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991.
In this paper the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation is investigated. The integrability test is performed yielding a positive result. Through the Painlevé–Bäcklund transformation, we derive four types of lump-kink solutions composed of two quadratic functions and N exponential functions. It is shown that fission and fusion interactions occur in the lump-kink solutions. Furthermore, a new variable separation solution with two arbitrary functions is obtained, the localized excitations including lumps, dromions and periodic waves are analyzed by some graphs. 相似文献
992.
993.
Recyclable MoO3 nanobelts for photocatalytic degradation of Rhodamine B by near infrared irradiation
Molybdenum trioxide (MoO3) represented an excellent photocatalytic performance with many applications, including degradation of organic contaminants and splitting of water. This paper presented a new route to synthesize MoO3 nanobelts with high aspect ratios and crystallinity by a hydrothermal technique. This work showed that the as-synthesized nanobelts exhibited strong photocatalytic activity to degrade an organic dye of Rhodamine B (RhB) in aqueous solution under the exposure of the light source in the near infrared wavelength range, significantly improving the photocatalytic activity of the nanobelts. The results also showed that for a small concentration of RhB at 7.5 mg/L a complete photodegradation (for a given MoO3 nanobelts quantity of 0.1 g) can be reached after exposing for 60 min. For all concentrations of the RhB solution, the photodegradation exhibited an exponential dependence on the exposure time followed by a sudden shutdown, but no complete photodegradation can be reached. Also, the residual quantity of RhB in solution after the photocatalytic reaction was determined by the initial RhB concentration. The photocatalytic degradation can be interpreted by the pseudo–first-order equation for the absorption of liquid/solid based on solid capacity; thus, photocatalytic degradation can be attributed to the interaction between the photoexcited electrons in the substrate and the antibonding orbital of the RhB in solution. The sudden shutdown was due to the inability of the photoexcited electrons in the substrate hopping to the antibonding orbital of RhB in the presence of the RhB intermediate products from the degraded RhB. In addition, this work showed that the photocatalytic reaction can be recovered after a thermal treatment of postreacted MoO3 nanobelts, enhancing the utilization efficiency of the catalysis. 相似文献
994.
Franziska Kühn 《Mathematische Nachrichten》2019,292(2):358-376
We present an existence result for Lévy‐type processes which requires only weak regularity assumptions on the symbol with respect to the space variable x. Applications range from existence and uniqueness results for Lévy‐driven SDEs with Hölder continuous coefficients to existence results for stable‐like processes and Lévy‐type processes with symbols of variable order. Moreover, we obtain heat kernel estimates for a class of Lévy and Lévy‐type processes. The paper includes an extensive list of Lévy(‐type) processes satisfying the assumptions of our results. 相似文献
995.
996.
Basak Karpuz 《Mathematical Methods in the Applied Sciences》2019,42(9):2993-3001
In this paper, we give new sufficient conditions for both oscillation and nonoscillation of the delay dynamic equation where and satisfy τ(t) ≤ σ(t) for all large t and . As an important corollary, we obtain the time scale invariant integral condition for nonoscillation: for all large t. Also, with some examples, we show that newly presented results are sharp. 相似文献
997.
Rong Chen Zhijun Qiao Shouming Zhou 《Mathematical Methods in the Applied Sciences》2019,42(18):6999-7010
Considered herein is a two‐component Novikov equations (called Geng‐Xue system for short) with cubic nonlinearities. The persistence properties and some unique continuation properties of the solutions to the system in weighted Lp spaces are established. Moreover, a wave‐breaking criterion for strong solutions is determined in the lowest Sobolev space by using the localization analysis in the transport equation theory, and we also give a lower bound for the maximal existence time. 相似文献
998.
Julia Calatayud Juan Carlos Corts Marc Jornet 《Mathematical Methods in the Applied Sciences》2019,42(18):7259-7267
In this paper, we address the problem of approximating the probability density function of the following random logistic differential equation: P′(t,ω)=A(t,ω)(1?P(t,ω))P(t,ω), t∈[t0,T], P(t0,ω)=P0(ω), where ω is any outcome in the sample space Ω. In the recent contribution [Cortés, JC, et al. Commun Nonlinear Sci Numer Simulat 2019; 72: 121–138], the authors imposed conditions on the diffusion coefficient A(t) and on the initial condition P0 to approximate the density function f1(p,t) of P(t): A(t) is expressed as a Karhunen–Loève expansion with absolutely continuous random coefficients that have certain growth and are independent of the absolutely continuous random variable P0, and the density of P0, , is Lipschitz on (0,1). In this article, we tackle the problem in a different manner, by using probability tools that allow the hypotheses to be less restrictive. We only suppose that A(t) is expanded on L2([t0,T]×Ω), so that we include other expansions such as random power series. We only require absolute continuity for P0, so that A(t) may be discrete or singular, due to a modified version of the random variable transformation technique. For , only almost everywhere continuity and boundedness on (0,1) are needed. We construct an approximating sequence of density functions in terms of expectations that tends to f1(p,t) pointwise. Numerical examples illustrate our theoretical results. 相似文献
999.
The inverse problem of determining 2D spatial part of integral member kernel in integro‐differential wave equation is considered. It is supposed that the unknown function is a trigonometric polynomial with respect to the spatial variable y with coefficients continuous with respect to the variable x. Herein, the direct problem is represented by the initial‐boundary value problem for the half‐space x>0 with the zero initial Cauchy data and Neumann boundary condition as Dirac delta function concentrated on the boundary of the domain . Local existence and uniqueness theorem for the solution to the inverse problem is obtained. 相似文献
1000.