We study mean-field type optimal stochastic control problem for systems governed by mean-field controlled forward–backward stochastic differential equations with jump processes, in which the coefficients depend on the marginal law of the state process through its expected value. The control variable is allowed to enter both diffusion and jump coefficients. Moreover, the cost functional is also of mean-field type. Necessary conditions for optimal control for these systems in the form of maximum principle are established by means of convex perturbation techniques. As an application, time-inconsistent mean-variance portfolio selection mixed with a recursive utility functional optimization problem is discussed to illustrate the theoretical results.

We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation. As applications, the small deviations and Chung’s law of the iterated logarithm are obtained.

In this article, we address two issues related to the perturbation method introduced by Zhang and Lu (J Comput Phys 194:773–794, 2004), and applied to solving linear stochastic parabolic PDE. Those issues are the construction of the perturbation series, and its convergence.

With the notion of weakly weighted sharing and relaxed weighted sharing, we investigate the uniqueness problems of certain type of difference polynomials sharing a small function. The results of the paper extend and generalize some recent results due to Meng (Math. Bohem. 139:89–97, 2014).

In this paper, we consider the convergence of the generalized Kähler-Ricci flow with semi-positive twisted form $\theta $ on Kähler manifold $M$. We give detailed proofs of the uniform Sobolev inequality and some uniform estimates for the metric potential and the generalized Ricci potential along the flow. Then assuming that there exists a generalized Kähler-Einstein metric, if the twisting form $\theta $ is strictly positive at a point or $M$ admits no nontrivial Hamiltonian holomorphic vector field, we prove that the generalized Kähler-Ricci flow must converge in $C^\infty $ topology to a generalized Kähler-Einstein metric exponentially fast, where we get the exponential decay without using the Futaki invariant.

Due to the shortages of current methods for the recovery of sharp features of mesh models with holes, this paper presents two novel algorithms for the recovery of features (especially sharp features) in mesh models. One algorithm defines an energy that is regarded as the difference between the initial features and the ideal features. The optimal solution of the energy optimization problem modifies the initial features. The algorithm has good performance on sharp features. The other method establishes a plane cluster for each initial feature point to obtain a corresponding modified feature point. If necessary, we can obtain the modified feature line by fitting these modified points. Both methods depend little on the result of filling model holes and result in better features, which maintain the sharp geometric characteristic and the smoothness of the model. The experimental results of the two algorithms demonstrate their superiority and rationality compared with the existing methods.

In this paper, we determine the finite minimal non-supersolvable groups decomposable into the product of two normal supersolvable subgroups.