Existence of Four Periodic Solutions of a Ratio-Dependent Predator-Prey Model with Exploited Terms

We study a non-autonomous ratio-dependent predator-prey model with exploited terms. This model is of periodic coefficients, which incorporates the periodicity of the varying environment. By means of the coincidence degree theory, we establish sufficient conditions for the existence of at least four positive periodic solutions of this model.

Problem-solving model guided by stimulus-organism-response theory:State of mind and coping styles of depressed mothers after cesarean delivery

BACKGROUND The use of a problem-solving model guided by stimulus-organism-response(SOR)theory for women with postpartum depression after cesarean delivery may inform nursing interventions for women with postpartum depression.AIM To explore the state of mind and coping style of women with depression after cesarean delivery guided by SOR theory.METHODS Eighty postpartum depressed women with cesarean delivery admitted to the hospital between January 2022 and October 2023 were selected and divided into two groups of 40 cases each,according to the random number table method.In the control group,the observation group adopted the problem-solving nursing model under SOR theory.The two groups were consecutively intervened for 12 weeks,and the state of mind,coping styles,and degree of post-partum depression were analyzed at the end of the intervention.RESULTS The Edinburgh Postnatal Depression Scale and Hamilton Depression Scale-24-item scores of the observation group were lower than in the control group after care,and the level of improvement in the state of mind was higher than that of the control group(P<0.05).The level of coping with illness in the observation group after care(26.48±3.35)was higher than that in the control group(21.73±3.20),and the level of avoidance(12.04±2.68)and submission(8.14±1.15)was lower than that in the control group(15.75±2.69 and 9.95±1.20),with significant differences(P<0.05).CONCLUSION Adopting the problem-solving nursing model using SOR theory for postpartum depressed mothers after cesarean delivery reduced maternal depression,improved their state of mind,and coping level with illness.

Active contour model based measurement of distance of material serial sections

The measurement of thickness of material removed between serial sections is a crucial step of three-dimensional reconstruction. Active contour model is an efficient method for contour detection of objects on an image. Based on the segmentation of the FeAl/ZrO2 composite image by using adaptive threshold, the gradient vector flow (GVF) snake was used to detect the contour of the indent. The horizontal diagonal length and the vertical diagonal length of the indent contour were acquired by measuring the distance from the uppermost snaxel to the lowermost snaxel and that from the leftmost snaxel to the rightmost snaxel respectively. Then the final diagonal length was gotten by averaging the vertical diagonal length and the horizontal diagonal length. The Vickers indenter was made by a square pyramidal-shaped diamond with opposite faces at an angle of 136°, so the geometrical relation was established between the thickness of material removed between two successive serial sections and the difference of diagonal length on the two serial sections. Based on the relation, the thickness of material removed between two successive serial sections was calculated using the two successive diagonals.

Determination of Polarity Terms of Some Nitrogen-Containing Surfactants and Simulated Hydrophobic Tail Models by Gas Chromatography

Some polarity terms of two groups of nitrogen-containing surfactants （six alkanolamides and nine polyoxyethylenated long chain amines） are measured through gas chromatography. The apparent methanol carbon number (CMeOH) and polarity index （IP） values are determined on the investigated surfactants as stationary phases in packed columns. Similarly, CMeOH and IP values are determined on simulated hydrophobic tail （SHT） models. The obtained results reveal that the introduction of SHT approach permits the distinction between the polarities of different surfactants and their head groups. The measured polarity terms are discussed as related to hydrophile-lipophile balance （HLB） number and the hydrophobic group carbon number （RCN）. Some equations relating the measured polarity values and these variable have been developed.

Comparison of Two Recurrent Neural Networks for Rainfall-Runoff Modeling in the Zou River Basin at Atchérigbé (Bénin)

Hydrological models are developed to simulate river flows over a watershed for many practical applications in the field of water resource management. The present paper compares the performance of two recurrent neural networks for rainfall-runoff modeling in the Zou River basin at Atchérigbé outlet. To this end, we used daily precipitation data over the period 1988-2010 as input of the models, such as the Long Short-Term Memory (LSTM) and Recurrent Gate Networks (GRU) to simulate river discharge in the study area. The investigated models give good results in calibration (R2 = 0.888, NSE = 0.886, and RMSE = 0.42 for LSTM;R2 = 0.9, NSE = 0.9 and RMSE = 0.397 for GRU) and in validation (R2 = 0.865, NSE = 0.851, and RMSE = 0.329 for LSTM;R2 = 0.9, NSE = 0.865 and RMSE = 0.301 for GRU). This good performance of LSTM and GRU models confirms the importance of models based on machine learning in modeling hydrological phenomena for better decision-making.

Capacity model of on-rampmerging section of urban expressway

To establish the empirical capacity model of an on- ramp merging section, the Erlang distribution is first selected to define the time headway distribution, and then the gap acceptance theory is applied to develop the basic capacity model of the on-ramp merging section. Since not all the time headways on the shoulder lane can be made full use of by on- ramp vehicles, a modified capacity model is developed, which takes the usage probability of time headway into consideration. Then, a model of capacity discount coefficient ~： is developed. Finally, based on the modified capacity model and the model of capacity discount coefficient, an empirical merge capacity model which contains the shoulder lane volume, critical gap, and the distance from nose to merging point, is constructed. Results show that, compared with other models, the proposed model is more reasonable since it takes merging section geometry into consideration, and it is easy to apply. The merge capacity varies with the shoulder lane volume, the critical gap, the distance between the nose and the merging point, and the design velocity of the shoulder lane and ramp.

Damage statistical mechanics model of top coal in steep top caving coal

Damage statistical mechanics model of horizontal section height in the top caving was constructed in the paper. The influence factors including supporting pressure, dip angle and characteristic of coal on horizontal section height were analyzed as well. By terms of the practice project analysis, the horizontal section height increases with the increase of dip angle β and thickness of coal seam M. Dip angle of coal seam β has tremendous impact on horizontal section height, while thickness of coal seam M has slight impact. When thickness of coal seam is below 10m, horizontal section height increases sharply. While thickness exceeds 15m, it is not major factor influencing on horizontal section height any long.

3D geological modeling for mineral resource assessment of the Tongshan Cu deposit,Heilongjiang Province,China

Three-dimensional geological modeling （3DGM） assists geologists to quantitatively study in three-dimensional （3D） space structures that define temporal and spatial relationships between geological objects. The 3D property model can also be used to infer or deduce causes of geological objects. 3DGM technology provides technical support for extraction of diverse geoscience information, 3D modeling, and quantitative calculation of mineral resources. Based on metallogenic concepts and an ore deposit model, 3DGM technology is applied to analyze geological characteristics of the Tongshan Cu deposit in order to define a metallogenic model and develop a virtual borehole technology; a BP neural network and a 3D interpolation technique were combined to integrate multiple geoscience information in a 3D environment. The results indicate： （1） on basis of the concept of magmatic-hydrothermal Cu polymetallic mineraliza- tion and a porphyry Cu deposit model, a spatial relational database of multiple geoscience information for mineralization in the study area （geology, geophysics, geochemistry, borehole, and cross-section data） was established, and 3D metallogenic geological objects including mineralization stratum, granodiorite, alteration rock, and magnetic anomaly were constructed; （2） on basis of the 3D ore deposit model, 23,800 effective surveys from 94 boreholes and 21 sections were applied to establish 3D orebody models with a kriging interpolation method; （3） combined 23,800 surveys involving 21 sections, using VC＋＋ and OpenGL platform, virtual borehole and virtual section with BP network, and an improved inverse distance interpolation （IDW） method were used to predict and delineate mineralization potential targets （Cu-grade of cell not less than 0.1%）; （4） comparison of 3D ore bodies, metallogenic geological objects of mineralization, and potential targets of mineralization models in the study area, delineated the 3D spatial and temporal relationship and causal processes among the ore bodies, alteration rock, metallo- genic stratum, intrusive rock, and the Tongshan Fault. This study provides important technical support and a scientific basis for assessment of the Tongshan Cu deposit and surrounding exploration and mineral resources.

A New RCS Statistical Model of Radar Target

In this paper, the drawbacks of conventional target fluctuation models used in radar target modeling are set out. It is usually difficult to statistically model a real target because there are very few parameters which can be used to approximate the probability density function (PDF) of a real target's radar cross section (RCS) in conventional target models. A new method of statistical modeling is suggested, according to which the first nth central moment of real target's RCS, combined with the Legendre orthogonal polynomials, is used to reconstruct the PDF of the target's RCS. The relationship between the coefficients of the Legendre polynomials and the central moments of RCS are deduced mathematically. Through a practical computing example, the error-of-fit is shown as a function of the orders of Legendre coefficients. By comparing the errors-of-fit caused by both the new model and the conventional models, it is concluded that the new nonparametric method for statistical modeling of radar targets is superior.

A Simplified Nonlinear Model of Vertical Vortex-Induced Force on Box Decks for Predicting Stable Amplitudes of Vortex-Induced Vibrations

Wind-tunnel tests of a large-scale sectional model with synchronous measurements of force and vibration responses were carried out to investigate the nonlinear behaviors of vertical vortex-induced forces （VIFs） on three typical box decks （i.e., fully closed box, centrally slotted box, and semi-closed box）. The mechanisms of the onset, development, and self-limiting phenomenon of the vertical vortex-induced vibration （VlV） were also explored by analyzing the energy evolution of different vertical VIF components and their contributions to the vertical VIV responses. The results show that the nonlinear components of the vertical VIF often differ from deck to deck; the most important components of the vertical VIF, governing the stable amplitudes of the vertical VIV responses, are the linear and cubic components of velocity contained in the self-excited aerodynamic damping forces. The former provides a constant negative damping ratio to the vibration system and is thus the essential power driving the development of the VIV amplitude, while the latter provides a positive damping ratio proportional to the square of the vibration velocity and is actually the inherent factor making the VIV amplitude self-limiting. On these bases, a universal simplified nonlinear mathematical model of the vertical VIF on box decks of bridges is presented and verified in this paper; it can be used to predict the stable amplitudes of the vertical VIV of long-span bridges with satisfactory accuracy.

Bayesian-MCMC-based parameter estimation of stealth aircraft RCS models

When modeling a stealth aircraft with low RCS（Radar Cross Section）, conventional parameter estimation methods may cause a deviation from the actual distribution, owing to the fact that the characteristic parameters are estimated via directly calculating the statistics of RCS. The Bayesian–Markov Chain Monte Carlo（Bayesian-MCMC） method is introduced herein to estimate the parameters so as to improve the fitting accuracies of fluctuation models. The parameter estimations of the lognormal and the Legendre polynomial models are reformulated in the Bayesian framework. The MCMC algorithm is then adopted to calculate the parameter estimates. Numerical results show that the distribution curves obtained by the proposed method exhibit improved consistence with the actual ones, compared with those fitted by the conventional method. The fitting accuracy could be improved by no less than 25% for both fluctuation models, which implies that the Bayesian-MCMC method might be a good candidate among the optimal parameter estimation methods for stealth aircraft RCS models.

Analysis of Factors Influencing Insomnia and Construction of a Prediction Model:A Cross-sectional Survey on Rescuers

Objective To determine the factors influencing insomnia and construct early insomnia warning tools for rescuers to informbest practices for early screening and intervention.Methods Cluster sampling was used to conduct a cross-sectional survey of 1,133 rescuers from one unit in Beijing,China.Logistic regression modeling and R software were used to analyze insomniarelated factors and construct a PRISM model,respectively.Results The positive rate of insomnia among rescuers was 2.74%.Accounting for participants’age,education,systolic pressure,smoking,per capita family monthly income,psychological resilience,and cognitive emotion regulation,logistic regression analysis revealed that,compared with families with an average monthly income less than 3,000 yuan,the odds ratio(OR)values and the[95%confidence interval(CI)]for participants of the following categories were as follows:average monthly family income greater than 5,000 yuan:2.998(1.307–6.879),smoking:4.124(1.954–8.706),and psychological resilience:0.960(0.933–0.988).The ROC curve area of the PRISM model(AUC)=0.7650,specificity=0.7169,and sensitivity=0.7419.Conclusion Insomnia was related to the participants’per capita family monthly income,smoking habits,and psychological resilience on rescue workers.The PRISM model’s good diagnostic value advises its use to screen rescuer early sleep quality.Further,advisable interventions to optimize sleep quality and battle effectiveness include psychological resilience training and smoking cessation.

3D Geological Modeling with Multi-source Data Integration in Polymetallic Region:A Case Study of Luanchuan,Henan Province,China

The development of 3D geological models involves the integration of large amounts of geological data,as well as additional accessible proprietary lithological, structural,geochemical,geophysical,and borehole data.Luanchuan,the case study area,southwestern Henan Province,is an important molybdenum-tungsten -lead-zinc polymetallic belt in China.

Size effect on longitudinal MOE of microtomed wood sections and relevant theoretical explanation

It has been repeatedly observed that the mechanical properties of microtomed wood sections are significantly lower than those of samples of normal size, but few investigations have been conducted to deal with this topic, especially based on theoretical approaches. We measured the longitudinal MOE of Chinese fir on microtomed sections ranging in thickness from 70 to 200 μm and compared these with the values of samples of normal size. The results indicate that the MOE of microtomed wood sections increases with thickness from 70 to 200 μm, but is significantly less than that of normal samples. A size effect coefficient of 2.63 is inferred based on statistical data for samples of normal size and 200 μm thick microtomed sections. Finally, an explanation based on a complete shear restraint model of cell walls and a single fiber multi-ply model is proposed for the size effect on stiffness of microtomed wood sections.

AModel for the Optimization of the Shale Gas HorizontalWell Section Based on the Combination of Different Weighting Methods in the Frame of the Game Theory

Existing“evaluation indicators”are selected and combined to build a model to support the optimization of shale gas horizontal wells.Towards this end,different“weighting methods”,including AHP and the so-called entropy method,are combined in the frame of the game theory.Using a relevant test case for the implementation of the model,it is shown that the horizontal section of the considered well is in the middle sweet spot area with good physical properties and fracturing ability.In comparison with the FSI(flow scanner Image)gas production profile,the new model seems to display better abilities for the optimization of horizontal wells.

Cellular automation model for analyzing capacity of branch road section

In order to reduce the traffic pressure of urban arterial road with the rational utilization of the branch road,the vehicle meeting behavior on the branch road without divided lane was described,and the cellular automation (CA) model was put forward by introducing meeting behavior to reflect the relation between safe meeting speed and road width.The numerical simulation results depict several relation curves between road section capacity,speed and road width under different directional distributions of traffic flow,as well as the curves between the major and minor direction saturation flow,speed and road width.These relation characteristics indicate that except the one-way road section capacity and speed remaining unchanged,other road section capacities and speeds under different directional distributions increase with the increase of road width.On narrow road,the two-way traffic capacity and speed are less than those of one-way traffic;on wide road,the two-way traffic capacity doubles that of one-way traffic,but their speeds are almost the same.As the directional distribution moves to an even distribution of 50/50,the major direction saturation flows and speeds as well as the minor direction speeds tend to decease,while the minor direction saturation flow tends to increase.

Penalty model for delay of bidding section construction period in South-to-North Water Diversion Eastern Route Project from perspective of programs

According to the multi-project and program management theory, this paper analyzes the program generation principle and establishes a program based on progress goals. On the basis of the present situation of calculation of penalty for delay of the bidding section construction period with the critical path method, we studied the effects of contractor-induced delay of the bidding section construction period in detail, including the effects on the construction period of the bidding section itself, the earliest start times of the next bidding section and other subsequent bidding sections, and the construction period of the program, and then constructed a penalty model for delay of the bidding section construction period from the perspective of programs. Using the penalty model, we conducted a practical analysis of penalty for delay of the construction period of the Baoying station program in the South-to-North Water Diversion Project. The model can help determine the amount of penalty for delay of the construction period in bidding sections scientifically and reasonably,

EXISTENCE AND UNIQUENESS OF THE POSITIVE STEADY STATE SOLUTION FOR A LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH A CROWDING TERM

This paper deals with a Lotka-Volterra predator-prey model with a crowding term in the predator equation.We obtain a critical value λ1^D(Ω0),and demonstrate that the existence of the predator inΩ0 only depends on the relationship of the growth rateμof the predator and λ1^D(Ω0),not on the prey.Furthermore,whenμ<λ1^D(Ω0),we obtain the existence and uniqueness of its positive steady state solution,while whenμ≥λ1^D(Ω0),the predator and the prey cannot coexist inΩ0.Our results show that the coexistence of the prey and the predator is sensitive to the size of the crowding regionΩ0,which is different from that of the classical Lotka-Volterra predator-prey model.

Correction of the Littlest Higgs Model to Higgs Production Process e-γ→veW-H in e-γ Collisions

The littlest Higgs model is the most economical one among various little Higgs models. In the context of the littlest Higgs （LH） model, we study the process e-γ → veW^-H and calculate the contributions of the LH model to the cross section of this process. The results show that in most of the parameter spaces preferred by the electroweak precision data, the value of the relative correction is larger than 10%. Such correction to the process e-γ →veW^-H is large enough to be detected via e-γ collisions in the future high energy linear e^＋ e^- collider （ILC） experiment with the c.m. energy √s = 500 GeV and a yearly integrated luminosity ￡ = 100fb^-1, which will give an idea/way to test the model.

Collins Model and Phase Diagram of 2D Ternary System

The Collins model is introduced into the two-dimensional (2D) alternative ternary system having the Lennard-Jones (L-J) potential. The Gibbs free energy of this ternary system is calculated, and according to thermodynamic theory, a group of equations that determine the solid-liquid diagram of ternary system are derived, someisothermal sectional diagrams of the 2D ternary system are obtained. The results are quite similar to the behavior ofthree-dimensional substances.