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.

HB-Continuous Mappings in L-Topological Space

In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.

Changes in Soil Enzyme Activity and Nutrient Content in Different Years of Continuous Cropping Tobacco Fields

In order to find out changes in the main fertility indicators of continuous cropping tobacco fields in Henan Province with years of continuous cropping,5 typical tobacco fields( Jia County,Shaoling District,Fangcheng County,Xiangcheng County,and Song County) were studied. Indicators in question included activity of main enzymes( sucrase,urease,catalase,and acid phosphatase),p H value,organic matters,total nitrogen,available phosphorus and available potassium. The results indicate that in most tobacco fields,the activity of sucrase and urease increased in two years of continuous cropping,later,it showed a declining trend with increase in years of continuous cropping; in some fields,it directly declined with increase in years of continuous cropping; the activity of catalase increased in two years of continuous cropping,later,it showed a declining trend with increase in years of continuous cropping,and it became stable after three years of continuous cropping;generally,the activity of acid phosphatase declined with increase in the years of continuous cropping within 3 years continuous cropping,later,it became stable. Except Fangcheng County,the soil p H value of other districts( counties) generally declined with increase in years of continuous cropping,and it was in the range of 5. 6-6. 8. With the increase in continuous cropping,the soil organic matters( SOM) in tobacco fields of Jia County and Song County declined,changes of SOM in tobacco fields of Fangcheng County and Xiangcheng County were not obvious,and SOM showed the trend of first decline then rise in Shaoling District. In most tobacco fields( Jia County,Xiangcheng County,and Song County),the total nitrogen showed a declining trend; in Shaoling District,it showed a trend of first decline then rise; in Fangcheng County,it showed a rising trend. The available phosphorus firstly slightly declined then rose in tobacco fields of Shaoling District and Song County; it showed a trend of first rise then decline in Jia County; there were no obvious changes in Fangcheng County and Xiangcheng County. Changes in the available potassium were different in tobacco fields. In sum,there are certain rules for changes in soil enzyme activity and nutrient content in tobacco fields in Henan Province,but changes are not completely the same. It is concluded that the site conditions and farming activities exert a certain influence on soil enzyme activity,p H value,organic matters,and nitrogen,phosphorus and potassium content. Therefore,to solve obstacles in continuous cropping of tobacco fields,different regions should take different measures.

JOINT HOLDER CONTINUITY OF PARABOLIC ANDERSON MODEL

We obtain the H?lder continuity and joint H?lder continuity in space and time for the random field solution to the parabolic Anderson equation ■ in d-dimensional space, where ■ is a mean zero Gaussian noise with temporal covariance γ0 and spatial covariance given by a spectral density μ(ξ). We assume that ■ and ■ , where αi, i = 1, · · ·, d(or α) can take negative value.

Effects of prostaglandin E combined with continuous renal replacement therapy on septic acute kidney injury

BACKGROUND The effects of prostaglandin E(PGE)combined with continuous renal replacement therapy(CRRT)on renal function and inflammatory responses in patients with septic acute kidney injury(SAKI)remain unclear.AIM To investigate the effects of PGE combined with CRRT on urinary augmenter of liver regeneration(ALR),urinary Na+/H+exchanger 3(NHE3),and serum inflammatory cytokines in patients with SAKI.METHODS The clinical data of 114 patients with SAKI admitted to Yichang Second People's Hospital from May 2017 to January 2019 were collected.Fifty-three cases treated by CRRT alone were included in a control group,while the other 61 cases treated with PGE combined with CRRT were included in an experimental group.Their urinary ALR,urinary NHE3,serum inflammatory cytokines,renal function indices,and immune function indices were detected.Changes in disease recovery and the incidence of adverse reactions were observed.The 28-d survival curve was plotted.RESULTS Before treatment,urinary ALR,urinary NHE3,blood urea nitrogen(BUN),serum creatinine(SCr),CD3+T lymphocytes,CD4+T lymphocytes,and CD4+/CD8+T lymphocyte ratio in the control and experimental groups were approximately the same.After treatment,urinary ALR and NHE3 decreased,while BUN,SCr,CD3+T lymphocytes,CD4+T lymphocytes,and CD4+/CD8+T lymphocyte ratio increased in all subjects.Urinary ALR,urinary NHE3,BUN,and SCr in the experimental group were significantly lower than those in the control group,while CD3+T lymphocytes,CD4+T lymphocytes,and CD4+/CD8+T lymphocyte ratio were significantly higher than those in the control group(P<0.05).After treatment,the levels of tumor necrosis factor-α,interleukin-18,and high sensitivity C-reactive protein in the experimental group were significantly lower than those in the control group(P<0.05).The time for urine volume recovery and intensive care unit treatment in the experimental group was significantly shorter than that in the control group(P<0.05),although there was no statistically significant difference in hospital stays between the two groups.The total incidence of adverse reactions did not differ statistically between the two groups.The 28-d survival rate in the experimental group(80.33%)was significantly higher than that in the control group(66.04%).CONCLUSION PGE combined with CRRT is clinically effective for treating SAKI,and the combination therapy can significantly improve renal function and reduce inflammatory responses.

THE HLDER CONTINUITY FOR THE GRADIENT OF SOLUTIONS TO ONE-SIDED OBSTACLE PROBLEMS

The Hǒlder continuity is proved for the gradient of the solution Jo the one-sided obstacle problem of the following variational inequality in the case 1<p<2

Directly electrospinning submillimeter continuous fibers on tubes to fabricate H2S detectors with fast and high response

The fast and high response detection of neurotoxic H_(2)S is of great importance for the environment.In this paper,directly electrospinning technology on the ceramic tube is developed to improve the response of H_(2)S detector based on superlong SnO_(2)fibers.The submillimeter continuous fibers are deposited directly on ceramic tubes by in-situ electrospinning method and can keep morphology of fibers during calcination.By employing this technology,CuO-doped SnO_(2)fiber H_(2)S detectors are fabricated,and 10%atom CuO-doped SnO_(2)H_(2)S detector shows the highest response of 40 toward 1 ppm H_(2)S at 150℃while the response is only 3.6 for the H_(2)S detector prepared in traditional route.In addition,the in-situ electrospinning H_(2)S detectors show faster response and recovery compared to the H_(2)S detectors fabricated by the conventional way.The high and fast response of H_(2)S detectors based on in-situ electrospinning can be ascribed to the continuous fiber structure and CuO modification.The present in-situ electrospinning technology may provide a new strategy for the development of other gasdetectors and bio-detectors with fast and high response.

Strong Feller Property for SDEs with Super-linear Drift and Hölder Diffusion Coefficients

In this paper,we investigate the strong Feller property of stochastic differential equations(SDEs)with super-linear drift and Hölder diffusion coefficients.By utilizing the Girsanov theorem,coupling method,truncation method and the Yamada-Watanabe approximation technique,we derived the strong Feller property of the solution.

Hlder continuity for solutions of elltptic equations involving measures

The Hoider continuity is proved to bounded solutions of degenerate elliptic e-quations involving measures. The structural conditions of the equation are more general and therestrictions on the structural coofficients are weaker.

H型钢表面裂纹成因分析

H型钢由异型坯轧制生产,异型坯形状独特,连铸生产中横向表面温度极不均匀,应力、应变状况复杂,对冶炼和连铸工艺均有较高要求。SS400异型坯生产中钢水未经精炼处理,部分炉次钢水碳含量处于包晶反应严重的碳含量范围,硫、磷含量较高,w(Mn)/w(S)较低,总氧和大型夹杂物含量较高;浸入式水口为直孔型,结晶器中上升流股较弱,坯壳生长不均匀;拉速较慢,并采用双水口浇铸,结晶器中上升流股更弱,弯月面处钢水供热不足,处于低温状态,保护渣也因温度低而熔融欠佳;二冷强度偏高,矫直辊前异型坯腹板表面温度处于低温脆性区,因此轧制成品H型钢的表面裂纹较多。

Heyting系统及其H-空间化表示形式

Steven Vickers将拓扑的方法与逻辑理论的结果相结合于专著《Topology via Logic》中建立了拓扑系统,并将这一理论应用于计算机理论的研究.本文借助于拓扑系统的思想和方法,以及Frame结构和Heyting代数的共有性质,以Heyting代数为主体建立了一种新型的代数系统—Heyting系统,建立了Heyting系统之间的恰当的联系方法—H-连续映射;给出了Heyting系统的H-空间化表示形式并对相关性质进行了讨论.本文的工作进一步丰富了Heyting代数的研究方法和拓扑系统的研究内容.

H型钢X-H三机架往复连轧过程三维有限元分析

针对H型钢X-H方法生产过程,采用有限元分析软件ANSYS/LS-DYNA,建立仿真模型,完成了H型钢三机架往复连轧过程。详细描述了计算模型的建立、边界加载以及材料的定义。在模拟结果的基础上,深入分析了稳定轧制阶段轧件断面金属的流动情况、变形规律以及轧制力的特点,得到了金属沿着H型钢轧槽表面往内流动、出现冲击载荷等结论。可为H型钢的多机架往复的连轧仿真分析,以及X-H轧制工艺研究提供数值参考。

APP在H型高血压出院患者延续护理中的应用

目的探讨APP在H型高血压出院患者延续护理中的应用效果。方法选取2014年4月-2015年3月在我院高血压科住院的120例H型高血压患者,按入院先后顺序随机分为观察组和对照组各60例。观察组患者由延续护理小组成员在常规出院健康宣教的基础上利用APP对其进行延续护理;对照组延用原来的常规出院健康宣教。比较出院6个月复查时两组患者的血压、同型半胱氨酸(Hcy)指标变化。结果在随访的120例患者中,有6人失访,失访率为5%。出院6个月复查时,观察组患者血压、同型半胱氨酸指标均优于对照组,差异有统计学意义(P<0.05)。结论运用APP对H型高血压出院患者进行延续护理的效果较好,值得推广。

H型高血压延续性护理研究进展

对H型高血压的定义、危险因素、危害进行概述,综述了医院、社区延续性护理对H型高血压的研究进展,以期提高对H型高血压的关注,早期发现并实施全面、系统、有效的延续性护理干预,降低心脑血管事件风险。

连铸连轧过程中SPA-H钢板表面的氧化锈蚀

利用光学显微镜、扫描电镜、能谱和XRD衍射物相分析等手段,研究了SPA-H钢经连铸连轧后表面黄色锈斑的形成原因。结果表明,黄色锈斑的外层主要由Fe2O3、里层由FeO组成,在钢板表面呈条带状分布;而无黄色锈斑的钢板表面主要是由FeO组成。黄色锈斑是由于在轧制过程中,钢表面的高温氧化产物(FeO)破裂,在随后的冷却过程中破裂处特别是裂纹的尖端形成大量的Fe2O3所致,高温氧化产物FeO的应变速率和该氧化膜的横向生长比较高,高温氧化膜开裂后,裂纹不能自愈,较低温度时合金表面发生了线性氧化。

具连续偏差变元的向量抛物型方程的H-振动性

考虑一类具连续偏差变元的向量抛物型偏微分方程的振动性,利用Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维泛函微分不等式不存在最终正解的问题,给出了该类方程在Robin边值条件下所有解H-振动的若干充分条件,这里H是RM中的单位向量.

H酸连续化合成工艺综述

本文简单介绍了H酸的传统合成工艺,并指出了该工艺存在的问题。综述了国内外有关H酸生产的新工艺。认为精萘连续磺化、硝化、催化加氢还原、选择性催化水解制备H酸是未来发展方向。

H型钢坯连续铸造工艺概况及发展现状

阐述了H型钢坯连铸技术,介绍了H型钢坯连铸关键设备及技术,总结了H型钢坯连铸主要工艺特点,概括了国内外H型钢坯连铸技术发展历程及现状,分析了H型铸坯存在的质量缺陷及影响因素,并提出了改善铸坯质量的措施,为H型钢坯连铸领域科研及生产提供参考。

机器人非线性连续变增益H_∞控制器设计

本文针对 n关节的刚性机器人 ,提出了一种设计连续变增益控制器的新方法 .这种方法结合了变增益和 H∞ 理论 ,通过在平衡点附近线性化系统 ,利用具有极点配置的状态反馈 H∞ 技术 ,对应每个运动区域 ,设计满足H∞ 性能和动态特性的状态反馈增益 ,这些增益通过泰勒级数展开拟合成与运动点有关的连续函数 .随着系统状态的变化 ,拟合成的增益函数可使控制器获得连续的增益 ,使得所设计的控制器同样适合系统状态变化较快的对象 ,而且系统随状态的变化始终具有很高的动态性能 ,克服了传统变增益控制器中存在的不足 .仿真结果验证了此控制器的有效性 .