Abstract:
The paper examines the key issues on system decoupling in service operations of mass customization by conducting a case study in catering services. It firstly justifies the effectiveness of applying concept of mass customization into service system decoupling to deal with the operation dilemma and then reveals the nature of decoupling decisions for mass customization purpose after discussions on the importance of modularization and the role of technologies including IT in the decoupling process. Based on these analyses, a Judgment-Matrix-based model on how to make the decoupling decisions in balancing the multiple operation objectives is then proposed and further research directions are finally suggested.

Abstract:
This paper used the Hyper Mesh and LS-DYNA software to establish a dummy-seat finite element simulation model. The head, chest and neck injury of the dummy were analyzed respectively in the frontal impact and rear impact. It was indicated that modification of seat was needed to meet the requirements. The simulation results showed that the original model cannot provide effective protection for the occupants and need for structural improvements. According to the simulation results of deformation and stress conditions of the seat parts, the original seat structure was improved and optimized for four improvement schemes, including the structure optimization of the seat side panel, the center hinge, framework under the cushion and the backrest lock. The results indicated that the optimized seat improved the occupant protection performance by reducing occupant damage parameters compared with original seat, which illustrated that the optimization basically met the target.

Abstract:
We first propose a new separability criterion based on algebraic-geometric invariants of bipartite mixed states introduced in [1], then prove that for all low ranks r

Abstract:
We prove a lower bound for Schmidt numbers of bipartite mixed states. This lower bound can be applied easily to low rank bipartite mixed states. From this lower bound it is known that generic low rank bipartite mixed states have relatively high Schmidt numbers and thus entangled. We can compute Schmidt numbers exactly for some mixed states by this lower bound as shown in Examples. This lower bound can also be used effectively to determine that some mixed states cannot be convertible to other mixed states by local operations and classical communication. The results in this paper are proved by ONLY using linear algebra, thus the results and proof are easy to understand.

Abstract:
We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear subspaces if the state is separable. Some examples are studied based on our criterion

Abstract:
We introduce algebraic sets in the complex projective spaces for the mixed states in bipartite quantum systems as their invariants under local unitary operations. The algebraic sets of the mixed state have to be the union of the linear subspaces if the mixed state is separable. Some examples are given and studied based on our criterion

Abstract:
Our previous work about algebraic-geometric invariants of the mixed states are extended and a stronger separability criterion is given. We also show that the Schmidt number of pure states in bipartite quantum systems, a classical concept, is actually an algebraic-geometric invariant.

Abstract:
From the consideration of measuring bipartite mixed states by separable pure states, we introduce algebraic sets in complex projective spaces for bipartite mixed states as the degenerating locus of the measurement. These algebraic sets are independent of the eigenvalues and only measure the "position" of eigenvectors of bipartite mixed states. They are nonlocal invariants ie., remaining invariant after local unitary transformations. The algebraic sets have to be the sum of the linear subspaces if the mixed states are separable, and thus we give a "eigenvalue-free" criterion of separability.Based on our criterion, examples are given to illustrate that entangled mixed states which are invariant under partial transposition or fufill entropy and disorder criterion of separability can be constructed systematically.We reveal that a large part of quantum entanglement is independent of eigenvalue spectra and develop a method to measure this part of quantum enatnglement.The results are extended to multipartite case.

Abstract:
We introduce algebriac sets in the products of complex projective spaces for multipartite mixed states, which are independent of their eigenvalues and only measure the "position" of their eigenvectors, as their non-local invariants (ie. remaining invariant after local untary transformations). These invariants are naturally arised from the physical consideration of checking multipartite mixed states by measuring them with multipartite separable pure states. The algebraic sets have to be the sum of linear subspaces if the multipartite mixed state is separable, and thus we give a new separability criterion of multipartite mixed states. A continuous family of 4-party mixed states, whose members are separable for any 2:2 cut and entangled for any 1:3 cut (thus bound entanglement if 4 parties are isolated), is constructed and studied from our invariants and separability criterion. Examples of LOCC-incomparable entangled tripartite pure states are given to show it is hopeless to characterize the entanglement properties of tripartite pure states by only using the eigenvalue speactra of their partial traces. We also prove that at least $n^2+n-1$ terms of separable pure states, which are "orthogonal" in some sence, are needed to write a generic pure state in $H_A^{n^2} \otimes H_B^{n^2} \otimes H_C^{n^2}$ as a linear combination of them.