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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
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该文研究了振荡Robin混合边值齐次化问题解的收敛率.该工作的困难之处在于Robin边值上出现的振荡因子以及边界交叉项的处理.该文利用对偶方法巧妙得对振荡积分进行了估计.文中建立了解的H1和L2收敛率,所得结果明显地依赖于维数.该文可以视为将对偶方法和光滑算子,延拓到处理振荡Robin混合边值问题的情形. 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
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In this paper we analyze some classes of abstract simplicial complexes relying on algebraic models arising from module theory. To this regard, we consider a left-module on a unitary ring and find models of abstract complexes and related set operators having specific regularity properties, which are strictly interrelated to the algebraic properties of both the module and the ring.Next, taking inspiration from the aforementioned models, we carry out our analysis from modules to arbitrary sets. In such a more general perspective, we start with an abstract simplicial complex and an associated set operator. Endowing such a set operator with the corresponding properties obtained in our module instances, we investigate in detail and prove several properties of three subclasses of abstract complexes.More specifically, we provide uniformity conditions in relation to the cardinality of the maximal members of such classes. By means of the notion of OSS-bijection, we prove a correspondence theorem between a subclass of closure operators and one of the aforementioned families of abstract complexes, which is similar to the classic correspondence theorem between closure operators and Moore systems. Next, we show an extension property of a binary relation induced by set systems when they belong to one of the above families.Finally, we provide a representation result in terms of pairings between sets for one of the three classes of abstract simplicial complexes studied in this work. 相似文献
8.
Ran Zhang Natalia Pavlovna Bondarenko Chuan Fu Yang 《Mathematical Methods in the Applied Sciences》2021,44(1):124-139
In this paper, we consider the Sturm–Liouville equation with the jump conditions inside the interval (0,π). The inverse problem is studied, which consists in recovering operator coefficients from two spectra, corresponding to different boundary conditions. We prove the uniqueness theorem and provide necessary and sufficient conditions for solvability of the inverse problem. We also obtain the oscillation theorem for the eigenfunctions of the considered discontinuous boundary value problem. 相似文献
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.
Marta Wojciechowska Piotr Stepnowski Marek Gołębiowski 《Biomedical chromatography : BMC》2022,36(5):e5346
This paper presents the effect of insecticides on the composition of the surface compounds of one of the most harmful insects, Tenebrio molitor, by analysis using GC–MS. As a result of the use of insecticides, the composition of the chemical compounds on the surface of insects changes, depending on the insecticides used. The most numerous groups of the marked compounds were fatty acids, alkanes, esters and sterols. The content of the identified compounds in the larvae increased at both 24 and 48 h after the application of insecticides, in comparison with the control samples. The content of identified compounds in the samples taken from the females increased 24, 48 and 72 h after the application of insecticides in comparison with the control samples. By contrast, in samples prepared from males, the content of identified compounds decreased 24 h after the application of insecticides, compared with the control samples. The highest content of chemical compounds was for fatty acids and alkanes after the use of insecticides. The content of fatty acids after the application of the insecticide with deltamethrin was 62.1 ± 3.3–466.9 ± 5.9 μg/g, and after the application of the insecticide with cyfluthrin was 49.9 ± 1.9–458.3 ± 4.2 μg/g. However, the content of alkanes after the use of deltamethrin was 115.6 ± 4.2–4672.0 ± 32.1 μg/g, and after the use of cyfluthrin was 189.4 ± 3.8–3975.0 ± 10.2 μg/g. 相似文献