28,016 research outputs found
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
Rigidity Theorem for integral pinched shrinking Ricci solitons
We prove that an -dimensional, , compact gradient shrinking Ricci
soliton satisfying a -pinching condition is isometric to a
quotient of the round , 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
Inverse spectral problems for the Sturm-Liouville operator with discontinuity
In this work, we consider the Sturm-Liouville operator on a finite interval
with discontinuous conditions at . We prove that if the potential
is known a priori on a subinterval with , then parts of two
spectra can uniquely determine the potential and all parameters in
discontinuous conditions and boundary conditions. For the case , parts
of either one or two spectra can uniquely determine the potential and a part of
parameters.Comment: 13 page
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 then only the left reflection coefficient uniquely
determine the potential.Comment: 9 page
Some rigidity results for complete manifolds with harmonic curvature
Let be an -dimensional complete Riemannian manifold
with harmonic curvature and positive Yamabe constant. Denote by and
the scalar curvature and the trace-free Riemannian curvature
tensor of , respectively. The main result of this paper states that
goes to zero uniformly at infinity if for , the
-norm of is finite. Moreover, If is positive, then
is compact. As applications, we prove that is isometric
to a spherical space form if for , is positive and the
-norm of is pinched in , where is an
explicit positive constant depending only on , and the Yamabe
constant.
In particular, we prove an -norm of pinching theorem
for complete, simply connected, locally conformally flat Riemannian -manifolds with constant negative scalar curvature.
We give an isolation theorem of the trace-free Ricci curvature tensor of
compact locally conformally flat Riemannian -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
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
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 . 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 , 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 , then
for the case , infinitely many eigenvalues and resonances can be missing
for the unique determination of the potential, and for the case , 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 , 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
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