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1.
On Regularization of a Source Identification Problem in a Parabolic PDE and its Finite Dimensional Analysis 下载免费PDF全文
Subhankar Mondal & M. Thamban Nair 《偏微分方程(英文版)》2021,34(3):240-257
We consider the inverse problem of identifying a general source term, which is a function of both time variable and the spatial variable, in a parabolic PDE from the knowledge of boundary measurements of the solution on some portion of the lateral boundary. We transform this inverse problem into a problem of solving a compact linear operator equation. For the regularization of the operator equation with noisy data, we employ the standard Tikhonov regularization, and its finite dimensional realization is done using a discretization procedure involving the space $L^2(0,\tau;L^2(Ω))$. For illustrating the specification of an a priori source condition, we have explicitly obtained the range space of the adjoint of the operator involved in the operator equation. 相似文献
2.
本文考虑一类离散型随机$R_0$ 张量互补问题,利用Fischer-Burmeister函数将问题转化为约束优化问题,并用投影Levenberg-Marquardt方法对其进行了求解。在一般的条件下得到了该方法的全局收敛性,相关的数值实验表明了该方法的有效性。 相似文献
3.
使用Galerkin方法,结合Sobolev空间理论和不等式技巧,给出了广义神经传播方程解的存在唯一性定理,然后利用吸引子存在性定理,采用半群方法证明了方程整体吸引子的存在性. 相似文献
4.
Hacer Bilgin Ellidokuzoğlu & Serkan Demiriz 《分析论及其应用》2021,37(4):557-571
Başar and Braha [1], introduced the sequence spaces $\breve{\ell}_\infty$, $\breve{c}$ and $\breve{c}_0$ of Euler-Cesáro bounded, convergent and null difference sequences and studied their some properties. Then, in [2], we introduced the sequence spaces ${[\ell_\infty]}_{e.r}, {[c]}_{e.r}$ and ${[c_0]}_{e.r}$ of Euler-Riesz bounded, convergent and null difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. The main purpose of this study is to introduce the sequence space ${[\ell_p]}_{e.r}$ of Euler-Riesz $p-$absolutely convergent series, where $1 \leq p <\infty$, difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. Furthermore, the inclusion $\ell_p\subset{[\ell_p]}_{e.r}$ hold, the basis of the sequence space ${[\ell_p]}_{e.r}$ is constructed and $\alpha-$, $\beta-$ and $\gamma-$duals of the space are determined. Finally, the classes of matrix transformations from the ${[\ell_p]}_{e.r}$ Euler-Riesz difference sequence space to the spaces $\ell_\infty, c$ and $c_0$ are characterized. We devote the final section of the paper to examine some geometric properties of the space ${[\ell_p]}_{e.r}$. 相似文献
5.
Presenting the devices invented by Toepler, Holtz, Wimshurst, and Wommelsdorf, the history of the influence machines, the progress made, and the remaining deficits are discussed. The theoretical considerations published in the literature lack generalizable statements on the efficiency. Based on R. W. Pohl's model (1927), an elementary analysis is made, with the result that the upper limit of the theoretically achievable efficiency of influence machines is only 50%. 相似文献
6.
The aim of this work was to evaluate the influence of US on the properties of the fluconazole emulsions prepared using imidazolium-based ILs ([Cn C1im]Br). The effects of the preparation method (mechanical stirring or US), US amplitude, alkyl chain length (of [C12C1im]Br or [C16C1im]Br), and IL concentration on the physicochemical properties were evaluated. Properties such as droplet size, span index, morphology, viscosity encapsulation efficiency, and drug release profile were determined. The results showed that US-prepared emulsions had a smaller droplet size and smaller polydispersity (Span) than those prepared by mechanical stirring. Additionally, the results showed that emulsions prepared with [C16C1im]Br and US had spherical shapes and increased stability compared to emulsions prepared by MS, and also depended on the IL concentration. The emulsion prepared by US at 40% amplitude had increased encapsulation efficiency. US provided a decrease in the viscosity of emulsions containing [C12C1im]Br; however, in general, all emulsions had viscosity close to that of water. Emulsions containing [C16C1im]Br had the lowest viscosities of all the emulsions. The emulsions containing the IL [C16C1im]Br had more controlled release and a lower cumulative percentage of drug release. The IL concentration required to prepare these emulsions was lower than the amount of conventional surfactant required, which highlights the potential synergic effects of ILs and US in preparing emulsions of hydrophobic drugs. 相似文献
7.
In the past decade, big data has become increasingly prevalent in a large number of applications. As a result, datasets suffering from noise and redundancy issues have necessitated the use of feature selection across multiple domains. However, a common concern in feature selection is that different approaches can give very different results when applied to similar datasets. Aggregating the results of different selection methods helps to resolve this concern and control the diversity of selected feature subsets. In this work, we implemented a general framework for the ensemble of multiple feature selection methods. Based on diversified datasets generated from the original set of observations, we aggregated the importance scores generated by multiple feature selection techniques using two methods: the Within Aggregation Method (WAM), which refers to aggregating importance scores within a single feature selection; and the Between Aggregation Method (BAM), which refers to aggregating importance scores between multiple feature selection methods. We applied the proposed framework on 13 real datasets with diverse performances and characteristics. The experimental evaluation showed that WAM provides an effective tool for determining the best feature selection method for a given dataset. WAM has also shown greater stability than BAM in terms of identifying important features. The computational demands of the two methods appeared to be comparable. The results of this work suggest that by applying both WAM and BAM, practitioners can gain a deeper understanding of the feature selection process. 相似文献
8.
9.
In this paper, we develop a simplified hybrid weighted essentially non-oscillatory (WENO) method combined with the modified ghost fluid method (MGFM)
[31] to simulate the compressible two-medium flow problems. The MGFM can turn
the two-medium flow problems into two single-medium cases by defining the ghost
fluids state in terms of the predicted the interface state, which makes the material
interface “invisible”. For the single medium flow case, we adapt between the linear
upwind scheme and the WENO scheme automatically by identifying the regions of
the extreme points for the reconstruction polynomial as same as the hybrid WENO
scheme [55]. Instead of calculating their exact locations, we only need to know the
regions of the extreme points based on the zero point existence theorem, which is
simpler for implementation and saves computation time. Meanwhile, it still keeps
the robustness and has high efficiency. Extensive numerical results for both one
and two dimensional two-medium flow problems are performed to demonstrate the
good performances of the proposed method. 相似文献
10.
GAO Jian-kui LI Yi-jie ZHANG Qin-nan LIU Bing-wei LIU Jing-bo LING Dong-xiong LI Run-hua WEI Dong-shan 《光谱学与光谱分析》2021,41(11):3347-3351
聚醚醚酮(PEEK)由于其耐热、耐腐蚀、耐辐照、抗疲劳、电绝缘性等优良性能,在许多领域可以代替金属、陶瓷等传统材料而得到广泛应用。特别是随着5G技术的发展和应用,PEEK已经成为5G热门材料。在PEEK材料实际应用中,温度的影响是一个非常重要和关键的因素。主要研究了PEEK太赫兹光谱以及温度对PEEK太赫兹光谱特性的影响。通过利用太赫兹透射光谱技术,同时结合控温装置,在温度从25~300 ℃均匀上升过程中,每间隔5 ℃测试得到PEEK片状样品的太赫兹时域光谱数据,利用光学参数提取算法可以得到PEEK的吸收系数、介电常数等光学参数,进一步得到特定频率下光学常数随温度的变化趋势,从而对材料进行表征和分析。在0.5~4 THz有效光谱范围内,实验结果表明,在常温(25 ℃)下,PEEK在3.5 THz具有一个明显的特征吸收峰。在25~300 ℃这个温度范围内,在1 THz频率下,PEEK的吸收系数、介电常数相对于室温分别有4.38%和5.0%的波动,同时PEEK在常温下在1 THz的介电损耗正切值为2.5×10-3,相比于PMMA和PE等高分子材料,PEEK的介电损耗正切值要低得多,且在升温过程保持相对稳定,表明PEEK在太赫兹频段的光谱特性具有很好的热稳定性和较低的介电损耗。研究结果表明,太赫兹光谱技术可以结合温控装置,通过材料的光学参数对高分子材料热稳定性进行研究和表征,同时还可以得到材料在不同温度下的介电性质。太赫兹光谱技术具有快速、高效、无标记、无损伤等优势,只需要压片就可以对固体样品进行测试,对于研究材料内部缺陷、稳定性以及材料的鉴别等具有很好的研究意义。同时本实验的测试数据可以为PEEK材料在不同温度下5G和6G等高频通信应用提供参考。 相似文献