Science China Mathematics

We consider the exact controllability problem from boundary for thin shells. Under some checkable geometric assumptions on the middle surface, we establish the observability inequalities via the Bochner technique for the Dirichlet control and the Neumann control problems. We also give several examples to verify the geometric assumptions.

We study the toric degeneration of Weyl group translated Schubert divisors of a partial flag variety $$F{\ell _{{n_1}, \ldots,{n_k};n}}$$ via Gelfand-Cetlin polytopes. We propose a conjecture that Schubert varieties of appropriate dimensions intersect transversally up to translation by Weyl group elements, and verify it in various cases, including the complex Grassmannian Gr(2, n) and the complete flag variety Fℓ1,2,3,4.

By making a convex combination of the modified secant equations proposed by Yuan and Wei et al., a hybrid secant equation and also, a modified BFGS algorithm is proposed. The hybridization parameter is effectively computed using the available information of recent iterations. Under proper conditions, it is shown that the proposed algorithm is globally, locally and superlinearly convergent. By using the performance profile introduced by Dolan and Moré, a comparison between the implementations of the proposed algorithm and two efficient modified BFGS algorithms proposed by Yuan and Wei et al., on a set of unconstrained optimization test problems from the CUTEr collection, is done. Numerical results demonstrating the efficiency of the proposed modified BFGS algorithm are reported.

We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.

Silicon nano-wires (SiNWs) and boron nitride nano-tubules (BN-NTs) were successfully synthesized by excimer laser ablation at high temperature. These one-dimensional nano-materials synthesized by this method have a very high yield, a uniform diameter distribution, and a high purity. Micro-structures of these nano-materials were investigated by transmission electron microscopy (TEM). The SiNWs have a high density of structural defects of microtwin, stacking faults, and low-angle boundary, which are closely related to the formation of SiNWs and the determination of morphology of the nano-wires. BN-NTs are mainly single atomic-layered and the outer surface of tubules is clean without any attachment. The formation of single atomic-layered tubule is attributed to the catalyst effect which makes the axial rate of BN-NTs much higher than the radial growth

The tensor complementarity problem is a special instance in the class of nonlinear complementarity problems, which has many applications in multi-person noncooperative games, hypergraph clustering problems and traffic equilibrium problems. Two most important research issues are how to identify the solvability and how to solve such a problem via analyzing the structure of the involved tensor. In this paper, based on the concept of monotone mappings, we introduce a new class of structured tensors and the corresponding monotone tensor complementarity problem. We show that the solution set of the monotone tensor complementarity problem is nonempty and compact under the feasibility assumption. Moreover, a necessary and sufficient condition for ensuring the feasibility is given via analyzing the structure of the involved tensor. Based on the Huber function, we propose a regularized smoothing Newton method to solve the monotone tensor complementarity problem and establish its global convergence. Under some mild assumptions, we show that the proposed algorithm is superlinearly convergent. Preliminary numerical results indicate that the proposed algorithm is very promising.

LetX 1,…,X n be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ωq in Rq+1,q ⩾ 1. Let $$f_n (x) = n^{ - 1} c(h)\sum\nolimits_{i = 1}^n {K[(1 - x'X_i )/h^2 ]} $$ be a kernel estimator off(x). In this paper we establish a central limit theorem for integrated square error off n under some mild conditions.

By catching the so-called strictly critical points, this paper presents an effective algorithm for computing the global infimum of a polynomial function. For a multivariate real polynomial f, the algorithm in this paper is able to decide whether or not the global infimum of f is finite. In the case of f having a finite infimum, the global infimum of f can be accurately coded in the Interval Representation. Another usage of our algorithm is to decide whether or not the infimum of f is attained when the global infimum of f is finite. In the design of our algorithm, the well-known Wu’s method plays an important role.

A new transuranium neutron-deficient isotope235Am was produced by 35 MeV proton to bombard the rare radioactive238Pu target. The products were transported and collected by the He-jet system. The Am isotopes were separated and purified by radiochemistry method and the y-ray, X-ray and y-X(y) coincidence of the samples was measured. The synthesis of235Am was definitely identified. Its measured half-life is (15±5) min.