Acyclic dominating partitions

Given a graph G=(V, E), let ${\mathcal{P}}$ be a partition of V. We say that ${\mathcal{P}}$ is dominating if, for each part P of ${\mathcal{P}}$, the set V\P is a dominating set in G (equivalently, if every vertex has a neighbor of a different part from its own). We say that ${\mathcal{P}}$ is acyclic if for any parts P, P′ of ${\mathcal{P}}$, the bipartite subgraph G[P, P′] consisting of the edges between P and P′ in ${\mathcal{P}}$ contains no cycles. The acyclic dominating number ad(G) of G is the least number of parts in any partition of V that is both acyclic and dominating; and we shall denote by ad(d) the maximum over all graphs G of maximum degree at most d of ad(G). In this article, we prove that ad(3)=2, which establishes a conjecture of P. Boiron, É. Sopena, and L. Vignal, DIMACS/DIMATIA Conference “Contemporary Trends in Discrete Mathematics”, 1997, pp. 1–10. For general d, we prove the upper bound ad(d)=O(dlnd) and a lower bound of ad(d)=Ω(d). © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 292–311, 2010     

具有稳定自治动态的一般非线性系统的镇定问题

针对一般非线性系统,在它的自治动态是稳定的条件下,应用Lyapunov方法获得它可全局渐近稳定的充分条件,同时在系统函数是解析的情况下,基于输出反馈控制律,构造出了类Luenberger观测器,使得闭环系统的平衡点全局渐近稳定.     

RELATIONS BETWEEN SOLUTIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SEMIMARTINGALE WITH NON-LIPSCHITZ COEFFICIENTS

In this paper, a class of stochastic differential equations (SDEs) driven by semi-martingale with non-Lipschitz coefficients is studied. We investigate the dependence of solutions to SDEs on the initial value. To obtain a continuous version, we impose the conditions on the local characteristic of semimartingale. In this case, it gives rise to a flow of homeomorphisms if the local characteristic is compactly supported.     

Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in ℝ<Superscript>2<Emphasis Type="Italic">n</Emphasis></Superscript>

In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface ∑ ⊂ R²ⁿ, there exist at least n non-hyperbolic closed characteristics with even Maslovtype indices on ∑ when n is even. When n is odd, there exist at least n closed characteristics with odd Maslov-type indices on ∑ and at least (n-1) of them are non-hyperbolic. Here we call a compact star-shaped hypersurface ∑ ⊂ R²ⁿ index perfect if it carries only finitely many geometrically distinct prime closed characteristics, and every prime closed characteristic (τ, y) on ∑ possesses positive mean index and whose Maslov-type index i(y, m) of its m-th iterate satisfies i(y, m) ≠-1 when n is even, and i(y, m) ∉ {-2, -1, 0} when n is odd for all m ∈ N.     

辽河减压渣油-正戊烷体系的相态变化特性

利用RUSKA公司无汞PVT装置,对辽河减压渣油-正戊烷体系的相行为进行了实验观察,测定了辽河渣油-正戊烷体系相态变化的边界线,如液-液相分界线、液-液-气三相区分界线等,绘制了体系的p-t相图;在140℃～190℃,1.0MPa～10.0MPa,溶剂质量比为3.0～6.0的条件下,对体系相特性的变化进行了分析和讨论。在实验条件下,辽河渣油-戊烷体系的p-t相图可以划分为四个区域:单一液相区、液-液两相区、液-液-气三相区、气-液两相区;溶剂质量比对由单一液相区转变为液-液两相分相压力的影响显著,溶剂质量比越大,分相压力越大;但溶剂质量比对液-液-气三相区影响不大。确定了辽河渣油-正戊烷体系溶剂脱沥青过程适宜的操作区域。     

Discovery of mass spectral characteristics and automatic identification of wax esters from gas chromatography mass spectrometry data

The mass spectral characteristics of wax esters were systemically summarized and interpreted through data mining of their standard mass spectra taken from NIST standard mass spectral library. Combining with the rules of retention indices described in the previous study, an automatic system was subsequently developed to identify the structural information for wax esters from GC/MS data. After tested and illustrated by both simulated and real GC/MS data, the results indicate that this system could identify wax esters except the polyunsaturated ones and the mass spectral characteristics are useful and effective information for identification of wax esters.     

The method of mixed volume element‐characteristic mixed volume element and its numerical analysis for three‐dimensional slightly compressible two‐phase displacement

Numerical simulation of oil‐water two‐phase displacement is a fundamental problem in energy mathematics. The mathematical model for the compressible case is defined by a nonlinear system of two partial differential equations: (1) a parabolic equation for pressure and (2) a convection‐diffusion equation for saturation. The pressure appears within the saturation equation, and the Darcy velocity controls the saturation. The flow equation is solved by the conservative mixed volume element method. The order of the accuracy is improved by the Darcy velocity. The conservative mixed volume element with characteristics is applied to compute the saturation, that is, the diffusion is discretized by the mixed volume element and convection is computed by the method of characteristics. The method of characteristics has strong computational stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation. Small time truncation error and accuracy are obtained through this method. The mixed volume element simulates diffusion, saturation, and the adjoint vector function simultaneously. By using the theory and technique of a priori estimates of differential equations, convergence of the optimal second order in norm is obtained. Numerical examples are provided to show the effectiveness and viability of this method. This method provides a powerful tool for solving challenging benchmark problems.     

Extensions,dilations, and spectral problems of singular Hamiltonian systems

In this paper, we construct a space of boundary values for minimal symmetric 1D Hamiltonian operator with defect index (1,1) (in limit‐point case at a(b) and limit‐circle case at b(a)) acting in the Hilbert space In terms of boundary conditions at a and b, all maximal dissipative, accumulative, and self‐adjoint extensions of the symmetric operator are given. Two classes of dissipative operators are studied. They are called “dissipative at a” and “dissipative at b.” For 2 cases, a self‐adjoint dilation of dissipative operator and its incoming and outgoing spectral representations are constructed. These constructions allow us to establish the scattering matrix of dilation and a functional model of the dissipative operator. Further, we define the characteristic function of the dissipative operators in terms of the Weyl‐Titchmarsh function of the corresponding self‐adjoint operator. Finally, we prove theorems on completeness of the system of root vectors of the dissipative operators.     

Symmetric and finitely symmetric polynomials on the spaces and

We consider on the space polynomials that are invariant regarding permutations of the sequence variable or regarding finite permutations. Accordingly, they are trivial or factor through c₀. The analogous study, with analogous results, is carried out on , replacing the permutations of by measurable bijections of that preserve the Lebesgue measure.