Effect of solvent on the initiation mechanism of living anionic polymerization of styrene:A computational study

For living anionic polymerization(LAP),solvent has a great influence on both reaction mechanism and kinetics.In this work,by using the classical butyl lithium-styrene polymerization as a model system,the effect of solvent on the mechanism and kinetics of LAP was revealed through a strategy combining density functional theory(DFT)calculations and kinetic modeling.In terms of mechanism,it is found that the stronger the solvent polarity,the more electrons transfer from initiator to solvent through detailed energy decomposition analysis of electrostatic interactions between initiator and solvent molecules.Furthermore,we also found that the stronger the solvent polarity,the higher the monomer initiation energy barrier and the smaller the initiation rate coefficient.Counterintuitively,initiation is more favorable at lower temperatures based on the calculated results ofΔG_(TS).Finally,the kinetic characteristics in different solvents were further examined by kinetic modeling.It is found that in benzene and n-pentane,the polymerization rate exhibits first-order kinetics.While,slow initiation and fast propagation were observed in tetrahydrofuran(THF)due to the slow free ion formation rate,leading to a deviation from first-order kinetics.

Applying Graph Theory and Mathematical-Computational Modelling to Study a Neurophysiological Circuit

The aim of the present study is to contribute to the knowledge about the functioning of the neuronal circuits. We built a mathematical-computational model using graph theory for a complex neurophysiological circuit consisting of a reverberating neuronal circuit and a parallel neuronal circuit, which could be coupled. Implementing our model in C++ and applying neurophysiological values found in the literature, we studied the discharge pattern of the reverberant circuit and the parallel circuit separately for the same input signal pattern, examining the influence of the refractory period and the synaptic delay on the respective output signal patterns. Then, the same study was performed for the complete circuit, in which the two circuits were coupled, and the parallel circuit could then influence the functioning of the reverberant. The results showed that the refractory period played an important role in forming the pattern of the output spectrum of a reverberating circuit. The inhibitory action of the parallel circuit was able to regulate the reverberation frequency, suggesting that parallel circuits may be involved in the control of reverberation circuits related to motive activities underlying precision tasks and perhaps underlying neural work processes and immediate memories.

Mathematical Modeling and Computational Semiotics： Methodological Approach to Formalization of Semiotic Concepts

This paper aims to conduct a research on the state of the art of artificial intelligence techniques to investigate the relationships between cognitive actions addressed in steps of mathematical modeling and computational semiotics activities. It also briefly reviews the main techniques of artificial intelligence, with particular emphasis on intelligent systems techniques. Such analysis uses semiotic concepts in order to identify the use of new techniques for modeling intelligent systems through the integrated use of mathematical and computational tools. At last, once understood that semiotics can bring contributions to the study of intelligent systems, a methodology for modeling computational semiotics based on the semiotic concepts formalization extracted from the semiotic theory of Charles Sanders Peiree is proposed.

Mathematics and Computer Graphic Design Arts

The relationship between arts and mathematics is very close, computer graphic design is based on digital methodology. The paper reveals the mathematical backgrounds behind graphic design by the example of computer-aided cubic modeling and mathematical exchange methodology. Furthermore, one can get incredible artistic effects if computer graphic designers pay more attention to the probability and use probable numbers and fractal operation in their design activities.Finally, the author also discusses the bidirections between arts and mathematics.

Microsoft Mathematics软件辅助高等数学教学的探讨

文章阐述了计算机辅助教学的重要意义和作用,并以高等数学课程为例分析了如何利用Microsoft Mathematics软件提供的绘图和解题功能辅助教师教学,同时帮助学生更好地学习高等数学课程。

Dynamic Factor Method of Computing Dynamic Mathematical Model for System Simulation

The computational methods of a typical dynamic mathematical model that can describe the differential element and the inertial element for the system simulation are researched. The stability of numerical solutions of the dynamic mathematical model is researched. By means of theoretical analysis, the error formulas, the error sign criteria and the error relationship criterion of the implicit Euler method and the trapezoidal method are given, the dynamic factor affecting the computational accuracy has been found, the formula and the methods of computing the dynamic factor are given. The computational accuracy of the dynamic mathematical model like this can be improved by use of the dynamic factor.

Mathematical Model of Heat Treatment and Its Computer Simulation

Computer simulation on heat treatment is the foundation of intelligent heat treatment. The simulations of temperature field, phase transformation, stress/strain complicate quenching operation were realized by using the model of three dimensional non linear finite element method and the treatment methods of abruptly changing interface conditions. The simulation results basically fit those measured in experiments. The intelligent sealed multipurpose furnace production line has been developed based on the combination of computer simulation on gaseous carburizing and computer control technology. More than 3000 batches of workpieces have been processed on this production line, and all are up to standard. The application of computer simulation technology can significantly improve the loading ability and relia bility of nitriding and carburizing workpieces, reduce heat treatment distortion, and shorten carburizing duration. It is recommended that the reliable product design without redundancy should be performed with the combination of the CAD of mechanical products, the CAE of materials selection and heat treatment, and the dynamic evaluation technology of product reliability.

Teaching Reform and Practice on Course Construction of Discrete Mathematics

Discrete mathematics studies the respective structures,laws and interrelationships of different discrete quantities,which has a wide range of applications in computer science and software engineering.It has the characteristics of research,practice and innovation.The teaching goals of the course of discrete mathematics include not only the understanding and mastery of knowledge,but also the study of methodology.However,current teaching mechanism has limitations in outdated course contents,rare real project examples and nonscientific scoring modes.This paper attempts to think about the course construction of discrete mathematics to improve the teaching effects and cultivate students’practical ability.

MATHEMATICAL MODEL AND COMPUTER SIMULATION OF MOISTURE TRANSFER PROCESS DURING SINTERING

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Learning to represent 2D human face with mathematical model

How to represent a human face pattern?While it is presented in a continuous way in human visual system,computers often store and process it in a discrete manner with 2D arrays of pixels.The authors attempt to learn a continuous surface representation for face image with explicit function.First,an explicit model(EmFace)for human face representation is pro-posed in the form of a finite sum of mathematical terms,where each term is an analytic function element.Further,to estimate the unknown parameters of EmFace,a novel neural network,EmNet,is designed with an encoder-decoder structure and trained from massive face images,where the encoder is defined by a deep convolutional neural network and the decoder is an explicit mathematical expression of EmFace.The authors demonstrate that our EmFace represents face image more accurate than the comparison method,with an average mean square error of 0.000888,0.000936,0.000953 on LFW,IARPA Janus Benchmark-B,and IJB-C datasets.Visualisation results show that,EmFace has a higher representation performance on faces with various expressions,postures,and other factors.Furthermore,EmFace achieves reasonable performance on several face image processing tasks,including face image restoration,denoising,and transformation.

The Program Application on the Relative Method of Fuzzy Mathematics

The method of fuzzy mathematics for simultaneous assessment of time and intensity of earthquake hazards has been studied.This method is based on fundamental statistical indices of regional seismicity.Applying the retrieval method of fuzzy information,we can classify the time and intensity into several intervals and classes of seismic activity,then the possible time interval of large earthquakes with magnitude of M≥Ms can be estimated in a given region.Based on the preceding idea,an FRPP program is constructed.For the automatic data processing when this method is used,it is very important to design the statistical process of each index decomposition so that the program could be fit to a different sample discussed.There are some functions in the FRPP program.The man-made impact on results is reduced to the minimum as far as possible.Computation time is saved.There is a menu on which time interval,index,intensity class,and output data all can be selected.The catalog input that can be displayed on the

Mathematica软件在《数学分析》中的应用

从求解不等式、极限、导数、微分、不定积分、定积分及绘图等方面介绍了Mathematica软件在《数学分析》中的应用。研究表明,将Mathematica应用于《数学分析》中,能够使学习变得更直观、更容易,对提高学生学习的积极性有明显促进作用。

Mathematica软件在高校数学教学中的应用

指出数学教学改革的发展应该使用计算机软件来解决诸多的数学问题;使用Mathematica软件解决高等数学中函数的绘制图像、求函数的导数、不定积分和定积分等等,以提高高等数学教学的效果和学生学习高等数学的兴趣和效率.

Mathematica软件在大学数学教学中的应用

Mathematica软件具有强大的计算、绘图和编程功能,在高等数学、线性代数、概率论与数理统计等大学数学课程中引入Mathematica软件进行辅助教学,可以提高教学效果,培养学生利用所学知识分析问题和解决问题的能力。

Mathematica软件在高等数学教学中的应用

Mathematica软件是一套专门进行数学计算的软件，在高等数学中引入Mathematica软件进行辅助教学，有利于增强教学的直观性．激发学生学习兴趣．提高学生解决数学综合问题的能力。

一类双调和方程边值问题的四阶和六阶Richardson外推法

首先,对双调和方程建立了具有二阶精度的差分格式,证明了该差分格式的解存在唯一性,并利用极值原理证明了其收敛性和稳定性;利用双重Richardson外推法对该差分格式做了一次外推和二次外推,在内结点处使得计算结果分别具有四阶精度和六阶精度。研究结果表明,外推算法在一定条件下对于提高差分格式解的精度有显著的作用。

一类变系数椭圆型Dirichlet边值问题的差分外推格式

对于变系数椭圆型偏微分方程的Dirichlet边值问题,首先,应用泰勒展开建立五点差分格式,并证明差分格式解的存在唯一性;其次,应用极值原理得到差分格式解的先验估计式,进一步证明其收敛性和稳定性;再次,应用Richardson外推法,建立具有四阶精度的外推格式;最后,应用Gauss-Seidel迭代方法对算例进行求解,数值结果表明Richardson外推法极大地提高了数值解的精度。

数学软件包Mathematica引入教学的探索

运用数学软件包可起到形象直观、节省时间、提高学生兴趣的作用。训练学生熟练地使用数学软件包已成为高等数学教学内容的一部分。

All-optical computing based on convolutional neural networks

The rapid development of information technology has fueled an ever-increasing demand for ultrafast and ultralow-en-ergy-consumption computing.Existing computing instruments are pre-dominantly electronic processors,which use elec-trons as information carriers and possess von Neumann architecture featured by physical separation of storage and pro-cessing.The scaling of computing speed is limited not only by data transfer between memory and processing units,but also by RC delay associated with integrated circuits.Moreover,excessive heating due to Ohmic losses is becoming a severe bottleneck for both speed and power consumption scaling.Using photons as information carriers is a promising alternative.Owing to the weak third-order optical nonlinearity of conventional materials,building integrated photonic com-puting chips under traditional von Neumann architecture has been a challenge.Here,we report a new all-optical comput-ing framework to realize ultrafast and ultralow-energy-consumption all-optical computing based on convolutional neural networks.The device is constructed from cascaded silicon Y-shaped waveguides with side-coupled silicon waveguide segments which we termed“weight modulators”to enable complete phase and amplitude control in each waveguide branch.The generic device concept can be used for equation solving,multifunctional logic operations as well as many other mathematical operations.Multiple computing functions including transcendental equation solvers,multifarious logic gate operators,and half-adders were experimentally demonstrated to validate the all-optical computing performances.The time-of-flight of light through the network structure corresponds to an ultrafast computing time of the order of several picoseconds with an ultralow energy consumption of dozens of femtojoules per bit.Our approach can be further expan-ded to fulfill other complex computing tasks based on non-von Neumann architectures and thus paves a new way for on-chip all-optical computing.

Past and Future of Mathematical Geology

This is a brief review of alternative methods of problem-solving in geoscience with emphasis on the role of mathematical geology. It is desirable to maintain a clear-cut distinction between reliable facts which can be stored in data banks and concepts that can be incorporated in the specifications of statistical models designed for specific purposes. If possible, subjective probabilities should be incorporated in hypotheses that are to be tested by statistical inference.