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In this paper, we study the asymptotic behavior of solutions to second grade fluid equations, a model for viscoelastic fluids, in an expanding domain. We prove that, the solutions converge to a solution of the incompressible Euler equations in the whole plane, as the elastic response α and the viscosity ν vanish, and the radius of domain becomes infinite. Meanwhile, we also establish precise convergence rates in terms of ν , α and the radius of the family of spatial domains.

By searching the randomized controlled trials (RCTs) of acupuncture and moxibustion from CNKI since its inception date to december 31 of 2019, the development status and hot trend of RCTs of acupuncture and moxibustion in China were summarized. The CiteSpace and VOSviewer software were used to perform keyword co-occurrence analysis, clustering analysis, time-zone analysis and citation-burst analysis, and visual map was drawn. As a result, a total of 60 995 articles were included, which were published in 1027 academic journals with 1787 keywords. The publication date was from 1975 to 2019. During the past 45 years, the publications of RCTs on acupuncture and moxibustion had shown an overall growth trend with characteristics of the times. The RCTs of manual acupuncture ranked the top, and its proportion of publications every 5 years was stable in the past 30 years. Since 1994, the hot words such as electroacupuncture, warming needling, auricular point sticking and various acupoint therapies had emerged; meanwhile, the spectrum of diseases had broadened, and an evolutionary trend corresponding to therapies and disease systems had been formed. In recent decade, the RCTs using moxibustion therapy have increased significantly, and the hot words such as "sub-health" "winter diseases being treated in summer" and "acupoint application/ moxibustion during the dog days" had indicated that acupuncture clinical research was further inclined to the field of chronic disease prevention and health services, which was in line with social development and the needs of the times.通过检索中国期刊全文数据库（CNKI）自建库至2019年12月31日收录的针灸随机对照试验（RCT）文献，总结国内针灸RCT发展现状及热点趋势。应用CiteSpace与VOSviewer软件进行关键词共现、聚类、共现时区及突现词分析，并绘制可视化图谱。结果共纳入60 995篇文献，发表于1027部学术期刊，包括1787个关键词，发表时间为1975-2019年。45年间，针灸RCT发文量整体呈增长态势且具时代特点，疗法选择以手针居首，且近30年每5年发文量占比趋于稳定；自1994年起，电针、温针灸、耳穴贴压及各类穴位疗法等热词涌现，疾病谱拓宽，形成疗法与疾病系统相对应的演进趋势；近10年来，灸法的发文量显著增长，同时“亚健康”“冬病夏治”“三伏贴/灸”等热词的兴起标志着针灸临床研究进一步向慢病防治及健康服务领域倾斜，符合社会发展与时代需求。.

In this paper, we are concerned with the initial-boundary value problem to the 2D magneto-micropolar system with zero angular viscosity in a smooth bounded domain. We prove that there exists a unique global strong solution of such a system by imposing natural boundary conditions and regularity assumptions on the initial data, without any compatibility condition., Comment: 21 pages

In this paper, we study the approximation of π through the semiperimeter or area of a random n-sided polygon inscribed in a unit circle in ℝ2. We show that, with probability 1, the approximation error goes to 0 as n → ∞, and is roughly sextupled when compared with the classical Archimedean approach of using a regular n-sided polygon. By combining both the semiperimeter and area of these random inscribed polygons, we also construct extrapolation improvements that can significantly speed up the convergence of these approximations.

We investigate the boundary layer effects of the 3-D incompressible Boussinesq system for Rayleigh–Benard convection with vanishing diffusivity limit. By adopting the multi-scale analysis and the a...

The main purpose of this paper is to study the initial layer problem and the infinite Prandtl number limit of Rayleigh-Bénard convection with an ill prepared initial data. We use the asymptotic expansion methods of singular perturbation theory and the two-time-scale approach to obtain an exact approximating solution and the convergence rates $O(\varepsilon^{\frac{3}{2}})$ and O(ε2).

In this paper, we study the global regularity to a three-dimensional logarithmic sub-dissipative Navier-Stokes model. This system takes the form of \begin{document} ${\partial _t}u +(\mathcal {D}^{-1/2}u)·\nabla u + \nabla p =-\mathcal {A}^2u$ \end{document} , where \begin{document} $\mathcal {D}$ \end{document} and \begin{document} $\mathcal {A}$ \end{document} are Fourier multipliers defined by \begin{document} $\mathcal {D}=|\nabla|$ \end{document} and \begin{document} $\mathcal {A}= |\nabla|\ln^{-1/4}(e + λ \ln (e + |\nabla|)) $ \end{document} with \begin{document} $λ≥q0$ \end{document} . The symbols of the \begin{document} $\mathcal {D}$ \end{document} and \begin{document} $\mathcal {A}$ \end{document} are \begin{document} $m(ξ) =\left| ξ \right|$ \end{document} and \begin{document} $h(ξ) = \left| ξ \right| / g(ξ)$ \end{document} respectively, where \begin{document} $g(ξ) = {\ln ^{{1 / 4}}}(e + λ \ln (e + |ξ|))$ \end{document} , \begin{document} $λ≥0$ \end{document} . It is clear that for the Navier-Stokes equations, global regularity is true under the assumption that \begin{document} $h(ξ) =|ξ|^α$ \end{document} for \begin{document} $α≥q 5/4$ \end{document} . Here by changing the advection term we greatly weaken the dissipation to \begin{document} $ h(ξ)={{\left| ξ \right|} / g(ξ)}$ \end{document} . We prove the global well-posedness for any smooth initial data in \begin{document} $H^s(\mathbb{R}^3)$ \end{document} , \begin{document} $ s≥q3 $ \end{document} by using the energy method.

This paper is devoted to the study of the two-dimensional andthree-dimensional ideal incompressible magneto-hydrodynamic (MHD)equations in which the Faraday law is inviscid. We consider thelocal existence and uniqueness of classical solutions for the MHDsystem in Holder space when the general initial data belongs to \begin{document}$C^{1,α}(\mathbb{R}^n)$\end{document} for \begin{document}$n=2$\end{document} and \begin{document}$n=3$\end{document} .

We consider the global existence of the two-dimensional Navier-Stokes flow in the exterior of a moving or rotating obstacle. Bogovski$\check{i}$ operator on a subset of $\mathbb{R}^2$ is used in this paper. One important thing is to show that the solution of the equations does not blow up in finite time in the sense of some $L^2$ norm. We also obtain the global existence for the 2D Navier-Stokes equations with linearly growing initial velocity.

Single crystal YAG doped with a rare earth element has been commercially available for six decades. Polycrystalline YAG of high quality, suitable for use as laser gain media or optical windows has been available since 2004, and only from a single vendor. II-VI Incorporated seeks to be the premier supplier of high quality polycrystalline Yttrium Aluminum Garnet for laser gain media and infrared windows here in the United States. We present recent optical property characterization of polycrystalline (ceramic) YAG synthesized by II-VI. Optical transmission (1064 nm) data, FTIR and UV-vis-NIR spectroscopy, and photothermal common-path interferometer (PCI) absorption data are presented. Mechanisms for absorption and scatter produced by residual pores and impurities are discussed. Ceramic YAG properties are compared with single crystal (boule grown) YAG.

Background Previous studies have shown that miR-144-3p might be a potential biomarker in non-small cell lung cancer (NSCLC). Nevertheless, the comprehensive mechanism behind the effects of miR-144-3p on the origin, differentiation, and apoptosis of NSCLC, as well as the relationship between miR-144-3p and clinical parameters, has been rarely reported. Methods We investigated the correlations between miR-144-3p expression and clinical characteristics through data collected from Gene Expression Omnibus (GEO) microarrays, the relevant literature, The Cancer Genome Atlas (TCGA), and real-time quantitative real-time PCR (RT-qPCR) analyses to determine the clinical role of miR-144-3p in NSCLC. Furthermore, we investigated the biological function of miR-144-3p by Gene Ontology (GO), Kyoto Encyclopedia of Genes and Genomes (KEGG) analyses. Protein-protein interaction (PPI) network was created to identify the hub genes. Results From the comprehensive meta-analysis, the combined SMD of miR-144-3p was − 0.95 with 95% CI of (− 1.37, − 0.52), indicating that less miR-144-3p was expressed in the NSCLC tissue than in the normal tissue. MiR-144-3p expression was significantly correlated with stage, lymph node metastasis and vascular invasion (all P

The classical Archimedean approximation of π uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in R 2 . When n vertices are randomly selected on the circle, a random inscribed polygon can be constructed by connecting adjacent vertices and it is known that its semiperimeter and area both converge to π almost surely as n → ∞ and their distributions are also asymptotically Gaussian. In this paper, we consider the case of random circumscribing polygons that are tangent to the circle at each of the prescribed random points. These random versions of the circumscribing Archimedean polygons, however, are more complicated than their inscribed relatives. On the one hand, when all points fall on a semicircle, such a circumscribing polygon does not actually “circumscribe” the circle at all, but instead falls completely outside the circle; on the other hand, even if it behaves normally, its area or semiperimeter can still be unbounded. Nevertheless, we show that such undesirable cases happen with exponentially small probability as n becomes large, and like the case of inscribed polygons, in the limit as n → ∞ , similar convergence results can be established for the semiperimeters or areas of these random circumscribing polygons.

The quasi-neutral limit of the full Navier–Stokes–Fourier–Poisson system in the torus T d ( d ≥ 1 ) is considered. We rigorously prove that as the scaled Debye length goes to zero, the global-in-time weak solutions of the full Navier–Stokes–Fourier–Poisson system converge to the strong solution of the incompressible Navier–Stokes equations as long as the latter exists. In particular, the effect of large temperature variations is taken into account.

In order to validate the good linear response of an instrument entitled Sky Radiometer(abbreviated to DTL-1) and check the great accuracy of radiance, the experiments which checked the DTL-1 using the large diameter integrating sphere system verified that the instrument had fine linearity and working stability. At the same time, the sky radiance in Hefei was measured, and the validity and correctness of DTL-1 were verified using fibre-optical spectrometer. The results indicated that the instrument had fine work ability, including good linear response, and could satisfy the scientific research and the actual application. However, the linear response of the instrument entitled Sky Radiometer in different region will be validated.

Background: The aim of this research is to further evaluate the efficacy and safety of percutaneous coronary intervention (PCI) in patients with acute myocardial infarction (AMI) complicated with chronic renal insufficiency (CRI) by meta-analysis, to provide scientific and effective medical evidence for PCI in patients with AMI complicated with CRI, and to support the clinical application of PCI. Methods: Electronic databases will be searched, including PubMed, Cochrane Library, Embase, CNKI, CBM, VIP, and Wanfang Data. Patients with AMI complicated by renal insufficiency treated with PCI will be included. The retrieval time is from inception to January 2019. The inclusion and exclusion criteria are formulated to search only the relevant literature. Endnote software management for literature will be adopted. The literature will be independently screened by 2 researchers. Excel 2016 will be applied to extract literature data with the “Research Information Registration Form.” The final selected literature will be assessed for bias risk. Stata 12.0 software will be used for the meta-analysis. Results: The systematic evaluation and meta-analysis will be carried out strictly in accordance with the requirements of the Cochrane System Evaluator Manual 5.3 on meta-analyses, which will provide a high-quality evaluation of the clinical efficacy and safety of PCI in patients with AMI and CRI. Ethics and dissemination: This study belongs to the category of systematic reviews, not clinical trials. Therefore, it does not require ethical approval. The results of this study will be published in influential international academic journals related to this topic. Conclusion: PCI is an effective and safe treatment for patients with AMI and CRI. This study will provide a definite evidence-based medical conclusion and provide a scientific basis for the clinical treatment of patients with AMI and CRI. PROSPERO registration number: CRD42019131367.

In order to calculate the amount of CO2 emissions from the iron and steel making in China, carbon flows in two iron and steel enterprises were investigated with Material Flow Analysis, through the production data and sampling of materials from each enterprise in this paper. Results show that the main carbon sources of CO2 emissions in blast furnace-basic oxygen furnace (BF-BOF) steelmaking are fossil fuel, and fossil fuel in electricity furnace (EAF) steelmaking account for 33% of the total carbon sources; The amount of CO2 emission of per ton crude steel from the BF-BOF steelmaking and EAF steelmaking is 1149.7 and 46.6 kg, respectively.

The fly ash was modified by Cl, Fe, Cu salts to investigate the mercury adsorption performance and analyze the impacts on it. Experiment results indicate that significant improvement of removal efficiencies with FeCl3、CuCl2 and CuBr2 impregnation onto fly ash. The modification adjusted the pore structure of fly ash and formed more pores to absorb Hg, also it was found that new active sites were generated after the treatment, which can oxidize Hg0 and improve chemical adsorption.

Hydrotalcites (HT-X) of different Mg/Al ratio (X is Mg/Al molar ratio, 3 and 4) was synthesized by co-precipitation method. Calcined HTLCs (CHT-X) at 500°C have been shown to recover their original layered structure by taking up chloride ion from aqueous solution. Adsorption of chloride by CHT-X was investigated in batch mode. The kinetics study showed that the pseudo-second-order kinetics model could be used to describe the adsorption process satisfactorily. The equilibrium isotherm showed that the Langmuir model gave a better fit to the experimental data than the Freundlich model. The maximum adsorption capacity of CHT-3 was 83.33 mg/g; CHT-4 was 90.09 mg/g .The samples of different Mg/Al ratio have different crystallite size, thus showing different adsorption capacity. As the Mg/Al ratio increases from 3 to 4; the electric charge density between the layers becomes weaker; the interlayer spacing increases; the sample shows greater adsorption capacity. The HT-X where characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), electron dispersive X-ray analysis (EDX).

In this paper, we first present a novel concept of 2-D basis interleaving array (also referred to as basis array for short). That is, an m × m interleaved array is said to be a basis array if the shortest distance among all pairs of elements in each of the so-called m-equivalent sets within the m × m array reaches the maximum. It is shown that this maximum is given by $${\lfloor \sqrt{2m} \rfloor}$$ and an m × m basis array can be constructed by using a simple cyclic translation method. The previously developed concept of successive packing is then generalized in the sense that it can be applied to any basis array to generate an interleaved array with a larger size. Except that optimality cannot be guaranteed, the concept of basis arrays and successive packing are extended to M-D cases. It is shown that for any M ? 2, the proposed technique can spread any error burst of block size $${m_{1}^{k} \times m_{2}^{k} \times \cdots \times m_{M}^{k}}$$ within an $${ m_{1}^{n} \times m_{2}^{n} \times \cdots \times m_{M}^{n}}$$ array (1 ? k ? n?1) so effectively that the error burst can be corrected with some simple random error-correcting code (provided the error-correcting code is available). It is shown that important prior results in M-D interleaving such as the t-interleaved array based approach by Blaum et al. and the successive packing approach by Shi and Zhang now become special cases of the framework based on basis arrays and successive packing, proposed in this paper.

Given an mtimesn array and k distinct colors with 2lesmlesn and 2lesk

We present an elementary theory of optimal interleaving schemes for correcting cluster errors in two-dimensional digital data. It is assumed that each data page contains a fixed number of, say n, codewords with each codeword consisting of m code symbols and capable of correcting a single random error (or erasure). The goal is to interleave the codewords in the mxn array such that different symbols from each codeword are separated as much as possible, and consequently, an arbitrary error burst with size up to t can be corrected for the largest possible value of t. We show that, for any given m, n, the maximum possible interleaving distance, or equivalently, the largest size of correctable error bursts in an mxn array, is given by [email protected][email protected]? if n= [email protected]?m^2/[email protected]?. Furthermore, we develop a simple cyclic shifting algorithm that can provide a systematic construction of an mxn optimal interleaving array for arbitrary m and n. This extends important earlier work on the complementary problem of constructing interleaving arrays that, given the burst size t, minimize the interleaving degree, that is, the number of different codewords in a 2-D (or 3-D) array such that any error burst with given size t can be corrected. Our interleaving scheme thus provides the maximum burst error correcting power without requiring prior knowledge of the size or shape of an error burst.

Given an mtimesn array of k single random error correction (or erasure) codewords, each having length l such that mn=kl, we construct optimal interleaving schemes that provide the maximum burst error correction power such that an arbitrarily shaped error burst of size t can be corrected for the largest possible value of t. We show that for all such mtimesn arrays, the maximum possible interleaving distance, or equivalently, the largest value of t such that an arbitrary error burst of size up to t can be corrected, is bounded by lfloorradic2krfloor if kleslceil(min{m,n})2/2rceil, and by min{m,n}+lfloor(k-lceil(min{m,n})2 /2rceil)/min{m,n}rfloor if kgeslceil(min{m,n})2/2rceil. We generalize the cyclic shifting algorithm developed by the authors in a previous paper and construct, in several special cases, optimal interleaving arrays achieving these upper bounds. Additionally, for codewords of variable lengths, we solve a related array coloring problem for which the same upper bounds hold and can be achieved

One of the key problems in the study of optimal interleaving schemes for correcting two-dimensional (2-D) cluster errors is how to place, say, n distinct symbols, each appearing m times, in an m/spl times/n array such that the resulting array has the maximum possible burst error-correcting power. In a previous paper, the authors have proved that for any given m, n, the maximum possible interleaving distance, and hence, the largest possible value t such that an arbitrary error burst of size t can be corrected in an m/spl times/n interleaved array, is given by t=/spl lfloor//spl radic/2n/spl rfloor/ for n = /spl les/ /spl lceil/m/sup 2//2/spl rceil/, and t=m+/spl lfloor/(n-/spl lceil/m/sup 2//2/spl rceil/)/m/spl rfloor/ for n /spl ges/ /spl lceil/m/sup 2//2/spl rceil/. In this work, we extend these results and show that for all m, n with n /spl ges/ m, an optimal m/spl times/n interleaving array can always be obtained by a Latin rectangle in which each row and each column contains each symbol at most once. This provides additional error-correcting power to the array in that all linear error bursts occupying a whole row or column can also be corrected.

In this paper we study the linearized relaxation model of Katsoulakis and Tzavaras in a half-space with arbitrary space dimension n ⩾1. Our main interest is to establish the asymptotic equivalence of the relaxation system and its corresponding multi-dimensional equilibrium conservation law. We identify and rigorously justify a necessary and sufficient condition (which we refer to as stiff Kreiss condition, or SKC in short) on the boundary condition to guarantee the uniform stability of the initial–boundary value problem of the relaxation system independent of the relaxation rate. The asymptotic convergence and the corresponding boundary layer behavior are studied by Fourier–Laplace transform and a detailed asymptotic analysis. The SKC is shown to be more restrictive than the classical uniform Kreiss condition for all n ⩾1.

In this paper we study the effects of small viscosity term and the far-field boundary conditions for systems of convection-diffusion equations in the zero viscosity limit. The far-field boundary conditions are classified and the corresponding solution structures are analyzed. It is confirmed that the Neumann type of far-field boundary condition is preferred. On the other hand, we also identify a class of improperly coupled boundary conditions which lead to catastrophic reflection waves dominating the inlet in the zero viscosity limit. The analysis is performed on the linearized convection-diffusion model which well describes the behavior at the far field for many physical and engineering systems such as fluid dynamical equations and electro-magnetic equations. The results obtained here should provide some theoretical guidance for designing effective far field boundary conditions.

In this paper, we give a systematic study of the boundary layer behavior for linear convection-diffusion equation in the zero viscosity limit. We analyze the boundary layer structures in the viscous solution and derive the boundary condition satisfied by the viscosity limit as a solution of the inviscid equation. The results confirm that the Neumann type of far-field boundary condition is preferred in the outlet and characteristic boundary condition. Under some appropriate regularity and compatibility conditions on the initial and boundary data, we obtain optimal error estimates between the full viscous solution and the inviscid solution with suitable boundary layer corrections. These results hold in arbitrary space dimensions and similar statements also hold for the strip problem.

The microphase adsorption-spectral correction (MPASC) technique is described and applied to the study of the interactions of Evans blue (EB) with cetyltrimethylammonium bromide (CTAB) and with four proteins: bovine serum albumin (BSA), myoglobin (Mb), hemoglobin (Hb) and ovalbumin (OVA). EB can be adsorbed on a cationic surfactant and on protein by electrostatic force and the aggregation obeys the Langmuir isotherm. Results have shown that the products are formed as follows: monomer aggregate EB·CTAB, micellar aggregate (EB·CTAB)78 and protein aggregates (EB68·BSA), (EB14·OVA), (EB126·Mb) and (EB58·Hb). The adsorption constant of the aggregates are calculated to be KEB·CTAB=2.95×106, KEB68·BSA=3.40×104, KEB14·OVA=5.20×102, KEB126·Mb=6.81×102 and KEB58·Hb=5.73×102, respectively. The aggregation of EB in proteins is sensitive in the presence of CTAB and selective in the presence of EDTA and it has been applied to the analysis of samples with satisfactory results.

In this paper we consider the initial-boundary value problem (IBVP) for the one-dimensional Jin-Xin relaxation model. The main interest is to study the boundary layer behaviors in the solutions to the IBVP of the relaxation system and their asymptotic convergence to solutions of the corresponding hyperbolic conservation laws in the limit of small relaxation rate. First we develop a general expansion theory for the relaxation IBVP using a matched asymptotic analysis. This formal procedure determines a unique equilibrium limit, and also reveals rich initial and boundary layer structures in the solutions of the relaxation system. Arbitrarily accurate solutions to the IBVP of the relaxation system are then constructed by combining the various orders of the equilibrium solutions, the initial and boundary layer solutions. The validity of the initial and boundary layers and the asymptotic convergence results are rigorously justified through a stability analysis for a broad class of boundary conditions in the case when the relaxation system is 2 × 2 2 \times 2 .