Extensions of the Fill–Fishkind formula and the infimum – parallel sum relation

Recently, in (Arias ML, Corach G, Maestripieri A. Range additivity, shorted operator and the Sherman–Morrison–Woodburry formula, Linear Algebra Appl. 2015;467), authors gave a generalization of a formula by Fill and Fishkind, regarding the Moore–Penrose inverse of the sum of two matrices, in the setting of arbitrary Hilbert spaces. We consider this formula under some weaker assumptions and derive certain conclusions generalizing the mentioned result. We also extend a formula connecting the infimum of two orthogonal projections and their parallel sum to a formula connecting the star-infimum and the parallel sum of operators which need not be positive, using the concept of parallel sum that was introduced in (Antezana J, Corach G, Stojanoff D. Bilateral shorted operators and parallel sums. Linear Algebra Appl. 2006;414).     

Dynamic maintenance decision-making for series–parallel manufacturing system based on MAM–MTW methodology

Proper maintenance schedule is required to improve manufacturing systems’ profitability and productivity. A novel dynamic maintenance strategy is thus developed to incorporate both the single-machine optimization and the whole-system schedule for series–parallel system. Firstly, multiple attribute value theory and maintenance effects are considered in the single-machine optimization. A developed multi-attribute model (MAM) is used to determine the optimal maintenance intervals. Then, a series–parallel structure of the system is investigated in terms of the whole-system schedule. Maintenance time window (MTW) programming is presented to make a cost-effective system schedule by dynamically utilizing maintenance opportunities. The maintenance scheme achieved by using the proposed MAM–MTW methodology is demonstrated through a case study in a hydraulic steering factory. It is concluded that proper consideration of maintenance effects and time window leads to a significant cost reduction.     

Acyclic edge coloring of 2‐degenerate graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a′(G). A graph is called 2‐degenerate if any of its induced subgraph has a vertex of degree at most 2. The class of 2‐degenerate graphs properly contains series–parallel graphs, outerplanar graphs, non ? regular subcubic graphs, planar graphs of girth at least 6 and circle graphs of girth at least 5 as subclasses. It was conjectured by Alon, Sudakov and Zaks (and much earlier by Fiamcik) that a′(G)?Δ + 2, where Δ = Δ(G) denotes the maximum degree of the graph. We prove the conjecture for 2‐degenerate graphs. In fact we prove a stronger bound: we prove that if G is a 2‐degenerate graph with maximum degree Δ, then a′(G)?Δ + 1. © 2010 Wiley Periodicals, Inc. J Graph Theory 69: 1–27, 2012     

Tunable optomechanically induced transparency and fast–slow light in a loop-coupled optomechanical system

We theoretically explore the tunability of optomechanically induced transparency(OMIT) phenomenon and fast–slow light effect in a loop-coupled hybrid optomechanical system in which two optical modes are coupled to a common mechanical mode. In the probe output spectrum, we find that the interference phenomena OMIT caused by the optomechanical interactions and the normal mode splitting(NMS) induced by the strong tunnel coupling between the cavities can be observed. We further observe that the tunnel interaction will affect the distance and the heights of the sideband absorption peaks. The results also show that the switch from absorption to amplification can be realized by tuning the driving strength because of the existence of stability condition. Except from modulating the tunnel interaction, the conversion between slow light and fast light also can be achieved by adjusting the optomechanical interaction in the output field. This study may provide a potential application in the fields of high precision measurement and quantum information processing.     

用蓝色光二极管测量掺钛蓝宝石飞秒激光脉冲宽度

用蓝色光二极管双光子跃迁光电流信号测量掺钛蓝玉石飞秒激光脉冲宽度，实验高精度地记录了二阶干涉自相关曲线及其精细结构，由于用蓝色二极管双光子跃迁代替了常用的二次谐波，而且光信号直接转化为电信号，从而使飞秒激光脉冲宽度的测量大为简化。     

Quantifying interference in multipartite quantum systems

The characterization of quantum correlations is crucial to the development of new quantum technologies and to understand how dramatically quantum theory departs from classical physics. Here we systematically study single- and multiparticle interference patterns produced by general two- and three-qubit systems. From this we establish on phenomenological grounds a new type of quantum correlation for these systems, which we name quantum interference, deriving some quantifiers that are given explicitly in terms of the density matrix elements of the complete system. By using these quantifiers, we show that, contrary to our expectations, entanglement is not a required property for a composite quantum system to manifest multiparticle interference.     

Collider search of light dark matter model with dark sector decay

We explore the possibility that the dark matter relic density is not produced by a thermal mechanism directly, but by the decay of other heavier dark-sector particles which themselves can be produced by the thermal freeze-out mechanism. Using a concrete model with light dark matter from dark sector decay, we study the collider signature of the dark sector particles associated with Higgs production processes. We find that future lepton colliders could be a better place to probe the signature of this kind of light dark matter model than hadron colliders such as LHC. Also, we find that a Higgs factory with center-of-mass energy 250 GeV has a better potential to resolve the signature of this kind of light dark matter model than a Higgs factory with center-of-mass energy 350 GeV.     

Parallel computation of two-point boundary-value problems via particular solutions

Nonlinear two-point boundary-value problems (TPBVP) can be reduced to the iterative solution of a sequence of linear problems by means of quasilinearization techniques. Therefore, the efficient solution of linear problems is the key to the efficient solution of nonlinear problems.Among the techniques available for solving linear two-point boundary-value problems, the method of particular solutions (MPS) is particularly attractive in that it employs only one differential system, the original nonhomogeneous system, albeit with different initial conditions. This feature of MPS makes it ideally suitable for implementation on parallel computers in that the following requirements are met: the computational effort is subdivided into separate tasks (particular solutions) assigned to the different processors; the tasks have nearly the same size; there is little intercommunication between the tasks.For the TPBVP, the speedup achievable is ofO(n), wheren is the dimension of the state vector, hence relatively modest for the differential systems of interest in trajectory optimization and guidance. This being the case, we transform the TPBVP into a multi-point boundary-value problem (MPBVP) involvingm time subintervals, withm–1 continuity conditions imposed at the interface of contiguous subintervals. For the MPBVP, the speedup achievable is ofO(mn), hence substantially higher than that achievable for the TPBVP. It reduces toO(m) if the parallelism is implemented only in the time domain and not in the state domain.A drawback of the multi-point approach is that it requires the solution of a large linear algebraic system for the constants of the particular solutions. This drawback can be offset by exploiting the particular nature of the interface conditions: if the vector of constants for the first subinterval is known, the vector of constants for the subsequent subintervals can be obtained with linear transformations. Using decomposition techniques together with the discrete version of MPS, the size of the linear algebraic system for the multi-point case becomes the same as that for the two-point case.Numerical tests on the Intel iPSC/860 computer show that substantial speedup can be achieved via parallel algorithms vis-a-vis sequential algorithms. Therefore, the present technique has considerable interest for real-time trajectory optimization and guidance.Dedicated to the Memory of Professor Jan M. SkowronskiThis paper, based on Refs. 1–3, is a much condensed version of the material contained in these references.The technical assistance of the Research Center on Parallel Computation of Rice University, Houston, Texas is gratefully acknowledged.     

Neutron scattering from PEEK

An alkali‐soluble polysaccharide, GM5‐1, from the mycelium of Ganoderma tsugae, was fractionated by the nonsolvent addition method. The weight‐average molecular mass (M _w) and intrinsic viscosity ([η]) of fractions were studied by laser light scattering and viscometry with dimethylsulfoxide (DMSO) containing 0.25M LiCl (0.25M LiCl/DMSO) as the solvent at 30°C. The dependences of [η] and the radius of gyration (?S ²?_z ^1/2) on M _w were found to be [η]=9.8×10^?2 M _w ^0.57 (cm³g^?1) and ?S ²?_z ^1/2=1.65×10^?2 M _w ^0.58 (nm) in the M _w range from 8.6×10⁵ to 2.6×10⁶. The analysis based on current theories for a wormlike chain showed that the chain conformational parameters of GM5‐1 were 4.2 nm for persistence length (q) and 833 nm^?1 for linear mass density (M_L) with an obvious excluded volume effect. The results suggested the alkali‐soluble polysaccharide behaves like a semiflexible chain in 0.25M LiCl/DMSO at 30°C.