Preliminary Research on the Mathematical Methods and Order of Problems in the“Fungcheng”Chapter of Yang Hui's Mathematical Methods(1261 CE)

Yang Hui was one of the most important authors of mathematical works during the thirteenth century.Mathematical Methods Explaining in Detail The Nine Chapters(Xiangjie jiuzhang suanfa詳解九章算法,1261 CE)is the earliest extant work attributed to Yang Hui.From the thirteenth to the fifteenth century,this work played a crucial role in the circulation and popularization of The Nine Chapters on Mathematical Procedures(Jiuzhang suanshu九章算术).However,the only surviving printed edition of Mathematical Methods is incomplete and contains many mistakes obstructing contemporary researchers'understanding of this work.The "Fangcheng" chapter of The Nine Chapters deals with problems related to solving what today are known as simultaneous sets of linear equations.However,interpreting the text in this chapter of Mathematical Methods and recovering the mathematical practices relating to fangcheng are difficult.Through detailed textual and mathematical analyses,the author of this paper explains Yang Hufs understanding and practice relating to〃the fangcheng method"and"the method of the positive and the negative".This paper includes an appendix that provides a detailed translation of the ambiguous text relating to"the method of the positive and the negative"and gives reasons supporting the interpretation provided here.Yang Hufs understanding of the concepts of"positive"and"negative"and his practice relating to these two concepts may easily be confused with their apparent counterparts in modem mathematics.Also,careful analysis of the mathematical methods in this work reveal that the order of problems in Yang Hufs Reclassifications of Mathematical Methods Explaining in Detail The Nine Chapters([Xiangjie jiuzhang suanfa zuanlei詳解九章算法纂類],namely,the last section of Mathematical Methods)were rearranged according to commentaries to specific methods that appear in Mathematical Methods.Some textual clues referring to the zzprevious question"(qianwen前問)in certain commentaries of Mathematical Methods indeed reflect the order of problems in Reclassifications.Yang Hui made especially detailed commentaries on the problems that he arranged in a sequence that differs with respect to the original order of problems as they appear in the ancient classic work,The Nine Chapters.All these discoveries reveal and serve to prove a close relationship between Yang Hufs Mathematical Methods and his Reclassifications.

Dispersive propagation of optical solitions and solitary wave solutions of Kundu-Eckhaus dynamical equation via modified mathematical method

In this research work,we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus(KE)equation with the help of modified mathematical method.We obtained the solutions in the form of dark solitons,bright solitons and combined dark-bright solitons,travelling wave and periodic wave solutions with general coefficients.In our knowledge earlier reported results of the KE equation with specific coefficients.These obtained solutions are more useful in the development of optical fibers,dynamics of solitons,dynamics of adiabatic parameters,dynamics of fluid,problems of biomedical,industrial phenomena and many other branches.All calculations show that this technique is more powerful,effective,straightforward,and fruitfulness to study analytically other higher-order nonlinear complex PDEs involves in mathematical physics,quantum physics,Geo physics,fluid mechanics,hydrodynamics,mathematical biology,field of engineering and many other physical sciences.

Accelerating Factor Xa inhibitor discovery with a de novo drug design pipeline

Small-molecule drugs are essential for maintaining human health. The objective of this study is to identify a molecule that can inhibit the Factor Xa protein and be easily procured. An optimization-based de novo drug design framework, Drug CAMD, that integrates a deep learning model with a mixed-integer nonlinear programming model is used for designing drug candidates. Within this framework, a virtual chemical library is specifically tailored to inhibit Factor Xa. To further filter and narrow down the lead compounds from the designed compounds, comprehensive approaches involving molecular docking,binding pose metadynamics(BPMD), binding free energy calculations, and enzyme activity inhibition analysis are utilized. To maximize efficiency in terms of time and resources, molecules for in vitro activity testing are initially selected from commercially available portions of customized virtual chemical libraries. In vitro studies assessing inhibitor activities have confirmed that the compound EN300-331859shows potential Factor Xa inhibition, with an IC_(50)value of 34.57 μmol·L^(-1). Through in silico molecular docking and BPMD, the most plausible binding pose for the EN300-331859-Factor Xa complex are identified. The estimated binding free energy values correlate well with the results obtained from biological assays. Consequently, EN300-331859 is identified as a novel and effective sub-micromolar inhibitor of Factor Xa.

Geological Environmental Adaptability of Qingdao Rural Urbanization Based on Fuzzy Mathematical Method

Fuzzy mathematics comprehensive evaluation method is used to evaluate the geological environment suitability of rural urbanization in Qingdao City,China.A total of 5 first-level evaluation factors are selected,including environmental geological condition,geological resources,engineering geological condition,geological disaster and environmental geological problem,and human engineering activity.And there are 27 second-level evaluation factors,such as topography,land type and vegetation,nature reserve,water source protection area,groundwater quality division,and major engineering project.Qingdao City is divided into four districts of suitable area,relatively suitable area,moderately suitable area and relatively unsuitable area of ecological environment.And their characteristics are introduced.Suggestions for the developing direction of urban construction are put forward.Region of Laoshan District lying to the west of the Shilaoren is suitable to set up high-rise building;west Hongshiya may establish a waste landfill site;Jiaozhou Bay,the downstream of Dagu River,and Jihongtan Reservoir should be built as the key geological environment protection area and water source protection area.And the north Hongdao should be strictly monitored in order to control the expansion of urban construction to Jihongtan Reservoir.Mocheng District and the area north of it,Jiaozhou District and the area east of it are the ideal urban construction development areas in Qingdao City in the future.

Influence on the Quality of Apocynum Venetum with Different Degumming Methods

The biochemical degumming and chemical degumming were employed to process apocynum venetum, and indices values for the residual gum content, fineness, strength of single fiber, average length, moisture regain and whiteness of degummed apocynum venetum fibers are evaluated with fuzzy mathematical method. The results obtained from this investigation show that the general index value of degummed apocynum venetum fibers with biochemical degumming （K1= 0.626 09） is prior to that with chemical degumming（K2=0.421 64）.

BLOCK PIVOT METHODS FOR SOLVING FRICTIONAL CONTACT PROBLEMS

Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number of steps when the friction coefficient is ''relative small''. Unlike most mathematical programming methods for contact problems, the block pivot methods permit multiple exchanges of basic and nonbasic variables.

SIMULTANEOUS DETERMINATION OF MULTICOMPONENT IN MIXED ACIDS BY MATHEMATICAL METHOD

A new method for the determination of components in mixed acids has been developed.The mathematical model is obtained from samples of known composition and is then used to predict the concentrations of components in unknown sample.The practical utility of this method is demonstrated for simultaneous determination of two systems of ternary mixed acids and the results are satisfactory.

Numerical Mathematics Theory,Methods and Applications

Aims and Scope: Numerical Mathematics:Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction,analysis and application of numerical methods for solving scientific problems.Important research and expository papers devoted to the numerical solution of mathematical problems arising in all areas of science and technology are expected.The journal originates from the journal Numerical Mathematics:A Journal of Chinese Universities (English Edition).

Numerical Mathematics Theory,Methods and Applications

Aims and Scope: Numerical Mathematics:Theory, Methods and Applications(NM-TMA) publishes high-quality original

Symplectic analysis for regulating wave propagation in a one-dimensional nonlinear graded metamaterial

An analytical method,called the symplectic mathematical method,is proposed to study the wave propagation in a spring-mass chain with gradient arranged local resonators and nonlinear ground springs.Combined with the linearized perturbation approach,the symplectic transform matrix for a unit cell of the weakly nonlinear graded metamaterial is derived,which only relies on the state vector.The results of the dispersion relation obtained with the symplectic mathematical method agree well with those achieved by the Bloch theory.It is shown that wider and lower frequency bandgaps are formed when the hardening nonlinearity and incident wave intensity increase.Subsequently,the displacement response and transmission performance of nonlinear graded metamaterials with finite length are studied.The dual tunable effects of nonlinearity and gradation on the wave propagation are explored under different excitation frequencies.For small excitation frequencies,the gradient parameter plays a dominant role compared with the nonlinearity.The reason is that the gradient tuning aims at the gradient arrangement of local resonators,which is limited by the critical value of the local resonator mass.In contrast,for larger excitation frequencies,the hardening nonlinearity is dominant and will contribute to the formation of a new bandgap.

Ecological Suitability Evaluation on Agricultural Land in Western Jilin Province Based on Fuzzy Mathematics

[Objective] This study was to evaluate the ecological suitability of agricultural land in western Jilin Province, with the aim to provide basis for the effective application of agricultural resources and the structural adjustment of land use. [Method] The evaluation index system was constructed based on fuzzy mathematic method according to the principles of systematic, dominant, effectiveness and feasibility; based on law of tolerance, reasonable evaluation criteria were determined according to the ecological amplitude of crops; based on GIS processing, the initial data completed the mathematical operation by using the VBA program in Excel. [Result] The area of agricultural land grade I was 5 512 km2, grade II of 25 985 km2, grade Ill of 7 907 km2, and area of land not suitable for agriculture was 6 312 km2. According to the evaluation results, the key areas for land use adjustment were Zhenlai County, Da＇an County, Tongyu County and western Changling County. The directions of land use adjustment included improving irrigation and drainage conditions, governing land salinization and conversion of cropland to forest and grassland. [Conclusion] This study provided basis for the effective application of agricultural resources and ecological environment construction in western Jilin Province.

Molecular Integral for the Double Electron-Repulsion Potential： A Closed Form Underived for Forty Years

A closed form of the title integral formula over the Gaussian-type orbitals is derived for the first time. The present closed form is analytical as the multiple hyper-geometric function of five variables.

A System of Simultaneous Equations (SEM) for the Study of the Effectiveness of the Japanese Monetary Policy

In this paper, the authors study the effectiveness of the Japanese monetary policy set by the Bank of Japan (BOJ) to contrast the three major crises that the country has experienced since the second half of the 90s: that of the lost decade, that of 2008 and that of the Covid-19 pandemic. To this end, they use a particular type of mathematical-statistical model that is widely applied today in the economic field, namely a simultaneous equation model (SEM). This simultaneous equation model is estimated through an Iteratively reweighted least squares (IRLS) using quarterly historical series in the sample period Q1 1994 - Q2 2020. All data are in real terms. The results, appropriately compared with those of other authors, suggest that the monetary policy has a (limited) impact only on the interbank market. The fiscal policy, instead, has a greater ability to influence the money supply, the private consumption and the inflation expectations.

某三级甲等公立医院数字减影设备的成本效益分析

目的对公立医院数字减影血管造影(digital subtraction angiography,DSA)设备进行成本效益分析,结合社会效益评价,为设备采购和管理提供科学依据。方法采用投资回收期法、投资收益率法、量本利分析法和净现值法对数字减影设备进行成本效益分析,运用模糊数学法建模和指标评分法进行社会效益评价。结果公立医院数字减影设备包括DSA数字血管造影机、DSA全数字化平板探测器血管造影机、血管造影X线系统,其中:血管造影X线系统投资收益率最高为19.07%,投资回收期仅2.80年,运行效益评价为优秀;DSA全数字化平板探测器血管造影机A的经济指标最低,原因在于其业务量仅达保本工作量的83.91%,但其社会效益评分最高(C值为7.3)。结论公立医院在采购和管理数字减影等大型设备时需进行充分的成本效益分析论证,兼顾公立医院的公益性和科研属性,实行经济效益和社会效益双评价。

Symplectic analysis for wave propagation in one-dimensional nonlinear periodic structures

The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.

A METHOD FOR DETERMINATION OF CONCENTRATION OF ATOMIC HYDROGEN PERMEATED IN MULTI-LAYER STRUCTURE WALL OF HYDROGENATION REACTORS

It was proposed how the concentration distribution was calculated in the treble lager wall of hgdrogenation reactor according to the principle of hydrogen diffusion at the steady state in this paper. Based on the steady hydrogen permeation current density i∞ measund with the hydrogen probe at a given temperature, the hydmpen concentrationson the key interfaces and hydrogen distribution at any given mdial profile in the single, double or treble layer wall of hydrogenation reactor could be found by applying the presented equations throoph suitable parmeters ioput. The theoretical bases were provided for developing the nondestructive probing technique of the concentration of atomic hydmpen in the wallS of hydrogenation reactors.

Performance Evaluation of Baseline-dependent Averaging Based on Full-scale SKA1-LOW Simulation

The Square Kilometre Array(SKA)is the largest radio interferometer under construction in the world.Its immense amount of visibility data poses a considerable challenge to the subsequent processing by the science data processor(SDP).Baseline dependent averaging(BDA),which reduces the amount of visibility data based on the baseline distribution of the radio interferometer,has become a focus of SKA SDP development.This paper developed and implemented a full-featured BDA module based on Radio Astronomy Simulation,Calibration and Imaging Library(RASCIL).Simulated observations were then performed with RASCIL based on a full-scale SKA1-LOW configuration.The performance of the BDA was systematically investigated and evaluated based on the simulated data.The experimental results confirmed that the amount of visibility data is reduced by about 50%to 85%for different time intervals(Δt_(max)).In addition,differentΔt_(max)have a significant effect on the imaging quality.The smallerΔt_(max)is,the smaller the degradation of imaging quality.

THE CHARACTERISTICS OF THUNDERSTORM FREQUENCY VARIATION AND THEIR POSSIBLE RELATION WITH THE ADJUSTMENT OF CROP DISTRIBUTION IN THE LEIZHOU PENINSULA

In order to research possible influences of the adjustment of plant distribution on the development frequency of thunderstorms over the Leizhou Peninsula, mathematic statistic methods, including correlation analyses, 11 kinds of fitting models and all-variable regression methods, were used for analyses and research. The results show that the average trend of the number of annual thunderstorm days is descending obviously, and there are thunderstorms in all seasons, in which warm post-midday thunderstorms have taken up the most part, and high frequency is found from May to September, and the starting and ending dates of thunderstorms have a great annual discrepancy. The vegetation structure has been improved along with the reduction of rice fields and the area increment of sugarcane and fruits planting, which results in the decrease of the number of thunderstorm days; the change in the characteristics of winter spare fields, which is caused by the planting of vegetables, limits the formation of thunderstorms in early winter and late spring. Meanwhile, the area adjustment of peanut planting has little influence on the variation of thunderstorm days. The adjustment of principal crop distribution, such as rice, sugarcane, fruits and vegetables, may have obvious influence on the formation of thunderstorms, and sugarcane has the largest effect, followed in turn by rice, vegetables and fruits, and the adjustment of crop distribution has little influence on the starting and ending dates of thunderstorms.

Ultra-compact broadband polarization beam splitter with strong expansibility

Based on the traditional directional coupler, we proposed a scheme to design on-chip polarization beam splitters using an inverse design method. In our scheme, the coupling area of the designed devices are only 0.48 μm× 6.4 μm. By manipulating the refractive index of the coupling region, the devices can work in C-band,L-band, O-band, or any other communication band. Different from conventional design methods, which need to adjust the design parameters artificially, if the initial conditions are determined, the proposed scheme can automatically adjust the design parameters of devices according to specific requirements. The simulation results show that the insertion losses of the designed polarization beam splitters can be less than 0.4 dB(0.35 dB) for TE(TM)mode at the wavelengths of 1310, 1550, and 1600 nm, and the extinction ratios are larger than 19.9 dB for the TE and TM modes at all three wavelengths. Besides, the extinction ratios of both polarization states are more than 14.5 dB within the wavelength range of 1286–1364 nm, 1497–1568 nm, and 1553–1634 nm. At the same time,the insertion losses are smaller than 0.46 dB.

Object-Oriented Analysis of ELIMINO

ELIMINO is a mathematical research system developed for theimplementation of Wu's method, a powerful method for polynomial equation systemsolving and geometric theorem proving. The aim of ELIMINO is to provide usera programmable interpreting environment to use Wu's method in scientific researchand engineering computation. In this paper, the development of ELIMINo systemis outlined and the techniques adopted are discussed, then some details about theobject-oriented analysis of ELIMINO are presented.