Relations between the Kahler cone and the balanced cone of a Kahler manifold

In this paper, we consider a natural map from the Kahler cone to the balanced cone of a Kahler manifold. We study its injectivity and surjecticity. We also give an analytic characterization theorem on a nef class being Kahler.Comment: Some corrects have been mad

Inverse spectral problems for the Sturm-Liouville operator with discontinuity

In this work, we consider the Sturm-Liouville operator on a finite interval $[0,1]$ with discontinuous conditions at $1/2$. We prove that if the potential is known a priori on a subinterval $[b,1]$ with $b\ge1/2$, then parts of two spectra can uniquely determine the potential and all parameters in discontinuous conditions and boundary conditions. For the case $b<1/2$, parts of either one or two spectra can uniquely determine the potential and a part of parameters.Comment: 13 page

Rigidity Theorem for integral pinched shrinking Ricci solitons

We prove that an $n$-dimensional, $n\geq4$, compact gradient shrinking Ricci soliton satisfying a $L^{\frac n2}$-pinching condition is isometric to a quotient of the round $\mathbb{S}^n$, which improves the rigidity theorem given by G. Catino (arXiv:1509.07416vl).Comment: arXiv admin note: text overlap with arXiv:1509.07416 by other author

Excited Binomial States and Excited Negative Binomial States of the Radiation Field and Some of their Statistical Properties

We introduce excited binomial states and excited negative binomial states of the radiation field by repeated application of the photon creation operator on binomial states and negative binomial states. They reduce to Fock states and excited coherent states in certain limits and can be viewed as intermediate states between Fock states and coherent states. We find that both the excited binomial states and excited negative binomial states can be exactly normalized in terms of hypergeometric functions. Base on this interesting character, some of the statistical properties are discussed.Comment: 7 pages, 4 figure

Determination of matrix potential from scattering matrix

(i) For the matrix Schr\"{o}dinger operator on the half line, it is shown that if the potential exponentially decreases fast enough then only the scattering matrix uniquely determines the self-adjoint potential and the boundary condition. (ii) For the matrix Schr\"{o}dinger operator on the full line, it is shown that if the potential exponentially decreases fast enough then the scattering matrix (or equivalently, the transmission coefficient and reflection coefficient) uniquely determine the potential. If the potential vanishes on $(-\infty,0)$ then only the left reflection coefficient uniquely determine the potential.Comment: 9 page

Statistical Properties and Algebraic Characteristics of Quantum Superpositions of Negative Binomial States

We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable non-classical properties and reduce to Schr\"odinger cat states in a certain limit. The algebras involved in the even and odd negative binomial states turn out to be generally deformed oscillator algebras. It is found that the even and odd negative binomial states satisfy a same eigenvalue equation with a same eigenvalue and they can be viewed as two-photon nonlinear coherent states. Two methods of generating such states are proposed.Comment: 11 pages and 2 figure

Some LpL^p rigidity results for complete manifolds with harmonic curvature

Let $(M^n, g)(n\geq3)$ be an $n$-dimensional complete Riemannian manifold with harmonic curvature and positive Yamabe constant. Denote by $R$ and $\mathring{Rm}$ the scalar curvature and the trace-free Riemannian curvature tensor of $M$, respectively. The main result of this paper states that $\mathring{Rm}$ goes to zero uniformly at infinity if for $p\geq \frac n2$, the $L^{p}$-norm of $\mathring{Rm}$ is finite. Moreover, If $R$ is positive, then $(M^n, g)$ is compact. As applications, we prove that $(M^n, g)$ is isometric to a spherical space form if for $p\geq \frac n2$, $R$ is positive and the $L^{p}$-norm of $\mathring{Rm}$ is pinched in $[0,C_1)$, where $C_1$ is an explicit positive constant depending only on $n, p$, $R$ and the Yamabe constant. In particular, we prove an $L^{p}(\frac n2\leq p<\frac{n-2}{2}(1+\sqrt{1-\frac4n}))$-norm of $\mathring{Ric}$ pinching theorem for complete, simply connected, locally conformally flat Riemannian $n(n\geq 6)$-manifolds with constant negative scalar curvature. We give an isolation theorem of the trace-free Ricci curvature tensor of compact locally conformally flat Riemannian $n$-manifolds with constant positive scalar curvature, which improves Thereom 1.1 and Corollary 1 of E. Hebey and M. Vaugon \cite{{HV}}. This rsult is sharped, and we can precisely characterize the case of equality.Comment: We revise the older version, and add some content

Solvability of the inverse scattering problem for the selfadjoint matrix Schrodinger operator on the half line

In this work we study the inverse scattering problem for the selfadjoint matrix Schrodinger operator on the half line. We provide the necessary and sufficient conditions for the solvability of the inverse scattering problem.Comment: 29 page

Inverse resonance problems for the Schroedinger operator on the real line with mixed given data

In this work, we study inverse resonance problems for the Schr\"odinger operator on the real line with the potential supported in $[0,1]$. In general, all eigenvalues and resonances can not uniquely determine the potential. (i) It is shown that if the potential is known a priori on $[0,1/2]$, then the unique recovery of the potential on the whole interval from all eigenvalues and resonances is valid. (ii) If the potential is known a priori on $[0,a]$, then for the case $a>1/2$, infinitely many eigenvalues and resonances can be missing for the unique determination of the potential, and for the case $a<1/2$, all eigenvalues and resonances plus a part of so-called sign-set can uniquely determine the potential. (iii) It is also shown that all eigenvalues and resonances, together with a set of logarithmic derivative values of eigenfunctions and wave-functions at $1/2$, can uniquely determine the potential.Comment: 12 page

Dynamically generated resonances from the vector meson-octet baryon interaction in the strangeness zero sector

The interaction potentials between vector mesons and octet baryons are calculated explicitly with a summation of t-, s-, u-channel diagrams and a contact term originating from the tensor interaction. Many resonances are generated dynamically in different channels of strangeness zero by solving the coupled-channel Lippman-Schwinger equations with the method of partial wave analysis, and their total angular momenta are determined. The spin partners N(1650)1/2^{-} and N(1700)3/2^-, N(1895)1/2^{-} and N(1875)3/2^-, and the state N(2120)3/2^- are all produced respectively in the isospin I=1/2 sector. In the isospin I=3/2 sector, the spin partners Delta(1620)1/2^- and Delta(1700)3/2^- are also associated with the pole in the complex energy plane. According to the calculation results, a J^P=1/2^- state around 2000 MeV is predicted as the spin partner of N(2120)3/2^-. Some resonances are well fitted with their counterparts listed in the newest review of Particle Data Group(PDG), while others might stimulate the experimental observation in these energy regions in the future.Comment: 28 pages, 12 figures, 8 tables. arXiv admin note: text overlap with arXiv:0905.0973 by other author