Abstract:
The dressing method based on the $2\times2$ matrix $\bar\partial$-problem is generalized to study the canonical form of AB equations. The soliton solutions for the AB equations are given by virtue of the properties of Cauchy matrix. Asymptotic behaviors of the $N$-soliton solution are discussed.

Abstract:
Resorting to the Lax matrix and elliptic variables, the discrete Chen-Lee-Liu hierarchy is decomposed into solvable ordinary differential equations. Based on the theory of algebraic curve, the continuous flow and discrete flow related to the discrete Chen-Lee-Liu hierarchy are straightened under the Abel-Jacobi coordinates. The meromorphic function $\phi$, the Baker-Akhiezer vector $\bar\psi $ and the hyperelliptic curve $\mathcal{K}_N$ are introduced, by which quasi-periodic solutions of the discrete Chen-Lee-Liu hierarchy are constructed according to the asymptotic properties and the algebro-geometric characters of $\phi,\ \bar\psi $ and $\mathcal{K}_N$.

Abstract:
We study the plus and minus type discrete mKdV equation. Some different symmetry conditions associated with two Lax pairs are introduced to derive the matrix Riemann-Hilbert problem with zero. By virtue of regularization of the Riemann-Hilbert problem, we obtain the complex and real solution to the plus type discrete mKdV equation respectively. Under the gauge transformation between the plus and minus type, the solutions of minus type can be obtained in terms of the given plus ones.

Abstract:
Binary symmetry constraints are applied to constructing B\"acklund transformations of soliton systems, both continuous and discrete. Construction of solutions to soliton systems is split into finding solutions to lower-dimensional Liouville integrable systems, which also paves a way for separation of variables and exhibits integrability by quadratures for soliton systems. Illustrative examples are provided for the KdV equation, the AKNS system of nonlinear Schr\"odinger equations, the Toda lattice, and the Langmuir lattice.

Abstract:
The Heisenberg hierarchy and its Hamiltonian structure are derived respectively by virtue of the zero curvature equation and the trace identity. With the help of the Lax matrix we introduce an algebraic curve $\mathcal{K}_{n}$ of arithmetic genus $n$, from which we define meromorphic function $\phi$ and straighten out all of the flows associated with the Heisenberg hierarchy under the Abel-Jacobi coordinates. Finally, we achieve the explicit theta function representations of solutions for the whole Heisenberg hierarchy as a result of the asymptotic properties of $\phi$.

Abstract:
We report the first measurement of charged pion, kaon and (anti-)proton production in jets from hadron colliders. The measurement was carried out with the ALICE detector using $2\times10^8$ minimum bias pp collisions at a centre-of-mass energy of $\sqrt{s}=7$ TeV at the LHC. We present the $\pi$, K and p transverse momentum ($p_\textrm{T}$) spectra, as well as the spectra of the reduced momentum (${z^\textrm{ch}\equiv p_\textrm{T}^\textrm{track}/p_\textrm{T, jet}^\textrm{ch}}$), in charged jets of $p_\textrm{T}$ between 5--20 $\textrm{GeV}/c$. The measurement is compared to Monte Carlo calculations.

Abstract:
A collision model, an automobile model and a multi-rigid-body model in
PC-crash are analyzed. By simulating a side collision accident between a car
and an electric bicycle (EB), a method that reproduces the car-electric bicycle
side collision accident based on PC-crash is presented according to some
important information such as the final position, the contacting location between
the cyclist and the car. A result is obtained by comparing with the reproduced
result, the deformation of accident vehicle and the surveillance video. The rollover
direction and fells-over sliding direction after the collision and the
contacting location and wrap motion of cyclist and electric bicycle are fitting
in with the real situation better compared with the reconstruction result in
PC-crash. Then the responsive-surface method and MONTEKARLO method are used in
MATLAB to analyze the uncertainty of the vehicle speed in reproduced scene
results. And the range of values of the pre-collision speed is obtained which
makes the reproduced result more objective and convincible that could provide
the basis of the accident assessment.

Abstract:
The maximum entropy principle (MEP), which has been popular in the modeling of droplet size and velocity distribution in sprays, is, strictly speaking, only applicable for isolated systems in thermodynamic equilibrium; whereas the spray formation processes are irreversible and non-isolated with interaction between the atomizing liquid and its surrounding gas medium. In this study, a new model for the droplet size distribution has been developed based on the thermodynamically consistent concept - the maximization of entropy generation during the liquid atomization process. The model prediction compares favorably with the experimentally measured size distribution for droplets, near the liquid bulk breakup region, produced by an air-blast annular nozzle and a practical gas turbine nozzle. Therefore, the present model can be used to predict the initial droplet size distribution in sprays.

Abstract:
A new solving approach for constraint problem was proposed in this study, the constraint problem needed to solve was decomposed not into single sub-problems but into three types of sub-problems, namely, rigid subset, scalable subset and radial subset and each type of subset corresponds a cluster of constraint problem. Based on cluster rewriting rule approach, a small set of rewriting rules were applied in constraint system and an incremental algorithm was presented, the solving approach could get the generic solution when no available rewriting rule was available. By this approach, we can determine that constraint system is well-constrained, under-constrained or over-constrained. The results reveal that the proposed method can efficiently process constraint problem.

Abstract:
In the process of modeling, users often change parameter values using trial-and error method in some CAD system. This study aims to present a novel approach that determines automatically suitable parameter intervals for semantic feature modeling system. A new algorithm of computing parameter range was proposed after analyzing geometric constraint graphs in this method, critical parameter value was found by decomposition for variant parameter and each sub-problem instance was solved in each interval. The results reveal that the proposed method can efficiently process constraint problem.