Minimizing hydraulic resistance of a plant root by shape optimization

Optimum plant root structure that minimizes a single root’s hydraulic resistance to water-uptake is studied in this paper with the constraint of constant root volume. Hydraulic resistances under the slender body approximation and without such a limitation are considered. It is found that for large stele-to-cortex permeability ratio, there exists an optimum root length-to-base-radius ratio that minimizes the hydraulic resistance. A remarkable feature of the optimum root structure is that the optimum dimensionless stele conductivity depends only on a single geometrical parameter, the stele-to-root base-radius ratio. Once the stele-to-root base-radius ratio and the stele-to-cortex permeability ratio are given, the optimum root length-to-radius ratio can be found. While these findings remain to be verified by experiments for real plant roots, they offer theoretical guidance for the design of bio-inspired structures that minimize the hydraulic resistance for fluid production from porous media.     

ProTaper根管治疗系统去除3 种不同根充糊剂效果评价

目的 评价ProTaper 根管治疗系统（D1、D2、D3）去除3 种不同根充糊剂效果。方法 收集口腔科门诊拔除的上颌前牙和前磨牙36 颗，将其高压灭菌保存，按随机数字表法分为3 组，每组各12 颗。A 组采用牙胶尖并用冷压技术和AH plus 糊剂；B 组采用牙胶尖并用冷压技术和氧化锌丁香油糊剂；C 组采用牙胶尖并用冷压技术和Cortisomol 糊剂。3组均采用ProTaper 再治疗器械去除牙胶等根充物，测量根管内充填物的残留量及镍钛器械操作时间。结果 3 组进行根管重新治疗后，均在根管内留下部分填充材料，A 组留下的根管壁残留充填物较B 组、C 组多。A 组和B 组、C 组间根管壁残留充填物与根管总面积比值的差异均有统计学意义（均P＜0.05）。3 组操作时间的差异无统计学意义。结论 ProTaper Universal再治疗器械不能彻底清除原充填材料，牙胶尖配合使用AH pus 糊剂充填会产生更多的根管壁残留充填物。     

Multiscale reliability of physical systems based on the principle of least variance

Multiscale reliability places priority on the shifting of space-time scale while dual-scale reliability concentrates on time limits. Both can be ranked by applying the principle of least variance, although the prevailing criteria for assessment may differ. The elements measuring reliability can be ideally assumed to be non-interactive or interactive as a rule. Different formulations of the latter can be adopted to yield weak, strong, and mixed reliability depending on the application. Variance can also be referred to the average based on the linear sum, the root mean square, or otherwise. Preference will again depend on the physical system under consideration. Different space-time scale ranges can be chosen for the appropriate time span to failure. Up to now, only partial validation can be made due to the lack of lower scale data that are generated theoretically.A set of R-integrals is defined to account for the evolution effects by way of the root functions from Ideomechanics. The approach calls for a “pulsating mass” model that can connect the physical laws for the small and large bodies, including energy dissipation at all scale level. Non-linearity is no longer an issue when characterization of matter is made by the multiscaling of space-time. Ordinary functions can also be treated with minor modifications.The key objective is not to derive new theories, but to explain the underlying physics of existing test data, and the reliability of diversified propositions for predicting the time span to failure. Present and past investigations have remained at the micro-macro or mi-ma scale range for several decades due to the inability to quantify lower scale data. To this end, the available mi-ma fatigue crack growth data are used to generate those at the na-mi and pi-na scale ranges. Reliability variances are computed for the three different scale ranges, covering effects from the atomic to the macroscopic scale. They include the initial crack or defect length and velocities. Specimen with large initial defects are found to be more reliable. This trend also holds for each of the na-mi and pi-na scale range. Also, large specimen data had smaller reliability variances than the smaller specimens making them more reliable. Variances for the nano- and pico-scale range had much more scatter and were diversified. Uncertainties and un-reliabilities at the atomic and sub-atomic scale are no doubt related, although their connections remain to be found.Reliability with high order precisions are also defined for multi-component systems that can involve trillions of elements at the different scale ranges. Such large scale computations are now within reach by the advent of super-speed computers, especially when reliability, risk, and among other factors may have to be considered simultaneously.     

气相色谱-质谱法与化学计量学分辨法分析当归须挥发油中化学成分

本文借助化学计量学分辨方法,建立了用气相色谱-质谱(GC-MS)联用法分析当归须挥发油成分的方法.对重叠色谱峰采用直观推导式演进特征投影算法进行分辨,从而获得每一组分的纯色谱和质谱,依靠每一组分纯质谱在NIST质谱库进行相似性检索而定性分析,用总体积积分法进行定量分析.在当归须挥发油中共分辨出86个色谱峰,通过质谱库检...     

Generalized q-Schur algebras and quantum Frobenius

The quantum Frobenius map and it splitting are shown to descend to maps between generalized q-Schur algebras at a root of unity. We also define analogs of q-Schur algebras for any affine algebra, and prove the corresponding results for them.     

求解非线性方程的抛物线迭代法

利用x2=g(x)进行迭代,从而求出非线性方程f(x)=0的根x*,是继用x=g(x)的简单迭代法的延拓,讨论抛物线迭代法的具体方法和步骤,给出收敛性定理.     

Dynamic Response Studies on Aggregation and Breakage Dynamics of Colloidal Dispersions in Stirred Tanks

Aggregation and breakage of aggregates of fully destabilized polystyrene latex particles in turbulent flow was studied experimentally in both batch and continuous stirred tanks using small‐angle static light scattering. It was found that the steady‐state values of the root‐mean‐square radius of gyration are fully reversible upon changes of stirring speed as well as solid volume fraction. Steady‐state values of the root‐mean‐square radius of gyration were decreasing with decreasing solid volume fraction as well as with increasing stirring speed. Moreover, it was found that the steady‐state structure and shape of the aggregates is not influenced by the applied stirring speed.     

Askey–Wilson type integrals associated with root systems

A new formula for an Askey–Wilson type integral associated with the root system F ₄ is studied. A simple proof of the evaluation formula for the original Askey–Wilson integral is also stated. 2000 Mathematics Subject Classification Primary—33D67, 33D60 This work was supported in part by Grant-in-Aid for Scientific Research (C) No. 15540045 from the Ministry of Education, Culture, Sports, Science and Technology (Japan).     

三I方法综述——它的提出、发展、应用和逻辑版本

对三I方法提出的背景、三I方法的推广与应用作了综述,介绍三I方法在数理逻辑学中的版本。     

Parity of ranks for elliptic curves with a cyclic isogeny

Let E be an elliptic curve over a number field K which admits a cyclic p-isogeny with p?3 and semistable at primes above p. We determine the root number and the parity of the p-Selmer rank for E/K, in particular confirming the parity conjecture for such curves. We prove the analogous results for p=2 under the additional assumption that E is not supersingular at primes above 2.