19,597 research outputs found
Algebraic Properties of the Real Quintic Equation for a Binary Gravitational Lens
It has been recently shown that the lens equation for a binary gravitational
lens, which is apparently a coupled system, can be reduced to a real
fifth-order (quintic) algebraic equation. Some algebraic properties of the real
quintic equation are revealed. We find that the number of images on each side
of the separation axis is independent of the mass ratio and separation unless
the source crosses the caustics. Furthermore, the discriminant of the quintic
equation enables us to study changes in the number of solutions, namely in the
number of images. It is shown that this discriminant can be factorized into two
parts: One represents the condition that the lens equation can be reduced to a
single quintic equation, while the other corresponds to the caustics.Comment: 7 pages (PTPTeX); accepted for publication in Prog. Theor. Phy
Non-linear vorticity-density coupling in Lagrangian dynamics
We present a general Lagrangian formalism that allows the treatment of
vorticity. We give solutions for the rotational perturbations up to the
third-order in a flat background universe. We show how the primordial vorticity
affects the evolution of the density fluctuation in high-density regions.Comment: 15 pages; submitted to Progress of Theoretical Physic
Fourier Domain Decoding Algorithm of Non-Binary LDPC codes for Parallel Implementation
For decoding non-binary low-density parity check (LDPC) codes,
logarithm-domain sum-product (Log-SP) algorithms were proposed for reducing
quantization effects of SP algorithm in conjunction with FFT. Since FFT is not
applicable in the logarithm domain, the computations required at check nodes in
the Log-SP algorithms are computationally intensive. What is worth, check nodes
usually have higher degree than variable nodes. As a result, most of the time
for decoding is used for check node computations, which leads to a bottleneck
effect. In this paper, we propose a Log-SP algorithm in the Fourier domain.
With this algorithm, the role of variable nodes and check nodes are switched.
The intensive computations are spread over lower-degree variable nodes, which
can be efficiently calculated in parallel. Furthermore, we develop a fast
calculation method for the estimated bits and syndromes in the Fourier domain.Comment: To appear in IEICE Trans. Fundamentals, vol.E93-A, no.11 November
201
Effect of the cosmological constant on the bending of light and the cosmological lens equation
We revisit the effect of cosmological constant on the light
deflection and its role in the cosmological lens equation. First, we re-examine
the motion of photon in the Schwarzschild spacetime, and explicitly describe
the trajectory of photon and deflection angle up to the second-order
in . Then the discussion is extended to the contribution of the cosmological
constant in the Schwarzschild-de Sitter or Kottler spacetime.
Contrary to the previous arguments, we emphasize the following points: (a) the
cosmological constant does appear in the orbital equation of light,
(b) nevertheless the bending angle of light does not change its form
even if since the contribution of is thoroughly
absorbed into the definition of the impact parameter, and (c) the effect of
is completely involved in the angular diameter distance .Comment: Revised version accepted for publication in Physical Review D. 5
pages including 3 figures and 4 references are adde
Duration and Interval Hidden Markov Model for Sequential Data Analysis
Analysis of sequential event data has been recognized as one of the essential
tools in data modeling and analysis field. In this paper, after the examination
of its technical requirements and issues to model complex but practical
situation, we propose a new sequential data model, dubbed Duration and Interval
Hidden Markov Model (DI-HMM), that efficiently represents "state duration" and
"state interval" of data events. This has significant implications to play an
important role in representing practical time-series sequential data. This
eventually provides an efficient and flexible sequential data retrieval.
Numerical experiments on synthetic and real data demonstrate the efficiency and
accuracy of the proposed DI-HMM
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