Resistance characterizations of equiarboreal graphs

A weighted (unweighted) graph $G$ is called equiarboreal if the sum of weights (the number) of spanning trees containing a given edge in $G$ is independent of the choice of edge. In this paper, we give some resistance characterizations of equiarboreal weighted and unweighted graphs, and obtain the necessary and sufficient conditions for $k$-subdivision graphs, iterated double graphs, line graphs of regular graphs and duals of planar graphs to be equiarboreal. Applying these results, we obtain new infinite families of equiarboreal graphs, including iterated double graphs of 1-walk-regular graphs, line graphs of triangle-free 2-walk-regular graphs, and duals of equiarboreal planar graphs.     

Existence and concentration of positive solutions for coupled Schrödinger equations

In this paper, we study the existence and concentration of positive solution of a class of coupled Schrödinger equations. We admit that the potentials may not be non-negative and suppose that the intersection of the sets has positive Lebesgue measure. By studying the modified functional of the associated functional carefully, we establish the existence of positive least energy solutions for the coupled Schrödinger system. Moreover, we prove the concentration phenomenon of the positive solution when the parameter goes to infinity.     

A curvilinear method based on minimal-memory BFGS updates

We present a new matrix-free method for the computation of negative curvature directions based on the eigenstructure of minimal-memory BFGS matrices. We determine via simple formulas the eigenvalues of these matrices and we compute the desirable eigenvectors by explicit forms. Consequently, a negative curvature direction is computed in such a way that avoids the storage and the factorization of any matrix. We propose a modification of the L-BFGS method in which no information is kept from old iterations, so that memory requirements are minimal. The proposed algorithm incorporates a curvilinear path and a linesearch procedure, which combines two search directions; a memoryless quasi-Newton direction and a direction of negative curvature. Results of numerical experiments for large scale problems are also presented.     

A different construction of Gaussian fields from Markov chains: Dirichlet covariances

We study a class of Gaussian random fields with negative correlations. These fields are easy to simulate. They are defined in a natural way from a Markov chain that has the index space of the Gaussian field as its state space. In parallel with Dynkin's investigation of Gaussian fields having covariance given by the Green's function of a Markov process, we develop connections between the occupation times of the Markov chain and the prediction properties of the Gaussian field. Our interest in such fields was initiated by their appearance in random matrix theory.     

The Invariant Eigen-Operator Method for Hamiltonians with Coordinates-Coordinates Coupling Terms

In this paper, we apply the method of “invariant eigen-operator” to study the Hamiltonian of harmonic oscillator with couplings and derive their invariant eigen-operator. We first discuss decoupling of coupled harmonic oscillators with the two different quality and frequencies. And then, we propose an operator Hamiltonian to describe the linear lattice chain with Born–von Karman boundary condition. The vibrating spectrum is thus obtained. The results show that, for the system of coupled harmonic oscillators by coordinate coupling or momentum coupling, the invariant eigen operator of system always has the form of or .     

Mechanism on oscillating lifted flames in nonpremixed laminar coflow jets

The oscillating lifted flame in a laminar nonpremixed nitrogen-diluted fuel jet is known to be a result of buoyancy, though the detailed physical mechanism of the initiation has not yet been properly addressed. We designed a systematic experiment to test the hypothesis that the oscillation is driven by competition between the positive buoyancy of flame and the negative buoyancy of a fuel stream heavier than the ambient air. The positive buoyancy was examined with various flame temperatures by changing fuel mole fraction, and the negative buoyancy was investigated with various fuel densities. The density of the coflow was also varied within a certain range by adding either helium or carbon dioxide to air, to study how it affected the positive and negative buoyancies at the same time. As a result, we found that the range of oscillation was well-correlated with the positive and the negative buoyancies; the former stabilized the oscillation while the latter triggered instability and became a source of the oscillation. Further measurements of the flow fields and OH radicals evidenced the important role of the negative buoyancy on the oscillation, detailing a periodic variation in the unburned flow velocity that affected the displacement of the flame.     

流动注射-电感耦合等离子体发射光谱法测定天然水中的钙和镁

本文采用流动注射－电感耦合等离子体发现光谱联用技术测定了天然水中的钙、镁元素。考察了试液的雾化和曝光时间及载气压力等因素对分析信号的影响。通过与气动连续进样的对比，测出了钙、镁在流动注射进样下的分散系数。本法在测定钙、镁含量高的水性时，不需对试样进行稀释处理。对五个水样中钙、镁的分析结果与EDTA络合滴定法相吻合。     

Field-induced functions of porous Si as a confined system

Electroluminescent porous Si (PS) diodes exhibit various useful functions under a high-electric field. The experimental PS diodes are composed of thin semitransparent metal films, PS layers (about 500 nm thick in minimum), p- or n-type Si substrates and ohmic back contacts. Definite nonlinear electrical behavior (negative resistance and nonvolatile bistable memory effects) and cold electron emission phenomena appear in these PS diodes associated with the EL emission. Both the negative resistance and memory effects are related to the charging of Si nanocrystallites by field-induced carrier injection. The electron emission observed in the PS diodes formed on n+–Si substrates is caused by hot electrons tunnelling through the top contact. By an appropriate structural control of PS, the effective drift length under a high-field conduction is significantly increased, and then electrons are emitted ballistically. These functions reflect the activity of PS as a nanocrystalline confined system.     

Global qualitative analysis of coupled three-level food chains

A coupled model for three-level food chain is considered, the coupling rule is discretized Laplacian diffusion type. The focus of this paper is on the global behavior of solutions. We will show that the differences of the same level population density approach zero as t→∞, provided that the coupling strength is sufficiently large.