11,754 research outputs found
On Weak Topology for Optimal Control of Switched Nonlinear Systems
Optimal control of switched systems is challenging due to the discrete nature
of the switching control input. The embedding-based approach addresses this
challenge by solving a corresponding relaxed optimal control problem with only
continuous inputs, and then projecting the relaxed solution back to obtain the
optimal switching solution of the original problem. This paper presents a novel
idea that views the embedding-based approach as a change of topology over the
optimization space, resulting in a general procedure to construct a switched
optimal control algorithm with guaranteed convergence to a local optimizer. Our
result provides a unified topology based framework for the analysis and design
of various embedding-based algorithms in solving the switched optimal control
problem and includes many existing methods as special cases
Preferred numbers and the distribution of trade sizes and trading volumes in the Chinese stock market
The distribution of trade sizes and trading volumes are investigated based on
the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen
Stock Exchange in the whole year 2003. We observe that the size distribution of
trades for individual stocks exhibits jumps, which is caused by the number
preference of traders when placing orders. We analyze the applicability of the
"-Gamma" function for fitting the distribution by the Cram\'{e}r-von Mises
criterion. The empirical PDFs of trading volumes at different timescales
ranging from 1 min to 240 min can be well modeled. The
applicability of the -Gamma functions for multiple trades is restricted to
the transaction numbers . We find that all the PDFs have
power-law tails for large volumes. Using careful estimation of the average tail
exponents of the distribution of trade sizes and trading volumes, we
get , well outside the L{\'e}vy regime.Comment: 7 pages, 5 figures and 4 table
The hidden-charm pentaquark and tetraquark states
In the past decade many charmonium-like states were observed experimentally.
Especially those charged charmonium-like states and bottomonium-like
states can not be accommodated within the naive quark model. These
charged states are good candidates of either the hidden-charm tetraquark
states or molecules composed of a pair of charmed mesons. Recently, the LHCb
Collaboration discovered two hidden-charm pentaquark states, which are also
beyond the quark model. In this work, we review the current experimental
progress and investigate various theoretical interpretations of these
candidates of the multiquark states. We list the puzzles and theoretical
challenges of these models when confronted with the experimental data. We also
discuss possible future measurements which may distinguish the theoretical
schemes on the underlying structures of the hidden-charm multiquark states.Comment: Review accepted by Physics Reports, 152 pages, 66 figures, and 29
table
Analytic smoothness effect of solutions for spatially homogeneous Landau equation
In this paper, we study the smoothness effect of Cauchy problem for the
spatially homogeneous Landau equation in the hard potential case and the
Maxwellian molecules case. We obtain the analytic smoothing effect for the
solutions under rather weak assumptions on the initial datum.Comment: 16 page
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