关于数直线R中分划R的子集

本文研究美国学者P.Bankston和R.J.McGovern提出的一个公开问题—数直线R中那些子集分划R?研究表明,R中的每一个0一维子集都分划R;对月中的1一维子集;本文给出了开集、闭集以及具有某种散性的子集分划R的充分必要条件。

数还是一个“点”吗?——“小数的近似数”教学实践与思考

数源于数,准确数的教学使学生建立“数对应数直线上一个点”的认知,而近似数的教学则打破了“数对应数直线上一个点”的认知,使学生认识到近似数表示一个区间内的所有数,是一次“由点到线”的数的概念的认知突破。文章结合“小数的近似数”教学实践,通过缘起、实录、反思三部分,阐述如何带领学生在多元表征互译中实现“由点到线”的数的概念的认知突破,进而全面理解近似数的意义,发展数感。

著名数学家朱梧槚的发现揭示课本有一系列重大错误——发现最小、大正数推翻百年集论破解2500年芝诺著名世界难题

论证有最大正数,各无穷序列都有末项,不存在对等于其真子集的无穷集,朱梧槚、肖奚安等4位数学家所言:"集合论中的无穷集都是自相矛盾的非集"不虚——意味一系列以非集为"无穷集"的"定理"和集论必是错上加错的更重大错误。证明元为正数且至少有两元的集必有最小元使困扰科学界2500年的芝诺著名"运动不存在"世界难题迎刃而解,从而揭示二千多年"点无大小"公理是几何学最重大根本错误——几百年解析几何一直存在极重大错误的根本原因。指出可证明各光滑曲线都是由充分短直线段连接成的,从而消除"△f≈df反例"悖论。逻辑学常识表明有标准数>R一切元。指出已知实数全体仅为实数全体的沧海一粟。试提出全新数学的冰山一角。

正数和负数

测量和计算有时不能得到整数的结果,这就要用分数和小数表示。除此之外,你还见过其他的数吗?留意一下中国地形图不难发现,上面世界最高峰——珠穆朗玛峰,图上标着8844m;还有一个吐鲁番盆地,图上标着-155m。你能说出它们的高度各是多少吗?图上标的数表示的高度是相对海平面说的,通常称为海拔高度。8844m表示珠穆朗玛峰比海平面高8844m,-155m表示吐鲁番盆地的高度比海平面低155m。从实际需要出发引入负数,是为了区分海平面以上与海平面以下高度,这是一对具有相反意义的量。

数频科学之椭圆周长的数频公式

椭圆周长的数频公式是数频科学的又一重要发现,它结束了经典数学没有椭圆周长等式及证明的历史,只有近似的积分式或无限项表达式,并不完全被证明是科学.这一公式在某一意义上见证了当今时代国际数学发展的科学进程.

Direct adaptive fuzzy control based on integral-type Lyapunov function

A new scheme of direct adaptive fuzzy controller for a class of nonlinear systems with unknown triangular control gain structure is proposed. The design is based on the principle of sliding mode control and the approximation capability of the first type fuzzy systems. By introducing integral-type Lyapunov function and adopting the adaptive compensation term of optimal approximation error, the closed-loop control system is proved to be globally stable, with tracking error converging to zero. Simulation results demonstrate the effectiveness of the approach.

Simulation and calculation of internal faults in long-stator linear synchronous motor based on winding function theory

To guarantee the safety of the high speed maglev train system, a novel model based on the winding function theory is proposed for the long-stator linear synchronous motor（LSM）, which is suitable for the real-time calculation of the running state. The accurate coupled mathematical models under different internal fault conditions of the LSM are derived based on the normal model. Then the fault currents and electromagnetic forces are simulated and calculated for the major potential internal faults of the LSM, such as the single-phase short circuit, the phase-phase short circuit and the single-phase open circuit. The characteristic curve between the electromagnetic force and the armature current of the LSM, which is compared with the results from the finite element method, proves the validation of the proposed method. The fault rule is determined and the proposed analytical model also shows its feasibility in the fast fault diagnosis through the comparison of the simulation results of currents and electromagnetic forces under different internal fault types and short circuit ratios.

Non-Lie Symmetry Groups of （2＋1）-Dimensional Nonlinear Systems

A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only speciai cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches.

Analysis of nonlinearities and effects in direct drive electro-hydraulic position servo system

The direct drive electro-hydraulic servo system is a new approach hydraulic system. It is much smaller and easier controlled than traditional systems and is a perfect energy saver. This paper will briefly introduce the popular nonlinearities in the electro-hydraulic system and analyse the effect of nonlinearities in direct drive electro-hydraulic position servo system by means of simulation research. Some valuable conclusions are given.

Mechanism and optimization of fuel injection parameters on combustion noise of DI diesel engine

Combustion noise takes large proportion in diesel engine noise and the studies of its influence factors play an important role in noise reduction. Engine noise and cylinder pressure measurement experiments were carried out. And the improved attenuation curves were obtained, by which the engine noise was predicted. The effect of fuel injection parameters in combustion noise was investigated during the combustion process. At last, the method combining single variable optimization and multivariate combination was introduced to online optimize the combustion noise. The results show that injection parameters can affect the cylinder pressure rise rate and heat release rate, and consequently affect the cylinder pressure load and pressure oscillation to influence the combustion noise. Among these parameters, main injection advance angle has the greatest influence on the combustion noise, while the pilot injection interval time takes the second place, and the pilot injection quantity is of minimal impact. After the optimal design of the combustion noise, the average sound pressure level of the engine is distinctly reduced by 1.0 d B(A) generally. Meanwhile, the power, emission and economy performances are ensured.

Numeric simulation analysis of load-settlement relation of pile in layer foundation

Considering the level distribution of soil layers, the soils surrounding pile are simulated with level finite layer elements. Supposing that the vertical deformation of the soil elements surrounding pile varies in the form of exponent function with radial distance, and considering the nonlinear constitutive relation of stress and strain, the stiffness matrix is established. The mechanics behavior of the pile—soil interface is simulated with a nonlinear interface element. This method can truly express the behavior of the pile-soil system. The load-settlement relation Q-S curves of two big diameter prototype piles on bearing test are analyzed, and satisfying results are obtained. This method is reasonable in theory and feasible in engineering.

Distribution of Vertical Turbulent Mixing Parameter Caused by Internal Tidal Waves and Solitary Waves in the South Yellow Sea

Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal waves is one of the mechanisms producing internal solitary waves (ISWs), which is different from the generation mechanism in the case where the semidiurnal tidal current flows over topographic drops. In this paper, the model of internal Kelvin wave with continuous stratification is given, and an elementary numerical study of nonlinear evolution of ITWs is made for the SYS, using the generalized KdV model (GKdV model for short) for a continuous stratified ocean, in which the different effects of background barotropic ebb and flood currents are considered. Moreover, the parameterization of vertical turbulent mixing caused by ITWs and ISWs in the SYS is studied, using a parameterization scheme which was applied to numerical experiments on the breaking of ISWs by Vlasenko and Hutter in 2002. It is found that the vertical turbulent mixing caused by internal waves is very strong within the upper layer with depth less than about 30m, and the vertical turbulent mixing caused by ISWs is stronger than that by ITWs.

Introduction of Linac quality management experience

The Elekta Precise medical Linac is a typical modern high energy accelerator which uses advanced digital technology and gets acknowledged around the world. It provides both X rays and electrons at various megavoltage energies including two photon energies （6 and 15 MV） and several electron energies （e.g. 6, 9, 12, 15, 18 and 22 MeV）. The commonly used dose rate for X rays is 500 MU/min, while that for electors is 400 MU/min. The accelerator is equipped with beam intensity modulation cm2. The width of MLC at 40 pairs of MLC for photon covering fields up to 40 × 40 the isocenter is 10 mm. The maximum leakage is less than 0.3%

Uncertainty Evaluation of Boar Fresh Semen Quality

According to JJF1059.2-2012 and CNAS-GL06, the measurement uncertainty of four indicators （semen volume, sperm motility and validity, progressive motility, abnormal sperm percentage） of boar fresh semen, as well as its influencing factors, was analyzed. The results showed that the measurement uncertainty of semen volume and progressive motility caused by inspectors was low, and their measurement results reliability was high. There were small differences in measurement results of semen volume and progressive motility among inspectors. However, the measurement uncertainty of sperm motility and abnormal sperm percentage was relatively large, and great differences were found among different inspectors. Therefore, the training of inspectors＇ measuring sperm motility and abnormal sperm percentage should be strengthened, and the comparison of measurement results among inspectors should be performed in the future.

Economical Analysis of Milk Production in the Farms of Siedlce Region

Last years the most profitable line of activity in agriculture is considered with milk production. The-effectiveness of this project depends primarily on the direct costs and the obtained of purchase price. Therefore the aim of this work was to analyze the financial results of dairy farms in the east part of Mazovia region. Completing the research in 2010, to the owners of 36 farms were sent a questionnaire containing 18 questions. The obtained data were used to characterize the various research facilities. And then the whole population was devoted on the 6 production groups, depend on the number of physical units of dairy cows. Moreover, based on survey data, an analysis of the profitability of milk production was done. It was the following economic values： direct costs, revenue, gross margin and the index of production profitability. Also the statistical analysis by calculating the Pearson linear correlation coefficient （r） and coefficient of determination （R2） was done. The study showed that the highest annual yield of milk from a cow at the level of 7500 kg, reached the farmers with the area of l 9.7 ha of with the density of 1.82 BFU/ha and with 8 years of cow utilization. Respondents from this group also received the highest value of effectiveness index （184.60%）. In addition, the performed regression analysis showed significant positive correlation between the effectiveness index and the surface agricultural lands occurring in the farms, density of agricultural lands, and efficiency from a cow and the price of milk.

Objects Description and Extraction by the Use of Straight Line Segments in Digital Images

An advanced edge-based method of feature detection and extraction is developed for object description in digital images. It is useful for the comparison of different images of the same scene in aerial imagery, for describing and recognizing categories, for automatic building extraction and for finding the mutual regions in image matching. The method includes directional filtering and searching for straight edge segments in every direction and scale, taking into account edge gradient signs. Line segments are ordered with respect to their orientation and average gradients in the region in question. These segments are used for the construction of an object descriptor. A hierarchical set of feature descriptors is developed, taking into consideration the proposed straight line segment detector. Comparative performance is evaluated on the noisy model and in real aerial and satellite imagery.

The mathematical model and simulation of the electrostatic suspension system in the vertical direction

In order to research the vibration law of electrostatic suspension systems in the vertical direction, the mathematical model as a nonlinear differential equation is established. A series of simulation is carried out. The results show that the solution of the differential equation is a periodic function. The amplitude becomes bigger with the original velocity increased. The period becomes smaller with the original velocity increasing. The numerical methods are presented to derive the amplitude and the frequency, and the results coincide with that of the simulation. The condition during which the simple harmonic vibration arises is pointed out. The expressions for the amplitude and the period of simple harmonic vibration are derived respectively, and the results are the same with that of the simulation. This study is helpful for researching the vibration characteristics of the electrostatic suspension system. The external disturb should be controlled to lower the amplitude and the frequency of the vibration.

Sensitivity Study of Design Parameters of a Railway Route under Vertical Deformations

Studying the interaction of components is basic for a railroad project, which is also very important for creating maintenance procedures based on predictions from a model that assumes adequate performance. To determine these interactions, which can have a great number of combinations, the use of a computational model is of vital importance, in this case, the program FERROVIA 1.0 （RAILROAD 1.0） was used. A critical study developed the program FERROVIA 1.0, and its variables were characterized based on values observed in the literature. After initial characterization was carried out, a comparative study was performed on the sensitivity between these variables and the indications of significant behavior for a railway deformed by the known load of a wheel. A statistical program was used to correlate the elements. The intention was to launch the program FERROVIA 1.0 and later use it for 2,187 combinations. The data used in these correlations corresponded to the normal values for the elements used in railroad engineering practice. Our main goal is to understand the behavior of the track vertical deflection according to the variation of the scaling of the various elements of the railway,

数轴:发展低年级学生数感的支架——“100以内数的认识练习课”教学实践与思考

《课程标准(2011年版)》中对数感的表述是:"数感主要是指关于数与数量、数量关系、运算结果估计等方面的感悟。建立数感有助于学生理解现实生活中数的意义,理解或表述具体情境中的数量关系。"在这里,数感被表述为一种感悟。"感"是感知、感觉,是一种直接反应,有原始的、经验的成分;"悟"是理解、明白、觉醒,需要大脑的思维活动。