16,119 research outputs found
Multi-breathers and high order rogue waves for the nonlinear Schr\"odinger equation on the elliptic function background
We construct the multi-breather solutions of the focusing nonlinear
Schr\"odinger equation (NLSE) on the background of elliptic functions by the
Darboux transformation, and express them in terms of the determinant of theta
functions. The dynamics of the breathers in the presence of various kinds of
backgrounds such as dn, cn, and non-trivial phase-modulating elliptic solutions
are presented, and their behaviors dependent on the effect of backgrounds are
elucidated. We also determine the asymptotic behaviors for the multi-breather
solutions with different velocities in the limit , where the
solution in the neighborhood of each breather tends to the simple one-breather
solution. Furthermore, we exactly solve the linearized NLSE using the squared
eigenfunction and determine the unstable spectra for elliptic function
background. By using them, the Akhmediev breathers arising from these
modulational instabilities are plotted and their dynamics are revealed.
Finally, we provide the rogue-wave and higher-order rogue-wave solutions by
taking the special limit of the breather solutions at branch points and the
generalized Darboux transformation. The resulting dynamics of the rogue waves
involves rich phenomena: depending on the choice of the background and
possessing different velocities relative to the background. We also provide an
example of the multi- and higher-order rogue wave solution.Comment: 45 pages, 16 figure
Using Fuzzy Linguistic Representations to Provide Explanatory Semantics for Data Warehouses
A data warehouse integrates large amounts of extracted and summarized data from multiple sources for direct querying and analysis. While it provides decision makers with easy access to such historical and aggregate data, the real meaning of the data has been ignored. For example, "whether a total sales amount 1,000 items indicates a good or bad sales performance" is still unclear. From the decision makers' point of view, the semantics rather than raw numbers which convey the meaning of the data is very important. In this paper, we explore the use of fuzzy technology to provide this semantics for the summarizations and aggregates developed in data warehousing systems. A three layered data warehouse semantic model, consisting of quantitative (numerical) summarization, qualitative (categorical) summarization, and quantifier summarization, is proposed for capturing and explicating the semantics of warehoused data. Based on the model, several algebraic operators are defined. We also extend the SQL language to allow for flexible queries against such enhanced data warehouses
The Advance in Partial Distribution: A New Mathematical Tool for Economic Management
In this paper, the Partial Distribution (PD) and multivariate Partial Distribution (MPD) are presented in their concepts, properties and applications, and PD is compared with the lognormal and the levy distribution. Though the levy distribution is better to describe the exchange returns in security market on a moderately large volatility range, the lognormal is better in a region of low values of volatility. We shall try to elucidate that Partial Distribution is better than lognormal distribution and levy distribution in many respects, and PD and MPD have some interesting properties which some other probability distributions have not. From PD and MPD, lots of interesting results can be acquired and many interesting economic propositions could be interpreted in analytic way. These properties could describe analytically many of phenomena in economic management better, and the results based on PD and MPD could be applied to solve many problems in economic management.Partial Distribution; multivariate Partial Distribution; mathematical tool, economic management
Shifts of neutrino oscillation parameters in reactor antineutrino experiments with non-standard interactions
We discuss reactor antineutrino oscillations with non-standard interactions
(NSIs) at the neutrino production and detection processes. The neutrino
oscillation probability is calculated with a parametrization of the NSI
parameters by splitting them into the averages and differences of the
production and detection processes respectively. The average parts induce
constant shifts of the neutrino mixing angles from their true values, and the
difference parts can generate the energy (and baseline) dependent corrections
to the initial mass-squared differences. We stress that only the shifts of
mass-squared differences are measurable in reactor antineutrino experiments.
Taking Jiangmen Underground Neutrino Observatory (JUNO) as an example, we
analyze how NSIs influence the standard neutrino measurements and to what
extent we can constrain the NSI parameters.Comment: a typo in Eq.(25) fixed after published version, discussion and
conclusion unchange
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