Smarandache函数在两数列上的下界估计

设S(n)是Smarandache函数,其中n是一正整数.讨论Smarandache函数S(n)在数列F((2k),1)=F(n,1)=n2n+1(n=2k)与数列G(2n,1)=(2n)2n+1上的下界估计.基于初等方法证明了:当偶数n≥6时,有S(F((2k),1))=S(F(n,1))≥6×2n+1;当n≥4时,有S(G(2n,1))≥6×2n+1.     

基于回波平移序列的快速三维磁共振温度成像方法

高强度聚焦超声（HIFU）是一种无创的热消融疗法，为保证其安全性和有效性，需要一种精度高、速度快的测温方法在其治疗过程中对温度进行监控.基于质子共振频率位移（PRFS）的磁共振温度成像（MRT）对温度具有较高的灵敏度，且与温度具有良好的线性关系，因此常被用于引导HIFU治疗.然而在实际应用中，HIFU治疗的最大隐患在于可能造成表皮灼伤，并且灼伤区域可能与焦点区域相隔较远.因此MRT的监控范围十分重要.本文基于三维回波平移成像序列，结合可控混叠的空间并行成像技术，实现了时间分辨率为3 s的快速三维温度成像.为了验证该方法的精度，本文首先设计了仿体降温实验，利用光纤温度计验证回波平移序列测温的准确度和精确度.然后在室温条件下扫描离体猪肉组织，对比加速前后的MRT的测温精确度.在HIFU加热条件下扫描离体猪肉组织，对比加速前后的MRT的测温准确度.结果显示，本文提出的方法可以在3 s内完成三维温度精准测量，对于HIFU治疗的安全监控具有重要意义.     

基于有限体积虚拟区域方法的两相流动直接模拟

为提高计算效率，提出有限体积法离散下的虚拟区域颗粒两相流动直接模拟方法.在控制方程中加入相应的虚拟区域源项，保证了颗粒内部的刚体运动特性.该源项中含有颗粒信息部分及流体信息部分.在每次迭代后，对源项中的流体信息部分进行更新，从而更好地保证颗粒内速度的刚体分布.计算静止颗粒圆柱绕流及单个颗粒的沉降过程，验证了算法的准确性.     

Direct meta-C−H Perfluoroalkenylation of Arenes Enabled by a Cleavable Pyrimidine-Based Template

The development of efficient and mild methods for the synthesis of organofluorine compounds is of foremost interest in various fields of chemistry. A direct pyrimidine-based selective meta-C−H perfluoroalkenylation of arenes involving several commercially available perfluoroolefins is described. The synthetic versatility of the protocol is demonstrated by an extensive substrate scope including different benzylsulfonyl, alkylarene and phenylacetic acid scaffolds. The generality of this methodology including the meta-C−H perfluoroalkenylation of Ibuprofen, the facile cleavage of the directing group and gram-scale reactions are presented.     

Thermoresponsive polymersome from a double hydrophilic block copolymer

The article describes synthesis and thermally triggered self‐assembly of a Poly (ethylene oxide)‐block‐poly (N‐insopropylacrylamide) (PEO‐b‐PNIPAm) in aqueous medium. At rt, the polymer remains as unimer, however, at lower critical solution temperature (LCST) of PNIPAm (32 °C), it forms a rather large undefined aggregate which at slightly elevated temperature (～40 °C) converges to well defined polymersome structure (Critical aggregation concentration = 0.45 mg/mL) with hydrodynamic diameter of 40–50 nm. By lowering the temperature, initial swelling of the compact vesicle followed by reversible disassembly to unimer was noticed. The polymersome exhibits encapsulation ability to a hydrophilic dye Calcein which can be spontaneously released by lowering the temperature below cloud point. Likewise a hydrophobic dye namely 8‐Anilino‐1‐naphthalenesulfonic acid (ANS) can also be encapsulated and released by thermal trigger. Detail photoluminescence studies reveal ANS dye can be used as a generalized probe molecule for detecting LCST of a thermoresponsive polymer by “fluorescence on” above LCST even by cursory observation. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2444–2451     

A novel chaotic image encryption scheme using DNA sequence operations

In this paper, we propose a novel image encryption scheme based on DNA (Deoxyribonucleic acid) sequence operations and chaotic system. Firstly, we perform bitwise exclusive OR operation on the pixels of the plain image using the pseudorandom sequences produced by the spatiotemporal chaos system, i.e., CML (coupled map lattice). Secondly, a DNA matrix is obtained by encoding the confused image using a kind of DNA encoding rule. Then we generate the new initial conditions of the CML according to this DNA matrix and the previous initial conditions, which can make the encryption result closely depend on every pixel of the plain image. Thirdly, the rows and columns of the DNA matrix are permuted. Then, the permuted DNA matrix is confused once again. At last, after decoding the confused DNA matrix using a kind of DNA decoding rule, we obtain the ciphered image. Experimental results and theoretical analysis show that the scheme is able to resist various attacks, so it has extraordinarily high security.     

Time‐dependent finite element simulations of a shear‐thinning viscoelastic fluid with application to blood flow

A new finite element method is developed to simulate time‐dependent viscoelastic shear‐thinning flows characterized by the generalized Oldroyd‐B model. The focus of the algorithm is improved stability through a free‐energy dissipative scheme by using low‐order piecewise‐constant finite element approximations for stress. The algorithm is further modified by incorporating a pressure‐projection method, a DG‐upwinding scheme, a symmetric interior penalty DG method to solve the elliptic pressure‐update equation and a geometric multigrid preconditioner. The improved stability and cost to accuracy is compared when using higher order discontinuous bilinear approximation, where in addition, we consider the influence of a slope limiter for these elements. The algorithm is applied to the 2D start‐up‐driven cavity problem, and the stability of the free energy is illustrated and compared between element choices. An application of the model to modelling blood in small arterioles and channels is considered by simulating pulsatile blood flow through a stenotic arteriole. The individual influences of viscoelasticity and shear‐thinning within the generalized Oldroyd‐B model are investigated by comparing results to the Newtonian, generalized Newtonian and Oldroyd‐B models. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite deformation swelling of a temperature-sensitive hydrogel cylinder under combined extension-torsion

The swelling behavior of a temperature-sensitive poly-N-isopropylacrylamide(PNIPAM) hydrogel circular cylinder is studied subjected to combined extension-torsion and varied temperature. In this regard, a semi-analytical solution is proposed for general combined loading. A finite element(FE) analysis is conducted, subjecting a hydrogel cylinder to the combined extension-torsion and the varied temperature to evaluate the validity and accuracy of the solution. A user-defined UHYPER subroutine is developed and verified under free and constrained swelling conditions. The FE results illustrate excellent agreement with the semi-analytical solution. Due to the complexity of the problem, some compositions and applied loading factors are analyzed. It is revealed that for larger cross-linked density and larger ending temperature, the cylinder yields higher stresses and smaller radial swelling deformation. Besides, the radial and hoop stresses increase by applying larger twist and axial stretch. The hoop stresses intersect at approximately R/Rout = 0.58, where the hoop stress vanishes. Besides, the axial force has direct and inverse relationships with the axial stretch and the twist, respectively. However, the resultant torsional moment behavior is complex, and the position of the maximum point varies significantly by altering the axial stretch and the twist.     

基于三维接触有限元分析的管片等效抗弯刚度和错台研究

针对盾构隧道管片接头等效抗弯刚度预测研究中，对梁-弹簧与三维模型整体等效性考虑的不充分，以三维接触有限元计算结果作为测量信息，借助基于挠度等效的反问题求解，提出了一种确定管片接头等效抗弯刚度的新方法；并利用不同轴力-偏心距组合下的反演结果，建立了基于Kriging代理模型的轴力-弯矩-等效抗弯刚度的非线性关系，提出了由此关联的管片结构非线性问题的数值求解方法。与三维有限元结果相比，所提方法可较为准确地预测管片结构的内力和变形，表现出良好的整体等效性。此外，借助三维接触有限元分析，进一步深入探讨了螺栓孔间隙与衬垫本构关系对管片纵向错台量的影响。     

Integral operators commuting with dilations and rotations in generalized Morrey-type spaces

We find conditions for the boundedness of integral operators $K$ commuting with dilations and rotations in a local generalized Morrey space. We also show that under the same conditions, these operators preserve the subspace of such Morrey space, known as vanishing Morrey space. We also give necessary conditions for the boundedness when the kernel is non-negative. In the case of classical Morrey spaces, the obtained sufficient and necessary conditions coincide with each other. In the one-dimensional case, we also obtain similar results for global Morrey spaces. In the case of radial kernels, we also obtain stronger estimates of $Kf$ via spherical means of $f$. We demonstrate the efficiency of the obtained conditions for a variety of examples such as weighted Hardy operators, weighted Hilbert operator, their multidimensional versions, and others.