Existence of a Hölder Continuous Extension on Embedded Balls of the 3-Torus for the Periodic Navier Stokes Equations

This article gives a general model using specific periodic special functions, which is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of cells of the 3-Torus. Satisfying a divergence-free vector field and periodic boundary conditions respectively with a general spatio-temporal forcing term which is smooth and spatially periodic, the existence of solutions which have finite time singularities can occur starting with the first derivative and higher with respect to time. The existence of a subspace of the solution space where v3 is continuous and {C, y1, y12}, is linearly independent in the additive argument of the solution in terms of the Lambert W function, (y12=y2, C∈R) together with the condition v2=-2y1v1. On this subspace, the Biot Savart Law holds exactly [see Section 2 (Equation (13))]. Also on this subspace, an expression X (part of PNS equations) vanishes which contains all the expressions in derivatives of v1 and v2 and the forcing terms in the plane which are related as with the cancellation of all such terms in governing PDE. The y3 component forcing term is arbitrarily small in ε ball where Weierstrass P functions touch the center of the ball both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3 only governing PDE resulting. With viscosity present as v changes from zero to the fully viscous case at v =1 the solution for v3 reaches a peak in the third component y3. Consequently, there exists a dipole which is not centered at the center of the cell of the Lattice. Hence since the dipole by definition has an equal in magnitude positive and negative peak in y3, then the dipole Riemann cut-off surface is covered by a closed surface which is the sphere and where a given cell of dimensions [-1, 1]3 is circumscribed on a sphere of radius 1. For such a closed surface containing a dipole it necessarily follows that the flux at the surface of the sphere of v3 wrt to surface normal n is zero including at the points where the surface of sphere touches the cube walls. At the finite time singularity on the sphere a rotation boundary condition is deduced. It is shown that v3 is spatially finite on the Riemann Sphere and the forcing is oscillatory in y3 component if the velocity v3 is. It is true that . A boundary condition on the sphere shows the rotation of a sphere of viscous fluid. Finally on the sphere a solution for v3 is obtained which is proven to be Hölder continuous and it is shown that it is possible to extend Hölder continuity on the sphere uniquely to all of the interior of the ball.

From Hölder Continuous Solutions of 3D Incompressible Navier-Stokes Equations to No-Finite Time Blowup on [ 0,∞ ]

This article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of arbitrary r balls of the 3-Torus. The continuity equation is satisfied together with spatially periodic boundary conditions. The yicomponent forcing terms consist of a function F as part of its expression that is arbitrarily small in an r ball where it is associated with a singular forcing expression both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3(vifor all velocity components) only governing PDE resulting. The extension of three restricted subspaces in each of the principal directions in the Cartesian plane is shown as the Cartesian product ℋ=Jx,t×Jy,t×Jz,t. On each of these subspaces vi,i=1,2,3is continuous and there exists a linear independent subspace associated with the argument of the W function. Here the 3-Torus is built up from each compact segment of length 2R on each of the axes on the 3 principal directions x, y, and z. The form of the scaled velocities for non zero scaled δis related to the definition of the W function such that e−W(ξ)=W(ξ)ξwhere ξdepends on t and proportional to δ→0for infinite time t. The ratio Wξis equal to 1, making the limit δ→0finite and well defined. Considering r balls where the function F=(x−ai)2+(y−bi)2+(z−ci)2−ηset equal to −1e+rwhere r>0. is such that the forcing is singular at every distance r of centres of cubes each containing an r-ball. At the centre of the balls, the forcing is infinite. The main idea is that a system of singular initial value problems with infinite forcing is to be solved for where the velocities are shown to be locally Hölder continuous. It is proven that the limit of these singular problems shifts the finite time blowup time ti∗for first and higher derivatives to t=∞thereby indicating that there is no finite time blowup. Results in the literature can provide a systematic approach to study both large space and time behaviour for singular solutions to the Navier Stokes equations. Among the references, it has been shown that mathematical tools can be applied to study the asymptotic properties of solutions.

A new type of internal solitary waves with a re-appearance period of 23 h observed in the South China Sea

The South China Sea （SCS）, in particular the northern SCS, is one of ocean areas where energetic internal solitary waves （ISWs）occur most frequently （Cai et al., 2012; Zheng, 2017）. Based on the re-appearance period （RP） at an observation station, Ramp et al.（2004） divided the ISWs into two types：Type-a and Type-b. Type-a ISWs arrive regularly at the same time every day, i.e., the RP is about 24 h, and Type-b ISWs arrive about one hour late every day, i.e., the RP is about 25 h.

Confirmation of 24 h 50 min Lunar Periodicity, Apparently Inexplicable by Classical Factors, in Precession of Allais Pendulum

During 36 days the motion of two pendulums, which were restarted every hour, was continuously recorded. 869 “runs” were thus made, providing each time the precession during the run, as well as other parameters of the motion. Spectral analysis of precession and ellipticity revealed a lunar component of 24 h 50 min, which can only result from an astral action, through mechanisms yet to be discovered. Indeed, an analysis was carried out of the influence of all classical perturbing factors: direct or indirect action of classical gravity, temperature, Earth’s magnetic field, etc.… None of them can explain this component, given its amplitude and phase. Its amplitude excludes also an explanation by general relativity. This is consistent with a major result that Allais claimed to have obtained during each one of the six continuous one-month-long experiments he carried out from 1954 to 1960. The numerous and very precise data provided by an automatic alidade give additional information to those gathered by Allais. All that confirms all the scientific interest that there would be to resume long-duration pendulum observations on a much more important scale: continuous observations for at least 2 years, and if possible more.

Introductory Statement by H.E. Ambassador Li Baodong,Head of Chinese Delegation,at the Consideration of the Committee Against Torture on China's 4th and 5th Periodic Reports

Mr. Chairman, Distinguished Members of the Committee, First of all, I would like to extend, on behalf of the Chinese delegation, our greetings and respects to all the distinguished members of the Committee. The Committee has made enormous efforts and played an important role in promoting the purposes and principles of the Convention and reinforcing the global efforts to ban and prevent torture. The Chinese Government appreciates your endeavor and will continue to support the work of the Committee.

Introductory Remarks by H.E. Duan Jielong,Head of Chinese Delegation,at the Consideration of the Committee on Elimination of All Forms of Racial Discrimination on China's 10th to 13th Periodic Reports

Madam Chairwoman, Mr. Rapporteur, Distinguished Members of the Committee, First of all, I would like to extend, on behalf of the Chinese delegation, our heartfelt greetings and respects to all the distinguished members of the Committee. The Committee has made enormous efforts and played an important role in promoting the objectives and principles of the International Convention on Elimination of All Forms of Racial Discrimination. The Chinese Government appreciates your endeavour and will continue to support the work of the Committee.

ActiGraph(GT3X/±系列)加速度计睡眠筛查方法研究进展

基于加速度计的24 h活动行为研究中,计算不同活动行为时间之前,必须先将加速度计数据分为清醒时期(研究身体活动和久坐行为)和睡眠时期(研究睡眠时间和睡眠质量)。但目前关于加速度计数据对清醒-睡眠期的分离尚无公认的标准方法,也缺乏对这些方法的系统梳理。研究从425篇相关文献中归纳出9种在自由生活条件下可用的清醒-睡眠期分离方法,通过解释这些方法的原理、优势与不足,为使用GT3X/±加速度计的研究人员提供选择睡眠筛查方法的建议:1)选择自动睡眠筛查算法时,腕部设备推荐使用GGIR内置的睡眠日记/HDCZA算法+van Hees 2015算法,腰部设备则可以选择Tracy ProChildren、Tudor-Locke、McVeigh或Bellettiere-McVeigh算法;2)选择Actilife进行睡眠筛查时,研究对象年龄<30岁时推荐使用Sadeh算法,≥30岁时推荐使用Cole-Kripke算法,且均需要睡眠日记的辅助。研究为24 h活动行为研究提供了数据处理方面的建议,也为未来开发新的清醒-睡眠期分离方法提供了方向,但仍需更多的研究来比较与验证这些睡眠筛查方法,以促进研究方法的标准化。

基于地脉动H/V谱比法的红土场地卓越周期

为研究地脉动H/V谱比法在确定红土场地卓越周期中的适用性,对不同类别红土场地开展系统的地脉动测试。首先利用地脉动H/V谱比法中水平分量的不同组合方式处理地脉动测试数据,得到HVSR曲线;然后分析HVSR曲线,获取场地卓越周期,进而确定场地类别,划分场地岩土类型;最后结合钻孔勘探信息,验证了地脉动H/V谱比法在确定红土场地卓越周期中具有良好的适用性,且H/V谱比法中采用东西和南北向水平分量的矢量和组合方式可更加简便和准确地获取场地卓越周期。

Analysis on Predominant Periods Distribution by Microtremor Observations for Seismic Disaster Prevention in Yokohama, Japan Using GIS

In recent years, predictions of damage from earthquakes have been made on a prefectural scale, and expectations exist that more detailed damage forecasts should be made even on a city/town/village scale. It is important to know detailed ground characteristics to do damage prediction on a fine scale. Using GIS is the best way to communicate this planar disaster prevention information to the general public. Yokohama City is the second largest city in Japan and developed as part of the capital region of Metropolitan Tokyo. Recently, the population of this city has reached about 3,000,000, and economic and cultural facilities, social infrastructure, and residential complexes are concentrated in this city. The capital region, including Yokohama City, was attacked by the 1923 Great Kanto Earthquake (M7.9) and Yokohama City was devastated by this earthquake. From the research so far, it is known that the H/V spectrum obtained from microtremor observation has a good correlation with the ground characteristics. The authors have been conducting high-density tremor observations that have been ongoing since the 1990s, mainly in Kanagawa Prefecture, Japan. Here, we have organized the predominant periods obtained from the observation results for Yokohama City. The entirety of Yokohama City was divided into 250 m × 250 m meshes and their centers were used as microtremor observation sites. Excluding sites that could not be used due to geographical conditions, observations were made at approximately 5700 sites. So, we compared the data obtained separately, such as the period, terrain classification, and amplification characteristics. The distribution maps of predominant periods in Yokohama City show that the city contains a lot of artificially transformed land, and consequently, the distribution of predominant periods is not uniform. However, it can be seen that the periods become gradually longer, moving from the higher elevation eastern part toward the lower elevation western part. Investigation of the site amplification factors and detailed topographical classifications indicates a clear correlation with the predominant period distribution.

Structure and tribological properties of Si/a-C:H(Ag)multilayer film in stimulated body fluid

Si/a-C:H(Ag)multilayer films with different modulation periods are prepared to test their potential applications in human body.The composition,microstructure,mechanical and tribological properties in the simulated body fluid are investigated.The results show the concentration of Ag first decreases and then increases with the modulation period decreasing from 984 nm to 250 nm.Whereas the C content has an opposite variation trend.Notably,the concentration of Ag plays a more important role than the modulation period in the properties of the multilayer film.The a-C:H sublayer of the film with an appropriate Ag concentration(8.97 at.%)(modulation period of 512 nm)maintains the highest sp3/sp2 ratio,surface roughness and hardness,and excellent tribological property in the stimulated body fluid.An appropriate number of Ag atoms and size of Ag atom allow the Ag atoms to easily enter into the contact interface for load bearing and lubricating.This work proves that the Ag nanoparticles in the a-C:H sublayer plays a more important role in the tribological properties of the composite-multilayer film in stimulated body fluid condition.

Effect of Qinggan Huayu granule on H22 liver ascitic tumor mice

Objective:To evaluate the therapeutic effect of Qinggan Huayu granule on mice with H22 liver cancer ascites tumor.Methods:A H22 liver cancer ascites mouse model was established by intraperitoneally injecting H22 liver cancer cells.Mice were randomly divided into the model group,the Ganfule group(1.35 g/kg),the fluorouracil group(50 mg/kg i.p),the Qinggan Huayu granule groups at low(0.67 g/kg),medium(1.34 g/kg),and high(2.68 g/kg)doses.Then the mice were administered continuously for 10 days and body weight and abdominal circumference were monitored every 3 days.On day 11,eight rats in each group were randomly selected for dissection to detect the amount of peritoneal water,peritoneal permeability and histopathological changes.The remaining mice were observed for survival.In addition,the vascular endothelial growth factor A(VEGFA)and vascular endothelial growth factor receptor 2(VEGFR2)were determined by Western blotting.Results:Compared with the model group,the weight growth of mice in the fluorouracil group and the medium-dose and high-dose Qinggan Huayu granule groups was slower(P<0.05).Moreover,the abdominal circumference of mice in each treatment group was increased slowly.There were significant differences in abdominal circumference between the fluorouracil group,the medium-dose group and the control group from day 6(P<0.05)while the abdominal circumference of the high dose group was significantly smaller than that of the control group from day 12(P<0.05).Moreover,compared with the model group,the amount of ascites in the medium-and high-dose Qinggan Huayu granule groups was decreased significantly(P<0.05).The optical density value of ascites supernatant in medium-and high-dose Qinggan Huayu granule group and the fluorouracil group decreased significantly(P<0.05)and the survival period of the medium-dose Qinggan Huayu granule group and the fluorouracil group was prolonged prominently(P<0.05).There was no significant difference in the low-dose Qinggan Huayu granule group and the Ganfule group.Peritoneal histopathological assay showed more complete peritoneal structure,less edema and less angiogenesis of the peritoneum in the fluorouracil group and the medium-and high-dose Qinggan Huayu granule group,which was better than that of the Ganfule group and the low-dose group.Compared with the model group,the expressions of VEGFA and VEGFR2 in the medium-dose Qinggan Huayu granule group decreased significantly(P<0.05,P<0.01).Conclusion:Qinggan Huayu granule can inhibit ascites production in the mice model with H22 liver cancer ascites tumor,prolong the survival of mice,and reduce peritoneal permeability and suppress the increase of peritoneal neovascularization.The mechanism may be related to the inhibition of VEGF/VEGFR pathway.

Higher Viral Load and Prolonged Viral Shedding Period is Associated with Impaired Th17 Cell Response in Patients with H1N1 Influenza A

Objective To explore whether age,disease severity,cytokines and lymphocytes in H1N1 influenza A patients correlate with viral load and clearance.Methods Total of 70 mild and 16 severe patients infected with H1N1 influenza A virus were enrolled in this study.Results It was found that the patients under 14 years old and severe patients displayed significantly higher viral loads and prolonged viral shedding periods compared with the patients over 14 years old and mild patients,respectively(P < 0.05).Moreover,the patients under 14 years old and severe patients displayed significantly lower Th17 cell frequency than the patients over 14 years old and mild patients(P < 0.01).The viral shedding period inversely correlated with the frequency of IL-17+IFN-γ-CD4+ T cells.Additionally,the decreased concentration of serum TGF-β correlated with the decreased frequency of IL-17+IFN-γ-CD4+ T cells.Conclusions Both younger and severe patients are associated with higher viral loads and longer viral shedding periods,which may partially be attributed to the impaired Th17 cell response.

Effects of hexametazidine on physiological properties of guinea-pig papillary muscles

Effects of hexametazidine [1,4-di(2,3,4-trimethoxybenzyl)piperazine] on the physiological properties of guinea-pig papillary muscles were investigated. Hexametazidine possesses a concentration-dependent negative inotropic effect (IC_(50)=81.8±16.9μmol/L).The effect of hexametazidine(30.8μmol/L)was antago- nized completely by increasing the concentration of Ca^(2+)from 1.8 to 5.4mmol/L. Hexametazidine(30.8μmol/L)increased the threshold concentration of adrenaline for inducing the automaticity of the muscles from 3.95±1.80 to 6.67±4.84μmol/L (P<0.05).It prolonged the functional refractory period from 218±14 to 254±20ms (P<0.05)at the concentration of 61.6μmol/L.Hexametazidine(6.2μmol/L)antago- nized the positive inotropic effect of isoprenaline competitively and of histamine non-competitively(pA 2 and pD2′ values were 5.45 and 4.13, respectively).

基于^(1)H-NMR代谢组学的绝经期综合征血清代谢标志物研究

目的:基于核磁共振氢谱(1H-NMR)代谢组学分析,结合模式识别寻找女性进入围绝经期以及罹患绝经综合征疾病的特异性血清代谢标志物。方法:选择80例绝经综合征患者、40例同龄围绝经期和40例育龄期健康女性为对照,利用^(1)H-NMR技术进行血清样本检测,运用PLS-DA、OPLS-DA分析对体内代谢产物进行比较研究。结果:绝经综合征患者与围绝经期、育龄期健康女性三组之间具有统计学差异的血清代谢物包括:乳酸、醋酸、谷氨酸、丙酮酸、肌酸、氧化三甲胺(TMAO)、N-乙酰糖蛋白、丙氨酸和胆碱。其中,进入围绝经期的健康女性,较育龄期有乳酸、醋酸等6个血清代谢产物显著下调,但尚不具备诊断价值。与围绝经期健康女性比较,绝经综合征患者丙氨酸、TMAO上调,谷氨酸、丙酮酸、N-乙酰糖蛋白和胆碱下调趋势显著,且谷氨酸、丙酮酸、N-乙酰糖蛋白和胆碱的变化趋势具有一定的诊断价值。结论:围绝经期是女性从生殖期过渡到老年期的一个特殊生理阶段,健康女性虽然较育龄期存在一定特征性代谢物的变化,但尚不具有诊断价值;但绝经综合征患者在疾病状态下所呈现的差异性代谢标志物,具有一定的诊断价值,可以为临床宏微观结合诊断绝经综合征提供一定的客观依据。

利用H/V谱比法研究三河和唐山地震震区地壳浅部沉积结构

利用一条穿过三河和唐山地震区的密集地震探测剖面数据,采用H/V谱比法获得了三河、唐山地震区及邻近区域的地壳浅部沉积结构特征、场地共振频率及易破坏程度等参数.结果表明:研究区松散沉积层厚度约为100—800 m,呈现出NW浅而SE深的变化特征;探测剖面西北部通县隆起的沉积层厚度约为350—450 m,沉积层界面起伏平缓;大厂凹陷沉积层厚度约为300—600 m,横向变化特征显著.测线东南部唐山地震区地壳浅部存在上下两组较明显的沉积界面:上层界面深度约为100 m,呈水平展布;下层界面深度约为300—800 m,且向东南方向逐渐加深.三河和唐山地震区的场地放大系数约为3—4,场地易破坏程度均大于20,显示出地表建筑物易破坏程度较高的特征.

面向纳米栅格扫描的时滞压电微动平台耦合补偿

针对栅格纳米扫描特别是高速扫描应用中,带测量滞后的压电纳米平台轴间周期耦合补偿的问题,提出一种无需复杂逆模型求解的鲁棒周期干扰观测控制策略。建立压电平台的机电耦合多扰动模型用以描述平台系统的动力学行为。在此基础上,构建周期干扰观测控制结构。通过推导的性能优化函数和鲁棒稳定性条件,将最优控制器参数求解问题转化为延时系统的混合灵敏度优化问题,并通过无穷维H∞控制方法进行求解。最后,在压电纳米平台上进行综合的实验探究。结果表明,建立的动力学模型能够有效拟合平台的实验响应;相较于无干扰观测器的方法和传统的周期干扰观测控制方法,提出的鲁棒优化方法在基频的抗干扰性能分别有超过99%和50%的提升。提出的鲁棒周期干扰控制方法有优越的抗干扰和不确定补偿性能。

H原子在完美δ-Pu金属体相中的扩散行为

采用密度泛函理论的广义梯度近似方法计算了H原子在δ-Pu金属体相中可能稳定存在间隙位置的嵌入能.计算结果表明,八面体间隙是H原子最稳定存在位置,无自旋极化和自旋极化水平的嵌入能分别为-3.12和-2.22eV.四面体间隙位的嵌入能相对稍大,是次稳定存在位置.通过能量分析推测了单个H原子在完美δ-Pu金属中可能的扩散路径和扩散能垒.最可能扩散路径为相邻不同间隙位的交替扩散,八面体间隙到四面体间隙的扩散能垒为1.06eV,而四面体间隙到八面体间隙的扩散能垒为0.38eV.另外沿平行晶轴方向四面体间隙到四面体间隙交替直线扩散的能垒为1.83eV,八面体间隙到八面体间隙交替扩散路径的能垒最高,为2.52eV.

线性离散周期系统满意估计

针对线性离散周期系统的状态估计问题,运用提升原理提取期望极点指标,同时期望估计误差系统满足稳态误差方差/H∞混合指标,采用代数Riccati矩阵不等式法与数值递推算法对误差系统进行了上述指标的满意估计设计,并根据满意控制的基本理论将上述满意估计问题转化为线性矩阵不等式(LMI)的线性规划问题,从而运用LMI技术求解并设计了可行的满意估计,数值算例验证了相关算法.

H.264中整数余弦变换和周期量化的原理与分析

H.264是联合视频组正在研究制定的新一代视频压缩编码标准。H.264在它的前身H.26L的基础上进行了改进,提出了一种新的整数余弦变换方法,在降低编解码器复杂性的同时提高了编码效率。针对新整数余弦变换的特点,并考虑到H.26L中量化表的类周期性质,H.264又提出了一种新的周期量化方法。分析了H.264中这种新的整数余弦变换和周期量化的推导过程,挖掘了其扩展的可能性,最后通过在复杂度、精度和性能三个方面与H.26L中的对应算法进行比较后指出这种新算法使得H.264与H.26L相比更加简单而有效。

悬索在外激励作用下的1∶3内共振分析(II)∶数值结果

本研究的第一部分已经推导了悬索在第一阶面内对称模态主共振和第三阶面内对称模态主共振下的平均方程,其中考虑了这两阶模态之间1∶3内共振。本文对平均方程的稳态解、周期解以及混沌解进行了研究。利用Newton-Naphson方法和拟弧长的延拓算法确定了主共振情况下的幅频响应曲线,通过利用Jacobian矩阵的特征值判断幅频响应曲线中解的稳定性。在这些幅频响应曲线中,都存在超临界Hopf分叉,导致平均方程的周期解。以这些超临界Hopf分叉为起点,利用打靶法和拟弧长的延拓算法确定了两种主共振情况下的周期解分支,同时通过利用Floquet理论判断这些周期解的稳定性。然后利用数值结果研究了两种主共振情况下的周期解经过倍周期分叉通向混沌的过程。最后利用Runge-Kutta法研究了悬索两自由度离散模型的非线性响应。