一个R2上含双曲函数核的Hilbert型不等式

通过引入参数，构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开，建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用，通过赋予参数不同的值，建立了一些有意义的特殊结果。     

Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network

In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy’s law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D–1D coupled model.     

A novel UPLC–MS/MS method for simultaneous quantification of trigonelline, 4-hydroxyisoleucine,and diosgenin from Trigonella foenum-graecum extract: Application to pharmacokinetic study in healthy and type 2 diabetic rats

Trigonelline (TR), 4-hydroxyisoleucine (4-HI), and diosgenin (DG) are the main bioactives of the purified standardized extract of the popular plant Trigonella foenum-graecum L. (TFG), and it has been proven effective for the treatment of various diseases. However, to the best of our knowledge, no study has investigated the pharmacokinetic parameters of purified standardized T. foenum-graecum extract in normal and diabetic Wistar rats. The present study has developed and validated a rapid, reliable, and sensitive simultaneous ultra-performance liquid chromatography MS method to estimate these bioactives. The chromatographic separation was achieved using methanol, acetonitrile, and 0.1% formic acid with the ideal gradient flow system on a BEH Shield RP 18 column. A positive electrospray ionization mode was selected to estimate m/z values of TR (138.14 > 94.63), 4-HI (148.19 > 74.08), and DG (415.54 > 271.33). The method was robust and reproducible over the linearity range of 60–5000, 6–5000, and 15–5000 ng/mL for TR, 4-HI, and DG, respectively. Using this novel validated method, we investigated the pharmacokinetic parameters of bioactives using Phoenix WinNonlin version 8.0 (Certera) in normal and diabetic rats. The assay was successfully applied for the estimation of pharmacokinetic parameters using noncompartmental analysis. This investigation shows that the absorption rate increased, whereas distribution and elimination processes slowed down in diabetic rats compared with normal rats.     

von Neumann’s trace inequality for Hilbert–Schmidt operators

von Neumann’s inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”.     

白云石制备似立方体状方解石型碳酸钙晶体及其机理研究

以轻烧白云石粉、氯化铵和二氧化碳为原料,在未使用晶型控制剂的情况下,通过蒸氨-沉钙过程制备出了似立方体状碳酸钙。研究了反应温度、溶液中钙离子浓度、通气速率、搅拌速度以及陈化时间对碳酸钙中方解石相含量以及晶体形貌的影响,并探索了沉钙反应的晶型控制机理。结果表明,在反应温度40 ℃、钙离子浓度0.05 mol/L、通碳速率100 mL/min、搅拌速度400 r/min和陈化时间2 h的条件下,制备出形貌规整、粒径分布均匀的似立方体状碳酸钙,平均粒径为5~10 μm。该研究为提升白云石的使用价值、生产高附加价值的碳酸钙产品,以及提高白云石资源的利用率提供理论基础。     

Sobolev-Lorentz范数约束下的次临界型Adams不等式

本文在Sobolev-Lorentz空间W²L^2,q(R⁴)的范数约束下得到了一个最佳的二阶次临界型Adams不等式.进一步,当次临界指标逼近最佳常数时,得到了Adams泛函的上、下界的估计.本文主要采用了Lam和Lu[A new approach to sharp MoserTrudinger and Adams type inequalities:a rearrangement-free argument,J.Diff Equ.,2013,255(3):298-325]的分割水平集方法.