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On the (N+1)-dimensional local fractional reduced differential transform method and its applications
Jian-Gen Liu Xiao-Jun Yang Yi-Ying Feng Ping Cui 《Mathematical Methods in the Applied Sciences》2020,43(15):8856-8866
In this paper, we generalize the (N+1)-dimensional local fractional reduced differential transform method (LFRDTM) within the local fractional derivative sense. First, we show some new properties, lemmas, theorems and corollariesfor the (N+1)-dimensional LFRDTM. Second, these new properties, lemmas and theorems can be proved immediately after. Thirdly, we used two examples to state that this approach is efficient and simple to find numerical solutions to higher dimensional local fractional partial differential equations. Finally, we can be seen that this work can be looked as an extension of the prior work. 相似文献
53.
Florian Wagener 《Natural Resource Modeling》2020,33(3):e12258
Natural resources are not infinitely resilient and should not be modeled as being such. Finitely resilient resources feature tipping points and history dependence. This paper provides a didactical discussion of mathematical methods that are needed to understand the optimal management of such resources: viscosity solutions of Hamilton–Jacobi–Bellman equations, the costate equation and the associated canonical equations, exact root counting, and geometrical methods to analyze the geometry of the invariant manifolds of the canonical equations. Recommendations for Resource Managers
- Management of natural resources has to take into account the possible breakdown of resilience and induced regime shifts.
- Depending on the characteristics of the resource and on its present and future economic importance, either for all initial states the same kind of management policy is optimal, or the type of the optimal management policy depends on the initial state.
- Modeling should reflect the finiteness of the data.
54.
Qiong-Tao Xie 《理论物理通讯》2020,72(6):65105-64
An analytical method is developed to study the two-mode quantum Rabi model. For certain specific parameter conditions, especially for the resonant conditions, we obtain an infinite number of the exact solutions of the eigenfunctions and associated energies. It is shown that there exist new types of the exact energies which do not correspond to the level-crossings. Our analytical method may find applications in some related models. 相似文献
55.
《Physics letters. A》2020,384(36):126913
A new approach to find exact solutions to one–dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions having vanishing and non–vanishing Bohm potentials. For most of the potentials, no solutions to the Schrödinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some quantum, such as accelerated Airy wavefunctions, are due to the presence of non–vanishing Bohm potentials. New examples of this kind are found and discussed. 相似文献
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César Adolfo Melo Hernández Edgar Yesid Lancheros Mayorga 《Mathematische Nachrichten》2020,293(4):721-734
In this paper, information about the instability of equilibrium solutions of a nonlinear family of localized reaction-diffusion equations in dimension one is provided. More precisely, explicit formulas to the equilibrium solutions are computed and, via analytic perturbation theory, the exact number of positive eigenvalues of the linear operator associated to the stability problem is analyzed. In addition, sufficient conditions for blow up of the solutions of the equation are also discussed. 相似文献
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