A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution

To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order derivative based total $\alpha$-order variation model, which can outperform the currently popular high order regularization models. There exist several previous works using total $\alpha$-order variations for image restoration; however first no analysis is done yet and second all tested formulations, differing from each other, utilize the zero Dirichlet boundary conditions which are not realistic (while non-zero boundary conditions violate definitions of fractional-order derivatives). This paper first reviews some results of fractional-order derivatives and then analyzes the theoretical properties of the proposed total $\alpha$-order variational model rigorously. It then develops four algorithms for solving the variational problem, one based on the variational Split-Bregman idea and three based on direct solution of the discretise-optimization problem. Numerical experiments show that, in terms of restoration quality and solution efficiency, the proposed model can produce highly competitive results, for smooth images, to two established high order models: the mean curvature and the total generalized variation.Comment: 26 page

Assignments of ΛQ\Lambda_Q and ΞQ\Xi_Q baryons in the heavy quark-light diquark picture

We apply a new mass formula which is derived analytically in the relativistic flux tube model to the mass spectra of $\Lambda_Q$ and $\Xi_Q$ (\emph{Q} = \emph{c} or \emph{b} quark) baryons. To this end, the heavy quark-light diquark picture is employed. We find that all masses of the available $\Lambda_Q$ and $\Xi_Q$ states can be understood well. The assignments to these states do not appear to contradict the strong decay properties. $\Lambda_c(2760)^+$ and $\Xi_c(2980)$ are assigned to the first radial excitations with $J^P = 1/2^+$. $\Lambda_c(2940)^+$ and $\Xi_c(3123)$ might be the 2\emph{P} states. The $\Lambda_c(2880)^+$ and $\Xi_c(3080)$ are the good 1\emph{D} candidates with $J^P = 5/2^+$. $\Xi_c(3055)$ is likely to be a 1\emph{D} state with $J^P = 3/2^+$. $\Lambda_b(5912)^0$ and $\Lambda_b(5920)^0$ favor the 1\emph{P} assignments with $J^P = 1/2^-$ and $3/2^-$, respectively. We propose a search for the $\tilde{\Lambda}_{c2}(5/2^-)$ state which can help to distinguish the diquark and three-body schemes.Comment: 9 tables, more discussions and references adde

Converting a CAD Model into a Manufacturing Model for the Components Made of a Multiphase Perfect Material

To manufacture the component made of a multiphase perfect material (including homogeneous and multi heterogeneous materials), it CAD model should be processed and converted into layered manufacturing model for further transformation of numerical control (NC) coding. This paper develops its detailed approaches and corresponding software. The process planning is made first and includes: (1) determining the build orientation of the component; and (2) slicing the component into layers adaptively according to different material regions since different materials have different optimal layer thickness for manufacturing. After the process planning, the layered manufacturing models with necessary information, including fabrication sequence and material information of each layer, are fully generated.Mechanical Engineerin

Quantum phase transition in the one-dimensional period-two and uniform compass model

Quantum phase transition in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudo-spin transformation method and the trace map method. The exact solutions are presented, the fidelity, the nearest-neighbor pseudo-spin entanglement, spin and pseudo-spin correlation functions are then calculated. At the critical point, the fidelity and its susceptibility change substantially, the gap of pseudo-spin concurrence is observed, which scales as $1/N$ (N is system size). The spin correlation functions show smooth behavior around the critical point. In the period-two chain, the pseudo-spin correlation functions exhibit a oscillating behavior, which is absent in the unform chain. The divergent correlation length at the critical point is demonstrated in the general trend for both cases.Comment: 5 pages, 6 figure

Signatures of Bose-Einstein condensation in an optical lattice

We discuss typical experimental signatures for the Bose-Einstein condensation (BEC) of an ultracold Bose gas in an inhomogeneous optical lattice at finite temperature. Applying the Hartree-Fock-Bogoliubov-Popov formalism, we calculate quantities such as the momentum-space density distribution, visibility and peak width as the system is tuned through the superfluid to normal phase transition. Different from previous studies, we consider systems with fixed total particle number, which is of direct experimental relevance. We show that the onset of BEC is accompanied by sharp features in all these signatures, which can be probed via typical time-of-flight imaging techniques. In particular, we find a two-platform structure in the peak width across the phase transition. We show that the onset of condensation is related to the emergence of the higher platform, which can be used as an effective experimental signature.Comment: 5 pages, 3 figure