8,367 research outputs found
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
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
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 . 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
Improved Performance of RF Energy Powered Wireless Sensor Node with Cooperative Beam Selection
RF energy harvesting is a promising potential solution to provide convenient
and perpetual energy supplies to low-power wireless sensor networks. In this
paper, we investigate the energy harvesting performance of a wireless sensor
node powered by harvesting RF energy from existing multiuser MIMO system.
Specifically, we propose a random unitary beamforming (RUB) based cooperative
beam selection scheme to enhance the energy harvesting performance at the
sensor. Under a constant total transmission power constraint, the multiuser
MIMO system tries to select a maximal number of active beams for data
transmission, while satisfying the energy harvesting requirement at the sensor.
We derive the exact closed-form expression for the distribution function of
harvested energy in a coherence time over Rayleigh fading channels. We further
investigate the performance tradeoff of the average harvested energy at the
sensor versus the sum-rate of the multiuser MIMO system.Comment: 17pages, 5 figure
Reconstruction and Solvability for Discontinuous Hochstadt-Lieberman Problems
We consider Sturm-Liouville problems with a discontinuity in an interior
point, which are motivated by the inverse problems for the torsional modes of
the Earth. We assume that the potential on the right half-interval and the
coefficient in the right boundary condition are given. Half-inverse problems
are studied, that consist in recovering the potential on the left half-interval
and the left boundary condition from the eigenvalues. If the discontinuity
belongs to the left half-interval, the position and the parameters of the
discontinuity also can be reconstructed. In this paper, we provide
reconstructing algorithms and prove existence of solutions for the considered
inverse problems. Our approach is based on interpolation of entire functions
Recovering Nonlocal Differential Pencils
Inverse problems for differential pencils with nonlocal conditions are
investigated. Several uniqueness theorems of inverse problems from the
Weyl-type function and spectra are proved, which are generalizations of the
well-known Weyl function and Borg's inverse problem for the classical
Sturm-Liouville operator.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1410.2017.
substantial text overlap with arXiv:1503.0174
Recovering Dirac Operator with Nonlocal Boundary Conditions
In this paper inverse problems for Dirac operator with nonlocal conditions
are considered. Uniqueness theorems of inverse problems from the Weyl-type
function and spectra are provided, which are generalizations of the well-known
Weyl function and Borg's inverse problem for the classical Dirac operator.Comment: 11 page
Wireless Transmission of Big Data: Data-oriented Performance Limits and Their Applications
The growing popularity of big data and Internet of Things (IoT) applications
bring new challenges to the wireless communication community. Wireless
transmission systems should more efficiently support the large amount of data
traffics from diverse types of information sources. In this article, we
introduce a novel data-oriented approach for the design and optimization of
wireless transmission strategies. Specifically, we define new performance
metrics for individual data transmission session and apply them to compare two
popular channel-adaptive transmission strategies. We develop several
interesting and somewhat counterintuitive observations on these transmission
strategies, which would not be possible with conventional approach. We also
present several interesting future research directions that are worth pursuing
with the data-oriented approach.Comment: 14 pages, 4 figure
Characterizing Energy Efficiency of Wireless Transmission for Green Internet of Things: A Data-Oriented Approach
The growing popularity of Internet of Things (IoT) applications brings new
challenges to the wireless communication community. Numerous smart devices and
sensors within IoT will generate a massive amount of short data packets. Future
wireless transmission systems need to support the reliable transmission of such
small data with extremely high energy efficiency. In this article, we introduce
a novel data-oriented approach for characterizing the energy efficiency of
wireless transmission strategies for IoT applications. Specifically, we present
new energy efficiency performance limits targeting at individual data
transmission sessions. Through preliminary analysis on two channel-adaptive
transmission strategies, we develop several important design guidelines on
green transmission of small data. We also present several promising future
applications of the proposed data-oriented energy efficiency characterization.Comment: 14 pages, 4 figure
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