南宋数学文献家荣棨与《黄帝九章算经细草》

南宋数学文献家荣棨是汴京人,以收集和整理镂版数学典籍尤其是《九章算术》为职业。关于荣棨籍贯,宋史典籍有"汴阳坊"与"汴京"两种解释,可证明其为汴京人无疑。尽管算学作为"五学"之一在宋代官办教育体制中渐趋式微,但民间具有博雅才学与镂版书籍资本的热心志士通过对算学典籍的校勘整理在宋元数学发展史上发挥了传承数学文化的独特作用。荣棨得到的"古本"《黄帝九章算经细草》与元丰监本《九章算经》相比,增加了贾宪的"细草",通过将此版本《黄帝九章算经细草》镂版行世,遂成为南宋杨辉《详解九章算法》的底本。正因为《黄帝九章算经细草》的刊印,贾宪三角及其贾宪在算法的抽象、创新和程序化方面所取得的诸多成就才有可能在杨辉《详解九章算法》中保存下来。

《算学宝鉴》用韵与16世纪山西汾阳方言

明中叶山西汾阳数学家王文素所著《算学宝鉴》中存有大量算学诗歌,用韵十分灵活,基本不遵平水韵。经过系联、分析韵脚字,归纳为14部,同时得到若干特殊韵例。参照现代山西方言,结合其他文献资料,《算学宝鉴》用韵反映了16世纪汾阳方言的若干特点——阳声韵:臻深曾梗通摄通押,宕与曾梗通摄通押,咸山摄合流;阴声韵:之灰通押,支鱼通押;入声韵:塞音韵尾合并,喉塞音-.已经产生。

从《中国算学史》上卷到《中国数学史》——纪念钱宝琮诞辰130周年

中国数学史学科主要奠基人之一钱宝琮主编的《中国数学史》是这一学科的经典,在海内外有着广泛的影响,但学术界对其形成过程未有系统梳理。本文利用新的史料,讨论了钱宝琮的学术生涯,明确提出他于1932年出版的个人专著《中国算学史》(上卷)是他1964年主编的集体著作《中国数学史》的先行作品,而后者可称前者的完璧之作。文章系统考察了《中国算学史》(上卷)的缘起,和它发展成为《中国数学史》的曲折历程。

基于算用结合的小学数学“活学”课堂构建

随着新课程改革的不断推进,对小学数学教学提出了新标准,加入“算用结合”“活学”课堂这一新的教学要求。“算用结合”能有效提高教学质量,培养学生的思维能力,促进学生学习。本文结合自身的教学实践,浅析在教学中进行算用结合的策略。

新型碳浓度测试演算系统的设计

以8031单片机构成的微机系统，对渗碳、碳氮共渗等热处理过程中碳浓度的测量、演算以及对多种参数实现精确控制，从而提高了工作表面热处理质量。

Syntheses,crystal structures,and quantum chemistry calculation of two Ni(Ⅱ)coordination polymers

Two new coordination polymers,[Ni(Hpdc)(bib)(H_(2)O)]_(n)(1)and{[Ni(bib)_(3)](ClO_(4))_(2)}_(n)(2),were prepared by mixing Ni^(2+),3,5⁃pyrazoledicarboxylic acid(H3pdc)/p⁃nitrobenzoic acid and 1,4⁃bis(imidazol⁃1⁃ylmethyl)butane(bib)by a hydrothermal method,respectively.X⁃ray crystallography reveals a 2D network constructed by six⁃coordinated Ni(Ⅱ)centers,bib,and Hpdc2-ligands in complex 1,while a 2D network is built by Ni(Ⅱ)and bib ligands in 2.Furthermore,the quantum⁃chemical calculations have been performed on‘molecular fragments’extracted from the crystal structure of 1 using the PBE0/LANL2DZ method in Gaussian 16 and the VASP program.CCDC:2343794,1;2343798,2.

Large and nonlinear electric field response in a two-dimensional ferroelectric Rashba material

The achievement of electrical spin control is highly desirable.One promising strategy involves electrically mod-ulating the Rashba spin orbital coupling effect in materials.A semiconductor with high sensitivity in its Rashba constant to external electric fields holds great potential for short channel lengths in spin field-effect transistors,which is crucial for preserving spin coherence and enhancing integration density.Hence,two-dimensional(2D)Rashba semiconductors with large Rashba constants and significant electric field responses are highly desirable.Herein,by employing first-principles calculations,we design a thermodynamically stable 2D Rashba semiconductor,YSbTe_(3),which possesses an indirect band gap of 1.04 eV,a large Rashba constant of 1.54 eV·Åand a strong electric field response of up to 4.80 e·Å^(2).In particular,the Rashba constant dependence on the electric field shows an unusual nonlinear relationship.At the same time,YSbTe_(3)has been identified as a 2D ferroelectric material with a moderate polarization switching energy barrier(~0.33 eV per formula).By changing the electric polarization direction,the Rashba spin texture of YSbTe_(3)can be reversed.These out-standing properties make the ferroelectric Rashba semiconductor YSbTe_(3)quite promising for spintronic applications.

Improvement of High-Speed Detection Algorithm for Nonwoven Material Defects Based on Machine Vision

Defect detection is vital in the nonwoven material industry,ensuring surface quality before producing finished products.Recently,deep learning and computer vision advancements have revolutionized defect detection,making it a widely adopted approach in various industrial fields.This paper mainly studied the defect detection method for nonwoven materials based on the improved Nano Det-Plus model.Using the constructed samples of defects in nonwoven materials as the research objects,transfer learning experiments were conducted based on the Nano DetPlus object detection framework.Within this framework,the Backbone,path aggregation feature pyramid network(PAFPN)and Head network models were compared and trained through a process of freezing,with the ultimate aim of bolstering the model's feature extraction abilities and elevating detection accuracy.The half-precision quantization method was used to optimize the model after transfer learning experiments,reducing model weights and computational complexity to improve the detection speed.Performance comparisons were conducted between the improved model and the original Nano Det-Plus model,YOLO,SSD and other common industrial defect detection algorithms,validating that the improved methods based on transfer learning and semi-precision quantization enabled the model to meet the practical requirements of industrial production.

Advancing automated pupillometry:a practical deep learning model utilizing infrared pupil images

AIM:To establish pupil diameter measurement algorithms based on infrared images that can be used in real-world clinical settings.METHODS:A total of 188 patients from outpatient clinic at He Eye Specialist Shenyang Hospital from Spetember to December 2022 were included,and 13470 infrared pupil images were collected for the study.All infrared images for pupil segmentation were labeled using the Labelme software.The computation of pupil diameter is divided into four steps:image pre-processing,pupil identification and localization,pupil segmentation,and diameter calculation.Two major models are used in the computation process:the modified YoloV3 and Deeplabv 3+models,which must be trained beforehand.RESULTS:The test dataset included 1348 infrared pupil images.On the test dataset,the modified YoloV3 model had a detection rate of 99.98% and an average precision(AP)of 0.80 for pupils.The DeeplabV3+model achieved a background intersection over union(IOU)of 99.23%,a pupil IOU of 93.81%,and a mean IOU of 96.52%.The pupil diameters in the test dataset ranged from 20 to 56 pixels,with a mean of 36.06±6.85 pixels.The absolute error in pupil diameters between predicted and actual values ranged from 0 to 7 pixels,with a mean absolute error(MAE)of 1.06±0.96 pixels.CONCLUSION:This study successfully demonstrates a robust infrared image-based pupil diameter measurement algorithm,proven to be highly accurate and reliable for clinical application.

Preoperative CT radiomics models for predicting composition of in vivo urinary calculi

Objective To observe the value of preoperative CT radiomics models for predicting composition of in vivo urinary calculi.Methods Totally 543 urolithiasis patients were retrospectively enrolled and divided into calcium oxalate monohydrate stone group(group A,n=373),anhydrous uric acid stone group(group B,n=86),carbonate apatite group(group C,n=30),ammonium urate stone group(group D,n=28)and ammonium magnesium phosphate hexahydrate stone group(group E,n=26)according to the composition of calculi,also divided into training set and test set at the ratio of 7∶3.Radiomics features were extracted and screened based on plain CT images of urinary system.Five binary task models(model A—E corresponding to group A—E)and a quinary task model were constructed using least absolute shrinkage and selection operator algorithm for predicting the composition of calculi in vivo.Then receiver operating characteristic curves were drawn,and the area under the curves(AUC)were calculated to evaluate the predictive efficacy of binary task models,while the accuracy,precision,recall and F1 score were used to evaluate the predictive efficacy of the quinary task model.Results All binary task models had good efficacy for predicting the composition of urinary calculi in vivo,with AUC of 0.860—0.948 in training set and of 0.856—0.933 in test set.The accuracy,precision,recall and F1 score of the quinary task model for predicting the composition of in vivo urinary calculi was 82.25%,83.79%,46.23%and 0.596 in training set,respectively,while was 80.63%,75.26%,43.48%and 0.551 in test set,respectively.Conclusion Binary task radiomics models based on preoperative plain CT had good efficacy for predicting the composition of in vivo urinary calculi,while the quinary task radiomics model had high accuracy but relatively poor stability.

Automated body composition analysis system based on chest CT for evaluating content of muscle and adipose

Objective To establish a body composition analysis system based on chest CT,and to observe its value for evaluating content of chest muscle and adipose.Methods T7—T8 layer CT images of 108 pneumonia patients were collected(segmented dataset),and chest CT data of 984 patients were screened from the COVID 19-CT dataset(10 cases were randomly selected as whole test dataset,the remaining 974 cases were selected as layer selection dataset).T7—T8 layer was classified based on convolutional neural network(CNN)derived networks,including ResNet,ResNeXt,MobileNet,ShuffleNet,DenseNet,EfficientNet and ConvNeXt,then the accuracy,precision,recall and specificity were used to evaluate the performance of layer selection dataset.The skeletal muscle(SM),subcutaneous adipose tissue(SAT),intermuscular adipose tissue(IMAT)and visceral adipose tissue(VAT)were segmented using classical fully CNN(FCN)derived network,including FCN,SegNet,UNet,Attention UNet,UNET++,nnUNet,UNeXt and CMUNeXt,then Dice similarity coefficient(DSC),intersection over union(IoU)and 95 Hausdorff distance(HD)were used to evaluate the performance of segmented dataset.The automatic body composition analysis system was constructed based on optimal layer selection network and segmentation network,the mean absolute error(MAE),root mean squared error(RMSE)and standard deviation(SD)of MAE were used to evaluate the performance of automatic system for testing the whole test dataset.Results The accuracy,precision,recall and specificity of DenseNet network for automatically classifying T7—T8 layer from chest CT images was 95.06%,84.83%,92.27%and 95.78%,respectively,which were all higher than those of the other layer selection networks.In segmentation of SM,SAT,IMAT and overall,DSC and IoU of UNet++network were all higher,while 95HD of UNet++network were all lower than those of the other segmentation networks.Using DenseNet as the layer selection network and UNet++as the segmentation network,MAE of the automatic body composition analysis system for predicting SM,SAT,IMAT,VAT and MAE was 27.09,6.95,6.65 and 3.35 cm 2,respectively.Conclusion The body composition analysis system based on chest CT could be used to assess content of chest muscle and adipose.Among them,the UNet++network had better segmentation performance in adipose tissue than SM.

Deep learning model based on PET/CT and combination with Cox proportional hazard model for predicting progression of lung invasive adenocarcinoma after surgery

Objective To observe the efficacy of deep learning(DL)model based on PET/CT and its combination with Cox proportional hazard model for predicting progressive disease(PD)of lung invasive adenocarcinoma within 5 years after surgery.Methods The clinical,PET/CT and 5-year follow-up data of 250 patients with lung invasive adenocarcinoma were retrospectively analyzed.According to PD or not,the patients were divided into the PD group(n=71)and non-PD group(n=179).The basic data and PET/CT findings were compared between groups,among which the quantitative variables being significant different between groups were transformed to categorical variables using receiver operating characteristic(ROC)curve and corresponding cut-off value.Multivariant Cox proportional hazard model was used to select independent predicting factors of PD of lung invasive adenocarcinoma within 5 years after surgery.The patients were divided into training,validation and test sets at the ratio of 6∶2∶2,and PET/CT data in training set and validation set were used to train model and tuning parameters to build the PET/CT DL model,and the combination model was built in serial connection of DL model and the predictive factors.In test set,the efficacy of each model for predicting PD of lung invasive adenocarcinoma within 5 years after surgery was assessed and compared using the area under the curve(AUC).Results Patients'gender and smoking status,as well as the long diameter,SUV max and SUV mean of lesions measured on PET images,the long diameter,short diameter and type of lesions showed on CT were statistically different between groups(all P<0.05).Smoking(HR=1.787[1.053,3.031],P=0.031)and lesion SUV max>4.15(HR=5.249[1.062,25.945],P=0.042)were both predictors of PD of lung invasive adenocarcinoma within 5 years after surgery.In test set,the AUC of PET/CT DL model for predicting PD was 0.847,of the combination model was 0.890,of the latter was higher than of the former(P=0.036).Conclusion DL model based on PET/CT had high efficacy for predicting PD of lung invasive adenocarcinoma within 5 years after surgery.Combining with Cox proportional hazard model could further improve its predicting efficacy.

Thermodynamic calculation of high zinc-containing Al-Zn-Mg-Cu alloy

Phase fraction and solidification path of high Zn-containing Al-Zn-Mg-Cu series aluminum alloy were calculated by calculation of phase diagram （CALPHAD） method. Microstructure and phases of Al-9.2Zn-1.7Mg-2.3Cu alloy were studied by X-ray diffraction （XRD）, differential scanning calorimetry （DSC） and scanning electron microscopy （SEM）. The calculation results show that η（MgZn2） phase is influenced by Zn and Mg. Mass fractions of η（MgZn2） in Al-xZn-1.7Mg-2.3Cu are 10.0%, 9.8% and 9.2% for x=9.6, 9.4, 8.8 （mass fraction, %）, respectively. The intervals of Mg composition were achieved for θ（Al2Cu）＋η（MgZn2）, S（Al2CuMg）＋η（MgZn2） and θ（Al2Cu）＋S（Al2CuMg）＋η（MgZn2） phase regions. Al3Zr, α（Al）, Al13Fe4, η（MgZn2）, α-AlFeSi, Al7Cu2Fe, θ（Al2Cu）, Al5Cu2MgsSi6 precipitate in sequence by no-equilibrium calculation. The SEM and XRD analyses reveal that α（Al）, η（MgZn2）, Mg（Al,Cu,Zn）2, θ（Al2Cu） and Al7Cu2Fe phases are discovered in Al-9.2Zn-1.7Mg-2.3Cu alloy. The thermodynamic calculation can be used to predict the major phases present in experiment.

Iron reduction in aluminum by electroslag refining

The effect of electroslag refining on iron reduction from commercial aluminum was investigated.Cast electrodes of commercial aluminum were electroslag refined using KCl-NaCl-Na3AlF6 slag containing Na2B4O7.Experimental results indicate that the iron content decreases with increasing Na2B4O7 addition and remelting time,and the iron content decreases from 0.400% to 0.184% under 9% Na2B4O7 addition for 30 min remelting.The elastic modulus,yield strength and ultimate tensile strength commercial aluminum are improved,and the tensile elongation is increased by 43% after electroslag refining.The chemical reaction between melt and slag to form Fe2B is the main reason for iron reduction and the thermodynamic calculation of the chemical reaction theoretically accounts for the formation of Fe2B.

Biomimetic asymmetric Michael addition reactions in water catalyzed by amino-containing β-cyclodextrin derivatives

Nineβ‐cyclodextrin derivatives containing an amino group were synthesized via nucleophilic sub‐stitution from mono（6‐O‐p‐tolylsulfonyl）‐β‐cyclodextrin and used in asymmetric biomimetic Mi‐chael addition reactions in water at room temperature. The mechanism responsible for the moder‐ate activity and enantioselectivity of the β‐cyclodextrin derivatives was explored using nuclear magnetic resonance spectroscopy, namely 2D 1H rotating‐frame overhauser effect spectroscopy （ROESY）, ultraviolet absorption spectroscopy, and quantum chemical calculations, which provide a useful technique for investigating the formation of inclusion complexes. The effects of the pH of the reaction medium, theβ‐cyclodextrin derivative dosage, the structure of the modifying amino group, and various substrates on the yield and enantioselectivity were investigated. The results indicated that these factors had an important effect on the enantiomeric excess （ee） in the reaction system. Experiments using a competitor for inclusion complex formation showed that a hydrophobic cavity is necessary for enantioselective Michael addition. A comparison of the reactions using 4‐nitro‐β‐nitrostyrene and 2‐nitro‐β‐nitrostyrene showed that steric hindrance improved the enan‐tioselectivity. This was verified by the optimized geometries obtained from quantum chemical cal‐culations. An ee of 71%was obtained in the asymmetric Michael addition of cyclohexanone and 2‐nitro‐β‐nitrostyrene, using （S）‐2‐aminomethylpyrrolidine‐modified β‐CD as the catalyst, in an aqueous buffer solution, i.e., CH3COONa‐HCl （pH 7.5）.

Plotting and application of predominance area diagram of In-S-O system based on topological rules

The mathematical topological rule was proposed to plot the predominance area diagram.Based on the phase rules,the components of In-S-O system were analyzed and the coexisting points of three condensed phases were determined.Combined with the topological rules and thermody namic calculation,four relation diagrams between the coexisting points of three condensed phases,which were denoted as α,β stable plane-topological diagram and unstable plane-topological diagram,were plotted for the In-S-O system.The results show that α stable plane topological diagram is in accordance with the predominance area diagram of In-S-O system plotted by traditional methods,which indicates that the new method is feasible to plot the predominance area diagram of In-S-O system.Meanwhile,β unstable plane-topological diagram can be used to elucidate the indium production with the bath smelting process.

Mathematical Definitions of Operators for Cartographic Generalization

This paper puts forword 11 cartographic generalization operator models and introduces their mathematical definitions,and thus a precise mathematical form and quantitative description has been given to these formerly limited qualitative concepts.The meaning of mathematical definition of operators for cartographic generalization and the application prospect in computer_aided cartography (CAC) is stated.ract The Jurassic strata in Jingyan of Sichuan containing the Mamenchinsaurus fauna are dealt with and divided in this paper. The Mamenchisaurus fossils contained there are compared in morphological features and stratigraphically with other types of the genus on by one. The comprehensive analysis show that the Mamenchisaurus fauna of Jingyan appeared in the early Late Jurassic and is primitive in morphology. The results of the morphological identification and stratigraphical study agree with each other. Their evolutionary processes in different apoches of the Late Jurassic also made clear. Key words Jingyan, Sichuan, Mamenchisaurus Fauna, stratigraphy, evolution

Identification of dynamic systems using support vector regression neural networks

A novel adaptive support vector regression neural network （SVR-NN） is proposed, which combines respectively merits of support vector machines and a neural network. First, a support vector regression approach is applied to determine the initial structure and initial weights of the SVR-NN so that the network architecture is easily determined and the hidden nodes can adaptively be constructed based on support vectors. Furthermore, an annealing robust learning algorithm is presented to adjust these hidden node parameters as well as the weights of the SVR-NN. To test the validity of the proposed method, it is demonstrated that the adaptive SVR-NN can be used effectively for the identification of nonlinear dynamic systems. Simulation results show that the identification schemes based on the SVR-NN give considerably better performance and show faster learning in comparison to the previous neural network method.

乾嘉天算专门之学在科举考试中的渗透

尽管一般认为明清时期的科举考试被理学笼罩而呈现僵化状态,但也时常与不同时期的文化和学术相关联。康熙帝虽热衷于以天文学和数学为大宗的西学,却明确表示科举考试不能以天文、算法命题,以免阻碍天算"实学"的发展。然而,乾嘉考据学派兴起,把明末以降的西学纳入儒学知识考据的范畴,形成具有汉学范式的天算专门之学,进而渗透到科举考试当中。天算专门之学不但出现在乾嘉之际的会试、乡试和学政举行的"观风试"试题中,还出现在考生的八股文和策论答卷中,并成为对考生学问进行评判的重要标准之一。