离散系统中的微分度量空间

收敛性是函数的一种接近性.邓聚龙提出了关联度以及关联空间的概念,用以描述离散系统中函数的接近程度.关联度的概念是灰色系统理论中的一个重要概念,在GM模型建立中起到关键作用.然而,关联映射不唯一,关联度与分辨系数有关,它的大小仅仅具有相对意义.本文提出了离散函数的微分度量以及微分度量空间等概念,用微分度量收敛来刻画离散函数的收敛.这种收敛与传统分析数学中的收敛是相容的。

Mobius变换的推广及其几何性质

先引入Mobius变换,讨论了此变换在复平面中的一些性质,接着把Mobius变换的实数形式推广到了n维空间,并证明了此推广即为共形变换.最后,讨论了Mobius变换在n维空间中的球几何和微分度量.

分式线性变换的一种推广及其几何性质

引入了分式线性变换的一种推广形式,讨论了其也可把圆映为圆.并把此变换利用实数形式推广到了n维空间,接着讨论了此变换在n维空间中的球几何和微分度量.

A New Three-Level Hierarchical Control Algorithm for Large-Scale Systems

This paper presents a new three-level hierarchical control parallel algorithm for large-scale systems by spatial and time decomposition. The parallel variable metric (PVM)method is found to be promising third-level algorithm. In the subproblems of second-level, the constraints of the smaller subproblem requires that the initial state of a subproblem equals the terminal state of the preceding subproblem. The coordinating variables are updated using the modified Newton method. the low-level smaller subproblems are solved in parallel using extended differential dynamic programmeing (DDP). Numerical result shows that comparing with one level DDP. the PVM /DDP algorithm obtains significant speed-ups.

NETWORK INTRUSION DETECTION METHOD BASED ON RS-MSVM

A new method called RS-MSVM （Rough Set and Multi-class Support Vector Machine） is proposed for network intrusion detection. This method is based on rough set followed by MSVM for attribute reduction and classification respectively, The number of attributes of the network data used in this paper is reduced from 41 to 30 using rough set theory. The kernel function of HVDM-RBF （Heterogeneous Value Difference Metric Radial Basis Function）, based on the heterogeneous value difference metric of heterogeneous datasets, is constructed for the heterogeneous network data. HVDM-RBF and one-against-one method are applied to build MSVM. DARPA （Defense Advanced Research Projects Agency） intrusion detection evaluating data were used in the experiment. The testing results show that our method outperforms other methods mentioned in this paper on six aspects： detection accuracy, number of support vectors, false positive rate, falsc negative rate, training time and testing time.

Soil Nutrient Distribution in Two Typical Paddy Terrace Wetlands Along an Elevation Gradient During the Fallow Period

Soil nutrient concentrations in the top soils from two paddy terraces were determined in order to investigate spatial distributions of soil nutrients along the elevations on the Yunnan plateau of China during the fallow period.Results showed that soil nutrients in both terraces were higher than the reference concentrations except for SOC,TN,TP and Fe.Soil macronutrients didn't show significant differences in both terraces except for Mg and Ca,so did soil micronutrients except for Mn.Spatial distribution patterns of soil nutrients along the increasing elevations were different in both terraces.However,soil nutrients in both terraces were generally not significantly influenced by the elevations and soil pH values.The findings of this study can contribute to soil fertility management and ecological protection of Hani terraces.

Mechanical properties and microscopic failure process of exemplary argillaceous interlayer from east China

The landslide disaster caused by the argillaceous interlayer not only destroys buildings,cultivated land,and roads but also seriously endangers human life and safety.This study concerns the mineral composition of selected argillaceous interlayer and their strength characteristics.To study the mineral composition of argillaceous interlayers,8 kinds of samples in the southern Jiangsu region of China were analyzed utilizing X-ray diffraction(XRD).The repeated direct shear strength tests(RDST)were carried out on the undisturbed specimens of the argillaceous interlayer.The results show that the argillaceous interlayer with high content of kaolinite shows ductile failure mode,which means that there is no obvious residual strength in the shear process.The arrangement of mineral particles on the shear surface of the specimens after different shear displacements was observed under the scanning electron microscope(SEM).It was observed that mineral particles on the shear surface showed a more directional arrangement with the increase of shear displacement.Furthermore,the influence of shear direction on the argillaceous interlayer with completely oriented mineral particles was studied through numerical experiments with four shear strength mechanisms proposition proposed.The influence of the mineral arrangement on the action occasion and magnitude of dilatancy component of shear strength is clarified in the shear mechanism.

Quality Characteristics and Microbiology Status in Kundi, an Intermediate Moisture Meat （IMM） Product

Meat and meat products are extremely perishable, so special care and handling must be exercised during slaughtering operation. Moreover, due to its high nutritive value, deterioration set in immediately after slaughtered, therefore it is necessary to preserved meat, using simple techniques. One of such method of preservation is drying method to produced Intermediate Moisture Meat （IMM）. The quality attributes and microbiological status of Kundi, a West African dried meat product （IMM） were studied over three months of storage period by comparing commercial products and laboratory Kundi products. Chemical and minerals composition and microbiological counts were reported. Moisture and water activity results indicated that the experimental Kundi was sufficiently dried to minimize microbial growth. Fat oxidation levels measured by free fatty acids （FFA, %） on extracted fats were unacceptably high for the commercial Kundi （2.64%）, which may be a reflection of the oil used in spraying the products. Processing of Kundi, appears to have relative higher amounts of minerals than fresh meat but their relative solubility were lower. Aflatoxin levels far exceeded established safe limits for commercial samples while laboratory samples fell under the safe limits, resulting from the mould growth in each product, with laboratory samples having lower growth than commercial samples.

STUDY ON DETERMINATION OF TRACE Cu（Ⅱ） BY DDCT CHELATING RESIN PRECONCENTRATION AND THIN LAYER RESIN PHASE SPECTROPHOTOMETRY

A new method for determination of Cu（Ⅱ） by DDCT chelating resin preconcentration and thin layer resin phase spectrophotometry was developed. The method has a high sensitivity （ε455= 3.6×10^5L/mol·cm）, which is 33 times higher than that of liquid phase spectrophotometry. It has a good selectivity （most coexisting ions could not influence determination） and an ideal precision [30μg Cu（Ⅱ）, n=6, RSD= l.67%]. The content of Cu（Ⅱ） in water, high purity rare earth and its oxide was determined. The detection limit of Cu（Ⅱ） is 5.3μg/L , and the linear range is 0-7.2μg/ml. The result is satisfactory.

Uncertainty Calculation of Roundness Assessment by Automatic Differentiation in Coordinate Metrology

Reomtly, Coordinate bieasuring Machines （CMMs） are widely used to measure roundness errors. Roundness is calculated from a large number of points collected from the profiles of the parts. According to the Guide to the Expression of Uncertainty in Measta- meat （GUM）, all measurement results must have a stated uncertainty associated the titan. However, no CMMs give the uncertainty value of the roundness, because no suitable measrement uncertainty calculation procedure exists. In the case of roundness raeasurement in coordinate metrology, this paper suggests the algorithms for the calculation of the measurement uncertainty of the roudness deviation based on the two mainly used association criteria, LSC and MZC. The calculation of the sensitivity coefficients for the uncertainty calculatiion can be done by autnatic differentiation, in order to avoid introducing additional emars by the traditional difference quotient approxima- tions. The proposed methods are exact and need input data only as the nrasured coordinates of the data points and their associated un- certainties.

Conformal vector fields on some Finsler manifolds

We study conformal vector fields on a Finsler manifold whose metric is defined by a Riemannian metric, a 1-form and its norm. We find PDEs characterizing conformal vector fields. Then we obtain the explicit expressions of conformal vector fields for certain spherically symmetric metrics on R^n.

Soil Respiration, Microbial Biomass and Nutrient Availability in Soil After Addition of Residues with Adjusted N and P Concentrations

Microbial activity and nutrient release are known to be influenced by organic matter properties,but it is difficult to separate the effect of C/N ratio from that of C/P ratio because in most plant residues both ratios are either high or low.An incubation experiment was conducted to investigate the effects of reducing the C/N and C/P ratios of slowly decomposable plant residues(young eucalyptus leaves,mature wheat straw,and sawdust) to those of rapidly decomposable residues(young kikuyu shoots) on soil respiration,microbial biomass,and N and P availability.The C/N and C/P ratios of the former were adjusted to 15 and 89,respectively,by adding N as(NH_4)_2SO_4,P as KH_2PO_4 or both and residues were added at 10 g C kg-1 to a silt loam.Soil respiration was measured over21 d;microbial biomass C(MBC) and available N and P were measured on days 0,7,and 21.Compared to the unamended soil,addition of kikuyu increased cumulative respiration 20-fold,MBC concentration 4 to 8-fold,and available P concentration up to4-fold,whereas the increase in available N concentration was small and transient.Cumulative respiration and MBC concentration were low in the sawdust-amended soil and were not influenced by reducing the C/N and C/P ratios.Cumulative respiration with original wheat and eucalyptus was 30%-40%of that with kikuyu.Reducing the C/N ratio alone or both C/N and C/P ratios increased cumulative respiration and MBC concentration 2-fold compared to the original wheat and eucalyptus,whereas reducing the C/P ratio had little effect.Throughout the experiment,the available N concentration after addition of residues with reduced C/N ratio increased in the following order of eucalyptus < wheat < sawdust.By independently lowering the C/N and C/P ratios,microbial activity was more limited by C and N than P.However,lowering the C/N ratio of very slowly decomposable sawdust had no effect on soil respiration and MBC concentration,suggesting that other properties such as concentration of poorly decomposable C compounds limited decomposition.

Teichmller space of negatively curved metrics on complex hyperbolic manifolds is not contractible

We prove that for all n = 4k- 2 and k 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π1(T<0(M)). T<0(M) denotes the Teichm¨uller space of all negatively curved Riemannian metrics on M, which is the topological quotient of the space of all negatively curved metrics modulo the space of self-diffeomorphisms of M that are homotopic to the identity.

The change in thickness of the solidified liquid layer rather than the immobilized mass determines the frequency response of a quartz crystal microbalance

The "solidified liquid layer" model has been examined using a quartz crystal microbalance(QCM) with a polymeric matrix.The model is shown to give a reasonable explanation for the following experimental observations:(i) The opposite response of the QCM and surface plasmon resonance(SPR) for the activation process;(ii) the marked difference in the responses for IgG/anti-IgG interaction between QCM and SPR.Theoretical analysis and experimental results indicated that QCM is sensitive to the thickness change of the "solidified liquid layer" but not the mass of captured biomolecules(i.e.,the immobilized mass),implying caution must be taken in interpreting QCM results.

The distribution of the periodic orbits with open deviation in C^(1+α)non-uniformly hyperbolic systems

Let f ： M → M be a C^1＋α diffeomorphism on a smooth compact Riemannian manifold M and A be a Pesin set associated with the ergodic hyperbolic measure μ. Then f ： A → A forms a non-uniformly hyperbolic system. We concern with the distribution of the periodic orbits whose time averages are apart from the space average of μ. Finally, we derive a large deviation result for these periodic orbits with open deviation property.

Convergence analysis of the formal energies of symplectic methods for Hamiltonian systems

Based on Feng's theory of formal vector fields and formal flows, we study the convergence problem of the formal energies of symplectic methods for Hamiltonian systems and give the clear growth of the coefficients in the formal energies. With the help of B-series and Bernoulli functions, we prove that in the formal energy of the mid-point rule, the coefficient sequence of the merging products of an arbitrarily given rooted tree and the bushy trees of height 1(whose subtrees are vertices), approaches 0 as the number of branches goes to ∞; in the opposite direction, the coefficient sequence of the bushy trees of height m(m ≥ 2), whose subtrees are all tall trees, approaches ∞ at large speed as the number of branches goes to +∞. The conclusion extends successfully to the modified differential equations of other Runge-Kutta methods. This disproves a conjecture given by Tang et al.(2002), and implies:(1) in the inequality of estimate given by Benettin and Giorgilli(1994) for the terms of the modified formal vector fields, the high order of the upper bound is reached in numerous cases;(2) the formal energies/formal vector fields are nonconvergent in general case.

Mathematical modeling of micropolar fluid flow through an overlapping arterial stenosis

In this study a mathematical model for two-dimensional pulsatile blood flow through overlapping constricted tapered vessels is presented. In order to establish resemblance to the in vivo conditions, an improved shape of the time-variant overlapping stenosis in the elastic tapered artery subject to pulsatile pressure gradient is considered. Because it contains a suspension of all erythrocytes, the flowing blood is represented by micropolar fluid. By applying a suitable coordinate transformation, tapered cosine-shaped artery turned into non-tapered rectangular and a rigid artery. The governing nonlinear partial differential equations under the imposed realistic boundary conditions are solved using the finite difference method. The effects of vessel tapering on flow characteristics consid- ering their dependencies with time are investigated. The results show that by increasing the taper angle the axial velocity and volumetric flow rate increase and the microrota- tional velocity and resistive impedance reduce. It has been shown that the results are in agreement with similar data from the literature.