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T. Ya. Ershova - One of the best experts on this subject based on the ideXlab platform.

  • On the convergence of the Dirichlet grid problem with a singularity for a singularly perturbed convection–diffusion equation
    Moscow University Computational Mathematics and Cybernetics, 2016
    Co-Authors: T. Ya. Ershova
    Abstract:

    The Dirichlet problem for a singulary perturbed convection–diffusion equation in a rectangle when a discontinuity at the flow exit the first derivative of the boundary condition gives rise to an inner layer for the solution. On piecewise-uniform Shishkin grids that condense near regular and characteristic layers, the solution obtained using the classical five-Point Difference scheme with a directed Difference is shown to converge with respect to the small parameter to solve the original problem in the grid norm L _∞ ^ h almost with the first order. This theoretical result is confirmed via numerical analysis.

  • A mixed boundary value problem for a singularly perturbed reaction-diffusion equation in an L-shaped domain
    Moscow University Computational Mathematics and Cybernetics, 2012
    Co-Authors: T. Ya. Ershova
    Abstract:

    A mixed boundary value problem for a singularly perturbed reaction-diffusion equation in an L -shaped domain is considered for when the solution has singularities at the corners of the domain. The densification of the Shishkin mesh near the inner corner where different boundary conditions meet is such that the solution obtained by the classical five-Point Difference scheme converges to the solution of the initial problem in the mesh norm L _∞ ^ h uniformly with respect to the small parameter with almost second order, i.e., as a smooth solution. Numerical analysis confirms the theoretical result.

  • Solution of the Dirichlet problem for a singularly perturbed reaction-diffusion equation in a square on a Bakhvalov grid
    Moscow University Computational Mathematics and Cybernetics, 2009
    Co-Authors: T. Ya. Ershova
    Abstract:

    The Dirichlet problem for a singularly perturbed reaction-diffusion equation in a square is solved with the help of the classic five-Point Difference scheme and a grid that is the tensor product of 1D Bakhvalov grids. Without imposing additional matching conditions in the corners of the domain, it is shown that the grid solution to the problem has the accuracy O ( N ^−2) in the norm L _∞ ^ h , where N is the number of grid nodes along each direction. The accuracy is uniform with respect to a small parameter. A simulation confirms the theoretical prediction.

Wladimir Andreff - One of the best experts on this subject based on the ideXlab platform.

Mary Giffear - One of the best experts on this subject based on the ideXlab platform.

  • safety efficacy and immunogenicity of vgx 3100 a therapeutic synthetic dna vaccine targeting human papillomavirus 16 and 18 e6 and e7 proteins for cervical intraepithelial neoplasia 2 3 a randomised double blind placebo controlled phase 2b trial
    The Lancet, 2015
    Co-Authors: Cornelia L Trimble, Matthew P Morrow, Kimberly A Kraynyak, Xuefei Shen, Michael J Dallas, Jian Yan, Lance Edwards, Lamar R Parker, Lynette Denny, Mary Giffear
    Abstract:

    Summary Background Despite preventive vaccines for oncogenic human papillomaviruses (HPVs), cervical intraepithelial neoplasia (CIN) is common, and current treatments are ablative and can lead to long-term reproductive morbidity. We assessed whether VGX-3100, synthetic plasmids targeting HPV-16 and HPV-18 E6 and E7 proteins, delivered by electroporation, would cause histopathological regression in women with CIN2/3. Methods Efficacy, safety, and immunogenicity of VGX-3100 were assessed in CIN2/3 associated with HPV-16 and HPV-18, in a randomised, double-blind, placebo-controlled phase 2b study. Patients from 36 academic and private gynaecology practices in seven countries were randomised (3:1) to receive 6 mg VGX-3100 or placebo (1 mL), given intramuscularly at 0, 4, and 12 weeks. Randomisation was stratified by age ( vs ≥25 years) and CIN2 versus CIN3 by computer-generated allocation sequence (block size 4). Funder and site personnel, participants, and pathologists were masked to treatment. The primary efficacy endPoint was regression to CIN1 or normal pathology 36 weeks after the first dose. Per-protocol and modified intention-to-treat analyses were based on patients receiving three doses without protocol violations, and on patients receiving at least one dose, respectively. The safety population included all patients who received at least one dose. The trial is registered at ClinicalTrials.gov (number NCT01304524) and EudraCT (number 2012-001334-33). Findings Between Oct 19, 2011, and July 30, 2013, 167 patients received either VGX-3100 (n=125) or placebo (n=42). In the per-protocol analysis 53 (49·5%) of 107 VGX-3100 recipients and 11 (30·6%) of 36 placebo recipients had histopathological regression (percentage Point Difference 19·0 [95% CI 1·4–36·6]; p=0·034). In the modified intention-to-treat analysis 55 (48·2%) of 114 VGX-3100 recipients and 12 (30·0%) of 40 placebo recipients had histopathological regression (percentage Point Difference 18·2 [95% CI 1·3–34·4]; p=0·034). Injection-site reactions occurred in most patients, but only erythema was significantly more common in the VGX-3100 group (98/125, 78·4%) than in the placebo group (24/42, 57·1%; percentage Point Difference 21·3 [95% CI 5·3–37·8]; p=0·007). Interpretation VGX-3100 is the first therapeutic vaccine to show efficacy against CIN2/3 associated with HPV-16 and HPV-18. VGX-3100 could present a non-surgical therapeutic option for CIN2/3, changing the treatment outlook for this common disease. Funding Inovio Pharmaceuticals.

Reiner Vanselow - One of the best experts on this subject based on the ideXlab platform.

Robert M. M. Mattheij - One of the best experts on this subject based on the ideXlab platform.

  • Estimating the Discretization Error in three Point Difference Schemes for Second Order Linear Singularly Perturbed BVP
    North-holland Mathematics Studies, 2008
    Co-Authors: Robert M. M. Mattheij
    Abstract:

    Abstract Consider the problem (1)-ey″ + py′ + gy = r, y(-1),y(1) given, and a Difference scheme on a set of nodalPoints t i , i = 0,…,N (2) a i u i+1 + b i u i + c i u i-1 = r i (where u i denotes an approximant to y(t i )). By using a technique developped in [5] for estimating homogeneous solutions of (2), we show how we can obtain useful estimates for the local Green's functions {G i (j)} of (2) ({G i (j)} is a solution of (2) with B C G O (j) = G N (j) = 0, r i = δ ij ). Once the local discretization error is computed, an estimate for the global error simply follows using these {G i (j)}. This method provides for a good insight into the error propagation. It is also a useful alternative for positivity arguments (notably when (2) is not positive). We give several examples of applications.

  • Estimates for the inverse of tridiagonal matrices arising in boundary-value problems☆
    Linear Algebra and its Applications, 2002
    Co-Authors: Robert M. M. Mattheij, M.d. Smooke
    Abstract:

    By considering tridiagonal matrices as three-term recurrence relations with Dirichlet boundary conditions, one can formulate their inverses in terms of Green's functions. This analysis is applied to three-Point Difference schemes for 1-D problems, and five-Point Difference schemes for 2-D problems. We derive either an explicit inverse of the Jacobian or a sharp estimate for both uniform and nonuniform grids.