一类具有欧拉形式的中立型微分方程的振动性

研究具有欧拉形式的无界时滞中立型微分方程解的振动性，给出了方程振动的几个充分条件。     

Hybrid optoelectronic bistability in a fiber Bragg grating by use of a tunable fiber laser

We report the observation of hybrid optoelectronic bistability in a fiber Bragg grating (FBG) by use of an electro-optically tuned cw fiber laser in which another wavelength-matched FBG is employed to constitute a tunable resonant cavity. The potential application of such a device as a fiber-optic sensor is also discussed.     

Synthesis of carbon nitride nanotubes with the C(3)N(4) stoichiometry via a benzene-thermal process at low temperatures

In this communication, we first report the direct synthesis of high-quality carbon nitride nanotubes (CNNTs) with inner diameters of 50-100 nm and wall thicknesses of 20-50 nm with the C(3)N(4) stoichiometry on a high-yield of 40%via a simple benzene-thermal process involving the reaction of C(3)N(3)Cl(3) with NaN(3) in a Teflon-lined autoclave at 220 [degree]C without using any catalyst or template.     

Cycles in 2-connected graphs

Let be a class of graphs on n vertices. For an integer c, let be the smallest integer such that if G is a graph in with more than edges, then G contains a cycle of length more than c. A classical result of Erdös and Gallai is that if is the class of all simple graphs on n vertices, then . The result is best possible when n-1 is divisible by c-1, in view of the graph consisting of copies of K_c all having exactly one vertex in common. Woodall improved the result by giving best possible bounds for the remaining cases when n-1 is not divisible by c-1, and conjectured that if is the class of all 2-connected simple graphs on n vertices, thenwhere , 2tc/2, is the number of edges in the graph obtained from K_c+1-t by adding n-(c+1-t) isolated vertices each joined to the same t vertices of K_c+1-t. By using a result of Woodall together with an edge-switching technique, we confirm Woodall's conjecture in this paper.     

EPR parameters and defect structures of the off-center Ti ion on the Sr site in neutron-irradiated SrTiO3 crystal

The EPR parameters (g factors and hyperfine structure constants A) for the tetragonal Ti³⁺ center in cubic phase and the rhombic Ti³⁺ center in tetragonal phase in the neutron-irradiated SrTiO₃ crystals are calculated from the third-order perturbation formulas of EPR parameters for d¹ ions. These low-symmetry Ti³⁺ centers in both phases of SrTiO₃ are due to the Ti³⁺ ion at “off center” on the Sr²⁺ site. From the calculation, the defect models (including the direction and magnitude of the Ti³⁺ off-center displacement) of the two Ti³⁺ centers in SrTiO₃ are estimated and the EPR parameters of both Ti³⁺ centers are reasonably explained on the basis of the defect models. The results are discussed.     

A note on 3‐partite graphs without 4‐cycles

Let $C_4$ be a cycle of order 4. Write $ex\left(n,n,n,C_4\right)$ for the maximum number of edges in a balanced 3‐partite graph whose vertex set consists of three parts, each has $n$ vertices that have no subgraph isomorphic to $C_4$. In this paper, we show that $ex\left(n,n,n,C_4\right)\ge \frac{3}{2}n\left(p+1\right)$, where $n=\frac{p\left(p?1\right)}{2}$ and $p$ is a prime number. Note that $ex\left(n,n,n,C_4\right)\le \left(\frac{3\sqrt{2}}{2}+o\left(1\right)\right)n^{\frac{3}{2}}$ from Tait and Timmons's works. Since for every integer $m$, one can find a prime $p$ such that $m\le p\le \left(1+o\left(1\right)\right)m$, we obtain that $\underset{n\to \infty }{\lim }\frac{ex\left(n,n,n,C_4\right)}{\frac{3\sqrt{2}}{2}{n}^{\frac{3}{2}}}=1$.     

Pressure controllable phase transition in MoTe2 by the interlayer band occupancy

High pressure can effectively control the phase transition of MoTe₂ in experiment, but the mechanism is still unclear. In this work, we show by first-principles calculations that the phase transition is suppressed and $1T^{\prime }$ phase becomes more stable under high pressure, which originates from the pressure-induced change of the interlayer band occupancies near the Fermi energy. Specifically, the interlayer states of $1T^{\prime }$ phase tend to be fully occupied under high pressure, while they keep partially occupied for the $T_d$ phase. The increase of the band occupancies makes the $1T^{\prime }$ phase more favorable in energy and prevents the structure changing from $1T^{\prime }$ to $T_d$ phase. Moreover, we also analyze the superconductivity under high pressure based on BCS theory by calculating the density of states and phonon spectra. Our results may shed some light on understanding the relationship between the interlayer band occupancy and crystal stability of MoTe₂ under high pressures.     

Enantiomeric separation of chiral pesticides by high performance liquid chromatography on cellulose tris-3,5-dimethyl carbamate stationary phase under reversed phase conditions

Twenty chiral pesticides were tested, of which seven samples were directly separated by HPLC using cellulose tris-3,5-dimethyl carbamate (CDMPC) chiral stationary phase under RP conditions. The influence of mobile phase composition and column temperatures from 0 degrees C to 40 degrees C on the separations were investigated. The mobile phases were methanol/water or ACN/water at a flow rate of 0.8 mL/min with UV detection at 230 or 210 nm. Epoxiconazole, terallethrin, benalaxyl, and diclofopmethyl were observed to obtain the baseline separation under suitable conditions and other pesticides pyriproxyfen, lactofen, and quizalofop-ethyl were separated partially. The retention factors (k) and selectivity factor (alpha) for the enantiomers of most investigated pesticides decreased upon increasing the temperature except for the selectivity factors (alpha) of pyriproxyfen in methanol/water. The ln alpha - 1/T plots for racemic chiral pesticides were linear at the range of 0-40 except for that of pyriproxyfen enantiomers in methanol/water and the chiral separations were controlled by enthalpy. Better separations were not always at low temperature. The elution orders of the eluting enantiomers were determined by a circular dichroism (CD) detector.