N=2^t点DFT的快速卷积算法

从所周知,循环卷积和离散富里叶变换(DFT)可以互相计算,只要得到其中一个的快速算法就可导出另一个的快速算法。循环卷积目前已有乘法量为O(N)的最佳算法(特别是当N较小时),为此关键是如何将DFT转化为循环卷积,当DFT的长度N=p(p为素数),Rader利用有限域GF(p)的乘法群是循环群就成功地将p点DFT转化为Q(p)(F(p)为户的Euler函数)点循环卷积;当N=p~e时,由于商环Z/(p~e)存在F(p~c)阶元素,人们也成功地将p~c点DFT转化为P(p~(c-1))一系列循环卷积,即一个y(p~c)点循环卷积,二个P(p~(c-1))点     

Microstructure evolution and dielectric properties of Ba<Subscript>5-x</Subscript>Na<Subscript>2x</Subscript>Nb<Subscript>10</Subscript>O<Subscript>30</Subscript> ceramics with different Ba–Na Ratios

The tetragonal tungsten bronzes of Ba5−xNa_2x Nb₁₀O₃₀ (BNN, 0.5≤ x≤1.3) ceramics were synthesized using the solid state reaction method. The sintering behavior and dielectric characteristics of the BNN ceramics, as a function of the Ba-Na ratio, were examined. Densification of the samples with excess compositions of Ba and Na was higher than that of the stoichiometric BNN sample. The maximum dielectric constant and the Curie temperature showed highest values at the stoichiometric composition and decreased as the composition shifted away from the stoichiometry. in order to obtain a quantitative evaluation of the diffuse phase transition (DPT) behavior of the BNN ceramics, γ and C/κ_max were calculated. The weakest DPT behavior was observed in the stoichiometric composition. An increase in the DPT is in correlation with the increase in the number of ways of cation distribution by the disordered occupation of Ba and Na and the vacancies in the A1 and A2 sites of the tungsten bronze structure.     

NMR-based characterization of a novel yellow chlorophyll catabolite, Ed-YCC,isolated from Egeria densa

A novel yellow chlorophyll catabolite, Ed-YCC, was isolated from leaves detached from Egeria densa shoots, in which chlorophyll degradation and anthocyanin synthesis were induced in 0.1 M fructose solution under light illumination as a plant senescence process, a model of autumnal leaf coloration. Structure elucidation was accomplished by various NMR techniques including 2D-INADEQUATE.     

An efficient method to synthesize HMX by nitrolysis of DPT with N_2O_5 and a novel ionic liquid

A novel polyethylene glycol(PEG)-200-based dicationic acidic ionic liquid(PEG200-DAIL)was used to synthesize HMX from DPT by nitrolysis with N2O5.It was found that either N2O5 or PEG200-DAIL could improve the yield.Furthermore,the combined use of PEG200-DAIL and N2O5 could increase the yield of HMX to 64%with the used quantity of HNO3 decreased.dramatically     

Comprehensive relativistic ab initio and density functional theory studies on PtH, PtF, PtCl, and Pt(NH(3))(2)Cl(2)

Platinum monohydride is taken as an example to compare the performance of various relativistic and correlation approaches, such as all-electron DPT (direct perturbation theory), ECP (effective core potential); RSPT2, RSPT3 (second- and third-order multireference Rayleigh-Schr?dinger perturbation theory), CCSD(T) (coupled-cluster with singles, doubles, and perturbative triples), as well as the four-component relativistic density functional theory. It is shown that first-order DPT performs significantly better than the (first-order) Breit-Pauli Hamiltonian. The performance of different approaches for the excitation energies of the platinum diatomics is discussed critically. The molecular spectroscopic constants for PtF and PtCl are predicted for the first time. The geometric data for several isomers of cis- and trans-Pt(NH(3))(2)Cl(2) are reported. The corresponding energetic data are calculated at relativistic all-electron and ECP-CCSD(T) as well as four-component relativistic density functional levels of theory. Contrary to previous results, it is found that the two C(2v) isomers of cis-Pt(NH(3))(2)Cl(2) are marginally separated in energy, which could be ascribed to Cl-H interactions.     

不饱和类锗烯H2C=GeLiCl的DFT研究

采用密度泛函理论方法, 在B3LYP/6-311G(d, p)水平上研究了不饱和类锗烯H2C=GeLiCl的结构及异构化反应. 结果表明, 不饱和类锗烯H2C=GeLiCl有三种平衡构型, 其中非平面的p-配合物型构型能量最低, 是其存在的主要构型. 对平衡构型间异构化反应的过渡态进行了计算,求得了转化势垒. 计算预言了最稳定构型的振动频率和红外吸收强度.     

Electrical studies on Zr-modified Bi3.25La0.75Ti3O12: a promising FRAM ceramic

Zr-modified Auruvillius family of lanthanum bismuth titanate, namely Bi_3.25La_0.75Ti_3?xZr_xO₁₂ (BLTZ, x = 0, 0.1, 0.3, 0.5, 0.7 and 1), was prepared by solid-state reaction method. Dielectric properties of the ceramics were studied as a function of temperature. Hysteresis measurements were also performed. Among the composition, Bi_3.25La_0.75Ti_2.9Zr_0.1O₁₂ (BLTZ1) showed large remnant polarization compared to the promising ceramic, namely Bi_3.25La_0.75Ti₃O₁₂. The results were corroborated with the pyroelectric, electric polarization and Raman spectroscopic data.     

Double proton transfer and one-electron oxidation behavior in double H-bonded glycinamide-glycine complex in the gas phase

The behaviors of double proton transfer (DPT) occurring in a representative glycinamide-glycine complex have been investigated employing the B3LYP/6-311++G** level of theory. Thermodynamic and especially kinetic parameters, such as tautomerization energy, equilibrium constant, and barrier heights have been discussed, respectively. The relevant quantities involved in the DPT process including geometrical changes, interaction energies, and deformation energies have also been studied. Analogous to that of tautomeric process assisted with a formic acid molecule, the participation of a glycine molecule favors the proceeding of the proton transfer (PT) for glycinamide compared with that without mediator-assisted case. The DPT process proceeds with a concerted mechanism rather than a stepwise one because no zwitterionic complexes have been located during the DPT process. The barrier heights are 12.14 and 0.83 kcal/mol for the forward and reverse directions, respectively. However, both of them have been reduced by 3.10 and 2.66 kcal/mol to 9.04 and -1.83 kcal/mol with further inclusion of zero-point vibrational energy (ZPVE) corrections, where the disappearance of the reverse barrier height implies that the reverse reaction should proceed with barrierless spontaneously, analogous to those of DPTs occurring between glycinamide and formic acid (or formamide). Additionally, the oxidation process for the double H-bonded glycinamide-glycine complex has also been investigated. The oxidated product is characterized by a distonic radical cation due to the fact that one-electron oxidation takes place on glycine fragment and a proton has been transferred from glycine to glycinamide fragment spontaneously. As a result, the vertical and adiabatic ionization potentials for the neutral complex have been determined to be about 8.71 and 7.85 eV, respectively, where both of them have been reduced by about 0.54 (1.11) and 0.75 (1.13) eV relative to those of isolated glycinamide (glycine) due to the formation of the intermolecular H-bond.     

Synthesis of Deuterium Labeled Tryptamine Derivatives

The synthesis of deuterium labeled tryptamine derivatives, [2‐(1H‐indol‐3‐yl)‐[²H₄]‐ethyl]‐dimethylamine (DMT), [²H₁₀]‐diethyl‐[2‐(1H‐indol‐3‐yl)‐ethyl]‐amine (DET), [2‐(1H‐indol‐3‐yl)‐ethyl]‐[²H₆]‐dipropyl‐amine (DPT) and [²H₂]‐alpha‐methyltryptamine (AMT) is described. The isotopically labeled compounds are used as internal standards in gas chromatography‐mass spectrometry (GC‐MS) assays.     

Convenient synthesis of 4H-1,2,4-triazole-3-thiols using di-2-pyridylthionocarbonate

We report here the convenient synthesis of 4H-1,2,4-triazole-3-thiols using di-2-pyridyl-thionocarbonate as the thiocarbonyl transfer reagent. This method is suitable for microplate parallel synthesis and produces samples in screening-ready condition. It uses two large sets of building-blocks: amines and hydrazides.