Table of contents

Wanyang Dai

Editor, Proceedings of the Third International Conference on Physics, Mathematics and Statistics

Professor, Department of Mathematics, Nanjing University, China

Email: nan5lu8@nju.edu.cn

The Third International Conference on Physics, Mathematics and Statistics (ICPMS2020) was originally planned to be held in Kunming, China during May 20-22, 2020. Due to the COVID-19 pandemic, for the safety and health of the participants, ICPMS2020 on-site conference was changed to online meeting during June 23-24, 2020 via online platform. The conference is an annual forum, aims to provide a platform for scholars and researchers worldwide to share their research achievements, discuss the hot issues and exchange the new experiences.

On behalf of the Organizing Committees of ICPMS2020

Technical Program Committee

List of Conference Chair, Conference Co-chair, TPC Chair and TPC member available in this pdf.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

This study introduces a simple method that enables cross-sectional visualization in the measurement of the planer-laser induced fluorescence (PLIF) method. The concentration field of the high Schmidt number scalar mixing layer generated by grid-generated turbulence is measured by a water-channel experiment in this tudy. The high Schmidt scalar mixing layer is produced by Rhodamine B aqueous solution and water. A small transparent prism, installed on the outside wall of the test section, aids in applying cross-sectional visualization. The small transparent prism is an isosceles triangular shaped prism filled with the working fluid through the test section of the water channel. The setting and details of the small transparent prism are shown in this study. By using the small transparent prism, the concentration field on the plane set into the test section is shown as a result of the cross-sectional visualization. In this result, a scalar structure like a mushroom is visualized around the mixing interface of the scalar mixing layer, as found in a previous experiment.

In order to meet the needs of society for energy-saving lamps, save energy and reduce costs, this paper designed a multi-function green sensor lamp. The system is based on microcomputer, using LED lighting technology, human body infrared sensing principle, photosensitive sensor principle and acoustic sensor principle to realize a new intelligent lighting tool for automatic control of light source lighting. The intelligent control of the illumination duration from both hardware and software enables the light control and voice-activated illumination functions, and has an anti-theft function, which can effectively improve home safety.

In this paper, we consider a two-way relaying channel with simultaneous wireless information and power transfer. The intermediate relay station forwards lattice codes under transmit power constraint. Meanwhile, it charges user terminals for static circuit consumption and uplink transmission power. We novelly propose an iterative algorithm to maximize the sum-rate with joint beam-forming and power splitting design in MPT assisted TWRC. The method achieves the highest achievable rate compared with separate optimization designs and time switching method. Moreover, an extremely small gap between the proposed method and the outer cut-set bound is observed.

The present study introduces a simple scheme for generating an axisymmetrically anisotropic incompressible initial flow. In addition, the proposed scheme is used to examine the effects of kinetic energy conservation errors on the time evolution of the anisotropic initial flows. In the analysis of the present study, an inviscid flow is analyzed. In this inviscid flow, the kinetic energy characteristics are known analytically. The kinetic energy conservation error is obtained using the Crank-Nicolson (CN) method. The scheme of the present study generates an axisymmetrically anisotropic initial flow by obtaining the weights of normal random vector components using an anisotropic parameter. The analysis of the flow field is performed using a fourth-order differential scheme that explicitly conserves kinetic energy with a fourth-order Runge-Kutta scheme. Because of the kinetic energy conservation error, the kinetic energy obtained using the CN method increases with time. The magnitude of the initial anisotropy obtained by this scheme decreases with time. This result is only slightly affected by kinetic energy conservation errors. On the other hand, kinetic energy conservation error affects the magnitude of the pressure-strain correlation term.

In this paper, a novel terahertz patch antenna is designed using a very thin layer of graphene as the radiating patch, to get tri-band operation. An attempt, is made to design both achiral and chiral graphene patch tri-band for 0.46/0.58/0.66-THz. The simulation has been carried out by using a full wave electromagnetic simulator based on FDTD method. We then expect these results to be of interest to scientists in the field of the interaction between the electromagnetic wave and grapheme to design potential application.

Aerodynamic shape optimization of natural-laminar-flow (NLF) nacelle for lange-range wide-body transport aircraft was investigated. Perturbed class function/shape function transformation (CST) method was used to parameter the three typical generatrix of the nacelle combined with the perturbation based transfinite interpolation method to achieve surface and space grid update. The k-ω SST (shear stress transport) turbulence model and ϒ – Re_θ transition models was use to predict the transition location.The gradient based optimization method called Sequential Quadratic Programming was selected for the high efficiency. Natural laminar flow design was performed on three dimensional nacelles and about 45%∼55% laminar flow region was achieved by the optimization design.

In this paper, factors affecting the completely melting time of phase change material (PCM) in a rectangular cavity are analyzed. The influence of three factors including inclination angle of the cavity, heating temperature, and geometry of the cavity on completely melting time is discussed under the boundary condition of single size heating and double sizes heating respectively, while other sides are considered to be adiabatic. A two-dimensional mathematical model is established for the simulation analysis and verified by experiments. In order to analyze the influence of all factors on the completely melting time, the orthogonal analysis method is adopted, and the range analysis method is used to determine the influence of three factors on the completely melting time. Based on the orthogonal analysis, it can be found that the heating temperature is the most significant factor during single side heating, while geometry of the cavity is the most important factor during double sides heating. The results will be helpful to optimize the structure of PCM component used for energy storage system or temperature control structure.

Based on the analysis of aerodynamic load and structural strength of the vehicle contact network monitoring device, the distribution of aerodynamic moments and surface pressure of the monitoring device is calculated by means of fluid-solid coupling. The calculated load is applied to the surface of the device for structural analysis, mainly to investigate the maximum deformation and maximum equivalent stress of the device. The study found that air flow separation occurred above the ear region when driving forward, the pressure was higher, and the air flow below the ear region flowed around the ear region. The pressure difference between the upper and lower ears produced a downward force of about 150N in a single ear region, and produced a large rolling moment, after checking its connection strength with the central body to meet the requirements for use.

Studying the ultra-high energy gamma ray source is an important way to reveal the origin of the cosmic ray, which is also a main topic of many ground gamma ray experiments. To expect the observation ability during the design of the experiment, as well as to test the analyse methods in the observation, a Monte Carlo procedure for the signal and background generation is necessary. In this paper, such a procedure is introduced. And the source significance for a Blazar source Mrk421 is expected based on this procedure. Finally, an unfolding method for the source spectrum measurement is also established bashed on this Monte Carlo data, which gives fitting errors around ±10.0% both for the flux and the spectrum index.

The problem of quantitative assessment of soil pollution of the capital metropolis by controlling physical-chemical factors of solid and liquid phases of soil is investigated. The metals were used as an integral indicator of pollution taking into account the mass fraction and the variation of soil bulk density. Multiple regression (R²=0.91-0.95) of layered heavy metals, as well as accumulation of biophilic elements of the exchange fund from two main predictors – dispersion (effective specific surface area of solid phase, determined by the original thermal desorption method) and pH of salt extract was revealed.

Phased array ultrasonic scanning is currently the most advanced non-destructive test for detecting flaws in a steel welding. However, large uncertainty exists in the detection results. Technically, this uncertainty is induced by the sparsity of detection resolution compared to the scale of the flaws. Consequently, it is essential to enrich the resolution of detection results and quantify the corresponding statistical uncertainty before evaluating the number and equivalent of the flaws in the steel welding. In this paper an uncertainty quantification framework is built with Bayesian compressive sensing method from which the equivalent of the flaws in the steel welding with certain degree of confidence can finally be given.

Two dimensional materials have special properties including small size effect, surface effect and quantum confinement effect caused by limited dimensionality, and their energy band can be tuned while doping by impurity elements. Recently, two dimensional transition metal dichalcogenides (TMDCs) are thought to be the most prospective material to fit Moore's law. Among them, MoS₂ is the most common and important materials in research and it might have the best photoelectric property among all known two dimensional materials. In this article, we simulated n-doped monolayer MoS₂ with chlorine atoms with the method of density functional theory and studied the effect on its electronic structure like electronic density of states and energy band structures. The results showed that this chlorine doping can introduce a defect energy level in the band structure of the monolayer MoS₂ and make it become n-type semiconductor. Our work lays a foundation for further research on the doping of other two-dimensional materials besides MoS₂ together with the study on the materials' electronic structure.

In the fast tunnel detection of multi-camera, a disease distributed in multiple images is prone to be misidentified as multiple diseases, which affects the evaluation of the status of the tunnel. This paper proposes a high-precision stitching method driven by data and scene based on multi-camera sequence images. Firstly, geometric rough calculation is performed to generate the theoretical stitching mode using the geometric positional relationship between the cameras in the scene and the image relationship is renewed after theoretical stitching. Secondly, feature points are extracted and matched for adjacent overlapping images by SURF algorithm. Therefore, pixel-level data registration is performed to achieve the image stitching. Finally, an integrated stitching mode is proposed based on the theoretical stitching and pixel-level data registration, which utilizes the stitched sequence images with high physical resolution to extract cross-section information. Practical results show that the method can achieve image stitching of the tunnels with high accuracy and good reliability.

The paper proposes a simple band stop frequency selective surface (FSS) design method based on spoof surface plasmon polaritons (spoof-SPPs). The novel FSS design is obtained by combing three-dimension (3-D) FSS and ultra-thin periodic corrugated metallic strip which supports spoof-SPPs. By placing electric-LC (ELC) resonators on the FSS surface at the bottom centre of the corrugated strip, the tight coupling occurs and we show that the SPP modes are rejected near the resonance frequencies of ELC resonators. The steep roll-off at both sides of the stopband can be demonstrated by the ELC resonators, which can find potential applications in wideband antenna radome. In addition, the 3-D FSS shows relatively stable performance with different oblique incidence angles.

With the development of cyber-physical power system, cyber security has a serious impact on the operation of power system. In this paper, a stochastic cascading failure model considering the structural and dynamical characteristics of cyber-physical power system is proposed. The model takes into account the community structure of networks, the heterogeneity of network nodes and the complex interdependence of coupling networks. Moreover, the malware spreading in the cyber network and the power flow redistribution in the power grid are considered to describe the dynamic physical processes of the system, and a stochastic method is adopted to describe the operating state transition of network components. Simulation results indicate that the cascading failure of coupled system is the result of malware attacks repeatedly triggering the power grid, and cyber coupling will aggravate the severity of grid failure propagation.

The amplitude shift keying (ASK) is a significant technique in communications. We propose a terahertz encoder based on the 2-dimensional electron gas (2DEG) metamaterial, which can complete ASK in the 0.43 THz and 0.81 THz independently. The ON/OFF ratio of the encoder in each band is more than 86%. The research is helpful in promoting terahertz technology and next-generation communications.

This paper focuses on the issue of how to select the optimal deployment scheme for the dispersal of miss distance during acoustic rendezvous measurements. Firstly, the measurement theory of acoustic rendezvous is introduced, and then the error model of acoustic rendezvous measurement is deduced and theoretical analysis is carried out. Then, an error evaluation index is established based on the dispersion characteristics of miss distance. Finally, simulation experiments are conducted for the miss distance obeying uniform distribution and normal distribution. Simulation experiments verify the correctness of the method in this paper, which has important guiding significance for the miss distance test.

The range of Mach number of 1.3 to 1.5 is defined as low-supersonic flow in wind tunnel testing, which is necessary range for major fighters, aerospace vehicles, and missiles to reach the cruise state. It is also the most difficult test range for conventional ground simulation equipment due to sound barrier and uniformity of artificial air flows. In order to expand the test range of 2.4m transonic wind tunnel, researches on low supersonic flow filed calibration was carried out, and the geometrical parameters of perforated walls in test section were determined. Measured results of flow uniformity are compared with advanced wind tunnels using cross-shaped rake and cone-cylinder model. The results show that uniformed low supersonic flow in model testing area was obtained using newly developed nozzle together with perforated walls in 2.4m transonic wind tunnel, which effectively improve the simulation capability of the facility. Together with the capacity of 2m supersonic wind tunnel, seamless link of test data has been achieved in high speed regime, which has formed an integrated test platform for sub-, trans-, and supersonic speeds on the order of 2 meters.

The sound field of a 3D shallow sea environment with a conical submarine mountain is simulated and calculated using the finite element method. To verify the accuracy of the finite element calculation results, the effects of submarine mountain height and sound source depth on sound-propagation characteristics are evaluated. The simulation results indicate that owing to the reflection and concentration of acoustic energy due to the submarine mountain, before the sound wave reaches the subsea mountain, the impact of subsea mountain on the acoustic energy can reach 10 dB. In addition, the sound energy is hindered by the seamount. Therefore, the sound energy loss after the sound wave reaches the subsea mountain is higher than the sound energy loss in the absence of the seamount under the same circumstance, and the maximum is up to 20 dB. The larger the seamount height and sound source depth, the more significant the blocking and accumulation of the sound energy.

Embryogenesis is a spatio-temporal multicellular evolutional process involved with intracellular biochemical activities and intercellular biophysical interactions. Reproducible and precise multicellular structures contribute to robustness of embryonic development by cell-cell communication, morphogenesis and other significant biological events. Using Caenorhabditis elegans as animal model, recently several researches established mechanical models to reconstruct the multicellular structures of this developmental system, in which cells interact via repulsive or attractive potentials inside an ellipsoidal eggshell. However, those models ignored some practical details and lack of test in depth. In this paper, we improved an in silico modeling framework based on previous models by revising formulae of interactive force and applying in vivo experimental information of eggshell shape, cell volume, cell position and cell-cell connection relationship. Cell pairs with and without empirically repeated connection were regarded to have different types of attractive force, which could help stabilize cells into their experimentally observed locations accompanied by correct neighbour relationships. Both previous models and our revised ones were tested, verified and compared to each other. Our modeling framework not only reproduces the multicellular structure patterns in an artificially compressed embryo with ∼50 cells, but also exhibits a potential to uncover active adjustments and controls on cell positioning.

Intelligent aircraft trajectory planning is an important support to ensure the successful completion of the mission of the aircraft, and it is also a key component of the intelligent aircraft mission planning system. Due to system performance constraints and environmental constraints, the positioning system of the intelligent aircraft cannot be accurately positioned during flight, which will cause flight errors. Excessive flight errors will lead to the failure of the mission. Therefore, error correction plays an increasingly important role in trajectory planning. This paper studies the rapid trajectory planning of intelligent aircraft under the limitation of system positioning accuracy. Based on the optimization theory, with the error generation rules and correction rules of the intelligent aircraft in flight as constraints, establishes the optimization model, and uses the fast non-dominated multi-objective optimization algorithm (NSGA-II) with elite retention strategy. This paper corrects the vertical and horizontal errors during the flight, and finally designs a reasonable intelligent aircraft trajectory that meets the minimum trajectory length and the minimum number of corrections during the flight.

CO in combustion products of aeroengine is a sign product of incomplete combustion. Real-time monitoring of CO can feedback combustion efficiency, which is of great significance to the design of combustion chamber and the optimization of fuel ratio of aeroengine. In this paper, based on the mid infrared absorption spectroscopy, a single optical path calibration-free wavelength modulation method is proposed to measure the temperature and concentration of CO in a flat flame. Firstly, the spectrum of light intensity signal and the amplitude frequency response of different frequencies are analysed, and the appropriate scanning frequency and modulation frequency are selected. Secondly, the equalization of Butterworth filter in DPLA is proposed to extract the first and second harmonics. The filter can effectively reduce the influence of nonlinear phase. Furthermore, calibration-free wavelength modulation method is simulated to measure CO at different temperature and concentration. Finally, CO in flat flame with different equivalence ratio at 5mm was measured for verification. The relative error between the measurement results of calibration-free wavelength modulation and that of thermocouple measurement is within 3.6% in the range of concentration 0.11% ∼ 0.24%, which verified the feasibility and effectiveness of the measurement scheme, and provided a reference for the CO concentration measurement at the outlet of aeroengine.

In this paper, we give a proposal to design a microwave Surface Plasmon Polaritons (SPPs) coupler, which can completely transfer energy of SPPs with robustness against varying geometrical parameters and broadband frequency range of microwave, based on Stimulated Raman Adiabatic Passage (STIRAP). The STIRAP is one of the most famous quantum coherent control methods, and most importantly it can improve the robustness of the device and energy transmission efficiency. This work is not only promising in designing robust and broadband compact microwave couplers, but also leading larger potential applications in microwave and millimeter wave communication.

We demonstrate an active controlled electromagnetically induced transparency (EIT) device via thermal control in a hybrid metamaterial, which consists of two split-ring resonators (SRRs) with integrated InSb-metal and a cut wire (CW) in a unit cell. We can dynamically control the amplitude modulation of the EIT window, by varying the temperature of the InSb thereby changing the damping rate of the dark mode of SRRs. When the temperature of the InSb changes from 240K to 320K, the EIT window undergoes modulation from on to off, and the modulation depth reaches 86.8%. The results are not only promising in designing compact slow light devices in the terahertz regime but also leading some essential applications in terahertz communications.

Using covalent organic frameworks (COFs) to capture noxious gas has become an increasing research interest, especially for the purpose of environmental protection. A theoretical study on the interactions of carbon monoxide (CO), sulfur dioxide (SO₂) and nitric oxide (NO), respectively with COF-300 has been proposed, based on the theory of the continuum approximation using Lennard-Jones potential. We discover that COF-300 can store more SO₂ in comparison to CO and NO under an increasing pressure at 77K. The present methodology is computationally efficient and can be employed in other types of gases and nano-porous materials without conceptual difficulties.

The characteristics of resonant modes in the side-coupled asymmetric square-ring resonator based on a plasmonic waveguide are investigated. The 1-order modes and 2-order modes can be manipulated by adjusting the longitudinal distance Δz and transversal distance Δx of the metal block in the square air cavity. The coupling and splitting effect of the resonant modes in the asymmetric square ring resonator are exploring. The proposed structure is potential in sensing and filtering.

Circular ring is the most useful specimen in industry. However, any small crack exists on it will cause some damage about the equipment and even more some serious disaster. As we understand plastic hinge will appear if we increase the load of the ring. The ring will collapse when there are four plastic hinges. The sequence of formation of these hinges is also depended on the location of the crack of the ring. In this paper three different approaches i.e., theoretical, numerical, and experimental will be presented. The theoretical approach is based on the linear elastic fracture mechanics (LEFM) and the method of superposition. The boundary element method (BEM) will be employed in the numerical approach. Finally, the cracked ring specimen was made of Aluminum 6061-T6 whose property is close to the ideally elastic-plastic material property in the experimental approach. The results show the consistency of these three different approaches and provide reasonable information to inspect the circular ring used in daily life.

The entry and ejection of fuel into and out of high-pressure oil tube are the basis of many fuel engines. However, the intermittent working process of fuel entering and exiting will be leading to pressure changes in high-pressure oil tube. Furthermore, it will affect the efficiency of an engine. Therefore, it can be seen important to control high-pressure oil tube effectively. Also, it will be increasing the efficiency of an engine, while having a greatly impact on the development of engine manufacturing and energy industry. This paper is to focus on solving pressure control under high-pressure oil tube. The problems are stable pressure at the inlet of the high-pressure tubing and high-pressure oil tube with no pressure reducing valve and only one nozzle. Regarding the first one, we used the least square method to fit an elastic modulus and pressure data. Then, a differential equation model of pressure and time were set inside high-pressure oil tube. Meanwhile, we also worked on a delayed injection strategy and traversal search algorithm to have results. So, the optimal delayed injection time is 0.23 ms while the one-way valve opening time is 3.06 ms . The maximum offset pressure is about0.3 MPa. The second case which is based on the first case. In order to achieve pressure control, linking the pressure at the inlet of high-pressure oil tube to a cam and using the principle of mass conservation. So, it is stated that the pressure can be stabilized as much as possible when the angular velocity is 0.0275 rad/ms. Finally, we verified the feasibility of the model through simulation analysis.

The "concentric drum" project tests team members' ability of cooperation, and the team members can hit the ball more times by working together. It is a typical dynamic problem. In this paper, the complete elastic collision model and the drum surface segmentation model are established to complete the discrete model. Through the optimization of the system, the good solution results of the problem are obtained gradually. The "concentric drum" strategy based on the discrete model has a certain reference for the solution of dynamic problems.

Let D be a non-trivial 2-(v, k, λ) design with a flag-transitive, point-primitive automorphism group G of almost simple type. If Soc(G) = A₅, one of the alternating groups, then there are precisely 3 such non-isomorphic 2-designs.

Let G be a lollipop graph obtained by appending a cycle C_n to a pendent vertex of a path P_m. In this paper, the signed (| G |−1) - subdomination number of a lollipop graph G is determined by classified discussion and exhaustived method.

Recognizing and understanding the behavior of the campus crowd is of great significance for improving the comprehensive management capabilities of the campus. The increasingly abundant of mobile terminal WIFI signals provide a unique data source for studying the behavior of the campus crowd. A Wifi-based personnel activity monitoring system is developed in this paper. Through monitoring and analyzing the MAC address (Media Access Control Address), RSSI (Received Signal Strength Indication) and Wireless AP (Access Point) in and around the Science Museum, Huaizhou building of Yunnan University, the association between WIFI signal and the crowd behavior is studied. Time series analysis is used to make predictions, and some valuable information about the gathering and activity status of campus crowd behavior is obtained. It provides an experimental platform for studying the dynamic behavior of people in campus or other crowd areas.

In this paper, we discuss the optimal allocation problem in a multi-level experiment when the cost of running the experiment at each level is taken into consideration. An objective function with cost consideration is proposed and the properties of the objective function are discussed. The procedure to the algorithm to obtain the optimal allocation is presented. Numerical examples are used to illustrate the methodology developed here.

In the precision marketing of a new product, it is a challenge to allocate limited resources to the target customer groups with different characteristics. We presented a framework using distance-based algorithm, K-Nearest-Neighbour, and support vector machine to capture customers' preference towards promotion channel. Additionally, on-line learning programming was combined with machine learning strategies to fit a dynamic environment, evaluating its performance through a parsimonious model of minimum regret. A resource optimization model was proposed using classification results as input. In particular, we collected data from a loan agency that offers loans to small business merchants. Our sample contained 525,919 customers who will be introduced to a new financial product. By simulating different scenarios between resources and demand, we showed an up to 22.42% increase in the number of expected merchants when K-NN was performed with optimal resource allocation strategy. Our results also show that K-NN is the most stable method to perform classification, and that distance-based algorithm has the most efficient adoption with on-line learning.

Our paper mainly studies the integrated application of weight graph, correlation coefficient and Leontief function to regional drug trading. To be better understood, we establish our model on the analysis of drug transaction among 5 states in America, including Ohio, Kentucky, West Virginia, Virginia and Pennsylvania. First, we build the weight graph with 5 states as vertexes to calculate the transaction strength of each state with others to predict the drug diffusion trend. And based on equilibrium analysis, we find that only the drug market in Ohio hasn't reached balanced state, which means the drug sale will increases. Second, we select 13 socio-economic indicators, aiming to use correlation analysis to reflect their influence on drug diffusion. We find that more incomplete households, more population with bad marital status and with low educational attainment probably ascend the drug cases. Third, we apply Leontief function to analysing how the drug production change when the quantity of material, transportation, fixed capital, workforce and demand, 5 main parts in the complete industrial chain are changing. Therefore, it may help to come up with some practical ways of controlling the illegal drug transaction.

In this paper, we introduce a nearly unit root processes with ARFIMA(p; d; q)-GARCH(l;m) errors, and establish an asymptotic theorem for the autoregressive coefficient estimation of the proposed model under very mild conditions. It's shown that the DF-type tests are functionals of the Ornstein-Uhlenbeck process rather than those of standard Brownian motions in the unit root case.

Magnetoencephalography (MEG) is a kind of brain function detection technology without trauma, which detects the electromagnetic physiological signal in the brain. It is widely used in depression research. We used permutation entropy, improved permutation entropy, conditional entropy to study the difference of MEG between depressed patients and healthy people, respectively. We implement three different entropy algorithms and compare the relative differences of entropy values in different brain regions of healthy people and depression patients under positive, neutral and negative emotional stimuli. The experimental results show that the relative difference of conditional entropy > the relative difference of improved permutation entropy > the relative difference of permutation entropy, and the difference of entropy value in the frontal region of human brain is the most obvious, which may provide the basis for the diagnosis of depression.

For the inverse problem of dynamic load identification in short duration wind tunnels, high system ill-posedness is a main cause leading to instability and low accuracy. In this study, an efficient method is proposed to reduce ill-posedness and identify dynamic load stably. The load to be identified is written as superposition of specific basis functions and each basis function is determined by specific parameters. A genetic algorithm is built to solve the parameters and construct the load. Compared with Tikhonov regularization method, the basis function method proposed can reduce the ill-posedness and numerical studies demonstrate its efficiency and accuracy.

We use the information entropy based on linear model, K-nearest neighbour estimation and kernel estimation to study the brain, a complex nonlinear dynamic system, and distinguish the nonlinear dynamic complexity of epileptic and normal EEG signals in Bonn database. The entropy estimation method of linear model and K-nearest neighbour estimation can only distinguish the information entropy of epileptic period from that of other two cases, but it can't distinguish the information entropy of epileptic interval and normal EEG signals. However, kernel estimation can distinguish the information entropy of EEG signals in three states well, and the threshold range is [0.1,3]. With the increase of threshold, the discrimination effect is gradually significant until stable, and the discrimination effect is obvious when the threshold is 0.5. The result of analysis indicated that EEG information entropy was the highest in the epileptic seizure period, followed by the epileptic seizure interval, and the lowest in normal human brain.

Named entity recognition (NER) plays an essential role in natural language processing systems. Judicial NER is a fundamental component of judicial information retrieval, entity relation extraction, and knowledge map building. However, Chinese judicial NER remains to be more challenging due to the characteristics of Chinese and high accuracy requirements in the judicial filed. Thus, in this paper, we propose a deep learning-based method named BiLSTM-CRF which consists of bi-directional long short-term memory (BiLSTM) and conditional random fields (CRF). For further accuracy promotion, we propose to use Adaptive moment estimation (Adam) for optimization of the model. To validate our method, we perform experiments on judgment documents including commutation, parole and temporary service outside prison, which is acquired from China Judgments Online. Experimental results achieve the accuracy of 0.876, recall of 0.856 and F1 score of 0.855, which suggests the superiority of the proposed BiLSTM-CRF with Adam optimizer.

Aiming at the identification of adulterated olive oil, based on the fusion of near-infrared and Raman data on the feature level, a model for the identification of adulterated olive oil was established.24 pure olive oil samples and 248 adulterated olive oil samples were used for model establishment in the experiment. With three parameter optimization methods, support vector machine classification and regression models were established based on fusion of near-infrared and Raman data on the feature level with canonical correlation analysis (CCA). The results showed that the accuracy of correction and prediction sets of olive oil adulteration classification model based on the fusion of near-infrared and Raman data was high, and the correlation coefficient of prediction model based on the fusion of near-infrared and Raman data reached 99.13%. The results showed that the classification and prediction models were feasible and effective in the identification of adulterated olive oils, and this work shed light on the development and applications of fusion of spectral data.

S block is located in the eastern margin of Surat basin, with large area and great difference in geological conditions. How to optimize the sweet spot development zone is the key to achieve the economic and efficient development of the block. Based on the static and dynamic data, this paper conducts the sensitivity analysis for peak gas rate of well, Estimated ultimate recovery(EUR) of well and coal reservoir geological parameters. On the precondition of coal seam permeability higher than 100md, the coal seam thickness and gas content are the main factors affecting the development effect. According to the differences of key reservoir parameters, four types of reservoirs are divided: type 1 reservoir thickness≥20m, dry-ash-free gas content≥4m³/t; type 2 reservoir Thickness ≥20m, dry-ash-free gas content between 3.6-4m³/t; type 3 reservoir thickness between 10-20m, dry-ash-free gas content between 3.2-3.6m³/t; type 4 reservoir thickness between 10-20m, dry-ash-free gas content between 2.8-3.2m³/t. Considering the reserve abundance and exploitable value, reservoirs of type 1 and 2 are considered as the development sweet spot area, which provides guidance for optimum selection of development area of coalbed methane(CBM) in S block of Surat basin.

In this paper, we focus on deep semi-nonnegative matrix factorization (DSemiNMF) which has a wider application in the real world than traditional NMF. We propose an efficient algorithm based on the classic alternating direction method of multipliers (ADMM) for DSemiNMF. By utilizing structures in DSemiNMF, we derive an efficient updating rule for updating subproblems according to its KKT conditions. Numerical experiments are conducted to compare the proposed algorithm with state-of-the-art deep semi-NMF algorithm. Results show that our algorithm performs better and the deep model indeed results in better clustering accuracy than single-layer model.

Utilizing time-varying VAR model and impulse response analysis, we examine the dynamic impact of volatility from foreign companies listed and their contribution to the main stock market in Japanese, Korean, Hong Kong and Singapore markets during the period of 20002018. We find that the host markets have a positive response to volatility effects of foreign companies, more specifically, the increase of the foreign company volatility will cause the increase of the host market volatility. Results show that volatility of foreign companies from mature markets did not cause more volatility in host markets. Interestingly, foreign companies from emerging markets will bring stronger volatility spillover to host markets.

Considering the limitation of AHP-fuzzy comprehensive evaluation method on the isomorphism and mutual exclusion of comment sets, it is difficult to use this method to evaluate actual cases with different dimension comment sets or check comment grades. This paper propounded an improved AHP-fuzzy comprehensive evaluation method with heterogeneous and check comment set, and the proposed method was further applied to the comprehensive evaluation of the evaluation state of collegiate teaching quality. Results illustrated that the improved method excelled not only in analysing and comparing the membership degree of each evaluation grade of the ultimate evaluation factors, but also in examining and evaluating the expected compliancedegree of each evaluation factor. The evaluation results were demonstrated to be more objective, accurate and applicable in a much wider scope.

The LSMR (Least Squares Minimal Residual) method is an absorbing solver that can solve linear system Ax = b and least squares problem min ||Ax = b|| where A is a sparse and large matrix. This method is based on the Golub-Kahan bidiagonalization process and sometimes it may converge slowly like other methods. I n order to prevent this event, a right preconditioner for LSMR method is presented to solve large and sparse linear system which used for LSQR (Least Squares with QR factorization) method before. Numerical examples and comparing the preconditioned LSMR method to unpreconditioned LSMR method would show the effectiveness of the preconditioner. I t is obtained from this paper that PLSMR (Preconditioned LSMR) method has a better performance in reducing the number of iterations and relative residual norm in comparing with the original LSMR method.

Evolutionary equations containing fractional derivatives have been widely used in financial models and can describe anomalous diffusion and transmission dynamics in some complex systems. We assumes that option pricing obeys the infinite jump CGMY process and treats stock price fluctuations as a fractal transmission system, A time fractional CGMY option pricing (TFCGMY) model is obtained. The L1 approximation of the Caputo fractional derivative and the modified GL approximation are used to discretize the time and space fractional order operators; the first order space derivative is discretized using the central difference quotient. The TFCGMY model and the above numerical techniques are used for the pricing analysis of European call options. By comparing and analyzing the option pricing model with the Black-Scholes model and the CGMY model shows that the introduction of time fractional differentiation can better capture the jump characteristics of stock prices of options.

In this paper, we intend to develop an effective numerical method to solve a class of two-dimensional space-fractional advection-diffusion-reaction equations. After spatially discretizing this equation using the fractional centered difference formula, it leads to a system of nonlinear ordinary differential equations. The compact implicit integration factor method is applied to solve the resulting system to achieve good stability and robustness. Linear stability analysis and numerical experiments are given to verify that the compact implicit integration factor method has excellent efficiency and stability properties.

It is well known that nonsymmetric algebraic Riccati equation can be efficiently solved by using the structure-preserving doubling algorithm (SDA) with the shift-and-shrink transformation and the corresponding doubling algorithm is called the SDA-ss. In this paper, we propose an improved SDA-ss algorithm. Preliminary numerical experiments show that the algorithm is efficient to derive the minimal nonnegative solution of nonsymmetric algebraic Riccati equation with M-matrix.

Our aim in this paper is to study a three-order fuzzy difference equation. Firstly, the fuzzy set theory is used to transform the fuzzy difference equation into the corresponding ordinary difference equations with parameters α, α ∊ (0,1]. And then, the existence and uniqueness for the solution to the ordinary difference equations are obtained by the iteration method, the inequality technique and the mathematical induction. Finally, the existence and uniqueness for the solution of the fuzzy difference equation is proved.

In this paper a class of fuzzy linear matrix equation AXB=C in which A and B are crisp matrices and C is a fuzzy numbers matrix, is investigated by using the embedding approach. A new matrix method for calculating the solution is designed in detail and a sufficient condition for the existence of strong fuzzy solution is derived. An example is given to illustrate our proposed method. Our result enriches the fuzzy linear systems theory.

Credit supervision is not only an important institutional arrangement for the construction of social credit system, but also one of the main ways to give full play to the value and role of credit. The risk evaluation of enterprise credit supervision can provide important reference for classified supervision. The research on the risk evaluation model and indicators of enterprise credit supervision is of great significance to improve the scientificity and accuracy of enterprise credit supervision risk evaluation. Through the research and analysis of enterprise credit supervision risk evaluation model and evaluation index, the fuzzy matter-element evaluation model is constructed, and the comprehensive weight of enterprise credit supervision risk evaluation index is calculated by subjective and objective weighting methods respectively, and the main factors affecting the level of enterprise credit supervision risk are analyzed, so as to provide suggestions for enterprises to carry out credit supervision risk evaluation and strengthen credit supervision risk management It provides a scientific reference.

This study was focused on understanding the learning effect and influencing factors affecting students at home during the epidemic, better help the college students in improving their learning efficiency, and achieving the state of "no suspension of classes". At first, we considered the students of science and engineering of Shandong University of management as an example to collect the relevant data through the questionnaire; secondly, with the help of SPSS 23.0 software, factor analysis method is used to obtain three public factors affecting the learning outcomes of students: external interference factor, curriculum factor, and emotional factor. At last, the actual situation of students and the results of the questionnaire have been combined in this paper, which puts forward practical improvement measures from the viewpoint of teachers and students.

In this paper, we study oscillatory behavior of a class of second-order mixed nonlinear neutral delay differential equation. By using of extended Riccati transformation, integral averaging and inequality technique, a new oscillation criteria of the equation were established, which had extended the results in the recent literatures.

This paper concerns the reconstruction of the support of source function based on the Bayesian level set approach. The unknown source to be reconstructed is assumed to be piecewise constant with a known value. In this setting, the support of the source function can be characterized by the level set functions. In the Bayesian level set inversion, the solution of the inverse problem is posterior distribution. The Markov Chain Monte Carlo (MCMC) algorithm is applied to generate the samples of the posterior distribution. The numerical results show the effectiveness of the proposed method and the dependence of the posterior samples on the flexible and proper smoothness priors with the Whittle-Matérn Gaussian random fields.

The distance Laplacian matrix and the distance signless Laplacian matrix of a connected graph G are defined by L_D(G) = Tr_G−D(G) and Q_D(G) = Tr_G + D(G). By a harmonious labelings of vertex set, the distance matrix of windmill graphs $${K _n^{(m)}}$$ is described as a block matrix. In this paper, we obtain the eigenvalues and the corresponding eigenvectors of the distance matrix, the distance Laplacian matrix and the distance signless Laplacian matrix of windmill graphs $${K _n^{(m)}}$$.

Due to many factors affecting the production of low rank coalbed methane (CBM), it is difficult to predict the productivity. The difference of production ramp-up period is large, the fitting of peak production and peak date is difficult, and the efficiency of existing production prediction methods is limited. Based on the characteristics of typical curves of CBM, a new method is established in this paper. Based on the previous accurate history match of reservoir simulation and analysis of the characteristics of typical curves of production index, water gas ratio, pressure and cumulative water production of typical wells, a rate-cumulative water-method (RCM) mathematical model is established by using non-linear fitting method. The mathematical model is determined by historical fitting. The model parameters can predict the output of CBM quickly and accurately, and provide the production prediction data for the scheme formulation and field decision-making. Compared with other prediction methods, RCM improves the history fitting through correlation analysis, improves the reliability of prediction results. It can predict gas well production in both production ramp-up and declining periods. It does not need to update the reservoir model and is less time-consuming. So it is particularly suitable for predicting the production for a large number of wells in a short time. By comparing the production history of CBM wells in "A" block, the accuracy of RCM prediction result is verified.

In this paper, we find the entire solutions of two classes of nonlinear difference equations when the solution is an exponential polynomial by using the new obtained Clunie Lemma. Some examples are given to show the existence of the solutions.

In this paper, we consider a coupled chemotaxis-fluid system in a 3D unbounded domain with mixed boundary conditions. A blow-up criterion for such a system is established by using the proper elliptic estimates and Stokes estimates under some assumptions on the chemotactic sensitivity function.

Medical postgraduate students (MPS) can select the appropriate statistical methods to do the SPSS experiments and view the experimental results after they have taken SPSS course. It is vital for MPS to exactly convert SPSS experiment results into three-line table in their academic papers. This paper investigated the Ability of MPS in Expressing SPSS experiment Results with Three-Line Table (AERTLT). The enrolled MPS in Southwest Medical University filled in the questionnaire about AERTLT on Jan, 2019. Questionnaire data are analysed using Multiple Linear Regression (MLR). Complex decision factor R²=0.834254 and adjoint probability p<0.001 in MLR suggest the linear correlation between AERTLT and 16 factors passes test. Then backward deletion variable method is employed to repeatedly delete the factor whose coefficient is the minimum value in partial f-test. AERTLT can be expressed by four significant factors i.e. "Analytical results in comparison of mean and population mean", "Analytical results in regression analysis", "Comment description in three-line table", and "P-Error in insufficient sample size or unsatisfactory univariate analysis". These four factors are the key point for SPSS course to cultivate MPS in the medical universities and colleges.

In this paper, the binary images of 100 kinds of leaves are used for leaf recognition. Firstly, we screen 35 important features and use the grey clustering analysis to establish the quantitative feature system of leaves. Then we use the gradient descent tree algorithm (GBDT) to select core features and use probabilistic neural network (PNN) to recognize and classify leaves, constructing a hybrid GBDT-PNN model. In the end, we obtain the classification results of leaves to evaluate model performance and the influence of core features on the model. The results show that the accuracy rate of GBDT-PNN model using 12 core features is 92.75%. And the accuracy rate with all 35 features is 93.5%. It illustrates that the model has great performance and core features have high influence on the model. By comparing with other commonly used deep learning algorithms and models, it is verified that the GBDT-PNN image recognition and classification model is effective and has high accuracy.

Let ${\mathbb{D}}$ = {z : |z| < 1} be the unit disk in the complex plane C, Φ : ${\mathbb{D}}$ → C is a analytic map. We study the multiplication operator M_Φ on the logarithmic weighted BMOA space $BMO{A}_{\mathrm{log}}=\{g\in H({\mathbb{D}}):{\sup }_{a\in {\mathbb{D}}}{(\mathrm{log}\frac{2}{1-|a{|}^{2}})}^{2}{\int }_{{\mathbb{D}}}{|{g}^{{\rm{{\prime} }}}(z)|}^{2}(1-{|{\varphi }_{a}(z)|}^{2})dm(z)\lt {\rm{\infty }}\}$. We obtain that a sufficient condition for the operator M_Φ to be a bounded operator on BMOA_log. We also get that another necessary condition for the operator M_Φ to be bounded on BMOA_log.

Based on the thorough analysis of the factors affecting the credit level of commercial circulation enterprises, a scientific and systematic evaluation index system was established. By adopting the fuzzy matter-element analytical method, which especially suits the multi-index and incompatibility issue, the evaluation model was built. The comprehensive integrated weighting method was applied for the determination of the index weight. Meanwhile, the subjective and objective information were considered comprehensively to elaborate the inherent law of the commercial circulation enterprise credit risk evaluation, which provide a practical and effective method for judging the credit level of commercial circulation enterprises and analyzing the key influencing factors of credit evaluation, and also provide a direction and reference for improving the credit level of commercial circulation enterprises.

Euclidean dot product plays an important role in data analysis and relation comparison for its intuitive properties. However, for some complicated structures, for example, time series, it would be insufficient to construct a complete theory via this product. In order to resolve and accommodate these issues, we devise a dynamical-scanning inner product which would take the interaction, in particular in the sense of time shift, between two vectors into consideration and yield a relation that contains much more information. Though this device is based on Euclidean dot product, it is more much suitable and flexible for handling some complicated mathematical objects. In addition, we also construct a dynamical-scanning inner product for function spaces. In the end, we show how to apply our devices on both matrix representations and time series. These exploration might delve into some intrinsic properties of some mathematical concepts or models.

Football is one of the sports that can reflect the importance of teamwork. The passing on the football field can be regarded as a closely connected network. This paper takes Everton as the research object, and a passing network is set up with players as nodes. Based on the method of complex network, this paper summarizes the tactical style of the team from the perspective of the whole season. At the same time, this paper selects two representative games and analyzes them dynamically according to minutes, and finds out the problem that the team does not implement the passing tactics in place. In addition, this paper constructs node performance evaluation indicator system, from three aspects of attack, transmission and defense, using AHP to determine the weight, in order to evaluate player's personal ability. According to the network model and performance evaluation system, we give some suggestions from the formation, tactics and players. The 4-2-3-1 formation get the highest evaluation. The tactics of passing and defending counterattack should be designed. In addition, the Everton is necessary to introduce some midfields and left defenders.

In this paper, we focus on sparse dictionary learning that is widely used as a data processing technique in many real-world applications. Based on the frame of alternating direction method of multiplier (ADMM), we extend to an alternating direction and projection method for sparse dictionary learning. By introducing proximal mapping and the equivalence to the corresponding projection, a partial convergence result of this multi-block and nonconvex ADMM algorithm is given that the algorithm converges to a Karush-Kuhn-Tucker point whenever it converges.

The existing Poisson-disk sampling methods work well in traditional space, whatever two dimensional or three dimensional space. However, there are few methods on generating random points in non-Euclid space. For generating uniform points on the cylinder surface, we propose an algorithm which combines Poisson-Disk sampling algorithm with cylindrical distance constraints in this paper. Experiment results show that the quality of the point set generated by the proposed algorithm is better than that generated by the pseudo-random number method in both uniformity and stability.

This paper focuses on numerically solving the time fractional reaction-diffusion equation on the whole line. A numerical scheme is constructed based on Hermite pseudospectral method, we use finite difference scheme in time direction while Hermite-Gauss points in space. Several numerical results for the Hermite pseudospectral scheme are provided to confirm that a second-order time accuracy and spectral accuracy in space can be obtained.

We introduce and analyze an age-structured model with staged-progression. The results reveal that the disease-free equilibrium is globally stable if the basic reproductive number R₀ < 1, and the disease is uniformly persistent for R₀>1. Numerical simulations are performed based on hepatitis C, illustrating the effects of infection age on dynamical process.

In the paper, an extended one-dimensional lattice hydrodynamic model is proposed to investigate the related factors on a gyroidal road (i.e. a curved road with a slope). We investigate the related influences on uniform traffic jam analytically and numerically. Based on control theory, condition for no traffic jam is obtained analytically. Finally, simulations are carried out to verify the new lattice hydrodynamic model and numerical simulations are consistent with the theoretical results.Results show that the related factors including the friction coefficient, radius of curvature and slope of a gyroidal road have major effect on the stability of traffic flow respectively.

In order to ensure the efficiency of daily passage on campus and prevent the occurrence of safety accidents, an improved prediction method of optimized BP neural network based on modified particle swarm optimization algorithm (PSO) was proposed. In this modified PSO algorithm, we propose a mutation operator to avoid particles plunging into local optimization, using the modified PSO algorithm to optimize the solution of weight and threshold in BP neural network. The prediction method is applied to the time series of the observed campus traffic flow for effective verification, and the result shows that the method has better nonlinear fitting ability and higher prediction accuracy for the short-term traffic flow on campus.

This paper studies the valuation effect of time-varying and the difference between different markets of overseas companies cross-listing on the host market. Using the data of the Hong Kong market from 1991 to 2018, we adopt the event study method and multiple regression model to analyse the short- and long-term valuation effect, respectively. Furthermore, two-stage least squares (2SLS) regression are utilized to address the endogeneity. We find that the valuation of foreign company listings on the host market change with the duration and have a significant short-term positive spillover effect. However, the long-term spillover effect is related to the company's home market. This study provides new insights into foreign cross-listing company valuation, offering a few implications for the establishment of a Chinese International Board.

As one of the important oil crops in China, soybean plays a significant place in the national food security system. This article analyzes the comparative advantages of soybean producing areas in China and further divides the advantage of soybean production into the advantage of scale and the advantage of efficiency. In addition, it adopts the advantage index to objectively describe the advantageous areas of soybean production and the comparison of scale advantage and efficiency advantage in these areas since 1978. Through the research, the article obtains the following findings: (1) Since the Reform and Opening Up, scale advantage has still been the determinant to the soybean production advantages of an area. While soybean production has been even more concentrated in soybean producing areas of Heilongjiang and Inner Mongolia, the efficiency advantage index in these two provinces has not been improved in the same pace. (2) The status of efficiency advantage has been constantly rising in other producing areas with the most comparative advantage (other than Heilongjiang and Inner Mongolia) and those with the least comparative advantage. The disadvantageous producing areas have gradually bettered the suitability of soybean production through breeding of fine varieties and high-quality cultivation. (3) The disadvantageous soybean producing areas can become the advantageous areas of soybean production depending on efficiency advantage, and the soybean producing areas with scale advantage can further improve their efficiency of soybean planting. This research provides a scientific reference for the regional deployment of soybean planting in China as well as a scientific basis for policy making.

Patients with Type 2 Diabetes Mellitus (T2DM) die every eight seconds in the world. T2DM is still not eradicated at home and abroad at present, thus "just control". A balanced diet and aerobic exercise (intervention treatment) can reduce risk factors and the incidence of diabetes and diabetic complications, which prevents or delays the onset and progression. The survey of people's knowledge of balanced diet and aerobic exercise has been conducted in Luzhou, Neijiang, Nanchong and Ziyang of Sichuan province and Tongren of Guizhou province from June to September 2019. A total of 865 subjects' questionnaires have been collected. Taking prediabetes as baseline, people's knowledge difference of balanced diet and aerobic exercise is compared forwards in low- or high-risk stage and backwards in the diabetes stage and diabetic complication stage through Pearson χ² test and the correlation coefficient Cramer's V and Φ. The knowledge difference in prediabetes and high-risk (χ²=4.2996, p=0.0224, Cramer's Φ=0.1038) is statistically significant, and the difference in prediabetes and diabetic complications (χ²=231.5272, p< 0.0000001, Cramer's Φ=0.5905) is also statistically significant. Knowledge of balanced diet and aerobic exercise at prediabetes stage is significantly higher than that in high-risk and that in diabetic complications. Doctors, nurses and researchers should use the Internet and door-to-door to educate people about the importance of balanced diet and aerobic exercise during prediabetes and diabetic complications in T2DM.

In this paper, we discuss the exact controllability of a first-order hyperbolic equation with an intermediate point memory by boundary control. We choose a Volterra and Fredholm transformation transferring the original control system into a target control system with controllability property. Then, we prove the exact controllability of the original control system in terms of the invertibility of the transformation and the controllability of the target control system.

This paper aims to investigate economics welfare gain from main rice export countries, namely India, Thailand, and Vietnam, by measuring the demand and supply of exporters and importers estimated by the copula-based Simultaneous ECM Approach. This model exploits a benefit of copula functions which allow the error's distribution of both demand and supply equations to have more realistic distributions. The highlighted empirical results show the adjustment of importing countries to the equilibrium. Thai rice export market can adjust better than the other two countries. This means that the export market is very strong. In the supply side, India is the fastest country in adjusting to its equilibrium. For the economic welfare aspect, the most welfare benefits in Thai rice trade belong to importing countries. Whereas, the most welfare benefits in India rice trade belong to exporting countries.

In this paper we propose a generalized estimating equations method to joint model the mean and correlation structures for longitudinal binary data based on Gaussian copula, and apply it to a large cohort study for the UK's North Staffordshire Osteoarthritis Project (NorStOP), where the responses can be pre-processed to binary variables. The resulting estimators for the mean and correlation parameters are proven to be consistent and asymptotically normally distributed. Since the theory and simulation results were studied in our previous manuscript [1], we give a brief introduction of our approach but mainly focus on its application to the NorStOP data.

The empirical analysis of this paper focuses on two issues, one is the impact of China's aging process on China's domestic tourism economy, and to what extent; the other is how to define and measure the impact of tourism culture on tourism economy. This research takes the domestic tourism revenue as the dependent variable and takes the elderly dependency ratio as the indepedent variable. In the modelling process, "external conditions" and "internal desires" are introduced as control variables and regarded as the software and hardware parts of tourism culture respectively. The time dummy variable is used to catch outliers and structural abrupt changes. Furthermore, quantile regression is carried out for the selected models. Based on ADL model and quantile regression, this paper analyzed the influence of aging and tourism culture on the development of China's tourism economy and its changing trend.

According to the observation of schools in Indonesia, the quadratic function graph is a lesson for junior high school students. For it is an abstract concept, students have difficulties to understand and picture out the graph functions. The main purpose of this research is to design a learning media to improve students' learning achievement by using hawgent dynamic mathematic software. The method of this research is research and development method. The target audience of this research were 32 students in experimental class and 32 students in controlled class. The result of this research is the material expert, research and media experts obtaining "valid" criteria. This means that the software is better than traditional teaching methods as students are able to easily visualise and generalise the graphical form of the quadratic equation. This automatically increases student's learning achievement and makes them find math interesting.

We uses markov evaluation model to evaluate the effectiveness of STC teaching (STC teaching mode is a method of combining online services and offline services mode of "Self-directed learning-Traditional teaching-Collaborative learning"). In the 2018-2019 academic year, Control class group (traditional teaching mode) and experimental class group (STC teaching mode) will be taught for the Advanced Mathematics Teaching of college students of science. We use the score data of the two classes as the evaluation basis. The results show that the STC teaching effect is significant.

For a prime 2, let n be a positive integer, and F_2ⁿ be the finite field with 2ⁿ elements. In this paper, we propose several classes of permutation polynomials with the form (x^k + x)^s + x²ⁿ⁻² over finite fields F_2ⁿ which have the highest degree of algebra.

Interval Farkas type inequality is an important tool to prove the optimality condition of interval optimization model. This research gives a Farkas-type inequality for AE solvability of a specific mixed interval linear system including both equality and inequality by using logical quantifiers. Some Farkas-type inequalities for different solvability established in previous literatures are special cases of the main result of this paper.

With a closed environment and dense population, urban metros are difficult to evacuate quickly in the case of fire, which often leads to serious consequences such as stampedes. To deal with metro fires effectively, this paper presents a three-dimensional model for assessing the failure probability of personnel protection. First, scenario elements of metro fire evolution were selected based on typical cases and traditional performance-based evaluation methods, and a scenario element database was constructed. Second, based on this approach, a three-dimensional evolution model of the metro fire scenario was established to visually express the interaction relationship of each scenario element in plane dimensions. Finally, an evaluation model of the personnel protection failure risk index was constructed by coupling the metro fire, emergency management and trapped personnel, and the failure probability of personnel protection was calculated. This model can evaluate the real-time risk of death in the process of metro fire accidents and provide an important reference for emergency decisions and plan deployment.

Based on the deficiencies of the existing research on the credit line of supply chain enterprises, this paper taking data sharing as research perspective, established the credit model of supply chain enterprises using data sharing. Through the case study of L Corporation Group, it is found that: 1) the supply chain can integrate information advantages, increase credit line and reduce financing costs; 2) the credit line of supply chain enterprises raises with the increase of data sharing degree; 3) the existing credit models of the banks are conservative, the actual credit line of enterprises is insufficient. The credit model constructed in the paper fully considers the effects of data sharing of related transactions between enterprises on the credit line in the context of supply chain, which can provide ideas for realizing the win-win situation of maximizing the financing scale of supply chain enterprises and minimizing the risk of banks.

In this paper, we constructed a three-parameter general social collaboration network model (GCNM) using both similarity-based strategy and copying-based strategy. In this model, a connection can be introduced between two nodes if they are similar in attributes or similar in structure (i.e., have many common friends). This model can match various types of real-world social networks by just choosing different values for three parameters, and therefore, can reproduce observed real network characteristics. Particularly, three widely studied models (similarity-based, copying-based, and pure preferential attachment (PA)) are only the special cases of this new model. Specifically, this new model possesses following new characteristics which existing models have difficulty to fulfill in all: 1) it not only exhibits the high average clustering coefficient, but also the high global clustering coefficient and explicit community structure (great number of triangles); 2) it not only makes the connections between the new node and existing nodes, but also between existing nodes; and 3) it has not only linear, but also non-linear relationship between the linking probability and the degree (the connectivity of nodes). Numerical results, which are in good agreement with real-world datasets from different fields, demonstrated all of these.

We first consider the zeros of a big class generalized q-difference polynomials in entire function which come from the Hayman problem. Second, we research about uniqueness result of the class q-difference polynomials in entire function which share a value. Our results improved or generalize the previous known results.

It has been shown that a 4 x 4 tree sign pattern is spectrally arbitrary if and only if it is potentially stable and potentially nilpotent in [M. Arav, F. Hall, Z. Li, K. Kaphle, N. Manzagol, spectrally arbitrary tree sign patterns of order 4, Electron. J. Linear Algebra, 20 (2010), 180-197], where the authors asked whether the above important theorem can be extended to the 5 x 5 case. In this paper, we negatively answer this question by constructing a 5x5 potentially stable and potentially nilpotent tree sign pattern which is shown to be not spectrally arbitrary.

Being the country of origin of soybean, China was once the biggest producer of the world, and has become the largest importer by now. Various regions of China are seeing profound changes of soybean production. By analyzing the changes of soybean producing areas in China from 1978 to 2017, this article revealed the characteristics of soybean's spatial variation in terms of the planting area and yield per unit area in the four decades in China and comprehensively explained the present situation and future potential growth of soybean production in China based on soybean growth characteristics and the resources in various regions. The results show that: (1) Since the Reform and Opening Up, the traditional main producing areas still maintain their principal part but show certain changes of geographical distribution; (2) The regional distribution of soybean production shows an overall trend of "concentrated over vast areas and dispersed in small areas"; (3) The planting areas of soybean are increasing steadily in Heilongjiang, Inner Mongolia, Jilin, He'nan and Anhui, while those are decreasing rapidly in Huang-Huai-Hai area and the southern area.

Rumor spreading has a profound influence on daily lives. There are several factors influencing rumor spreading. In this paper, we assume that there are two kinds of individuals in the crowd: those who do not know the rumors and those who learn about the rumors. And in the latter category, there are two attitudes toward rumors: those who are convinced of rumors and those who hold an objective attitude. Those convinced and objective individuals form a public opinion environmental factor conducive to the spread of rumors. Based on the public opinion environmental influence whose intensity decays with time, a model with two attitudes toward rumors is established. With numerical simulations, we illustrated the conversion state of three categories because of public opinion environmental factors, analyzing the sensitivity of the model. The results showed that it is beneficial to control the rumor propagation when controlling the influence of those who are convinced of rumors and those who hold an objective attitude rather than constraining one of them individually. And it was commonsensical that increasing the attenuation intensity of the two attitude rumors was also an effective way conducive to the control.

This paper deals with the inverse Sturm-Liouville problem with one discontinuous point on the three-star graph, suppose the potential is known on all edges except one, the one which has discontinuous point, we deduce the distribution of the eigenvalues, and prove that one spectrum uniquely determines a part of jump information. And by the reasonable assumption, we prove that if all the eigenvalues are simple, then one spectrum uniquely determines the unknown potential, too.

Inspired by Kirchhoff dynamic analogy, we write the Kirchhoff equation of thin elastic rod in form of curvature expression. Compared it with nonlinear Schrödinger equation, we extend a Jacobi elliptic function analogy solution to elastic rod equation and give a new alternative way to solve the Kirchhoff equation.

Compatible modifications to original Menter model (OMM) are incorporated using an elliptic relaxation approach to accurately accounting non-local characteristics accompanied by near-wall turbulence. Coefficients/functions of improved Menter model (IMM) are parameterized with the elliptic relaxation function to imitate the combined effects of near-wall turbulence and non-equilibrium. The characteristic length scale involved in the elliptic relaxation scheme is constructed in terms of viscous and turbulent length scales in conjunction with a non-singular strain-rate invariant. Non-local effects are consequently reinforced by the mean flow and turbulent variables. A non-linear eddy-viscosity damping function is invoked to relax the viscous length-scale coefficient pertaining to the elliptic relaxation model. Comparisons indicate that the IMM substantially improves the accuracy of flow simulations compared to the OMM and widely used Spalart-Allmaras (SA) model. A good consensus is obtained between IMM and DNS (direct numerical simulation)/measured data.

In this paper, multivariable sign transfer entropy algorithm is used to calculate the multivariable sign transfer entropy values of the same brain region and different brain regions stimulated by different emotional images in patients with depression and healthy control group. The connectivity of the magnetic channels in the brain region and between brain regions is studied. And the conclusions of negative cognitive bias in depressed patients [1] and functional asymmetry of emotion of cerebral hemispheres are verified [2]. The results showed that: For different brain regions, the left occipital region →frontal region under positive emotional picture stimulation and neutral emotional picture stimulation can significantly distinguish the depressed patients' group from the healthy control group, the corresponding connection strength of depressed patients was significantly weaker than that of healthy control group.

Many inventory models have been established based on determined demand but ignore the fact that demand can be affected by random factors. A procurement model considering random demand, different trade credit and cash discount is established in this paper. Due to the randomness of demand, possibilities of salvage or stock out at the end of the cycle are considered, and these cases can be dealt as classic news vendor problem. The optimal procurement strategy for the expected profit is derived by some theoretical results in this paper, which are also illustrated by a series of numerical examples and the corresponding sensitivity analyses are also presented.

In this study, we attempt to understand the effects of the accuracy order of higher-order Runge-Kutta methods on the turbulence statistics of incompressible wall turbulence. A second-order central difference scheme is used to spatially discretize the governing equations, considering the widely used lower-order spatial discretization. The effects of the difference in the order of the Runge-Kutta scheme are investigated using a turbulent channel flow. The turbulence statistics obtained are compared with those reported in three previous studies. Based on our results, we infer that the rms values of the mean velocity, mean pressure, Reynolds stress, and velocity fluctuation of the turbulent channel flow are not affected by the difference in the accuracy order of the higher-order Runge-Kutta method. The fluctuation of the rms values of static pressure obtained by using the fourth-order Runge-Kutta method were consistent with those obtained in previous studies.