2-Riched Inorganic/Organic Hybrid SEI: in situ-Chemical Construction and Performance-Improving Mechanism for Aqueous Zinc-ion Batteries

Uncontrolled dendrites growth and serious parasitic reactions in aqueous electrolytes, greatly hinder the practical application of aqueous zinc-ion battery. On the basis of in situ-chemical construction and performance-improving mechanism, multifunctional fluoroethylene carbonate (FEC) is introduced into aqueous electrolyte to construct a high-quality and ZnF₂-riched inorganic/organic hybrid SEI (ZHS) layer on Zn metal anode (ZMA) surface. Notably, FEC additive can regulate the solvated structure of Zn²⁺ to reduce H₂O molecules reactivity. Additionally, the ZHS layer with strong Zn²⁺ affinity can avoid dendrites formation and hinder the direct contact between the electrolyte and anode. Therefore, the dendrites growth, Zn corrosion, and H₂ evolution reaction on ZMA in FEC-included ZnSO₄ electrolyte are highly suppressed. Thus, ZMA in such electrolyte realize a long cycle life over 1000 h and deliver a stable coulombic efficiency of 99.1 % after 500 cycles.     

An Isolable Bis(Germylene)-Stabilized Plumbylone

We report herein the synthesis of a stable plumbylone ( 3 ) by reduction of a bromodigermylplumbylene ( 2 ) with 2.2 equiv of potassium graphite (KC₈). The molecular structure of 3 was established by a single-crystal X-ray diffraction study and features a two-coordinated Pb center with an acute Ge−Pb−Ge bond angle. Computational studies showed that this complex ( 3 ) possesses a singlet electronic ground state with a Pb⁰ center. Its high thermal stability can be most likely ascribed to the delocalization of π electrons over the Ge−Pb−Ge moiety. A preliminary reactivity study demonstrates that complex 3 can deliver Pb⁰ atoms to an organic azide producing a tetrameric imido complex [(PbNDipp)₄] (Dipp=2,6-ⁱPr-C₆H₃, 4 ) and perform a metathesis reaction with GeCl₂⋅dioxane to produce a bis(germylene)-stabilized germylone ( 5 ), highlighting the synthetic utility of 3 .     

Detachable Porous Organic Polymers Responsive to Light and Heat

Stimuli-responsive porous materials have captured much attention due to the on-demand tunable properties. Most reported stimuli-responsive porous materials are based on molecule isomerism or host-guest interaction, and it is highly desired to develop new types based on different responsive mechanism. Herein, inspired by natural cells which have the ability to fuse and divide induced by external stimulation, we report a new type of stimuli-responsive porous material based on detachment mechanism. A detachable porous organic polymer, namely DT-POP-1, is fabricated from the polymerization of anthracene-containing monomer (AnMon) when irradiated by 365 nm UV light. DT-POP-1 can detach into the monomer AnMon when irradiated with 275 nm UV light or heat. Such polymerization/detachment is reversible. The detachment results in a big difference in porosity and adsorption capacity, making the present detachable porous polymer highly promising in adsorptive separation and drug delivery.