借展示之力,品数学之美——在培养学生展示能力中的一些体会

新课程标准把表达能力培养放在一个重要的地位,反思以往的课堂,学生展示能力的培养恰恰是教师容易忽视的地方,在笔者的教学过程中,主要让学生在“敢展示、规范展示”上下功夫,取得了一些成绩。

把丰富学生的数学生活作为数学教学的重要内容

“数学生活”是指与数学有关的生活。丰富学生的数学生活,就要善于将学生的日常生活与数学学习联系起来,引导学生用数学的眼光观察生活中的事物,使学生在生活中“学”数学、“做”数学、“用”数学、“品”数学。

RESEARCH OF THE PARAMETRIC ASSEMBLY METHOD

The parametric part assembly generation method is presented. Based on the parametric part generated by means of constructive-element, through interactively inputting the relationships of the location and the assembly, and by compiling operations like movement and rotation, the assembly drawing is created so as to implement the occurrence of the parameterizations of the assembly and the part drawing. The data structure of the assembly part and the key technologies of hidden line removal in the implementation of assembly process, etc. , are described in detail.

Mass Transfer During Osmotic Dehydration Using Acoustic Cavitation

An experimental study on intensifying osmotic dehydration was carried out ina state of nature and with acoustic cavitation of different cavitating intensity (0.5A, 0.7A and0.9A) respectively, in which the material is apple slice of 5mm thickness. The result showed thatacoustic cavitation remarkably enhanced the osmotic dehydration, and the water loss was acceleratedwith the increase of cavitating intensity. The water diffusivity coefficients ranged from1.8x10^(-10)m^2·s^(-1) at 0.5A to 2.6x10^(-10)m^2·s^(-1) at 0.9A, and solute diffusivitycoefficients ranged from 3.5x10^(-11) m^2·s^(-1) at 0.5A to 4.6X10^(-11)m^2·s^(-1) at 0.9A. On thebasis of experiments, a mathematical model was established about mass transfer during osmoticdehydration, and the numerical simulation was carried out. The calculated results agree well withexperimental data, and represent the rule of mass transfer during osmotic dehydration intensified byacoustic cavitation.

Fuzzy integral based measurement and assessment of medium and small enterprises'product innovation

A fuzzy integral based way of measurement assessment has been established by using linguistic varia-bles and combining fuzzy integral with hierarchy analysis for measurement of medium and small enterprises'product innovation. The conclusions drawn from analyses made with 20 medium and small enterprises providebases for governments to formulate applicable policies and for medium and small enterprises to enhance theirproduct innovation.

Adsorption of ^133Cs and ^87Sr on pumice tuff：A comparative study between powder and intact solid phase

This study examines the use of intact samples as an alternative to powder in conventional batch sorption studies to determine the distribution coefficient(K_d).Stable cesium(^(133)Cs) and strontium(^(87)Sr) were used under specified geochemical conditions to compare the Kdvalues of powder and block pumice tuff samples. The aim of the study was to infer any Kddifference under laboratory and field conditions. Kdvalues for block samples were found to be less than one order of magnitude lower than powder materials for both Cs and Sr on fresh tuff, and more than one order of magnitude lower in oxidized tuff. Destruction of micropores in oxidized tuff was estimated to be mainly responsible for reducing Kdvalues in oxidized tuff. However, approximately one order of magnitude difference in Kdvalues indicates that homogenously prepared intact samples can be used for sorption coefficient measurement at closer to in situ conditions. Pore size distribution analysis using mercury intrusion porosimetry revealed that lower Kdvalues on block samples result from lower surface area available as sorption sites due to inaccessible closed pores in the intact solid.

Applied research of mathematical models in enterprise product sale

Some products are only sold in some regions while some are sold in certain months, so there are a lot of data gaps. If we choose too much of this vacancy data, it may have impact on knowledge extraction. So to aim at specific sale database, we chose to study six kinds of representative products among them and these products are relatively comprehensive in all regions and month sales including two conventional products, two special products and two accessories; we also chose seven sale regions to make detailed analysis. We selected nine characteristics of sales in database which respectively are monthly sales volume, monthly revenue, monthly average selling price, profit, program sales volume, completed percentage of a program, sales month, sales territory and product type.

Vibrational Structure of Selected Compounds Derived from Biomass： Lignin Dimers, Selected Aldopentoses and Aldohexoses

The production of chemicals from biomass is a very challenging process due to its diverse chemical composition. Lignin, cellulose and hemicellulose are the three main biopolymers of wood biomass, with cell walls ＆plant origin. Lignin has been chosen for the present studies due to its range of different linkages and structures. The present work involved a computational study of the most dominant lignin dimers and their vibrational structures, based on the Density Functional Theory method. Full geometry optimization of the compartments used the StoBe code with cluster model and non-local functional （RPBE） approach. The calculations of the vibrational frequencies were performed with harmonic approximations as well as an anharmonicity fit in the Morse potential function, as implemented in the StoBe code. In the case oflignin, the calculations included three different precursors based on： coumaryl alcohol, coniferyl alcohol and sinapyl alcohol. To represent the cellulose and hemicellulose derivatives, selected aldopentoses and aldohexoses （arabinose, xylose, glucose, galactose, and mannose） were considered. Presented here are the theoretical investigations for a variety of biomass derived compounds, to give the possibility of obtaining a theoretical VBD （Vibrations Basis Database） for experimental spectra interpretation. Such a database could be further used in the preliminary composition assessment of biomass derived substrates, which will be discussed here in more detail.

Patterns and Technology -- A Creative Approach to Isometries

Today＇s math education basic syllabus gives an ever increasing emphasis to Geometry and Patterns. Curricula also advocate an approach that allows student to understand the concepts involved supported by dynamical computer tools. However, there is not much research work joining these paradigms. Therefore, a case study was developed, with 9th grade students （14-15 years old）, to evaluate the impact of a creative approach to isometries and symmetries-friezes, rosaceas （rosettes） and wallpapers-centered in patterns （reproduction, continuation, completion, description and creation） and using Geometer＇s Sketchpad software to solve, mainly in pairs, and discuss, with the whole class, the challenging tasks proposed, involving the formulation of hypothesis, argumentation and justification of the reasoning. The statistical analysis of the quantifiable data and content analysis of the qualitative data, collecting trough enquiry, direct observation and documental analysis （involving questionnaires, field notes, logbook, pre-tests and post-test, other works of the students including those computer related, and internal documents of the school） enable to conclude positively regarding the main research question underlying the study. In fact, it led to the conclusion that the teaching strategy implemented has contributed to deepen the student＇s knowledge and skills on geometry, mathematical communication and autonomy as well as to develop a closer relation with the field of geometry itself. This article focuses on one of the cases studied. The pair was selected due to be representative of most students and due to their communication skills.

Mathematical model of the adjustment of the optimal price of the substituting commodity

In this paper, from the two economic concepts of the price elasticity of demand and the cross elasticity of demand, under the assumption that the operator＇s management goal is to obtain the profit maximization, the author established the mathematical model of the adjustment of the optimal price of the substituting commodity.

Some Notes on the Dual Leibniz-Hopf algebra

The Leibniz-Hopf algebra is the free associative algebra with one generator in each positive degree and coproduct given by the Cartan formula. Quasi-symmetric functions are a generalisation of symmetric functions [7],and the algebra of quasi-symmetric functions appear as the dual of the Leibniz-Hopf algebra. The Leibniz-Hopf algebra and its dual are word Hopf algebras and play an important role in combinatorics, algebra and topology. We give some properties of words and consider an another view of proof for the antipode in the dual Leibniz-Hopf algebra.

Inheritance of Main Morphological Traits and Chemical Parameters＇ Analysis of Oriental Tobacco

This study was conducted to evaluate four different parental oriental varieties with their F1 crosses to estimate inheritance of some morphological traits, such as plant hight, number of leaves, total dry weigh and chemical compounds, especially nicotine and sugars during sun-curing period. The oriental varieties Kozarsko 541, Plovdiv 50 and Krumovgrad 17 from Bulgaria and Basma Xanthi 101 from Greece and their respective crosses with Basma Xanthi 101 were studied. The study was set up in 2014 and 2015 in experimental field of the Tobacco and Tobacco Products Institute, Plovdiv, using randomized block design with four replications. Common agricultural practices were applied during the growing season. The result indicated that in hybrid combination with parental varieties Kozarsko 541 and Plovdiv 50, except total dry weight, additive gene effects are important for traits height of plant and number of leaves. Height of plant and number of leaves are inherited partially dominant to parent with higher value and total dry weight inheritance was over dominant. In hybrid combination Krumovgrad 17 x Basma Xanthi 101, inheritance of the plant height and leaves number were over dominant type. Total dry weight is inherited partially dominant. In a word, prevailing mode for inheritance of plant hight and total dry weight was the over dominance and for number of leaves it was partial dominance. In sun-curing with yellowing stage, nicotine decreased and sugars increased in all tested varieties with a highest percentage in variety Kozarsko 541 （nicotine） and Krumovgrad 17 （sugars）.

Nonlinear Maps Preserving the Jordan Triple ＊-Product on Factor von Neumann Algebras

Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.

On the Semiprimitivity and Semiprimality Problems for Partial Smash Products

In this paper we discuss about the semiprimitivity and the semiprimality of partial smash products. Let H be a semisimple Hopf algebra over a field k and let A be a left partial H-module algebra. We study the H-prime and the H-Jacobson radicals of A and their relations with the prime and the Jacobson radicals of A#H, respectively. In particular, we prove that if A is H-semiprimitive, then A^fH is semiprimitive provided that all irreducible representations of A are finite-dimensional, or A is an affine PI-algebra over k and k is a perfect field, or A is locally finite. Moreover, we prove that A=#=H is semiprime provided that A is an H-semiprime PI-algebra, generalizing to the setting of partial actions the known results for global actions of Hopf algebras.

ROLE OF DIFFERENT SYSTEM DELAYS ON ECOLOGICAL FOOD CHAIN DYNAMICS:MATHEMATICAL MODELLING AND ANALYSIS

This paper studies a three tier ecological food chain model consisting of nutrient,autotroph,and herbivore populations.Regeneration of nutrient from dead autotroph and herbivore biomass bydecomposers present in the soil is included.The time required for maturation of the herbivore populationis incorporated as a distributed time delay.Next,the authors introduce the time lag requiredfor regeneration of nutrient from the dead herbivore as a discrete time delay.Stability and bifurcationbehavior of the one-and two-delay models are carried out and a comparative study of the significanceof these delays in controlling the system dynamics is performed.Numerical simulations are done tojustify analytical results.

On the Same n-Types for the Wedges of the Eilenberg-Maclane Spaces

Given a connected CW-space X, SNT（X） denotes the set of all homotopy types [X＇] such that the Postnikov approximations X（n） and X＇^（n） are homotopy equivalent for all n. The main purpose of this paper is to show that the set of all the same homotopy n- types of the suspension of the wedges of the Eilenberg-MacLane spaces is the one element set consisting of a single homotopy type of itself, i.e., SNT（Σ（K（Z, 2a1） ∨ K（Z, 2a2）∨… ∨ K（Z,2ak））） = ＊ for a1 〈 a2 〈 … 〈 ak, as a far more general conjecture than the original one of the same n-type posed by McGibbon and Moller （in [McGibbon, C. A. and Moller, J. M., On infinite dimensional spaces that are rationally equivalent to a bouquet of spheres, Proceedings of the 1990 Barcelona Conference on Algebraic Topology, Lecture Notes in Math., 1509, 1992, 285-293].）

HEPATITIS C VIRUS AND INTRAVENOUS DRUG MISUSE： A MODELING APPROACH

Hepatitis C virus （HCV） is a blood-borne infection that can lead to progressive liver fail- ure, cirrhosis, hepatocellular carcinoma and death. A deterministic mathematical model for assessing the impact of daily intravenous drug misuse on the transmission dynamics of HCV is presented and analyzed. A threshold quantity known as the reproductive number has been computed. Stability of the steady states has been investigated. The dynamical analysis reveals that the model has globally asymptotically stable steady states. The impact of daily intravenous drug misuse on the transmission dynamics of HCV has been discussed through the basic reproductive number and numerical simulations.