手性有机酸保留指数的手性指数及原子类型电拓扑指数模型

基于手性碳原子的取代基次序规则,提出分子手性指数(wj),结合原子类型电拓扑指数(En)研究18种手性羟基酸和氨基酸的薄层色谱保留指数(RM)的定量关系(QSRR).经最佳变量子集回归建立最佳四元数学模型,传统的相关系数(R2)为0.969,留一法(LOO)的交互验证系数(Q2)为0.943,结果证明具有良好的稳健性及预测能力.根据进入该模型的4个结构参数(wj,E13,E16,E17)可知,影响手性有机酸保留指数的主要因素是分子的二维结构特征(如襒O,—OH,—NH2)和分子的手性特征.综上所述,新建wj及En对手性有机酸的保留指数表征具有合理性与有效性,为预测手性有机酸的保留指数提供一种有效方法.     

子群的S-条件置换性对有限群结构的影响

Let G be a finite group. Fix a prime divisor p of IGI and a Sylow p-subgroup P of G, let d be the smallest generator number of P and Ma（P） denote a family of maximal subgroups P1, P2 , Pd of P satisfying ∩^di=1 Pi = Ф（P）, the Frattini subgroup of P. In this paper, we shall investigate the influence of s-conditional permutability of the members of some fixed .Md（P） on the structure of finite groups. Some new results are obtained and some known results are generalized.     

Singleton core in many-to-one matching problems

We explore two necessary and sufficient conditions for the singleton core in college admissions problems. One is a condition on the colleges’ preference profiles, called acyclicity, and the other is a condition on their capacity vectors. We also study the implications of our acyclicity condition. The student-optimal stable matching is strongly efficient for the students, given an acyclic profile of the colleges’ preference relations. Even when the colleges’ true preference profile is acyclic, a college may be better off by misreporting its preference when the college-optimal stable mechanism is used.     

The distance coloring of graphs

Let G be a connected graph with maximum degree Δ≥ 3.We investigate the upper bound for the chromatic number χγ(G) of the power graph Gγ.It was proved that χγ(G) ≤Δ(Δ-1)γ-1Δ-2+ 1 =:M + 1,where the equality holds if and only if G is a Moore graph.If G is not a Moore graph,and G satisfies one of the following conditions:(1) G is non-regular,(2) the girth g(G) ≤ 2γ- 1,(3)g(G) ≥ 2γ + 2,and the connectivity κ(G) ≥ 3 if γ≥ 3,κ(G) ≥ 4 but g(G) 6 if γ = 2,(4) Δis sufficiently larger than a given number only depending on γ,then χγ(G) ≤ M- 1.By means of the spectral radius λ1(G) of the adjacency matrix of G,it was shown that χ2(G) ≤λ1(G)2+ 1,where the equality holds if and only if G is a star or a Moore graph with diameter 2 and girth 5,and χγ(G)λ1(G)γ+1 ifγ≥3.     

A new nonlinear blind source separation method with chaos indicators for decoupling diagnosis of hybrid failures: A marine propulsion gearbox case with a large speed variation

The normal operation of propulsion gearboxes ensures the ship safety. Chaos indicators could efficiently indicate the state change of the gearboxes. However, accurate detection of gearbox hybrid faults using Chaos indicators is a challenging task and the detection under speed variation conditions is attracting considerable attentions. Literature review suggests that the gearbox vibration is a kind of nonlinear mixture of variant vibration sources and the blind source separation (BSS) is reported to be a promising technique for fault vibration analysis, but very limited work has addressed the nonlinear BSS approach for hybrid faults decoupling diagnosis. Aiming to enhance the fault detection performance of Chaos indicators, this work presents a new nonlinear BSS algorithm for gearbox hybrid faults detection under a speed variation condition. This new method appropriately introduces the kernel spectral regression (KSR) framework into the morphological component analysis (MCA). The original vibration data are projected into the reproducing kernel Hilbert space (RKHS) where the instinct nonlinear structure in the original data can be linearized by KSR. Thus the MCA is able to deal with nonlinear BSS in the KSR space. Reliable hybrid faults decoupling is then achieved by this new nonlinear MCA (NMCA). Subsequently, by calculating the Chaos indicators of the decoupled fault components and comparing them with benchmarks, the hybrid faults can be precisely identified. Two specially designed case studies were implemented to evaluate the proposed NMCA-Chaos method on hybrid gear faults decoupling diagnosis. The performance of the NMCA-Chaos was compared with state of art techniques. The analysis results show high performance of the proposed method on hybrid faults detection in a marine propulsion gearbox with large speed variations.     

Acyclic edge coloring of triangle-free 1-planar graphs

A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G, denoted by χ a(G), is the least number of colors such that G has an acyclic edge coloring. A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that χ a(G) ≤Δ(G) + 22, if G is a triangle-free 1-planar graph.     

Mathematical model for hysteresis phenomenon in moisture transport of concrete carbonation process

From civil engineering point of view it is very important to construct and analyze a mathematical model for a mechanism of concrete carbonation process. On this subject there are several mathematical results concerned with a one-dimensional model, in which hysteresis effects are neglected. Our aim is to give a model with hysteresis effects appearing in carbonation process. In this paper, as the first step of this research we focus only on moisture transport in the process and propose an initial boundary value problem for a system of partial differential equations as a mathematical model. Also, we give results on the existence of a solution to the problem, globally in time and the uniqueness in only one-dimensional case without proofs.     

On the skin friction coefficient in viscoelastic wall-bounded flows

Analysis of the skin friction coefficient for wall bounded viscoelastic flows is performed by utilizing available direct numerical simulation (DNS) results for viscoelastic turbulent channel flow. The Oldroyd-B, FENE-P and Giesekus constitutive models are used. First, we analyze the friction coefficient in viscous, viscoelastic and inertial stress contributions, as these arise from suitable momentum balances, for the flow in channels and pipes. Following Fukagata et al. (Phys. Fluids, 14, p. L73, 2002) and Yu et al. (Int. J. Heat. Fluid Flow, 25, p. 961, 2004) these three contributions are evaluated averaging available numerical results, and presented for selected values of flow and rheological parameters. Second, based on DNS results, we develop a universal function for the relative drag reduction as a function of the friction Weissenberg number. This leads to a closed-form approximate expression for the inverse of the square root of the skin friction coefficient for viscoelastic turbulent pipe flow as a function of the friction Reynolds number involving two primary material parameters, and a secondary one which also depends on the flow. The primary parameters are the zero shear-rate elasticity number, El₀, and the limiting value for the drag reduction at high Weissenberg number, LDR, while the secondary one is the relative wall viscosity, μ_w. The predictions reproduce both types A and B of drag reduction, as first introduced by Virk (Nature, 253, p. 109, 1975), corresponding to partially and fully extended polymer molecules, respectively. Comparison of the results for the skin friction coefficient against experimental data shows good agreement for low and moderate drag reduction which is the region covered by the simulations.     

Kinematics of rigidly rotating spiral waves

Spiral waves rigidly rotating in excitable media are studied by use of a free-boundary approach. This study reveals the selection principle which determines the shape and the rotation frequency of spiral waves in an unbounded medium with a given excitability. It is shown that a rigidly rotating spiral in a medium with a strongly reduced refractoriness is supported within a range of the medium excitability restricted by two universal limits. At the low excitability limit the spiral core radius diverges, while at the high excitability limit it vanishes. The simulations performed for the medium excitability higher than the high excitability limit reveal nonstationary rotating waves, which considerably differ from well-studied meandering spiral waves. It is shown how the proposed free-boundary approach can be extended to the case of an arbitrary refractoriness. The predictions of the free-boundary approach are in good agreement with the results from numerical simulations of the underlying reaction-diffusion model and with asymptotics derived earlier for highly and weakly excitable media.     

Innovation diffusion uncertainty,advertising and pricing policies

We develop and analyze a normative and structurally stochastic model of innovation diffusion by depicting the market at an aggregate level. Model dynamics are defined through the flow pattern of individuals that move from the innovation unaware stage, to the innovation aware, and ultimately to the adopter stages. The stochastic evolution of this stage-wise transition unfolds according to tractable stochastic processes and is influenced by such factors as price, word of mouth, and advertisement efforts. In this environment, techniques of contingent claims analysis and stochastic control theory are employed to obtain optimal pricing or advertising policies that maximize the value of the innovation. To account for their optimal adjustment over time, these policies are modeled as positive real-valued adapted processes. Given this setting, policy adjustments over time (i.e. advertising or pricing) are viewed as a value additive sequence of nested real options. We present closed-form analytic results regarding the optimal policies. Simulations provide a numeric insight to the models' behavior.