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Chinese Annals of Mathematics, Series B - In the present article, the authors find and establish stability of multiplier ideal sheaves, which is more general than strong openness. 相似文献
14.
Yves Pomeau 《Comptes Rendus Mecanique》2018,346(3):184-197
The equations for a self-similar solution to an inviscid incompressible fluid are mapped into an integral equation that hopefully can be solved by iteration. It is argued that the exponents of the similarity are ruled by Kelvin's theorem of conservation of circulation. The end result is an iteration with a nonlinear term entering a kernel given by a 3D integral for a swirling flow, likely within reach of present-day computational power. Because of the slow decay of the similarity solution at large distances, its kinetic energy diverges, and some mathematical results excluding non-trivial solutions of the Euler equations in the self-similar case do not apply. 相似文献
15.
Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint‐Venant‐Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technique that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue 2 objectives. First, we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. However, second, we reinterpret our scheme as a splitting technique and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least, when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated. 相似文献
16.
《Mathematical Methods in the Applied Sciences》2018,41(9):3246-3269
The purpose of this paper is to describe the oscillatory properties of second‐order Euler‐type half‐linear differential equations with perturbations in both terms. All but one perturbations in each term are considered to be given by finite sums of periodic continuous functions, while coefficients in the last perturbations are considered to be general continuous functions. Since the periodic behavior of the coefficients enables us to solve the oscillation and non‐oscillation of the considered equations, including the so‐called critical case, we determine the oscillatory properties of the equations with the last general perturbations. As the main result, we prove that the studied equations are conditionally oscillatory in the considered very general setting. The novelty of our results is illustrated by many examples, and we give concrete new corollaries as well. Note that the obtained results are new even in the case of linear equations. 相似文献
17.
Umie F.M. Haziz Rosenani A. Haque Shun-Ze Zhan Hassan H. Abdallah Mohd R. Razali 《应用有机金属化学》2020,34(10):e5818
The synthesis and characterizations for a series of dinuclear gold (I)-di-NHC complexes, 1–8 through the trans-metalation method of their respective silver (I)-di-NHC complexes, i–viii are reported (where NHC = N-heterocyclic carbene). The successful complexation of a series of unusual non-symmetrical and symmetrical di-NHC ligands, 3,3'-(ethane-1,2-diyl)-1-alkylbenzimidazolium-1'-butylbenzimidazolium (with alkyl = methyl, ethyl, propyl, butyl, pentyl, hexyl, heptyl, benzyl) with the gold (I) ions are suggested by elemental analysis, Fourier transform-infrared, 1H- and 13C-NMR data. The 13C-NMR spectra of 1–8 show a singlet sharp peak in the range of 190.00–192.00 ppm, indicating the presence of a carbene carbon that bonded to the gold (I) ion. From single crystal X-ray diffraction data, the structure of complex 6 with the formula of [di-NHC-Au (I)]2·2PF6 is obtained [where NHC = 3,3'-(ethane-1,2-diyl)-1-hexylbenzimidazolium-1'-butylbenzimidazolium]. The photophysical study in solid state of 6 displays an intense photoluminescence with a strong emission maxima, λem = 480 nm, upon excitation at 340 nm at room temperature. Interestingly, the emission maximum at 77 K shows a structural character with a strong peak at 410 nm, a medium at 433 nm and a weak at 387 nm, accompanied by a tail band to about 500 nm. 相似文献
18.
Some methods of training radial basis neural networks in solving the Navier‐Stokes equations 下载免费PDF全文
Bakhtgerey Sinchev Saulet Erbulatovna Sibanbayeva Axulu Mukhambetkaliyevna Mukhanova Assel Nurgulzhanovna Nurgulzhanova Nurgali Sabyrovich Zaurbekov Kairat Sovetovish Imanbayev Nadezhda Lvovna Gagarina Lyazzat Kemerbekovna Baibolova 《国际流体数值方法杂志》2018,86(10):625-636
The purpose of this research is to analyze the application of neural networks and specific features of training radial basis functions for solving 2‐dimensional Navier‐Stokes equations. The authors developed an algorithm for solving hydrodynamic equations with representation of their solution by the method of weighted residuals upon the general neural network approximation throughout the entire computational domain. The article deals with testing of the developed algorithm through solving the 2‐dimensional Navier‐Stokes equations. Artificial neural networks are widely used for solving problems of mathematical physics; however, their use for modeling of hydrodynamic problems is very limited. At the same time, the problem of hydrodynamic modeling can be solved through neural network modeling, and our study demonstrates an example of its solution. The choice of neural networks based on radial basis functions is due to the ease of implementation and organization of the training process, the accuracy of the approximations, and smoothness of solutions. Radial basis neural networks in the solution of differential equations in partial derivatives allow obtaining a sufficiently accurate solution with a relatively small size of the neural network model. The authors propose to consider the neural network as an approximation of the unknown solution of the equation. The Gaussian distribution is used as the activation function. 相似文献
19.
《Mathematical Methods in the Applied Sciences》2018,41(14):5691-5710
We consider a 2 time scale nonlinear system of ordinary differential equations. The small parameter of the system is the ratio ϵ of the time scales. We search for an approximation involving only the slow time unknowns and valid uniformly for all times at order O(ϵ2). A classical approach to study these problems is Tikhonov's singular perturbation theorem. We develop an approach leading to a higher order approximation using the renormalization group (RG) method. We apply it in 2 steps. In the first step, we show that the RG method allows for approximation of the fast time variables by their RG expansion taken at the slow time unknowns. Next, we study the slow time equations, where the fast time unknowns are replaced by their RG expansion. This allows to rigorously show the second order uniform error estimate. Our result is a higher order extension of Hoppensteadt's work on the Tikhonov singular perturbation theorem for infinite times. The proposed procedure is suitable for problems from applications, and it is computationally less demanding than the classical Vasil'eva‐O'Malley expansion. We apply the developed method to a mathematical model of stem cell dynamics. 相似文献
20.
In this paper, estimates for a trilinear operator associated with the Hartree type nonlinearity are proved. Moreover, as application of these estimates, it is proved that after a linear transformation, the Cauchy problem for the Hartree-type equation becomes locally well posed in the Bessel potential and homogeneous Besov spaces under certain regularity assumptions on the initial data. This notion of well-posedness and the functional framework to solve the equation were firstly proposed by Y. Zhou. 相似文献