260,103 research outputs found
Perturbation theory of von Neumann Entropy
In quantum information theory, von Neumann entropy plays an important role.
The entropies can be obtained analytically only for a few states. In continuous
variable system, even evaluating entropy numerically is not an easy task since
the dimension is infinite. We develop the perturbation theory systematically
for calculating von Neumann entropy of non-degenerate systems as well as
degenerate systems. The result turns out to be a practical way of the expansion
calculation of von Neumann entropy.Comment: 7 page
Ground resonance analysis using a substructure modeling approach
A convenient and versatile procedure for modeling and analyzing ground resonance phenomena is described and illustrated. A computer program is used which dynamically couples differential equations with nonlinear and time dependent coefficients. Each set of differential equations may represent a component such as a rotor, fuselage, landing gear, or a failed damper. Arbitrary combinations of such components may be formulated into a model of a system. When the coupled equations are formed, a procedure is executed which uses a Floquet analysis to determine the stability of the system. Illustrations of the use of the procedures along with the numerical examples are presented
Dielectric Breakdown Strength of Polyethylene Nanocomposites
The term “nanometric dielectrics” or simply “nanodielectrics” was introduced in 1994 when Lewis [1] anticipated the potential property changes that would benefit electrical insulation due to nano-sized inclusion. Such materials, containing homogenous dispersion of small amount (normally less than 10wt%) of nanoparticles (with at least one dimension in nanometre range) in host matrix, are of specific dielectric interest. Although much effort has been put forth to investigate the potential dielectric benefit of such newly emerging materials, many uncertainties remain unanswered, and much remains to be explored [2]. Current experimental work is to investigate the preparation of nanodielectrics via solution blending approach. Polyethylene blend composed of 20wt% of high density polyethylene (HDPE) in low density polyethylene (LDPE) is proposed as the base polymer, with varying content of nanosilica (between 0wt% and 10wt%) as the fillers. Although expensive, solution blending method, when compared with melt compounding method, is expected to provide better dispersion of nanoparticles in polymers, thus providing qualitative data in understanding the behaviour of nanodielectrics [3]. Upon successful preparation of polyethylene nanocomposites, breakdown strength based on ASTM Standard D149-87 is to be conducted to determine the feasibility of such dielectric materials in engineering point of view. Figure 1 illustrates the schematic diagram of the breakdown test configuration. The samples are placed between two 6.3mm diameter steel ball bearings immersed in silicone fluid. AC voltage at a preset ramp rate will be applied until the samples fail and the values of breakdown voltages will be recorded and analysed using two-parameter Weibull distribution. Based upon top-down research approach, the underlying physics and chemistry associated with dielectric property changes will then be explored
Development of displacement- and frequency-noise-free interferometer in 3-D configuration for gravitational wave detection
The displacement- and frequency-noise-free interferometer (DFI) is a multiple
laser interferometer array for gravitational wave detection free from both the
displacement noise of optics and laser frequency noise. So far, partial
experimental demonstrations of DFI have been done in 2-D table top experiments.
In this paper, we report the complete demonstration of a 3-D DFI. The DFI
consists of four Mach-Zehnder interferometers with four mirrors and two
beamsplitters. The displacement noises both of mirrors and beamsplitters were
suppressed by up to 40 dB. The non-vanishing DFI response to a gravitational
wave was successfully confirmed using multiple electro-optic modulators and
computing methods
Perturbational approach to the quantum capacity of additive Gaussian quantum channel
For a quantum channel with additive Gaussian quantum noise, at the large
input energy side, we prove that the one shot capacity is achieved by the
thermal noise state for all Gaussian state inputs, it is also true for
non-Gaussian input in the sense of first order perturbation. For a general case
of copies input, we show that up to first order perturbation, any
non-Gaussian perturbation to the product thermal state input has a less quantum
information transmission rate when the input energy tend to infinitive.Comment: 5 page
Convergence of the Poincare Constant
The Poincare constant R(Y) of a random variable Y relates the L2 norm of a
function g and its derivative g'. Since R(Y) - Var(Y) is positive, with
equality if and only if Y is normal, it can be seen as a distance from the
normal distribution. In this paper we establish a best possible rate of
convergence of this distance in the Central Limit Theorem. Furthermore, we show
that R(Y) is finite for discrete mixtures of normals, allowing us to add rates
to the proof of the Central Limit Theorem in the sense of relative entropy.Comment: 11 page
Markov bases and subbases for bounded contingency tables
In this paper we study the computation of Markov bases for contingency tables
whose cell entries have an upper bound. In general a Markov basis for unbounded
contingency table under a certain model differs from a Markov basis for bounded
tables. Rapallo, (2007) applied Lawrence lifting to compute a Markov basis for
contingency tables whose cell entries are bounded. However, in the process, one
has to compute the universal Gr\"obner basis of the ideal associated with the
design matrix for a model which is, in general, larger than any reduced
Gr\"obner basis. Thus, this is also infeasible in small- and medium-sized
problems. In this paper we focus on bounded two-way contingency tables under
independence model and show that if these bounds on cells are positive, i.e.,
they are not structural zeros, the set of basic moves of all
minors connects all tables with given margins. We end this paper with an open
problem that if we know the given margins are positive, we want to find the
necessary and sufficient condition on the set of structural zeros so that the
set of basic moves of all minors connects all incomplete
contingency tables with given margins.Comment: 22 pages. It will appear in the Annals of the Institution of
Statistical Mathematic
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