Monochromatic k-edge-connection colorings of graphs

A path in an edge-colored graph $G$ is called monochromatic if any two edges on the path have the same color. For $k\ge 2$, an edge-colored graph $G$ is said to be monochromatic $k$-edge-connected if every two distinct vertices of $G$ are connected by at least $k$ edge-disjoint monochromatic paths, and $G$ is said to be uniformly monochromatic $k$-edge-connected if every two distinct vertices are connected by at least $k$ edge-disjoint monochromatic paths such that all edges of these $k$ paths are colored with a same color. We use $m{c}_k\left(G\right)$ and $um{c}_k\left(G\right)$ to denote the maximum number of colors that ensures $G$ to be monochromatic $k$-edge-connected and, respectively, $G$ to be uniformly monochromatic $k$-edge-connected. In this paper, we first conjecture that for any $k$-edge-connected graph $G$, $m{c}_k\left(G\right)=e\left(G\right)-e\left(H\right)+\lfloor \frac{k}{2}\rfloor$, where $H$ is a minimum $k$-edge-connected spanning subgraph of $G$. We verify the conjecture for $k=2$. We also prove the conjecture for $G=K_{k+1}$ and $G=K_{k,n}$ with $n\ge k\ge 3$. When $G$ is a minimal $k$-edge-connected graph, we give an upper bound of $m{c}_k\left(G\right)$, i.e., $m{c}_k\left(G\right)\le k-1$. For the uniformly monochromatic $k$-edge-connectivity, we prove that for all $k$, $um{c}_k\left(G\right)=e\left(G\right)-e\left(H\right)+1$, where $H$ is a minimum $k$-edge-connected spanning subgraph of $G$.     

Path integral quantization corresponding to the deformed Heisenberg algebra

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.     

The 4D Klein-Gordon, Dirac and Quantization Equations from 5D Null Paths

Results from 5D induced-matter and membrane theory with null paths are extended to show that a particle obeys the 4D Klein-Gordon equation but with a variable mass. The Dirac equation also follows, but raises concerns about 4D quantization in the two natural 5D gauges, and reopens the question of a Regge-like trajectory for the spin angular momenta and squared masses of gravitationally-dominated systems.     

Boundedness of commutators on homogeneous Herz spaces

The boundedness on homogeneous Herz spaces is established for a large class of linear commutators generated by BMO(R ⁿ ) functions and linear operators of rough kernels which include the Calderón-Zygmund operators and the Ricci-Stein oRfiUatory singular integrals with rough kernels. Project supponed in pan by the National h’atural Science Foundation of China (Grant No. 19131080) and the NEDF of China.     

Integral Kernel Operators on Fock Space – Generalizations and Applications to Quantum Dynamics

A general theory of operators on Boson Fock space is discussed in terms of the white noise distribution theory on Gaussian space (white noise calculus). An integral kernel operator is generalized from two aspects: (i) The use of an operator-valued distribution as an integral kernel leads us to the Fubini type theorem which allows an iterated integration in an integral kernel operator. As an application a white noise approach to quantum stochastic integrals is discussed and a quantum Hitsuda–Skorokhod integral is introduced. (ii) The use of pointwise derivatives of annihilation and creation operators assures the partial integration in an integral kernel operator. In particular, the particle flux density becomes a distribution with values in continuous operators on white noise functions and yields a representation of a Lie algebra of vector fields by means of such operators.     

Wavelet Collocation Methods for a First Kind Boundary Integral Equation in Acoustic Scattering

In this paper we consider a wavelet algorithm for the piecewise constant collocation method applied to the boundary element solution of a first kind integral equation arising in acoustic scattering. The conventional stiffness matrix is transformed into the corresponding matrix with respect to wavelet bases, and it is approximated by a compressed matrix. Finally, the stiffness matrix is multiplied by diagonal preconditioners such that the resulting matrix of the system of linear equations is well conditioned and sparse. Using this matrix, the boundary integral equation can be solved effectively.     

Adsorption effects and NMR properties: Continuous chain approach

The NMR properties of nuclei linked to long linear polymer molecules are sensitive to the influence of hard walls. In this context, the residual energy of tensorial spin-spin interactions is calculated using a path integral approach. Several thermodynamic quantities of the polymer system (free energy, equation of state,...) are also expressed, taking chain stiffness effects and the presence of two repulsive walls into consideration.     

Cycle and circle tests of balance in gain graphs: Forbidden minors and their groups

We examine two criteria for balance of a gain graph, one based on binary cycles and one on circles. The graphs for which each criterion is valid depend on the set of allowed gain groups. The binary cycle test is invalid, except for forests, if any possible gain group has an element of odd order. Assuming all groups are allowed, or all abelian groups, or merely the cyclic group of order 3, we characterize, both constructively and by forbidden minors, the graphs for which the circle test is valid. It turns out that these three classes of groups have the same set of forbidden minors. The exact reason for the importance of the ternary cyclic group is not clear. © 2005 Wiley Periodicals, Inc. J Graph Theory     

可重构制造系统重组过程中设备选择模型的研究

根据生产任务选择加工设备进行制造资源重组是实现可重构制造系统的关键问题之一，由于设备的选择涉及到多种因素，既有定量指标，又有定性指标，传统的依靠人工经验的方法显得力不从心。本文首先结合实际情况，提出了一套设备选择评价体系，通过对模糊判断矩阵采用最小对数二乘法确定各评价因素的权重系数，针对定性指标和定量指标采用不同的方法确定其性能指标值，通过模糊积分对评判指标进行综合评判，最后进行了实例研究。所提出的方法有效地简化了决策过程，为可重构制造系统设备选择提供了一套行之有效的方法。     

Method of lines with boundary elements for 1‐D transient diffusion‐reaction problems

Time‐dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi‐implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006