UNIVERSAL INEQUALITIES FOR A HORIZONTALLAPLACIAN VERSION OF THE CLAMPED PLATE PROBLEM ON CARNOT GROUP

In this paper, we investigate a horizontal Laplacian version of the clamped plate problem on Carnot groups and obtain some universal inequalities. Furthermore, for the lower order eigenvalues of this eigenvalue problem on carnot groups, we also give some universal inequalities.

DIFFEOMORPHISMS WITH VARIOUS C^1 STABLE PROPERTIES

Let M be a smooth compact manifold and A be a compact invariant set. In this article, we prove that, for every robustly transitive set A, flA satisfies a Cl-genericstable shadowable property （resp., Cl-generic-stable transitive specification property or Cl-generic-stable barycenter property） if and only if A is a hyperbolic basic set. In particular, flA satisfies a Cl-stable shadowable property （resp., Cl-stable transitive specification property or Cl-stable barycenter property） if and only if A is a hyperbolic basic set. Similar results are valid for volume-preserving case.

Three-step semiquantum secure direct communication protocol

Quantum secure direct communication is the direct communication of secret messages without need for establishing a shared secret key first.In the existing schemes,quantum secure direct communication is possible only when both parties are quantum.In this paper,we construct a three-step semiquantum secure direct communication(SQSDC)protocol based on single photon sources in which the sender Alice is classical.In a semiquantum protocol,a person is termed classical if he(she)can measure,prepare and send quantum states only with the fixed orthogonal quantum basis{|0,|1}.The security of the proposed SQSDC protocol is guaranteed by the complete robustness of semiquantum key distribution protocols and the unconditional security of classical one-time pad encryption.Therefore,the proposed SQSDC protocol is also completely robust.Complete robustness indicates that nonzero information acquired by an eavesdropper Eve on the secret message implies the nonzero probability that the legitimate participants can find errors on the bits tested by this protocol.In the proposed protocol,we suggest a method to check Eves disturbing in the doves returning phase such that Alice does not need to announce publicly any position or their coded bits value after the photons transmission is completed.Moreover,the proposed SQSDC protocol can be implemented with the existing techniques.Compared with many quantum secure direct communication protocols,the proposed SQSDC protocol has two merits:firstly the sender only needs classical capabilities;secondly to check Eves disturbing after the transmission of quantum states,no additional classical information is needed.

On the canonical map of surfaces with q≥6

We carry out an analysis of the canonical system of a minimal complex surface S of general type with irregularity q > 0.Using this analysis,we are able to sharpen in the case q > 0 the well-known Castelnuovo inequality KS2≥3pg(S) + q(S)-7.Then we turn to the study of surfaces with pg=2q-3 and no fibration onto a curve of genus > 1.We prove that for q≥6 the canonical map is birational.Combining this result with the analysis of the canonical system,we also prove the inequality:KS2≥7χ(S) + 2.This improves an earlier result of Mendes Lopes and Pardini (2010).