Stimulation of Microvascular Networks on Sulfonated Polyrotaxane Surfaces with Immobilized Vascular Endothelial Growth Factor

Modulation of material properties and growth factor application are critical in constructing suitable cell culture environments to induce desired cellular functions. Sulfonated polyrotaxane (PRX) surfaces with immobilized vascular endothelial growth factors (VEGFs) are prepared to improve network formation in vascular endothelial cells. Sulfonated PRXs, whereby sulfonated α‐cyclodextrins (α‐CDs) are threaded onto a linear poly(ethylene glycol) chain capped with bulky groups at both terminals, are coated onto surfaces. The molecular mobility of sulfonated PRX surfaces is modulated by tuning the number of threading α‐CDs. VEGF is immobilized onto surfaces with varying mobility. Low mobility and VEGF‐immobilization reinforce cell proliferation, yes‐associated protein activity, and rhoA, pdgf, ang‐1, and pecam‐1 gene expression. Highly mobile surfaces and soluble VEGF weakly affect these cell responses. Network formation is strongly stimulated in vascular endothelial cells only on low‐mobility VEGF‐immobilized surfaces, suggesting that molecular mobility and VEGF immobilization synergistically control cell function.     

A MODAL TESTING METHOD FOR CANTILEVER BEAM1)

基于欧拉-伯努利梁理论得到悬臂梁自由振动的振型函数。通过数值计算得出实验用的悬臂梁前五阶振型的节点位置及其与梁长的比值。考虑传感器对悬臂梁固有频率的影响,建立梁-传感器模型进行仿真分析并得出悬臂梁前五阶固有频率。基于节点位置和测点位置,在实验中选择激励点。将具体实验的结果与梁-传感器仿真模型结果进行对比,通过前五阶固有频率的误差分析,发现仿真分析结果与实验结果误差最高为 1.3%。研究完整地叙述了悬臂梁的模态测试流程,可为工程技术人员的模态测试起一定的指导作用。     

砂土串囊式充气锚杆承载力的研究

在砂土地层中,串囊式充气锚杆的研究还比较少,其承载特性及受力机理尚不明确。本文基于莫尔-库仑模型和Vesic圆孔扩张理论法,分别对圆柱体、球体、组合体、椭球体假设下的串囊式充气锚杆的扩大段进行计算分析。并将计算结果与试验得到的实测值进行对比。结果表明:四种形状假设中椭球体的形状假设理论值与实测值的误差最小,仅为8.35%。通过拟合试验数据,并引入与端阻力和侧摩阻力有关的两个系数对承载力公式进行修正,得到了抗拔承载力的经验公式。     

Multifold factorizations of cyclic groups into subsets

Let $(G,+)$ be an abelian group. A finite multiset A over G is said to give a λ-fold factorization of G if there exists a multiset B over G such that each element of G occurs λ times in the multiset $A+B:=\{a+b:a\in A,b\in B\}$. In this article, restricting G to a cyclic group, we will provide sufficient conditions on a given multiset A under which the exact value or an upper bound of the minimum multiplicity λ of a factorization of G can be given by introducing a concept of ‘lcm-closure’. Furthermore, a couple of properties on a given factor A will be shown when A has a prime or prime power order (cardinality). A relation to multifold factorizations of the set of integers will be also glanced at a general perspective.     

Correlation between Boron Isotope of Coral Acropora and pH Value of Seawater Surface

A water circulation system with the almost same element composition and socket type was adopted in coral Acropora culture under different seawater pH value conditions and the data of the relationship between boron isotopic compositions of coral and seawater pH value by thermoelectric ionization mass spectrometer were obtained. According to the correlations between α_carb-3 of coral and the pH value of cultured seawater, α_carb-3 was not a constant but related to pH value, indicating that B(OH)₃ also incorporated carbonate. Therefore, the theoretical formula could not be used to calculate the seawater pH value from the δ¹¹B_carb value of the measured marine biological carbonate. The empirical equations obtained experimentally would be an alternative method to calculate the seawater pH value. In addition, the mixed precipitation of CaCO₃ and Mg(OH)₂ was found in aquaculture tanks with high pH value, and the δ¹¹B of the solid was significantly higher than that of cultured seawater. The result indicated that the presence of Mg(OH)₂ had a significant effect on the boron isotope fractionation, which deserved our attention.     

Shape morphing and topology optimization of fluid channels by explicit boundary tracking

An integrated shape morphing and topology optimization approach based on the deformable simplicial complex methodology is developed to address Stokes and Navier‐Stokes flow problems. The optimized geometry is interpreted by a set of piecewise linear curves embedded in a well‐formed triangular mesh, resulting in a physically well‐defined interface between fluid and impermeable regions. The shape evolution is realized by deforming the curves while maintaining a high‐quality mesh through adaption of the mesh near the structural boundary, rather than performing global remeshing. Topological changes are allowed through hole merging or splitting of islands. The finite element discretization used provides smooth and stable optimized boundaries for simple energy dissipation objectives. However, for more advanced problems, boundary oscillations are observed due to conflicts between the objective function and the minimum length scale imposed by the meshing algorithm. A surface regularization scheme is introduced to circumvent this issue, which is specifically tailored for the deformable simplicial complex approach. In contrast to other filter‐based regularization techniques, the scheme does not introduce additional control variables, and at the same time, it is based on a rigorous sensitivity analysis. Several numerical examples are presented to demonstrate the applicability of the approach.     

Extremal generalized centralizers in matrix algebras

We describe matrices with extremal generalized centralizers over algebraically closed fields.     

The improvement of numerical modeling in the solution of incompressible viscous flow problems using finite element method based on spherical Hankel shape functions

In this paper, the finite element method with new spherical Hankel shape functions is developed for simulating 2‐dimensional incompressible viscous fluid problems. In order to approximate the hydrodynamic variables, the finite element method based on new shape functions is reformulated. The governing equations are the Navier‐Stokes equations solved by the finite element method with the classic Lagrange and spherical Hankel shape functions. The new shape functions are derived using the first and second kinds of Bessel functions. In addition, these functions have properties such as piecewise continuity. For the enrichment of Hankel radial basis functions, polynomial terms are added to the functional expansion that only employs spherical Hankel radial basis functions in the approximation. In addition, the participation of spherical Bessel function fields has enhanced the robustness and efficiency of the interpolation. To demonstrate the efficiency and accuracy of these shape functions, 4 benchmark tests in fluid mechanics are considered. Then, the present model results are compared with the classic finite element results and available analytical and numerical solutions. The results show that the proposed method, even with less number of elements, is more accurate than the classic finite element method.