数学绘本“绘”出灵动课堂——湘潭九华和平小学数学组风采

湘江之滨,九华湖畔,有一所现代化小学——湘潭九华和平小学.近年来,学校数学组聚焦数学绘本的研究,组成了绘本教学研究共同体.老师们深入绘本进行研究,找准数学知识与数学绘本的契合点,将绘本与数学教学进行有机融合,引领学生开启数学绘本的大门,让学生在学习过程中获取绘本中蕴含的数学知识,感受绘本中浓浓的人文精神,数学绘本“绘”出了灵动课堂.

数学组块化在班级管理中的应用

组块化是指个体利用存储于长时记忆中的知识对进入短时记忆的新信息加以组织,使之构成自己所熟悉的、有意义的、较大的信息单位的策略。组块化可以在数学学科教学中应用,也可以在班级管理中应用。

Coloring of some integer distance graphs

An integer distance graph is a graph G(Z, D) with the integer set Z as vertexset, in which an edge joining two vertices u and v if and only if | u - v | ∈ D, where D is a setof natural numbers. Using a related theorem in combinatorics and some conclusions known to us in thecoloring of the distance graph, the chromatic number _X(G) is determined in this paper that is ofthe distance graph G(Z, D) for some finite distance sets D containing {2, 3} with D = 4 andcontaining {2, 3, 5} with | D | = 5 by the method in which the combination of a few periodiccolorings.

An Equation of Stirling Numbers of the Second Kind

In this paper, We propose and prove the following equation, where {3^n} is a stirling number of the second kind, when n ≥ 3 is given.

Constructing Pandiagonal Snowflake Magic Squares of Odd Order

The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.

Shallow Water Modal Evolution Due to Nonlinear Internal Waves

Acoustic modal behavior is reported for an L-shape hydrophone array during the passage of a strong nonlinear internal wave packet. Acoustic track is nearly parallel to the front of nonlinear internal waves. Through modal decomposition at the vertical array, acoustic modes are identified. Modal evolution along the horizontal array then is examined during a passing internal wave. Strong intensity fluctuations of individual modes are observed before and during the internal waves packet passes the fixed acoustic track showing a detailed evolution of the waveguide modal behavior. Acoustic refraction created either uneven distribution of modal energy over the horizontal array or additional returns observable at the entire L-shape array. Acoustic ray-mode simulations are used to phenomenologically explain the observed modal behavior.

The Roots of Adjoint Polynomial of the Graphs Contain Triangles

We denote h(G,x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles. By the properties, we prove the non-zero root of adjoint polynomial of Dn and Fn are single multiple.

Methods Comparison for Microsatellite Marker Development:Different Isolation Methods,Different Yield Efficiency

Microsatellite markers have become one kind of the most important molecular tools used in various researches. A large number of microsatellite markers are required for the whole genome survey in the fields of molecular ecology,quantitative genetics and genomics. Therefore,it is extremely necessary to select several versatile,low-cost,efficient and time-and labor-saving methods to develop a large panel of microsatellite markers. In this study,we used Zhikong scallop(Chlamys farreri) as the target species to compare the efficiency of the five methods derived from three strategies for microsatellite marker development. The results showed that the strategy of constructing small insert genomic DNA library resulted in poor efficiency,while the microsatellite-enriched strategy highly improved the isolation efficiency. Although the mining public database strategy is time-and cost-saving,it is difficult to obtain a large number of microsatellite markers,mainly due to the limited sequence data of non-model species deposited in public databases. Based on the results in this study,we recommend two methods,microsatellite-enriched library construction method and FIASCO-colony hybridization method,for large-scale microsatellite marker development. Both methods were derived from the microsatellite-enriched strategy. The experimental results obtained from Zhikong scallop also provide the reference for microsatellite marker development in other species with large genomes.

Diophantine Approximation with Four Squares of Primes and Powers of Two

Under certain condition, the inequality |λ_1p_1~2+λ_2p_2~2+λ_3p_3~2+λ_4p_4~2+μ_12^(x1)+…+μ_s2^(xs)+γ|＜ηhas infinitely many solutions in primes p_1,p_2,p_3,p_4 and positive integers x_1,…,x_s.

A New System of Variational Inclusions with （H,η）-accretive Operators in Banach Spaces

In this paper, we first introduce a new class of generalized accretive operators named （H,η）-accretive in Banach space. By studying the properties of （H,η）-accretive, we extend the concept of resolvent operators associated with m-accretive operators to the new （H,η）-accretive operators. In terms of the new resolvent operator technique, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.

Quantitative characterization of β-solidifying γ-TiAl alloy with duplex structure

For precise plastic deformation,microstructure control is essential especially for β-solidifying γ-TiAl alloy with duplex structure.Based on stereology,the microstructure of isothermally compressed γ-TiAl alloy was divided into β_(0) grains,remnant α_(2)/γ lamellar colonies,α_(2) and γ grains.The results show that the volume fraction of β_(0) grains slightly increases in the isothermally compressed γ-TiAl alloy with the increase of height reduction.Meanwhile,the volume fractions of remnant α_(2)/γ lamellar colonies and α_(2) grains decrease.However,the volume fraction of γ grains increases from 64.39% to 78.47%.According to the quantitative results,the α→γ phase transformation was investigated in-depth,and it is found that isothermal compression accelerates the α→γ phase transformation.The first α→γ phase transformation is similar to ledge-controlled transformation,through which remnant α_(2)/γ lamellar colonies finally convert intoγgrains in isothermal compression.The second is achieved by α/γ phase interface immigration.

Properties of Bio-oil from Fast Pyrolysis of Rice Husk

Physicochemical properties of bio-oil obtained from fast pyrolysis of rice husk were studied in the present work.Molecular distillation was used to separate the crude bio-oil into three fractions viz.light fraction,middle fraction and heavy fraction.Their chemical composition was analyzed by gas chromatograph and mass spectrometer（GC-MS）.The thermal behavior,including evaporation and decomposition,was investigated using thermogravimetric analyzer coupled with Fourier transform infrared spectrometer（TG-FTIR）.The product distribution was significantly affected by contents of cellulose,hemicellulose and lignin.The bio-oil yield was 46.36%（by mass） and the yield of gaseous products was 27%（by mass）.The chemicals in the bio-oil included acids,aldehydes,ketones,alcohols,phenols,sugars,etc.The light fraction was mainly composed of acids and compounds with lower boiling point temperature,the middle and heavy fractions were consisted of phenols and levoglucosan.The thermal stability of the bio-oil was determined by the interactions and intersolubility of compounds.It was found that the thermal stability of bio-oil was better than the light fraction,but worse than the middle and heavy fractions.

A Monte Carlo Model of Light Propagation in Nontransparent Tissue

To sharpen the imaging of structures, it is vital to develop a convenient and efficient quantitative algorithm of the optical coherence tomography (OCT) sampling. In this paper a new Monte Carlo model is set up and how light propagates in bio-tissue is analyzed in virtue of mathematics and physics equations. The relations,in which light intensity of Class 1 and Class 2 light with different wavelengths changes with their permeation depth,and in which Class 1 light intensity (signal light intensity) changes with the probing depth, and in which angularly resolved diffuse reflectance and diffuse transmittance change with the exiting angle, are studied. The results show that Monte Carlo simulation results are consistent with the theory data.

Combinatorial model of solute transport in porous media

Modeling of solute transport is a key issue in the area of soil physics and hydrogeology. The most common approach (the convection-dispersion equation) considers an average convection flow rate and Fickian-like dispersion. Here,we propose a solute transport model in porous media of continuously expanding scale, according to the combinatorics principle. The model supposed actual porous media as a combinative body of many basic segments. First, we studied the solute transport process in each basic segment body, and then deduced the distribution of pore velocity in each basic segment body by difference approximation, finally assembled the solute transport process of each basic segment body into one of the combinative body. The simulation result coincided with the solute transport process observed in test. The model provides useful insight into the solute transport process of the non-Fickian dispersion in continuously expanding scale.

HER2 gene status and the relationship with p21 protein expression in gastric cancer

Objective： We aimed to analysis the HER2 gene status and its relationship with p21 protein expression in gastric carcinoma. Methods： Fluorescence in situ hybridisation （FISH） and immunohistochemistry （IHC） techniques were used to detect HER2 gene status and p53 protein in 59 cases of gastric cancer. Results： FISH detection of HER2 gene amplification rate was 16.9% （10/59）, HER2 gene amplification in 49 cases without copy number gain and gene amplification were a total of 49.2% （29/59）. HER2 protein expression was 42.4% （25/59）, HER2 gene amplification rates in patients with ＋＋＋, ＋＋ HER2 protein expression were 3/3 and 5/8, while in patients with ＋ HER2 protein expression, it was 2/14, there was significant difference （P 0.05）. p21 protein expression rate was 49.2% （29/59）, HER2 gene amplification rates and p21 protein expression had significant difference in tumor invasion depth, lymph node metastasis （P 0.05）; had no statistical significance in histological type, age, gender differences （P 0.05）. Conclusion： HER2 gene amplification rate and gene copy number had positively correlation with p21 protein expression, HER2 gene status and expression of p21 protein combined detection can provide a reference value in gastric cancer metastasis, patient’s condition development and prognosis, it also can guide clinical development of individual treatment.

Numerical simulation of dynamic fracture properties of rocks under different static stress conditions

When underground cavities are subjected to explosive stress waves,a uniquely damaged zone may appear due to the combined effect of dynamic loading and static pre-load stress.In this study,a rate-dependent two-dimensional rock dynamic constitutive model was established to investigate the dynamic fractures of rocks under different static stress conditions.The effects of the loading rate and peak amplitude of the blasting wave under different confining pressures and the vertical compressive coefficient(K_(0))were considered.The numerical simulated results reproduced the initiation and further propagation of primary radial crack fractures,which were in agreement with the experimental results.The dynamic loading rate,peak amplitude,static vertical compressive coefficient(K_(0))and confining pressure affected the evolution of fractures around the borehole.The heterogeneity parameter(m)plays an important role in the evolution of fractures around the borehole.The crack propagation path became more discontinuous and rougher in a smallerheterogeneity parameter case.

New Operator Identities and Combinatorics Studied by Virtue of IWOP Technique

Using the coherent state representation we derive some new operator identities and study some mathematical relations in comblnatorics. The technique of integral within an ordered product （IWOP） of operators plays an essential role in realizing our goal.

Chromatic Uniqueness of the Complement of T_m(l, 4, m - 6)

In the paper, we prove that the complement of Tm(1,4,m-6)(m> 10) is chromatically unique if and only if m≠5k(k≥2).

A Construction of Relative Difference Set

In this paper, we give a construction of RDS in Galois ring by using some bent function, and obtain the equivalent relationship between RDS and a kind of bent function. At the same time, its existence is demonstrated.

Using Self-referencing Interlaced Submatrices to Determine the Number of Chemical Species in a Mixture

Determining the number of chemical species is the first step in analyses of a chemical or biological system. A novel method is proposed to address this issue by taking advantage of frequency differences between chemical information and noise. Two interlaced submatrices were obtained by downsampling an original data spectra matrix in an interlacing manner. The two interlaced submatrices contained similar chemical information but different noise levels. The number of relevant chemical species was determined through pairwise comparisons of principal components obtained by principal component analysis of the two interlaced submatrices. The proposed method, referred to as SRISM, uses two self-referencing interlaced submatrices to make the determination. SRISM was able to selectively distinguish relevant chemical species from various types of interference factors such as signal overlapping, minor components and noise in simulated datasets. Its performance was further validated using experimental datasets that contained high-levels of instrument aberrations, signal overlapping and collinearity. SRISM was also applied to infrared spectral data obtained from atmospheric monitoring. It has great potential for overcoming various types of interference factor. This method is mathematically rigorous, computationally efficient, and readily automated.