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We propose a simple differential method and a refined Roonizi’s method to fit single Gaussian function and integro-differential method to fit two Gaussian functions. The conventional method for fitting Gaussian functions is an iterative procedure. The proposed methods, being linear in estimated parameters, alleviate the problem of critical initial guess needed in iterative procedures. The experimental results confirm the methods perform better or in a competitive manner compared to Caruana’s, Guo’s, Roonizi’s and FAS algorithm for single Gaussian case. It is found that the proposed integro-differential method to fit two Gaussian functions is stable and identifies Gaussian parameters in an efficient way.

This article concerns the estimation algorithms of battery's parameters and state of charge (SOC) and it is twofold. First, we present a simple variable length block wise least square estimation algorithm by considering locally linear SOC and open circuit voltage (OCV) relation on the run. The proposed algorithm can estimate accurately the parameters and follow the parameter changes. After estimating the battery parameters, SOC is directly computed from the combination of estimated parameters and SOC-OCV relation. This estimation scheme, which assumes hysteresis effect is negligible, is an online method. Second, if the hysteresis effect is considered in the model, we present an additional least square optimization problem to estimate SOC accurately. In this case, some parameters are tuned up in an offline way. Our approach compared with the extended Kalman filter based estimation method. The algorithms are validated by experiments with real data obtained from lab tests.

The stability of smooth solutions of an anisotropic surface quasi-geostrophic equation with horizontal dissipation remains an open problem. In this work, we present a partial answer to this problem in a rougher function space. More precisely, if the initial data θ0 belong to anisotropic Sobolev space H0, s with [Formula: see text], then there exists a global small solution, provided that the initial data are small in H0, s. The stability problem in the space H0,1 or more regular spaces remains open. The main tools used are the Littlewood–Paley theory and standard techniques.

We consider the existence of a class of stretched solutions of 2 1 2 D Magnetohydrodynamics equations in R 3 , which are sometimes called the columnar or two and half dimensional flows. The third components of the state variables have the form u 3 = x 3 γ 1 ( x 1 , x 2 ) + φ 1 ( x 1 , x 2 ) and B 3 = x 3 γ 2 ( x 1 , x 2 ) + φ 2 ( x 1 , x 2 ) and the first two components of the state variables depend on x 1 and x 2 only. We prove the local existence of such a flow in Sobolev spaces and give the regularity criteria in terms of 2 D vorticity ω or 2 D magnetic density j (but not both). Next, we identify the global existence of a class of axisymmetric flow without swirl for both velocity and magnetic field as a corollary of the main theorem. Finally, we present some exact global solutions as well as singular solutions with a special structure for viscous case and some exact global solutions for full inviscid case.

This paper concerns the wellposedness problem of Hall-MHD system. The mild solution of Hall-MHD equations exists globally in the nonhomogeneous Lei–Lin space setting provided that the initial data satisfies ‖ u 0 ‖ X − 1 ∩ X 0 + ‖ B 0 ‖ X − 1 ∩ X 0 min μ 2 , ν 4 , where μ is the viscosity of the fluid and ν is the magnetic diffusion coefficient. Our global existence result covers rougher initial data and improves the previous results.

We consider the chemotaxis Navier–Stokes equations which are the Keller–Segel model coupled to the incompressible Navier–Stokes equations in dimension three. We prove the global existence of the solution in the critical Besov spaces with small initial data only, which is a new result and improves the previous result.

We consider the Keller–Segel model coupled with the incompressible Navier–Stokes equations in the dimension three. Based on the wellposedness result in the critical Besov spaces, we present a result on the extension criterion for the local in time solution in the same functional setting, which is a new result for the model.

We consider the Keller-Segel model coupled with the incompressible Navier-Stokes equations in dimension three. We prove the local in time existence of the solution for large initial data and the global in time existence of the solution for small initial data plus some smallness condition on the gravitational potential in the critical Besov spaces, which are new results for the model.