用矩阵的初等变换化实二次型为标准形

本文介绍了一种用正交变换化实二次型为标准的新方法。

二次型的性质和应用

本文对二次型的标准形、规范形、正定二次型的性质及二次型理论的重要应用做了补充与说明,并简化了正定二次型理论中重要定理的证明过程。

Two New ent-Kauranoids from Isodon tenuifolia

Two new ent-kauranoids, tenuifolin A (3beta,6alpha, 15beta-trihydroxy-1alpha, 7beta-diacetoxy-11beta, 16beta-epoxy-ent-kaurane) (1) and tenuifolin B (1alpha,6alpha, 11beta-trihydroxy-3beta,7beta-diacetoxy-ent-kaur-16-en-15-one) (2), together with four known compounds were isolated from the aerial parts of Isodon tenuifolia (W. W. Smith) Kudo collected from Zhongdian County, Yunnan Province, China. Their structures were determined by the spectral methods (including 2D NMR techniques).

3D Engineering Model Retrieval Based on Enhanced Shape Distributions

To reuse and share the valuable knowledge embedded in repositories of engineering models for accelerating the design process, improving product quality, and reducing costs, it is crucial to devise search engines capable of matching 3D models efficiently and effectively. In this paper, an enhanced shape distributions-based technique of using geometrical and topological information to search 3D engineering models represented by polygonal meshes was presented. A simplification method of polygonal meshes was used to simplify engineering model as the pretreatment for generation of sample points. The method of sampling points was improved and a pair of functions that was more sensitive to shape was employed to construct a 2D shape distribution. Experiments were conducted to evaluate the proposed algorithm utilizing the Engineering Shape Benchmark (ESB) database. The experiential results suggest that the search effectiveness is significantly improved by enforcing the simplification and enhanced shape distributions to engineering model retrieval.

Analyses of Multiplicity and Stability Patterns of Agglomeration Controlled Precipitation with Both Primary and Secondary Nucleations

The possibility of multiplicity in an isothermal continuous mixed suspension-mixed product removalcrystallizer is explored using the bifurcation theory. A process involving agglomeration controlled precipitationis considered in which secondary nucleation occurs simultaneously with primary nucleation. The determinantequations for the existence of multiple steady states are developed and the multiplicity boundaries dependent on thephysical and kinetic properties and operational parameters of the process are obtained by resolving these determinantequations. The number of steady states in the precipitator for various multiplicity regions is determined and thelinear stability of these steady states is analyzed by using the Routh criterion.

例谈矩阵的合同变换法

借助矩阵的合同变换法,给出了化实二次型为标准形的方法、求标准正交基的方法,并给出了正定二次型判定定理的新证明。

矩阵初等变换应用举例

本文介绍了矩阵初等变换的基本概念及性质,举例阐述了矩阵初等变换在求多项式最大公因式、二次型标准形、判断向量组的等价性三方面的应用。

Using Binomial Tree Pricing Model in a Fuzzy Market

A model of using binomial tree pricing formulae in a fuzzy market is proposed. In the fuzzy market, a price interval can be got according to the belief degree. The rule for the reasonability of the price interval is proposed. The explicit expression of the interval is discussed in some special settings.

A Morphologically Structured Model for Mycelial Growth and Secondary Metabolite Formation

A morphologically structured model is proposed to describe the batch fermentation of lovastatin according to the growth kinetics of filamentous microorganisms. Three kinds of hyphae are considered in the model: actively growing hyphae, non-growing hyphae and deactivated hyphae. Furthermore, actively growing hyphae consist of three morphological compartments: apical compartment which gives rise to hyphal tip extension; subapical compartment which is related to hyphal branching; and hyphal compartment which is only responsible for secondary metabolite formation. The kinetics of mycelial growth mechanism is summarized and applied in modeling lovastatin fermentation. A Michaelis-Menten kinetic model with substrate inhibition is proposed for product formation. As expected, the model simulations fit well with experimental data obtained either from a laboratory scale 10L fer-menter or from a pilot-plant scale fermenter.

Formation Mechanism and Size Prediction of Bubble in Opposite-Flowing T-Shaped Microchannel

Bubble formation in an opposite-flowing T-shaped microchannel with 40 μm in depth and 120 μm in width was real-time visualized and investigated experimentally by means of a high speed camera. N2 bubbles were generated in glycerol-water mixtures with different concentrations of surfactant sodium dodecyl sulfate (SDS). And the images were captured by the high speed camera linked to a computer. Results indicated that the bubble formation process can be distinguished into three consecutive stages, i.e., expansion, collapse and pinching off. The bubble size decreases with the increase of liquid flow rate and viscosity of liquid phase as well as the decrease of gas flow rate. The surface tension of the liquid phase has no measurable influence on the bubble size. Moreover, a new approach to predicting the size of bubbles formed in the T-shaped microchannel is proposed. And the predicted values agree well with the experimental data.

The Marine Dynamics and Changing Trend off the Modern Yellow River Mouth

Topography around the Yellow River mouth has changed greatly in recent years, but studies on the current state of ma- rine dynamics off the Yellow River mouth are relatively scarce. This paper uses a two-dimension numerical model （MIKE 21） to reveal the tidal and wave dynamics in 2012, and conducts comparative analysis of the changes from 1996 to 2012. The results show that M2 amphidromic point moved southeastward by 11 kin. It further reveals that the tides around the Yellow River mouth are relatively stable due to the small variations in the tidal constituents. Over the study period, there is no noticeable change in the distribution of tidal types and tidal range, and the mean tidal range off the river mouth during the period studied is 0.5-1.1 m. However, the tidal currents changed greatly due to large change in topography. It is observed that the area with strong tidal currents shifted from the old river mouth （1976-1996） to the modem river mouth （1996-present）. While the tidal current speeds decreased continually off the old river mouth, they increased off the modem river mouth. The Maximum Tidal Current Speed （MTCS） reached 1.4 m s-1, and the maximum current speed of 50-year return period reached 2.8 m s-1. Waves also changed greatly due to change in topography. The significant wave height （H1/3） of 50-year return period changed proportionately with the water depth, and the ratio of Hi/3 to depth being 0.4-0.6. H1/3 of the 50-year return period in erosion zone increased continually with increasing water depth, and the rate of change varied between 0.06 and 0.07myr-1. Based on the results of this study, we infer that in the future, the modem river mouth will protrude gradually northward, while the erosion zone, comprising the old river mouth and area between the modern river mouth and the old river mouth （Intermediate region） will continue to erode. As the modem river mouth protrudes towards the sea, there will be a gradual increase in the current speed and decrease in wave height. Conversely, the old river mouth will retreat, with gradual decrease in current speed and increase in wave height. As more coastal constructions spring up around the Yellow River mouth in the future, we recommend that variation in hydrodynamics over time should be taken into consideration when designing such coastal constructions.

高等代数中的两个逆问题及其求解

本文提出了高等代数中矩阵的特征根与特征向量及实二次型的标准型这两个问题的逆问题,并分析了两个逆问题的求解方法。

Steady-State Properties of Driven Polydisperse Granular Mixtures

We represent a two-dimensional model of polydisperse granular mixtures with a power-law size distribution. The model consists of smooth hard disks in a rectangular box with inelastic collisions,driven by a homogeneous heat bath at zero gravity.The width of particle size distribution is characterized by the only parameter,namely,the fractal dimension D.The energy dissipation of the mixture is increased as D increases or as e decreases.Furthermore,it is found that the steady-state properties of the mixture such as the collision rate,granular temperature,kinetic pressure and velocity distribution depend sensitively on size distribution parameter D.

Chip Formation in Micro-cutting

The miniaturisation context leads to the rise of micro-machining processes. Micro-milling is one of the most flexible and fast of them. Although it is based on the same principles as macro-cutting, it is not a simple scaling-down of it. This down-sizing involves new phenomena in the chip formation, such as the minimum chip thickness below which no chip is formed. This paper presents a review of the current state of the art in this field from an experimental and a numerical point of view. A 2D finite element model is then developed to study the influence of the depth of cut on the chip formation. After the model validation in macro-cutting, it highlights the phenomena reported in literature and allows to perform a minimum chip thickness estimation.

FEM Edge Effect and Capacitance Evaluation on Cylindrical Capacitors

The purpose of this paper is to show the influence of the edge-effect on the electric field distribution, and hence on the inner capacitance and outer capacitance of a cylindrical capacitor surrounded by an insulating medium. To generalize the results, a two-dimensional axisymmetric finite element model of a cylindrical capacitor has been generated and the problem has been resolved taking into account the distance between the conductors for a complete set of dimensions. The available obtained results have been compared with previous published works. Finally, using statistical tools, the mathematical expression for computing the relationship between capacitance and insulation gap and cylindrical plates dimensions has been obtained.

On universal sums of polygonal numbers

For m = 3, 4,..., the polygonal numbers of order m are given by pm(n) =(m- 2) n2 + n(n= 0, 1, 2,...). For positive integers a, b, c and i, j, k 3 with max{i, j, k} 5, we call the triple(api, bpj, cpk)universal if for any n = 0, 1, 2,..., there are nonnegative integers x, y, z such that n = api(x) + bpj(y)+ cpk(z). We show that there are only 95 candidates for universal triples(two of which are(p4, p5, p6) and(p3, p4, p27)), and conjecture that they are indeed universal triples. For many triples(api, bpj, cpk)(including(p3, 4p4, p5),(p4, p5, p6) and(p4, p4, p5)), we prove that any nonnegative integer can be written in the form api(x) + bpj(y) + cpk(z) with x, y, z ∈ Z. We also show some related new results on ternary quadratic forms,one of which states that any nonnegative integer n ≡ 1(mod 6) can be written in the form x2+ 3y2+ 24z2 with x, y, z ∈ Z. In addition, we pose several related conjectures one of which states that for any m = 3, 4,...each natural number can be expressed as pm+1(x1) + pm+2(x2) + pm+3(x3) + r with x1, x2, x3 ∈ {0, 1, 2,...}and r ∈ {0,..., m- 3}.

Further casbane-type diterpenes from the soft coral Sinularia depressa

AIM: To study the minor diterpenes from the soft coral Sinularia depressa. METHOD: The chemical constituents were isolated and purified by various chromatographic techniques, and the chemical structures, including absolute configuration, were established on the basis of detailed analysis of spectroscopic data and by literature comparison with the data of related known compounds. RESULTS: A new casbane-type diterpene, 2-epi-10-hydroxydepressin(1), was isolated and identified. CONCLUSION: Compound 1 is a new casbane-type diterpene.

Cartan-Fubini type extension of holomorphic maps respecting varieties of minimal rational tangents

A fundamental result in the theory of minimal rational curves on projective manifolds is Cartan- Fubini extension theorem proved by Hwang and Mok, which describes the extensibility of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents （VMRT）, under a mild geometric assumption on the second fundamental forms of VMRT＇s. Hong and Mok have developed Cartan-Fubini extension for non-equidimensional holomorphic immersions from a connected open subset of a Pano manifold of Picard number 1 into a uniruled projective manifold, under the assumptions that the map sends VMRT＇s onto linear sections of VMRT＇s and it satisfies a mild geometric condition formulated in terms of second fundamental forms on VMRT＇s. In the current paper, we give a generalization of Hong and Mok＇s result, under the same condition on second fundamental forms, assuming only that the holomorphic immersions send VMRT＇s to VMRT＇s. Our argument is different from Hong and Mok＇s and is based on the study of natural foliations on the total family of VMRT＇s. This gives a substantially simpler proof than Hong and Mok＇s argument.

Contact binaries:Ⅱ.The importance of deformation caused by rotation and tides to the light curve of a contact binary

The theoretical light curves of contact binaries are calculated with and without putting in the contact binary evolution model.Firstly,we do not use the contact binary evolution model.A comparison of the light curve is performed with and without the deformation caused by rotation and tides.It shows that the light curve presents many differences,especially on the bottom and top.Secondly,we adopt the contact binary model [Huang R Q,et al.Chin J Astron Astrophys,2007,7:235-244;Song H F,et al.Chin J Astron Astrophys,2007,7:539-550] and compute the theoretical light curve with and without rotational and tidal effects by studying three binary systems(with low-,intermediate-and high-mass components).The bottom and top of the theoretical light curves are discussed and compared to observations.The results show that taking into account the rotational effect has a better agreement with observations than without it.Therefore,the deformation of the light curve of contact binaries caused by rotation and tides is very important.Meanwhile,the rotational and tidal effect can advance the start of the semi-detached,contact phase and the time of mass-reversal.