通过超宽139La固体核磁共振波谱研究层状La(OH)2NO3

层状稀土氢氧化物是一类新型的稀土功能材料，本文采用固体核磁共振（SSNMR）方法研究了同时具备离子交换能力和非线性光学特性的层状La（OH）₂NO₃化合物，探讨了通过四极核CPMG（QCPMG）脉冲序列和变频谱图采集获取超宽¹³⁹La SSNMR谱图的方法，并描述了适用于此类实验的滤波方程和谱图重建方法.重建谱图同时包含四极核中心跃迁和卫星跃迁信息，本文使用QUEST软件对超宽¹³⁹La NMR谱图进行了模拟，获取的四极耦合常数C_Q和非对称因子η_Q均与CASTEP密度泛函理论计算值高度吻合.SSNMR实验结果证实层状La（OH）₂NO₃化合物属于非中心对称结构（P2₁），解决了对其结构长期以来存在的争论.     

关于不定方程x3-1=749y2

利用同余式、平方剩余、Pell方程的解的性质、递归序列证明了:不定方程x³-1=749y²仅有整数解(x,y)=(1,0).     

Efficient remainder rule

Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the given conditions, one may need to understand the concept of modulo arithmetic in number theory. The Chinese Remainder Theorem is a known method to solve these types of problems using modulo arithmetic. In this paper, an efficient remainder rule has been proposed based on basic mathematical concepts. These core concepts are as follows: basic remainder rules of divisions, linear equation in slope intercept form, arithmetic progression and the use of a graphing calculator. These are easily understood by students who have taken prealgebra or intermediate algebra.     

Nucleus Independent Chemical Shift (NICS) at Small Distances from the Molecular Plane: The Effect of Electron Density

When close to the molecular plane, the behavior of nucleus independent chemical shift (NICS) as a function of the distance from the molecular plane deviates from its behavior at larger distances. By using a dense grid of NICS-probes (BQs) it is shown that, when close to the molecular plane, maximal (absolute) NICS values are obtained above the atoms. These maxima move towards the center as the grid is elevated until the (absolute) maximum NICS is obtained at the center and stay there when the grid is further elevated. It is shown that this behavior is a result of the current density, which is influenced by the electron density, according to the Biot-Savart law, which, in turn, causes the induced magnetic field measured by the NICS. It is thus concluded that if magnetic aromaticity is studied, the NICS calculations should be carried out at a large enough distance so that only the π-ring current affects the NICS. At distances ≥2 Å, NICS(r)_π,zz=A+B*C^r. Using non-linear correlation for obtaining A, B and C and extrapolate to NICS(1)_π,zz and NICS(1.7)_π,zz is recommended as measures for aromaticity.     

Hypertension in Prenatally Undernourished Young-Adult Rats Is Maintained by Tonic Reciprocal Paraventricular–Coerulear Excitatory Interactions

Prenatally malnourished rats develop hypertension in adulthood, in part through increased α₁-adrenoceptor-mediated outflow from the paraventricular nucleus (PVN) to the sympathetic system. We studied whether both α₁-adrenoceptor-mediated noradrenergic excitatory pathways from the locus coeruleus (LC) to the PVN and their reciprocal excitatory CRFergic connections contribute to prenatal undernutrition-induced hypertension. For that purpose, we microinjected either α₁-adrenoceptor or CRH receptor agonists and/or antagonists in the PVN or the LC, respectively. We also determined the α₁-adrenoceptor density in whole hypothalamus and the expression levels of α_1A-adrenoceptor mRNA in the PVN. The results showed that: (i) agonists microinjection increased systolic blood pressure and heart rate in normotensive eutrophic rats, but not in prenatally malnourished subjects; (ii) antagonists microinjection reduced hypertension and tachycardia in undernourished rats, but not in eutrophic controls; (iii) in undernourished animals, antagonist administration to one nuclei allowed the agonists recover full efficacy in the complementary nucleus, inducing hypertension and tachycardia; (iv) early undernutrition did not modify the number of α₁-adrenoceptor binding sites in hypothalamus, but reduced the number of cells expressing α_1A-adrenoceptor mRNA in the PVN. These results support the hypothesis that systolic pressure and heart rate are increased by tonic reciprocal paraventricular–coerulear excitatory interactions in prenatally undernourished young-adult rats.     

Assessment of DFT functionals with fluorine–fluorine coupling constants†

Density functional theory (DFT) calculations of nuclear magnetic resonance (NMR) spin–spin coupling constants (SSCCs) provide an important contribution for understanding experimentally observed values. It is known that calculated SSCCs using DFT methods correlate well with those experimentally measured. Unlike most of SSCCs, in fluorine compounds, fluorine–fluorine SSCC J_FF shows that the Fermi contact (FC) term is not dominant, particularly for J_FF in polyfluorinated organic molecules. In order to devise a DFT approach that would correctly reproduce the variation of SSCCs within a series of fluorine compounds, we test several DFT-based approaches, using different exchange and correlation functionals. Isotropic contributions to NMR fluorine–fluorine coupling constants (FC, spin-dipolar, SD, paramagnetic spin-orbit, PSO, and diamagnetic spin-orbit, DSO) have been calculated. Results show that DFT methods give appropriate values for ⁿJ_FF (n = 4 to 7), while for geminal and vicinal J_FF present large deviations from experimental values. For the latter SSCCs (²J_FF and ³J_FF), the four contributions (FC, SD, PSO and DSO) are analysed as a function of the local and nonlocal exchange in 1,1- and 1,2-difluoroethylene. Although FC term is not dominant for these SSCCs, the variation of this contribution with exchange is remarkable. On the other hand, SD and PSO contributions can be suitably computed without and with exact exchange, respectively.     

Multi-guasiparticle excitations of ~(91)Ru

The level structure in neutron-deficient nucleus 91Ru was investigated via the 58Ni(36Ar,2 plnγ)Ru reaction at a beam energy of 111 MeV.Charged particles,neutrons,and y-rays were emitted in this reaction and detected by the DIAMANT CsI ball,Neutron Wall,and the EXOGAM Ge clover array,respectively.In addition to the previously reported levels in 91Ru,new low-to-medium spin states were observed.Angular correlation and linear polarization measurements were performed to unambiguously determine spins and parities of the excited states in 91 Ru.The low-spin states of 91 Ru exhibit a scheme of multi-quasiparticle excitations,which is very similar to that of the neighboring N=47 isotone.These excitations have been interpreted in terms of the shell model.The calculations performed in the configuration space(p3/2,f5/2,p1/2,g9/2)reproduce the experimental excitation energies reasonably well,supporting the interpretation of the newly assigned positive-parity states in terms of the three quasiparticle configurationsπ(g9/2)^-2v(g9/2^-1 and v(g9/2)^-3.     

Mesogenic and optical properties of α,α′‐bis(4‐alkoxyphenylethynyl)oligothiophenes

Liquid crystalline α,α′‐bis(4‐alkoxyphenylethynyl)oligothiophenes (bi‐ and ter‐thiophene) have been synthesized and their mesogenic behaviour and optical properties investigated. They all exhibited a nematic mesophase, and compounds with long alkoxy chains also showed lamellar phases. Increasing the number of thiophene units increased both the transition temperatures and the mesophase ranges. As for their optical properties, incorporating more thiophene units results in red‐shifted absorption and emission spectra, slightly enhanced quantum efficiency, and a larger Stoke's shift. Most importantly, in terms of the absorption and emission maxima, the incorporation of one 4‐alkoxyphenylethynyl moiety was found to be equivalent to adding one thiophene ring.     

A study of aromatic three membered rings

The resonance energies (REs) of neutral three membered ring analogs of the cyclopropenyl cation, computed using block localized wave function (BLW) methods, reveal considerable variations. The RE's of cyclopropenes substituted with exocyclic double bonded groups C?X, (X = O, NH, CH₂, S, PH, SiH₂) increase with the electronegativity of X in the same row (SiH₂ < PH < S and CH₂ < NH < O). The extra cyclic resonance energies (ECREs) (an energetic measure of aromaticity based on comparisons with the RE's of acyclic models) of these derivatives range from +10.5 kcal/mol for cyclopropenone (X = O) (somewhat aromatic; the benzene ECRE is 29.3 kcal/mol) to ?2.4 kcal/mol (slightly antiaromatic) for X = SiH₂. Additional disubstitution of the C?C double bond by X′ groups (X′ = CH₃, NH₂, OH, SiH₃, PH₂, SH) increases the REs considerably, but has only small effects on the ECREs. Even the ECRE of deltic acid (X = O, X′ = OH) is only increased to +13.3 kcal/mol. The conclusion based on ECRE's, that all 12 of the three membered rings are only marginally aromatic/antiaromatic, is supported by the satisfactorily plot (R² = 0.92) of ECRE against values of NICS(0)_πzz (a superior nucleus chemical independent shift magnetic index of aromaticity), which range only from ?6.1 ppm (diatropic) for deltic acid (cf., ?35.5 ppm for benzene and ?14.2 ppm for the parent cyclopropenium ion) to +8.9 ppm (paratropic) for the silicon derivative, X = SiH₂, X′ = SiH₃. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

奇完全数的几个命题

本文证明形如3m-1的正整数不是完全数,由此推出当所有的qi≡-1(mod 3)时,奇数n=p~αП_(i=1)~sq_i~(2β_i)若是完全数,那么1/2σ(p~α)必是合数.指出k倍完全数的素因子必须满足一个不等式.运用此不等式证明当a≥n-2时形如a~(2~n)+b~(2~n)(a>b>0,a,b,n∈N~+)的奇数不是完全数.还指出当a与b都与3互素时,对于任意的正整数m,n,奇数a~(2~n)+b~(2~m)不是完全数.