Abstract:
Objective: To observe the changes on skin wheal and erythema of skin prick test for the patients with allergic rhinitis during SLIT. Methods: Since March 2010 the 103 cases of SLIT attacked by allergic rhinitis patients, divided into four age groups, respectively measured the diameter of skin wheal and erythema before treatment, six months, one year and 2 years after SLIT. The data were analyzed by analysis of variance method; P < 0.01 showed the difference was statistically significant. Results: The results showed that the most changes of skin erythema diameter were statistically significant in N1, N2, N3 age group during test observation compare with the data before SLIT (p < 0.01); and the most changes of allergen wheal diameter were not statistically significant, but the N4 group had no significant change of wheal and erythema diameter. Conclusion: Although most of the skin test wheal did not change significantly during the treatment of SLIT, the erythema reaction decreased to a certain extent, indicating that the intensity of histamine release may be reduced during the treatment.

Abstract:
Objective: The partial inferior turbinectomy and septoplasty was applied to treat the
allergic perennial rhinitis (APR), and to observe the ultrastructure changes of the
nasal mucosa before and after the operations. Methods: For 36 cases of research objects
diagnosed with APR, the partial inferior turbinectomy and septoplasty was administered.
For 6 APR cases among them, the pre- and postoperative observation of
anterior nasal mucosa of the inferior turbinate on the same side under the electron
microscope was conducted for one year respectively. In addition, their pathological
alterations of tissues were also conducted. Results: In the pre-operative observation
under the electron microscope, it was found that the nasal mucosae epithelium cells
were nude without cilia. The lamina propria had edema, and mesenchyme presented
the infiltration of substantial eosinophilic granulocytes, basophilic granulocytes,
plasmacytes and mast cells. Additionally, abundant degranulation and vacuolation of
cytoplasts were observed. The plentiful glands, duct ectasia, edema and structural
changes were also found. Some gland cells had degenerated. After the operation, it
was found that the epithelium nudity still existed and the deficiency of cilia was not
improved. Only a very small amount of microvilli existed. The edema of lamina propria
was improved and eosinophilic granulocytes were rarely observed in mesenchyme.
However, the infiltration of basophilic granulocytes, plasmocytes and mast
cells was still observed. The particle structure was generally stable and the central
crystal was clear without degranulation. Meanwhile, the amount of glands was reduced
and the tissue structure tended to be recovered. Overall, the nasal mucosa
showed changes as chronic inflammation. Conclusions: For the treatment of APR
with the methods presented by our research institution, in one year before and after
the operation, ultrastructural changes of inferior turbinate mucosa tissues were observed
from the preoperatively pathological changes of typical APR to the chronic
inflammation with the primary infiltration of neutrophilic granulocyte and mast cells.

Abstract:
In this paper we study fast iterative solvers for the large sparse linear systems resulting from the stochastic Galerkin discretization of stochastic partial differential equations. A block triangular preconditioner is introduced and applied to the Krylov subspace methods, including the generalized minimum residual method and the generalized preconditioned conjugate gradient method. This preconditioner utilizes the special structures of the stochastic Galerkin matrices to achieve high efficiency. Spectral bounds for the preconditioned matrix are provided for convergence analysis. The preconditioner system can be solved approximately by geometric multigrid V-cycle. Numerical results indicate that the block triangular preconditioner has better performance than the traditional block diagonal preconditioner for stochastic problems with large variance.

Abstract:
Assume that $V_h$ is a space of piecewise polynomials of degree less than $r\geq 1$ on a family of quasi-uniform triangulation of size $h$. Then the following well-known upper bound holds for a sufficiently smooth function $u$ and $p\in [1, \infty]$ $$ \inf_{v_h\in V_h}\|u-v_h\|_{j,p,\Omega,h} \le C h^{r-j} |u|_{r,p,\Omega},\quad 0\le j\le r. $$ In this paper, we prove that, roughly speaking, if $u\not\in V_h$, the above estimate is sharp. Namely, $$ \inf_{v_h\in V_h}\|u-v_h\|_{j,p,\Omega,h} \ge c h^{r-j},\quad 0\le j\le r, \ \ 1\leq p\leq \infty, $$ for some $c>0$. The above result is further extended to various situations including more general Sobolev space norms, general shape regular grids and many different types of finite element spaces. As an application, the sharpness of finite element approximation of elliptic problems and the corresponding eigenvalue problems is established.

Abstract:
The paper aims to analyze the symbolic meaning of Blanche in Tennessee Williams’ A Streetcar Named Desire. William has consistently employed symbolism to universalize the significance of the realistic action he posits, not only because he thinks of symbolism as essential of art, but because it seems to be characteristic of his personal reactions to life in general. Blanche DuBois, the very name, her appearance and dressing, her illusionary vision of the world, and her lantern together with her desire all contribute to William’s symbolic portrait of a southern belle. Displaced in an unfavorable environment, Blanche finally collapses mentally and excluded out of the new industrial world.

Abstract:
In this paper, we consider elliptic boundary value problems with discontinuous coefficients and obtain the asymptotic optimal error estimate $\|u-u_k\|_{1,\Omega}\leqslant Ch|\ln h|^{1/2}\|u\|_{2,\Omega_1+\Omega_2}$ for triangle linear elements.

Abstract:
In this paper, we analyze the convergence and optimality of a standard adaptive nonconforming linear element method for the Stokes problem. After establishing a special quasi--orthogonality property for both the velocity and the pressure in this saddle point problem, we introduce a new prolongation operator to carry through the discrete reliability analysis for the error estimator. We then use a specially defined interpolation operator to prove that, up to oscillation, the error can be bounded by the approximation error within a properly defined nonlinear approximate class. Finally, by introducing a new parameter-dependent error estimator, we prove the convergence and optimality estimates.

Abstract:
In this paper we develop a family of preconditioners for the linear algebraic systems arising from the arbitrary Lagrangian-Eulerian discretization of some fluid-structure interaction models. After the time discretization, we formulate the fluid-structure interaction equations as saddle point problems and prove the uniform well-posedness. Then we discretize the space dimension by finite element methods and prove their uniform well-posedness by two different approaches under appropriate assumptions. The uniform well-posedness makes it possible to design robust preconditioners for the discretized fluid-structure interaction systems. Numerical examples are presented to show the robustness and efficiency of these preconditioners.

Abstract:
This paper provides the first provable $\mathcal{O}(N \log N)$ algorithms for the linear system arising from the direct finite element discretization of the fourth-order equation with different boundary conditions on unstructured grids of size $N$ on an arbitrary polygoanl domain. Several preconditioners are presented, and the conjugate gradient methods applied with these preconditioners are proven to converge uniformly with respect to the size of the preconditioned linear system. One main ingredient of the optimal preconditioners is a mixed-form discretization of the fourth-order problem. Such a mixed-form discretization leads to a non-desirable ---either non-optimal or non-convergent--- approximation of the original solution, but it provides optimal preconditioners for the direct finite element problem. It is further shown that the implementation of the preconditioners can be reduced to the solution of several discrete Poisson equations. Therefore, any existing optimal or nearly optimal solver, such as geometric or algebraic multigrid methods, for Poisson equations would lead to a nearly optimal solver for the discrete fourth-order system. A number of nonstandard Sobolev spaces and their discretizations defined on the boundary of polygonal domains are carefully studied and used for the analysis of those preconditioners.

Abstract:
In this paper, we develop two classes of mixed finite element discretization for stationary MHD models, one using $\bm B$ (the magnetic field) and $\bm E$ (the electric field) as the discretization variables while the other using $\bm B$ and $\bm j$ (the current density) as the discretization variables. We show that the Gauss's law for magnetic field, namely $\nabla\cdot\bm{B}=0$, and the energy law for the entire system are preserved for both of these finite element schemes. We further establish that both of these new finite element schemes are well-posed under certain conditions, but we conclude that the finite element scheme based on $\bm B$-$\bm j$ formulation seems to be superior than the one based on $\bm B$-$\bm E$ formulation as the former requires much weaker conditions than the latter does.