Decay rate for viscoelastic wave equation of variable coefficients with delay and dynamic boundary conditions

In this paper, we consider a viscoelastic wave equation of variable coefficients in the presence of past history with nonlinear damping and delay in the internal feedback and dynamic boundary conditions. Under suitable assumptions, we establish an explicit and general decay rate result without imposing restrictive assumption on the behavior of the relaxation function at infinity by Riemannian geometry method and Lyapunov functional method.     

双核烷基咪唑过氧磷钨酸盐相转移催化剂合成及催化烯烃环氧化性能

合成并表征了一类双核长链烷基咪唑阳离子修饰的过氧磷钨杂多酸盐催化剂[Dnmin]1.5PW4O24,考察了催化剂在过氧化氢为氧源的烯烃环氧化反应中的催化活性.研究表明,这类催化剂在反应过程中表现出相转移催化现象,并具有较高的催化活性和选择性.其中,双核十二烷基咪唑杂多酸盐催化剂[D12min]1.5PW4O24的活性最佳,其环己烯转化率和环氧环己烷选择性分别达到97.7%和96.3%.催化剂在经过简单离心分离后可重复使用,重复使用4次后环己烯转化率和环氧环己烷选择性仍可分别达到72.4%和97.2%.催化剂[D12min]1.5PW4O24在其它几种烯烃的环氧化反应中均表现出相转移催化特性,且具有较高的催化活性.     

Intrinsic decay rate estimates for abstract wave equation with memory

In this paper, we consider an abstract wave equation in the presence of memory. The viscoelastic kernel g(t) is subject to a general assumption , where the function H(·)∈C¹(R⁺) is positive, increasing and convex with H(0)=0. We give the decay result as a solution to a given nonlinear dissipative ODE governed by the function H(s). Copyright © 2017 John Wiley & Sons, Ltd.     

On the decay and blow‐up of solution for coupled nonlinear wave equations with nonlinear damping and source terms

In this work, we consider a nonlinear coupled wave equations with initial‐boundary value conditions and nonlinear damping and source terms. Under suitable assumptions on the damping terms and source terms and initial data in the stable set, we obtain that the decay estimates of the energy function is exponential or polynomial by using Nakao's method. By using the energy method, we obtain the blow‐up result of solution with some positive or nonpositive initial energy. Copyright © 2016 John Wiley & Sons, Ltd.     

Blow up and global solutions for a quasilinear riser problem

In this paper, we consider an initial–boundary value problem to a riser vibrating with dissipative term in the equation. It is proved that under suitable conditions that the solution with a negative initial energy blows up in finite time. And we show that the solution with a nonnegative initial energy is global.     

Analysis of triterpenoids in <Emphasis Type="Italic">Ganoderma lucidum</Emphasis> using liquid chromatography coupled with electrospray ionization mass spectrometry

Triterpenoids extracted from Ganoderma lucidum (Leyss. ex Fr.) Karst were separated and characterized using optimized reversed-phase liquid chromatography with diode array detection and electrospray ion trap tandem mass spectrometry (HPLC-DAD-ESI-MS(n)). They could be classified into five types depending on the fragmentation behavior. All triterpenoids gave [M - H](-) and [2M - H](-) ions by electrospray ionization monitored in the negative ion mode; in addition, compounds of types III and IV gave prominent [M - H - H(2)O](-) ions and the unsaturated bond at C-20, 22 would reduce the abundance of [M - H - H(2)O](-) ion. The key fragmentation information was cleavage at C- and D-rings despite the predominant losses of H(2)O and CO(2). Compounds with hydroxyls at C-7 and C-15 would produce a list of b, b - 1, b - 2, and b - 16 ions attributed to cleavage of D-ring; if the second alcohol at C-15 were oxidized to ketone, the prominent cleavage would occur at C-ring and produce a group of ions of a; if C-7 were oxidized to ketone, transference of two hydrogen atoms would occur during the cleavage of rings and a list of ions about a + 2 and/or b + 2 would appear instead. The above fragmentations and regularities in fragmentation pathways were reported for the first time, and were implemented for the analysis of triterpenoids in G. lucidum. The chloroform extract was separated on a Zorbax SB-C(18) column, eluting with an acetonitrile-0.2% acetic acid gradient. A total of 32 triterpenoids, including six new ones, were identified or tentatively characterized based on the tandem mass spectra of the HPLC peaks.     

Analysis of multiplex endogenous estrogen metabolites in human urine using ultra-fast liquid chromatography–tandem mass spectrometry: A case study for breast cancer

A rapid, sensitive, specific and accurate analytical method of ultra-fast liquid chromatography combined with tandem mass spectrometry (UFLC–MS/MS) was established for simultaneous quantitative analysis of 16 distinct endogenous estrogens and their metabolites (EMs) in postmenopausal female urine. The quantitative method utilized a hydrolysis/extraction/derivatization step and a UFLC system to achieve separation in 16 min. The lower limit of quantitation for each estrogen metabolite was 2 pg mL⁻¹ with the percent recovery of a known added amount of estrogen at 93.2–109.3%. The intra-batch accuracy and precision for all analytes were 87.5–107.7% and 0.6–11.7%, respectively, while inter-batch accuracy and precision were 87.0–105.8% and 1.2–10.2%, respectively. Using this developed and validated method, the comprehensive metabolic profiling of 16 EMs in urine samples of 86 postmenopausal female breast cancer patients and 36 healthy controls was investigated by systematic statistical analysis. As a result, the circulating levels of 6 EMs were found to be different by a comparison of patients and healthy controls. The parent estrogens, estrone (E1) and 17β-estradiol (E2), as well as 2-hydroxyestradiol (2-OHE2) and 4-hydroxyestradiol (4-OHE2) were produced in higher abundance, whereas 16α-hydroxyestrone (16α-OHE1) and 2-methoxyestradiol (2-MeOE2) were decreased in the breast cancer group. 2-OHE2 and 4-OHE2 in particular showed significant elevation in patients, which are consistent with the carcinogenic mechanism hypothesis that catechol estrogens can react with DNA via quinones, resulting in mutations to induce breast cancer. Thus, 2,4-hydroxylation may be the dominant metabolic pathway for parent estrogens rather than 16α-hydroxylation. The lower level of 2-MeOE2 in the breast cancer group was believed to correlate with its protective effect against tumor formation. This study could provide valuable information on the association of the EM metabolic pathway with carcinogenesis as well as identify potential biomarkers for estrogen-induced breast cancer risk.