ON THE BOUNDEDNESS OF SPHERES IN F-SPACES

In this paper, some results concerning the relationship between the bounded-ness of some spheres and the local boundedness of the .F*-space are presented. Moreover, some results about the compactness are also given.

BOUNDEDNESS PROPERTIES OF SOLUTIONS OF DOUBLY NONLINEAR PARABOLIC EQUATIONS

Consider a doubly nonlinear parabolic equation and prove the boundedness of its generalized solutions.

The Representation Problems of Conjugate Spaces of l^(0)({X_(i)})Type F-normed Spaces

Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4))by the author,for a sequence of normed spaces{X_(i)},the representation problem of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces are studied in this paper.The algebraic representation continued equalities l^(0)({X_(i)})*A=c^(0)_(00)({X_(i)})*A=c_(00)({X^(*)_(i)}),(l^(0)(X))^(*)A=(c^(0)(X))^(*)A=(c^(0)_0(X))^(*)A=(c^(0)_(00)(X))^(*)A=c_(00)(X^(*))are obtained in the first part.Under weak-star topology,the topological representation c^(0)_(00)({X_(i)})^(*),w^(*)=c^(0)_(00)({X^(*)_(i)})is obtained in the second part.For the sequence of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.

Electronic structures of vacancies in Co_(3)Sn_(2)S_(2)

Co_(3)Sn_(2)S_(2)has attracted a lot of attention for its multiple novel physical properties,including topological nontrivial surface states,anomalous Hall effect,and anomalous Nernst effect.Vacancies,which play important roles in functional materials,have attracted increasing research attention.In this paper,by using density functional theory calculations,we first obtain band structures and magnetic moments of Co_(3)Sn_(2)S_(2)with exchange–correlation functionals at different levels.It is found that the generalized gradient approximation gives the positions of Weyl points consistent with experiments in bulk Co_(3)Sn_(2)S_(2).We then investigate the electronic structures of defects on surfaces with S and Sn terminations which have been observed in experiments.The results show that the single sulfur vacancy on the S-terminated surface introduces localized bond states inside the bandgap near the Fermi level.For di-and tri-sulfur vacancies,the localized defect states hybridize with neighboring ones,forming bonding states as well as anti-bonding states.The Sn vacancy on the Sn-terminated surface also introduces localized bond states,which are merged with the valence bands.These results provide a reference for future experimental investigations of vacancies in Co_(3)Sn_(2)S_(2).

Projected gradient trust-region method for solving nonlinear systems with convex constraints

In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of computing trial directions by this method combining with the line search technique. Close to the solution set this method is locally Q-superlinearly convergent under an error bound assumption which is much weaker than the standard nonsingularity condition.

Shamanskii-Like Levenberg-Marquardt Method with a New Line Search for Systems of Nonlinear Equations

To save the calculations of Jacobian,a multi-step Levenberg-Marquardt method named Shamanskii-like LM method for systems of nonlinear equations was proposed by Fa.Its convergence properties have been proved by using a trust region technique under the local error bound condition.However,the authors wonder whether the similar convergence properties are still true with standard line searches since the direction may not be a descent direction.For this purpose,the authors present a new nonmonotone m-th order Armijo type line search to guarantee the global convergence.Under the same condition as trust region case,the convergence rate also has been shown to be m+1 by using this line search technique.Numerical experiments show the new algorithm can save much running time for the large scale problems,so it is efficient and promising.

On the Linear Convergence of the Approximate Proximal Splitting Method for Non-smooth Convex Optimization

Consider the problem of minimizing the sum of two convex functions,one being smooth and the other non-smooth.In this paper,we introduce a general class of approximate proximal splitting(APS)methods for solving such minimization problems.Methods in the APS class include many well-known algorithms such as the proximal splitting method,the block coordinate descent method(BCD),and the approximate gradient projection methods for smooth convex optimization.We establish the linear convergence of APS methods under a local error bound assumption.Since the latter is known to hold for compressive sensing and sparse group LASSO problems,our analysis implies the linear convergence of the BCD method for these problems without strong convexity assumption.