一元实函数极值问题求解的几种初等方法

在生产实践中,我们经常遇到在一定条件下,如何做到用料最省,质量最好,成本最低、效率最高这样一类问题。例如:制造一只铁皮罐头盒,可以做成各种形状、尺寸,但怎样设计才能使用料最少?这就是最小的问题。相应的,用面积一定的铁皮,做成怎样形状和尺寸的罐头盒,其容积最大?这又是最大的问题。研究极大或极小的问题,在数学上称为极值问题。关于极值问题的求法,中学数学教材中零星地、分散地讲了一些,并不系统。在中教材中首先涉及极值问题,是在讨论二次函数的图象及其性质的时候(即初中代数第四册)以后陆续在不等式和三角函数中谈到一些。微积分部分知识下放以后,利用函数的导数求极值便也成为方法之一。

小小项目开启学生大智慧——三元实小在“技术启迪智慧"项目活动评比中蝉联全国第一

苏州市三元实验小学和宁夏固原市原州区三营镇第一小学以结对方式,共同参与联合国儿童基金会开展的"技术启迪智慧"远程项目学习。去年4月两校组建"三缘三赢"

周期函数和它的一个充要条件

周期函数和它的一个充要条件周大光，章合利（苏州职大）论述周期函数的文章很多，本文归纳了一元实周期函数的一些性质，并给出函数周期性的一个充要条件。１周期函数的四则运算一般说来，两个周期函数的和、差、积、商不一定是周期函数。例如：Ｄ（ｘ）＋ｓｉｎｘ就不是...

FLOW STRESS MODELING FOR AERONAUTICAL ALUMINUM ALLOY 7050-T7451 IN HIGH-SPEED CUTTING

The high temperature split Hopkinson pressure bar （SHPB） compression experiment is conducted to obtain the data relationship among strain, strain rate and flow stress from room temperature to 550 C for aeronautical aluminum alloy 7050-T7451. Combined high-speed orthogonal cutting experiments with the cutting process simulations, the data relationship of high temperature, high strain rate and large strain in high-speed cutting is modified. The Johnson-Cook empirical model considering the effects of strain hardening, strain rate hardening and thermal softening is selected to describe the data relationship in high-speed cutting, and the material constants of flow stress constitutive model for aluminum alloy 7050-T7451 are determined. Finally, the constitutive model of aluminum alloy 7050-T7451 is established through experiment and simulation verification in high-speed cutting. The model is proved to be reasonable by matching the measured values of the cutting force with the estimated results from FEM simulations.

Correlation Analysis between Quality Characteristics and Fruit Mineral Element Contents in 'Fuji' Apples

[Objective] The aims were to explore the relationship between the contents of fruit mineral elements and quality features of the ＇Fuji＇ apple, screen major mineral elements of the fruit affecting fruit quality features, and set up optimum proposals of fruit mineral elements for good fruit qualities, so as to provide a theoretical basis for the reasonable orchard soil and foliar fertilizer applications to increase fruit quality and reduce the physiological diseases related to the ＇Fuji＇ apple. [Methods] The fruit mineral elements and quality indicators of ＇Fuji＂ apples were in- vestigated and analyzed, which were collected from the 153 commercial apple or- chards of ＂Fuji＇ apple located in 51 counties. The variable importance for projection （VlP） of partial least squares regression （PLS） method was used to analyze the model effect and weight analysis impact of the fruit mineral element contents to fruit quality, screen out major factors of fruit mineral elements influencing the different fruit qualities, and set up the regression equation of the fruit qualities and major fruit mineral elements. Linear programming was used to obtain optimum proposals of the fruit mineral elements to achieve good ＇Fuji＇ apple qualities. [Results] The mineral elements content and quality characteristics in ＂Fuji＇ apple fruit had great differences in the different produce regions in which the maximum content of nitro- gen, iron, zinc and boron in the ＇Fuji＇ fruit were12.06, 6.17, 7.7, and 10.08 times greater than the minimum respectively, and the differences for titratable acid and the SSC/TA ratio were 2.33 and 2.16 times respectively. The correlation analysis between the fruit mineral element contents and qualities showed that the nitrogen content of fruit had a significantly negative correlation with the soluble solid content, SSC/TA ratio and red color area, while the calcium and iron contents in the fruit were in significantly positive correlation with the soluble solid content and SSC/TA ratio. The model effect and weight analysis showed that the content of nitrogen and iron in the fruit had a greater influence on the integral fruit quality, followed by phosphorus, potassium and calcium. The variable importance for projection （VlP） technology of PLS found that the mean fruit weight was primarily affected by nitro- gen, phosphorus and potassium, and the soluble solid was primarily affected by ni- trogen, calcium and iron, while the red color area was primarily affected by nitro- gen, potassium, calcium, iron and zinc. The regression equation between fruit quality and mineral element contents showed that the mean fruit weight had a greater pos- itive effect coefficient with the content of phosphorus and potassium, and a greater negative effect coefficient with the content of nitrogen in the fruit. Moreover, the sol- uble solid had the largest negative effect coefficient with nitrogen and largest posi- tive effect coefficient with calcium and iron in the fruit. [Conclusion] The maximum content of soluble solid and titratable acid were 1.5 times more than the minimum, and nitrogen, iron, zinc and boron were 6 times more than in the ＇Fuji＇ apple fruit in the different produce regions. Therefore, it is a key technological measure to improve the overall qualities of the ＂Fuji＇ apple by decreasing the content of nitrogen, and increasing the contents of iron, phosphorus, potassium and calcium in the fruit.

Analysis of Static Temperature Field of Vehicle's Solid Rubber Tire

Aim To analyse the static temperature field ofthe solid rubber tire(SRT).Methods The mechanical and thermal FE models were developed and analyzed respectively with the FE software ANSYS.Results The maximum temperature becomes higher with the higher with the higher velocity of tire and scales down slightly with the higher convection coefficients.The mixed models are reasonable.Conclusion The study on static temperature field is important and reasonable.It gives the fundament for life analysis of SRT.

STUDY AND IMPROVEMENT OF MLS RELATIONAL DATA MODEL

The conception of multilevel security (MLS) is commonly used in the study of data model for secure database. But there are some limitations in the basic MLS model, such as inference channels. The availability and data integrity of the system are seriously constrained by it′s 'No Read Up, No Write Down' property in the basic MLS model. In order to eliminate the covert channels, the polyinstantiation and the cover story are used in the new data model. The read and write rules have been redefined for improving the agility and usability of the system based on the MLS model. All the methods in the improved data model make the system more secure, agile and usable.

论翻译(文摘)

夫译之为事难矣,译元将奈何?其平日冥心钩考,必先将所译者与所以译者两国之文字深嗜笃好,字栉句比,以考彼此文字孳生之源,同异之故。所有相当元实义,委曲推究,务审其音之高下,析其字句之繁简,尽其文体之变态,及其义理精深奥折之所由然。夫如是,则一书到手,经营反复,确知其意旨之所在,而文摹写其神情,仿佛其语气。

The Monotonicity Problems for Generalized Inverses of Matrices in H (n, ≥)

On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.

Establishment of a mdr1 Multidrug Resistant Model of Orthotopic Transplantation of Liver Carcinoma on Nude Mice

To develop a new method of inducing mdrl multidrug resistance by establishinga nude mice model of orthotopic transplantation of liver carcinoma by sporadic abdominalchemotherapy at intervals. Methods: Hepatocellular carcinoma HepG2 cell was cultured and injectedsubcutaneously to form the tumor-supplying mice. The tumor bits from the tumor-supplying mice wereimplanted under the envelope of the mice liver and induced by abdominal chemotherapy withPharmorubicin. Physical examination, ultrasonography, spiral CT and operative inspection were usedto examine tumor progression. RT-PCR and immunohistochemistry were adopted to detect the expressionof mdr1-mRNA and its encoded protein P-gp protein (P-gp). Results: There was no operative dead, therate of implanting tumor successfully was 88% (22/25), the rate of implanting secondly successfullywas 100% (3/3), and the rate of inducing successfully was 80% (16/20). The expression of mdrl-mRNAand the P-gp in the inducing group was 23 folds and 13 folds in the control group respectively.Conclusion: We have established an in vivo model of mdr using nude mice transplanted with orthotopicliver neoplasm coupled to chemotherapy.

Minor Self-conjugate and Skewpositive Semidefinite Solutions to a System of Matrix Equations over Skew Fields

Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and sufficient conditions for the existence of and the expressions for the msc solutions and the ssd solutions are obtained for the system.

FEM model for real-time guide wire simulation in vasculature

A model suitable for describing the mechanical response of thin elastic objects is proposed to simulate the deformation of guide wires in minimally invasive interventions. The main objective of this simulation is to provide doctors an opportunity to rehearse the surgery and select an optimal operation plan before the real surgery. In this model the guide wire is discretized with the multi-body representation and its elastic energy derivate from elastic theory is a polynomial function of the nodal displacements. The vascular structure is represented by a tetrahedron mesh extended from the triangular mesh of the artery, which can be extracted from the patient＇s CT image data. The model applies the energy decline process of the conjugate gradient method to the deformation simulation of the guide wire. Experimental results show that the polynomial relationship between elastic energy and nodal displacements tremendously simplifies the evaluation of the conjugate gradient method and significantly improves the model＇s efficiency. Compared with models depending on an explicit scheme for evaluation, the new model is not only non-conditionally stable but also more efficient. The model can be applied to the real-time simulation of guide wire in a vascular structure.

Discrete element modeling of migration and evolution rules of coarse aggregates in the static compaction process

To investigate migration and evolution rules of coarse aggregates in the static compaction process, an algorithm of generating digital coarse aggregates that can reflect real morphology（ such as shape, size and fracture surface） of aggregate particles, is represented by polyhedral particles based on the discrete element method（ DEM）. A digital specimen comprised of aggregates and air voids is developed. In addition,a static compaction model consisting of a digital specimen and three plates is constructed and a series of evaluation indices such as mean contact force σMCF, wall stress in direction of zcoordinate σWSZZ, porosity and coordination numbers are presented to investigate the motion rules of coarse aggregates at different compaction displacements of 7. 5, 15 and 30 mm. The three-dimensional static compaction model is also verified with laboratory measurements. The results indicate that the compaction displacements are positively related to σMCF and σWSZZ, which increase gradually with the increase in iterative steps. When the compaction proceeds, the digital specimen porosity decreases, but the coordination number increases. The variation ranges of these four indices are different at different compaction displacements. This study provides a method to analyze the compaction mechanism of particle materials such as asphalt mixture and graded broken stone.

Accuracy analysis of plane-strain bulge test for determining mechanical properties of thin films

The effect of a variety of geometrics, initial conditions and material properties on the deformation behavior of thin films in the plane-strain bulge test was systematically scrutinized by performing the finite element analysis, and then the accuracy of the plane-strain bulge test in determining the mechanical properties of thin films in terms of our finite element results was analyzed. The results indicate that although the determination of the plane-strain modulus in the light of the plane-strain bulge equation is fairly accurate, the calculation of the residual stress is not satisfied as expected, especially for low residual stress. Finally, an approach is proposed for analyzing bulge test data, which will improve the accuracy and reliability of this bulge test technique.

Numerical simulation of residual stress field in green power metallurgy compacts by modified Drucker-Prager Cap model

Compaction process simulation and residual stress prediction of green PM compact were carried out with elasto-plastic 3D FEA based on the modified Drueker-Prager Cap model in Abaqus. The model parameters of the investigated powder Distaloy AE were determined as functions of relative density through typical mechanical property tests of powder. The model was implemented as a user subroutine USDFLD. Single sided compaction of a d20 ram^5 mm disk green compact of Distaloy AE was simulated, and the residual stress of the disk after ejection was predicted with FEA. The FEA results of the compaction process and the residual stress of the disk show good agreement with compaction experiments and X-ray diffraction measurements, which validates the model and its parameters. The results indicate that the compressive residual stresses exist mainly in a thin layer on the side surface, but the residual stresses are very small on the top and bottom surfaces.

Design of the Testing System for Jet Elements

To analyze the errors of processing data, the testing principle for jet elements is introduced and the property of testing system is theoretically and experimentally studied. On the basis of the above, the method of processing data is presented and the error formulae, which are the functions of the testing system property, are derived. Finally, the methods of reducing the errors are provided. The measured results are in correspondence with the theoretical conclusion.

Loading System for Full-Scale Heavy-Duty Support Node Test with Multi-Directional Loading Requirements

This paper presents the design, analysis and experimental study of a loading system for heavy-duty nodes test based on a large-scale multi-directional in-plane loading device, which has been used in a full-scale heavy-duty support node test. Test loads of the support reached 6 567 kN with multi-directional loading requirements, which outrange the capacity of the available loading devices. Through the reinforcement of a large-scale multi-directional inplane loading device, the innovative design of a self-balanced load transferring device, and other arrangement considerations of the loading system, the test was implemented and the loading capacity of the ring was considerably enlarged. Due to the heavy loading requirements, some checking computations of the ring and the load transferring device outranged the limit of the Chinese national code "Code for Design of Steel Structures (GB 50017—2003)", thus elastic-plastic finite element (FE) analysis was carried out on the two devices, and also the real-time monitoring on the whole loading systems during experiments to ensure test safety. FE analysis and test results show that the loading system worked elastically during experiments.

Individualized Pixel Synthesis and Characterization of Combinatorial Materials Chips

Conventionally, an experimentally determined phase diagram requires studies of phase formation at a range of temperatures for each composition, which takes years of effort from multiple research groups. Combinatorial materials chip technology, featuring high-throughput synthesis and characterization, is able to determine the phase diagram of an entire composition spread of a binary or ternary system at a single temperature on one materials library, which, though significantly increasing efficiency, still requires many libraries processed at a series of temperatures in order to complete a phase diagram. In this paper, we propose a "one-chip method" to construct a complete phase diagram by individually synthesizing each pixel step by step with a progressive pulse of energy to heat at different temperatures while monitoring the phase evolution on the pixel in situ in real time. Repeating this process pixel by pixel throughout the whole chip allows the entire binary or ternary phase diagram to be mapped on one chip in a single experiment. The feasibility of this methodology is demonstrated in a study of a Ge-Sb-Te ternary alloy system, on which the amorphouscrystalline phase boundary is determined.

Histological and ultrastructural changes induced by selenium in early experimental gastric carcinogenesis

AIM： To investigate the effect and significance of selenium in early experimental gastric carcinogenesis. METHODS： Weaning male Wistar rats were divided randomly into normal control group, experiment control group, low selenium （2 mg/L） group and high selenium （4 mg/L） group. Wistar rat gastric carcinogenesis was induced by N-methyl-N-nitro-N-nitroso guanidine （MNNG） （20 mg/kg） gavage dally for 10 d. Na2SeO3 was given by piped drinking 1 wk prior to MNNG gavage. The rats were killed at the 43^rd wk. The surface characteristics of gastric mucosa were observed with naked eyes. Histopathologic changes of rat gastric mucosa were observed by HE staining and AB-PAS methods. The changes of cellular ultrastructure were observed under transmission electron microscope. Statistical analysis was carried out by SPSS. RESULTS： The incidence rate of gastric mucosa erosion, hemorrhage and intestinal metaplasia was 0, 45.5%, 66.7%, and 92.9%, respectively （92.9% vs 45.5%, P〈0.05） in the normal control group, experiment control group, low selenium group, and high selenium group. Leiomyoma formed in the process of inducement of rat gastric carcinoma. Dietary Na2SeO3 （2 and 4 mg/L） slightly increased the incidence rate of leiomyoma （0.23%, 46.6%, and 46.6%）. gastric mucosa did not change in the course of rat gastric carcinogenesis. Dietary Na2SeO3 by pipe drinking could expand the intracellular secretory canaliculus of parietal cells and increase the number of endocrine cells and lysosomes. CONCLUSION： Dietary Na2SeO3 by pipe drinking aggravates gastric erosion, hemorrhage and promotes intestinal metaplasia of gastric mucosa. The mechanism may be related with the function of parietal cells.

Automatic target tracking on multi-resolution terrain

We propose a high-performance path planning algorithm for automatic target tracking in the applications of real-time simulation and visualization of large-scale terrain datasets, with a large number of moving objects （such as vehicles） tracking multiple moving targets. By using a modified Dijkstra＇s algorithm, an optimal path between each vehicle-target pair over a weighted grid-presented terrain is computed and updated to eliminate the problem of local minima and losing of tracking. Then, a dynamic path re-planning strategy using multi-resolution representation of a dynamic updating region is proposed to achieve high-performance by trading-off precision for efficiency, while guaranteeing accuracy. Primary experimental results showed that our algorithm successfully achieved l0 to 96 frames per second interactive path-replanning rates during a terrain simulation scenario with 10 to 100 vehicles and multiple moving targets.