渗透在“函数”中的数学文化

“数学文化”概念的提出，是近几年来数学课程改革的重要标志之一．新课标要求将数学文化与高中数学内容有机地结合起来，使学生在学习数学的过程中真正受到文化感染，产生文化共鸣，体会数学的文化品位．这就要求我们对教学内容进行微观分析，将数学文化渗入课堂教学．本文就“函数”这一内容所渗透的文化现象作一些新的探讨，使学生在学习函数的过程中得到文化的熏陶．

大概念视域下高中数学单元整体教学策略研究——以“函数的基本性质”为例

“大概念”作为连接学科知识与核心素养的桥梁,揭示了学科的本质特征,还为学生提供了分析和解决问题的基本策略与方法。本文以“函数的基本性质”为例,以大概念为锚点,通过单元整体教学设计帮助学生深刻理解函数内涵,掌握函数性质,并且引导学生将函数相关知识灵活应用在实际问题之中,培养学生的数学学科核心素养,基于大概念的视角,教师将进一步探究优质教学策略,为一线教师提供有益的参考与借鉴。

“物”反应式满足:网生艺术的“函数”价值、气氛与收藏欲

法国理论家鲍德里亚,始终将研究视野根植时代、社会、媒介等生存环境的关系场域,尤其在早期理论代表作《物体系》中,提出一种由"物"反应式满足体系支配的社会形态,人逐渐转为"受到物的包围"的"官能性的人"。伴随网络媒介技术对人类生存的深度影响,诸多艺术从架上、银幕走向网络,形成网生艺术新类型。本文主要基于《物体系》及关联理论点,探讨当下网生艺术与人类发展的多维想象。

要重视数学概念的生成教学——听“函数的奇偶性”一课有感

一、背景描述 数学概念是反映数学对象的本质属性的思维形式，是数学基础知识的核心，是构建数学理论大厦的基石，是形成数学知识体系的主要元素，是导出数学定理和数学法则的逻辑基础，是数学思想与方法的载体．正确理解数学概念既是掌握数学基础知识的前提，也是进行判断、推理、计算和证明的依据，许多数学问题的解决常常离不开数学概念．

用本原性问题驱动数学概念教学——以高一数学“函数单调性”为例

“本原性”是哲学研究中的一个冷峻字眼，但它同时把我们带入到了一个追求本质、回归原初的境界．在当前数学课程改革的推进中，各种观点激荡对峙、各种教法令人眼花缭乱．无论是讲授还是活动、接受还是发现，对于教学形式的争论似乎让我们淡忘了“数学”的存在．上海市教科院的杨玉东博士和南京师范大学的徐文彬博士，他们在两个城市分别进行着主题相近的课题研究——即如何用本原性问题驱动数学课堂教学．对于“本原性问题”的追求也许只是个美好的愿望，但在此过程中，我们可以强烈地感受到他们对于“让学生学习到数学本质”的追求以及在寻求数学本质过程中的探询精神．本刊将陆续登载一系列他们课题的相关成果，希望引发读者的思考、争鸣．

用研究数学的方法熏陶学生——“函数的奇偶性”的教学设计与反思

学生来自四星级重点高中普通班,知识结构较好,学习能力较强,探究欲望较高.1.2教材分析所用教材为《普通高中课程标准实验教科书·数学（必修1）》（苏教版）,内容是第2章第2.2.2节“函数的奇偶性”,这是第2.2节“函数的简单性质”的第二部分,第一部分是函数的单调性.本章的核心教学目标之一是培养学生熟悉并能运用函数语言。

A whole process damage constitutive model for layered sandstone under uniaxial compression based on Logistic function

Bedding structural planes significantly influence the mechanical properties and stability of engineering rock masses.This study conducts uniaxial compression tests on layered sandstone with various bedding angles(0°,15°,30°,45°,60°,75°and 90°)to explore the impact of bedding angle on the deformational mechanical response,failure mode,and damage evolution processes of rocks.It develops a damage model based on the Logistic equation derived from the modulus’s degradation considering the combined effect of the sandstone bedding dip angle and load.This model is employed to study the damage accumulation state and its evolution within the layered rock mass.This research also introduces a piecewise constitutive model that considers the initial compaction characteristics to simulate the whole deformation process of layered sandstone under uniaxial compression.The results revealed that as the bedding angle increases from 0°to 90°,the uniaxial compressive strength and elastic modulus of layered sandstone significantly decrease,slightly increase,and then decline again.The corresponding failure modes transition from splitting tensile failure to slipping shear failure and back to splitting tensile failure.As indicated by the modulus’s degradation,the damage characteristics can be categorized into four stages:initial no damage,damage initiation,damage acceleration,and damage deceleration termination.The theoretical damage model based on the Logistic equation effectively simulates and predicts the entire damage evolution process.Moreover,the theoretical constitutive model curves closely align with the actual stress−strain curves of layered sandstone under uniaxial compression.The introduced constitutive model is concise,with fewer parameters,a straightforward parameter determination process,and a clear physical interpretation.This study offers valuable insights into the theory of layered rock mechanics and holds implications for ensuring the safety of rock engineering.

THE(p,q)-ANALOG OF MULTIVALENT BAZILEVIC FUNCTIONS ASSOCIATED WITH A LIMACON

This paper studies the problem of functional inequalities for analytic functions in classical geometric function theory.Using the di erential subordination principle and(p,q)-derivative operator,it introduces(p,q)-analog of a class of multivalently Bazilevic functions as-sociated with a limacon function,and obtains the corresponding coefficient estimates and the Fekete-Szego inequality,which extend and improve the related results for starlike functions,even q-starlike functions.

Continuity of truncated Hardy-Littlewood maximal function

This paper focuses on the continuity of the truncated Hardy-Littlewood maximal function.We first show that the truncated Hardy-Littlewood maximal function is lower semi-continuous.Then by investigating the behavior of the truncated Hardy-Littlewood maximal function when the truncated parameterγchanges,we obtain an equivalent condition of the continuity of the truncated Hardy-Littlewood maximal function.

Research on fast detection method of infrared small targets under resourceconstrained conditions

Infrared small target detection is a common task in infrared image processing.Under limited computa⁃tional resources.Traditional methods for infrared small target detection face a trade-off between the detection rate and the accuracy.A fast infrared small target detection method tailored for resource-constrained conditions is pro⁃posed for the YOLOv5s model.This method introduces an additional small target detection head and replaces the original Intersection over Union(IoU)metric with Normalized Wasserstein Distance(NWD),while considering both the detection accuracy and the detection speed of infrared small targets.Experimental results demonstrate that the proposed algorithm achieves a maximum effective detection speed of 95 FPS on a 15 W TPU,while reach⁃ing a maximum effective detection accuracy of 91.9 AP@0.5,effectively improving the efficiency of infrared small target detection under resource-constrained conditions.

关注概念的本质——“函数的奇偶性”教学实录与反思

1基本情况1.1授课对象学生来自四星级重点高中普通班,基础较好,有-定的自学能力、推理能力及抽象能力,也有一定的自主探究意识.1.2教材分析所用教材为《普通高中课程标准实验教科书·数学（必修1）》（苏教版）,内容是第2章第2.2.2节“函数的奇偶性”,这是第2.2节“函数的简单性质”的第二部分.本章的核心教学目标之一是培养学生学会用数量关系来刻画函数图象变化趋势及图象的对称性,

Data processing method for aerial testing of rotating accelerometer gravity gradiometer

A novel method for noise removal from the rotating accelerometer gravity gradiometer(MAGG)is presented.It introduces a head-to-tail data expansion technique based on the zero-phase filtering principle.A scheme for determining band-pass filter parameters based on signal-to-noise ratio gain,smoothness index,and cross-correlation coefficient is designed using the Chebyshev optimal consistent approximation theory.Additionally,a wavelet denoising evaluation function is constructed,with the dmey wavelet basis function identified as most effective for processing gravity gradient data.The results of hard-in-the-loop simulation and prototype experiments show that the proposed processing method has shown a 14%improvement in the measurement variance of gravity gradient signals,and the measurement accuracy has reached within 4E,compared to other commonly used methods,which verifies that the proposed method effectively removes noise from the gradient signals,improved gravity gradiometry accuracy,and has certain technical insights for high-precision airborne gravity gradiometry.

NORMALITY AND THE NUMBER OF ZEROS

In this paper,we study normal families of meromorphic functions.By using the idea in[11],we obtain some normality criteria for families of meromorphic functions that concern the number of zeros of the differential polynomial,which extends the related result of Li,and Chen et al..An example is given to show that the hypothesis on the zeros of a(z)is necessary.

Automatic road extraction framework based on codec network

Road extraction based on deep learning is one of hot spots of semantic segmentation in the past decade.In this work,we proposed a framework based on codec network for automatic road extraction from remote sensing images.Firstly,a pre-trained ResNet34 was migrated to U-Net and its encoding structure was replaced to deepen the number of network layers,which reduces the error rate of road segmentation and the loss of details.Secondly,dilated convolution was used to connect the encoder and the decoder of network to expand the receptive field and retain more low-dimensional information of the image.Afterwards,the channel attention mechanism was used to select the information of the feature image obtained by up-sampling of the encoder,the weights of target features were optimized to enhance the features of target region and suppress the features of background and noise regions,and thus the feature extraction effect of the remote sensing image with complex background was optimized.Finally,an adaptive sigmoid loss function was proposed,which optimizes the imbalance between the road and the background,and makes the model reach the optimal solution.Experimental results show that compared with several semantic segmentation networks,the proposed method can greatly reduce the error rate of road segmentation and effectively improve the accuracy of road extraction from remote sensing images.

FINITE RANGE SET WITH TRUNCATED MULTIPLICITY FOR MEROMORPHIC FUNCTIONS ON SOME COMPLEX DISC

In this paper,we consider the truncated multiplicity finite range set problem of meromorphic functions on some complex disc.By using the value distribution theory of meromorphic functions,we establish a second main theorem for meromorphic functions with finite growth index which share meromorphic functions(may not be small functions).As its application,we also extend the result of a finite range set with truncated multiplicity.

Vertical distribution characteristics of soil saturated hydraulic conductivity under different land use patterns in the Mu Us sandy land

Background,aim,and scope Soil saturated hydraulic conductivity(K_(s))is a key parameter in the hydrological cycle of soil;however,we have very limited understanding of K_(s) characteristics and the factors that inf luence this key parameter in the Mu Us sandy land(MUSL).Quantifying the impact of changes in land use in the Mu Us sandy land on K_(s) will provide a key foundation for understanding the regional water cycle,but will also provide a scientific basis for the governance of the MUSL.Materials and methods In this study,we determined K_(s) and the basic physical and chemical properties of soil(i.e.,organic matter,bulk density,and soil particle composition)within the first 100 cm layer of four different land use patterns(farmland,tree,shrub,and grassland)in the MUSL.The vertical variation of K_(s) and the factors that influence this key parameter were analyzed and a transfer function for estimating K_(s) was established based on a multiple stepwise regression model.Results The K_(s) of farmland,tree,and shrub increased gradually with soil depth while that of grassland remained unchanged.The K_(s) of the four patterns of land use were moderately variable;mean K_(s)values were ranked as follows:grassland(1.38 mm·min^(-1))<tree(1.76 mm·min^(-1))<farmland(1.82 mm·min^(-1))<shrub(3.30 mm·min^(-1)).The correlation between K_(s) and organic matter,bulk density,and soil particle composition,varied across different land use patterns.A multiple stepwise regression model showed that silt,coarse sand,bulk density,and organic matter,were key predictive factors for the K_(s) of farmland,tree,shrub,and grassland,in the MUSL.Discussion The vertical distribution trend for K_(s) in farmland is known to be predominantly influenced by cultivation,fertilization,and other factors.The general aim is to improve the water-holding capacity of shallow soil on farmland(0-30 cm in depth)to conserve water and nutrients;research has shown that the K_(s) of farmland increases with soil depth.The root growth of tree and shrub in sandy land exerts mechanical force on the soil due to biophysical processes involving rhizospheres,thus leading to a significant change in K_(s).We found that shallow high-density fine roots increased the volume of soil pores and eliminated large pores,thus resulting in a reduction in shallow K_(s).Therefore,the K_(s) of tree and shrub increased with soil depth.Analysis also showed that the K_(s) of grassland did not change significantly and exhibited the lowest mean value when compared to other land use patterns.This finding was predominantly due to the shallow root system of grasslands and because this land use pattern is not subject to human activities such as cultivation and fertilization;consequently,there was no significant change in K_(s) with depth;grassland also had the lowest mean K_(s).We also established a transfer function for K_(s) for different land use patterns in the MUSL.However,the predictive factors for K_(s) in different land use patterns are known to be affected by soil cultivation methods,vegetation restoration modes,the distribution of soil moisture,and other factors,thus resulting in key differences.Therefore,when using the transfer function to predict K_(s) in other areas,it will be necessary to perform parameter calibration and further verification.Conclusions In the MUSL,the K_(s) of farmland,tree,and shrub gradually increased with soil depth;however,the K_(s) of grassland showed no significant variation in terms of vertical distribution.The mean K_(s) values of different land use patterns were ranked as follows:shrub>farmland>tree>grassland;all land use patterns showed moderate levels of variability.The K_(s) for different land use patterns exhibited differing degrees of correlation with soil physical and chemical properties;of these,clay,silt,sand,bulk density,and organic matter,were identified as important variables for predicting K_(s) in farmland,tree,shrub,and grassland,respectively.Recommendations and perspectives In this study,we used a stepwise multiple regression model to establish a transfer function prediction model for K_(s) for different land use patterns;this model possessed high estimation accuracy.The ability to predict K_(s) in the MUSL is very important in terms of the conservation of water and nutrients.

Stability of second order Hopfield neural networks with time delays

Dynamical behaviors of a class of second order Hopfield neural networks with time delays is investigated.The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem and the counter proof method,and some sufficient conditions for the global asymptotic stability of the equilibrium point are obtained through the combination of a suitable Lyapunov function and an algebraic inequality technique.