Growth of apatite on chitosan-multiwall carbon nanotube composite membranes

Bioactive membranes for guided tissue regeneration would be of value for periodontal therapy. Chitosan-multiwall carbon nanotube (CS-MWNT) composites were treated to deposit nanoscopic apatite for MWNT proportions of 0-4 mass%. Fourier-transform infrared spectroscopy, scanning electron microscopy, energy-dispersive X-ray analysis, and X-ray diffraction were used for characterization. Apatite was formed on the CS-MWNT composites at low MWNT concentrations, but the dispersion of the MWNT affects the crystallite size and the Ca/P molar ratio of the composite. The smallest crystallite size was 9 nm at 1 mass% MWNT.     

An $$H^1$$-Galerkin mixed finite element method for time fractional reaction–diffusion equation

In this article, an \(H^1\)-Galerkin mixed finite element (MFE) method for solving time fractional reaction–diffusion equation is presented. The optimal time convergence order \(O(\varDelta t^{2-\alpha })\) and the optimal spatial rate of convergence in \(H^1\) and \(L^2\)-norms for variable \(u\) and its gradient \(\sigma \) are derived. Moreover, some numerical results are shown to support our theoretical analysis.     

Ockham’s Calculus of Strict Implication

In his main work Summa Logicae written around 1323, William of Ockham developed a system of propositional modal logic which contains almost all theorems of a modern calculus of strict implication. This calculus is formally reconstructed here with the help of modern symbols for the operators of conjunction, disjunction, implication, negation, possibility, and necessity.     

低钾血症对颅脑创伤患者预后的影响

目的 探讨低钾血症在颅脑创伤患者中的发病情况及其与预后的关系。方法 2010 年6月至2013 年6 月共有168 例住院期间出现低钾血症且年龄≥18 岁的颅脑创伤患者纳入研究。依据低钾血症严重程度的不同,将患者分成轻度组（3.00mmol/L≤血钾＜3.50mmol/L）、中度组（2.50mmol/L≤血钾＜3.00mmol/L）和重度组（血钾＜2.50mmol/L）,各组均采用患者血钾的最低值进行数据分析。高钠血症和低磷血症分别被定义为血钠＞147.00mmol/L 和血磷＜0.80mmol/L。结果 受试患者的血钾在1.10~3.40mmol/L,平均2.90mmol/L。当血钾出现最低值时,与其余两组比较,重度组患者具有更高的血钠和更低的血磷水平（均P＜0.01）。与轻度组（10.5%）或中度组（25.7%）相比,重度组患者的病死率（82.1%）显著上升（均P＜0.01）。多变量逻辑回归分析结果显示,低格拉斯哥昏迷评分（OR=1.28,95%CI=1.12~1.42,P＜0.01）、低血钾（OR=5.57,95%CI=2.76~10.93,P＜0.01）、低血磷（OR=2.76,95%CI=1.11~7.25,P＜0.01）以及高血尿素氮（OR=1.16,95%CI=1.07~1.24,P＜0.01）是导致患者死亡的独立危险因素。结论 颅脑创伤患者是出现低钾血症的高危人群,重度低钾血症的患者更容易合并高钠血症和低磷血症。重度低钾血症和低磷血症是颅脑创伤患者死亡的独立危险因素。     

Landauer–Büttiker and Thouless Conductance

In the independent electron approximation, the average (energy/charge/entropy) current flowing through a finite sample \({\mathcal{S}}\) connected to two electronic reservoirs can be computed by scattering theoretic arguments which lead to the famous Landauer–Büttiker formula. Another well known formula has been proposed by Thouless on the basis of a scaling argument. The Thouless formula relates the conductance of the sample to the width of the spectral bands of the infinite crystal obtained by periodic juxtaposition of \({\mathcal{S}}\). In this spirit, we define Landauer–Büttiker crystalline currents by extending the Landauer–Büttiker formula to a setup where the sample \({\mathcal{S}}\) is replaced by a periodic structure whose unit cell is \({\mathcal{S}}\). We argue that these crystalline currents are closely related to the Thouless currents. For example, the crystalline heat current is bounded above by the Thouless heat current, and this bound saturates iff the coupling between the reservoirs and the sample is reflectionless. Our analysis leads to a rigorous derivation of the Thouless formula from the first principles of quantum statistical mechanics.     

<Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript>-Classification of Gapped Parent Hamiltonians of Quantum Spin Chains

We consider the C ¹-classification of gapped Hamiltonians introduced in Fannes et al. (Commun Math Phys 144:443–490, 1992) and Nachtergaele (Commun Math Phys 175:565–606, 1996) as parent Hamiltonians of translation invariant finitely correlated states. Within this family, we show that the number of edge modes, which is equal at the left and right edge, is the complete invariant. The construction proves that translation invariance of the ‘bulk’ ground state does not need to be broken to establish C ¹-equivalence, namely that the spin chain does not need to be blocked.     

Nondestructive rare earth element imaging of fish teeth from deep‐sea sediments

X‐ray fluorescence computed tomography is an emerging imaging modality that allows for the nondestructive reconstruction of the internal distribution of elements within a sample. The common use of X‐ray excitation energy (up to approximately 20 keV) has necessitated the use of l ‐shell fluorescence for heavy elements. In this study, based on high energy X‐ray at BL13W1 of the Shanghai Synchrotron Radiation Facility, we employed high‐energy excitation for tomographic imaging of the heavy metals (rare earth elements) in fish teeth from deep‐sea sediments on the micrometer scale using K‐shell X‐ray fluorescence. The virtual cross‐sectional distribution of La, Ce, Pm, Pr, Nd, and Sm were obtained, thereby providing a feasible approach for analyzing the enrichment mechanism of rare earth elements. Copyright © 2015 John Wiley & Sons, Ltd.     

Symplectic invariants for curves and integrable systems in similarity symplectic geometry

In this paper, similarity symplectic geometry for curves is proposed and studied. Explicit expressions of the symplectic invariants, Frenet frame and Frenet formulae for curves in similarity symplectic geometry are obtained by using the equivariant moving frame method. The relationships between the Euclidean symplectic invariants, Frenet frame, Frenet formulae and the similarity symplectic invariants, Frenet frame, Frenet formulae for curves are established. Invariant curve flows in four-dimensional similarity symplectic geometry are also studied. It is shown that certain intrinsic invariant curve flows in four-dimensional similarity symplectic geometry are related to the integrable Burgers and matrix Burgers equations.     

Ragnar Frisch and interior-point methods

The distinguished econometrician Ragnar Frisch (1895–1973) also played an important role in optimization theory. In fact, he was a pioneer of interior-point methods. This note reconsiders his contribution, relating it to history and modern developments.