Bifurcation and Turing Pattern Formation in a Diffusion Modified Leslie-Gower Predator-Prey Model with Crowley-Martin Functional Response

In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results.

Effect of health education based on information-motivationbehavioral skills model on patients with unilateral vestibular dysfunction

BACKGROUND Vestibular dysfunction(VH)is a common concomitant symptom of late peri-pheral vestibular lesions,which can be trauma,poisoning,infection,heredity,and neurodegeneration,but about 50%of the causes are unknown.The study uses the information-motivation-behavioral skills(IMB)model for health education,effectively improve the quality of life,increase their self-confidence,reduce anxiety and depression,and effectively improve the psychological state of patients.AIM To explore the effect of health education based on the IMB model on the degree of vertigo,disability,anxiety and depression in patients with unilateral vestibular hypofunction.METHODS The clinical data of 80 patients with unilateral vestibular hypofunction from January 2019 to December 2021 were selected as the retrospective research objects,and they were divided into the control group and the observation group with 40 cases in each group according to different nursing methods.Among them,the control group was given routine nursing health education and guidance,and the observation group was given health education and guidance based on the IMB model.The changes in self-efficacy,anxiety and depression,and quality of life of patients with unilateral VH were compared between the two groups.RESULTS There was no significant difference in General Self-Efficacy Scale(GSES)scale scores between the two groups of patients before nursing(P>0.05),which was comparable;after nursing,the GSES scale scores of the two groups were higher than those before nursing.The nursing group was higher than the control group,and the difference was statistically significant(P<0.05).There was no significant difference in the scores of Hospital Anxiety and Depression Scale(HADS)and anxiety and depression subscales between the two groups before nursing(P>0.05).After nursing,the HADS score,anxiety,and depression subscale scores of the two groups of patients were lower than those before nursing,and the nursing group was lower than the control group,and the difference was statistically significant(P<0.05).After nursing,the Dizziness Handicap Inventory(DHI)scale and DHI-P,DHI-E and DHI-F scores in the two groups were decreased,and the scores in the nursing group were lower than those in the control group,and the difference was statistically significant(P<0.05).CONCLUSION Health education based on the IMB model can effectively improve patients'quality of life,increase self-efficacy of patients with unilateral vestibular hypofunction,enhance patients'confidence,enable patients to resume normal work and life as soon as possible,reduce patients'anxiety and depression,and effectively improve patients'psychological status.

Impact of stage-specific limb function exercises guided by a selfmanagement education model on arteriovenous fistula maturation status

BACKGROUND The exercise of limb function is the most economical and safe method to promote the maturation of arteriovenous fistula(AVF).However,due to the lack of a uni-fied exercise standard in China,many patients have insufficient awareness of the importance of AVF,leading to poor effectiveness of limb function exercise.The self-management education model can effectively promote patients to take pro-active health-related actions.This study focuses on the characteristics of patients during the peri-AVF period and conducts a phased limb function exercise under the guidance of the self-management education model to observe changes in fac-tors such as the maturity of AVF.AIM To assess the impact of stage-specific limb function exercises,directed by a self-management education model,on the maturation status of AVFs.METHODS This study is a randomized controlled trial involving 74 patients with forearm AVFs from the Nephrology Department of a tertiary hospital in Sichuan Province,China.Patients were randomly divided into an observation group and a control group using a random number table method.The observation group underwent tailored stage-specific limb func-tion exercises,informed by a self-management education model which took into account the unique features of AVF at various stages,in conjunction with routine care.Conversely,the control group was given standard limb function exercises along with routine care.The assessment involves the maturity of AVFs post-intervention,post-operative complications,and the self-management level of the fistula in both groups patients.Analyses were conducted using SPSS version 23.0.Count data were represented by frequency and percentage and subjected to chi-square test comparisons.Measurement data adhering to a normal distribution were presented as mean±SD.The independent samples t-test was utilized for inter-group comparisons,while the paired t-test was used for intra-group comparisons.For measurement data not fitting a normal distribution,the median and interquartile range were presented and analyzed using the Wilcoxon rank sum test.RESULTS At the 8-wk postoperative mark,the observation group demonstrated significantly higher scores in AVF symptom recognition,symptom prevention,and self-management compared to the control group(P<0.05).However,the variance in symptom management scores between the observation and control groups lacked statistical signi-ficance(P>0.05).At 4 wk after the operation,the observation group displayed a superior vessel diameter and depth from the skin of the drainage vessels in comparison to the control group(P<0.05).While the observation group did manifest elevated blood flow rates in the drainage vessels relative to the control group,this distinction was not statistically significant(P>0.05).By the 8-wk postoperative interval,the observation group outperformed the control group with notable enhancements in blood flow rates,vessel diameter,and depth from the skin of drainage vessels(P<0.01).Seven days following the procedure,the observation group manifested significantly diminished limb swelling and an overall reduced complication rate in contrast to the control group(P<0.05).The evaluation of infection,thrombosis,embolism,arterial aneurysm stenosis,and incision bleeding showed no notable differences between the two groups(P>0.05).By the 4-wk postoperative juncture,complications between the observation and control groups were statistically indistinguishable(P>0.05).CONCLUSION Stage-specific limb function exercises,under the guidance of a self-management education model,amplify the capacity of AVF patients to discern and prevent symptoms.Additionally,they expedite AVF maturation and miti-gate postoperative limb edema,underscoring their efficacy as a valuable method for the care and upkeep of AVF in hemodialysis patients.

A whole process damage constitutive model for layered sandstone under uniaxial compression based on Logistic function

Bedding structural planes significantly influence the mechanical properties and stability of engineering rock masses.This study conducts uniaxial compression tests on layered sandstone with various bedding angles(0°,15°,30°,45°,60°,75°and 90°)to explore the impact of bedding angle on the deformational mechanical response,failure mode,and damage evolution processes of rocks.It develops a damage model based on the Logistic equation derived from the modulus’s degradation considering the combined effect of the sandstone bedding dip angle and load.This model is employed to study the damage accumulation state and its evolution within the layered rock mass.This research also introduces a piecewise constitutive model that considers the initial compaction characteristics to simulate the whole deformation process of layered sandstone under uniaxial compression.The results revealed that as the bedding angle increases from 0°to 90°,the uniaxial compressive strength and elastic modulus of layered sandstone significantly decrease,slightly increase,and then decline again.The corresponding failure modes transition from splitting tensile failure to slipping shear failure and back to splitting tensile failure.As indicated by the modulus’s degradation,the damage characteristics can be categorized into four stages:initial no damage,damage initiation,damage acceleration,and damage deceleration termination.The theoretical damage model based on the Logistic equation effectively simulates and predicts the entire damage evolution process.Moreover,the theoretical constitutive model curves closely align with the actual stress−strain curves of layered sandstone under uniaxial compression.The introduced constitutive model is concise,with fewer parameters,a straightforward parameter determination process,and a clear physical interpretation.This study offers valuable insights into the theory of layered rock mechanics and holds implications for ensuring the safety of rock engineering.

Numerical Analysis of Permeability of Functionally Graded Scaffolds

In this work,we numerically study the hydrodynamic permeability of new-generation artificial porous materials used as scaffolds for cell growth in a perfusion bioreactor.We consider two popular solid matrix designs based on triply periodic minimal surfaces,the Schwarz P(primitive)and D(diamond)surfaces,which enable the creation of materials with controlled porosity gradients.The latter property is crucial for regulating the shear stress field in the pores of the scaffold,which makes it possible to control the intensity of cell growth.The permeability of functionally graded materials is studied within the framework of both a microscopic approach based on the Navier-Stokes equation and an averaged description of the liquid filtration through a porous medium based on the equations of the Darcy or Forchheimer models.We calculate the permeability coefficients for both types of solid matrices formed by Schwarz surfaces,study their properties concerning forward and reverse fluid flows,and determine the ranges of Reynolds number for which the description within the Darcy or Forchheimer model is applicable.Finally,we obtain a shear stress field that varies along the sample,demonstrating the ability to tune spatially the rate of tissue growth.

Effect of Shuanghuanglian Oral Solution on Liver Function in a Mouse Model of Non-alcoholic Steatohepatitis

[Objectives]To observe the effect of Shuanghuanglian oral solution on liver function in BABL/cJ mice in non-alcoholic steatohepatitis(NASH)model.[Methods]The BABL/cJ mice were randomly divided into three groups:a control group,a model group,and an experimental group.The experimental group was administered with 10%Shuanghuanglian oral solution at a dose of 0.1 mL/(10 g·d),while the control group and experimental group received an equivalent dosage of normal saline.All three groups were treated for a period of 28 d.The liver function of the mice in each group was examined after the treatment.[Results]The body mass,liver index,triacylglycerol(TG),total cholesterol(TC),aspartate aminotransferase(AST),and alanine aminotransferase(ALT)levels were all significantly reduced compared to the model group(P<0.05).[Conclusions]Shuanghuanglian oral solution has a beneficial effect on liver function in BABL/cJ mice.

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.

Electrostatic Attraction and Repulsion Explained and Modelled Mathematically Using Classical Physics—A Detailed Mechanism Based on Particle Wave Functions

The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.

Effects of Continuous Precision Nursing Model on Knowledge, Attitudes, and Practices (KAP) Behavior and Cardiac Function in Patients after Percutaneous Coronary Angiography and Stent Implantation

Objective:To explore the impact of a continuous precision nursing model on patients’Knowledge,Attitudes,and Practices(KAP)and cardiac function during the nursing process of patients undergoing percutaneous coronary angiography and stent implantation.Methods:Ninety patients who underwent percutaneous coronary angiography and stent implantation in our hospital from April 2022 to April 2023 were selected and randomly divided into the control group(45 cases),in which routine nursing support was carried out during the treatment process,and the observation group(45 cases),in which continuous precision nursing model was carried out during the treatment process.Comparisons were made between the two groups of patients on their KAP,cardiac function,and quality of life during recovery.Results:There was no difference in the left ventricular ejection fraction(LVEF),cardiac output(CO),and cardiac index(CI)levels before intervention.After the intervention,the levels of cardiac function in the observation group were higher than those of the control group(P<0.05).There was no difference in the Exercise of Self-Care Agency(ESCA)self-care ability scale scores before the intervention.After the intervention,the observation group had higher ESCA scores than the control group(P<0.05).Conclusion:Implementation of a continuous precision nursing model in the care of patients undergoing percutaneous coronary angiography and stent implantation improved the patient’s cardiac function,and KAP,and promoted recovery.

Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

Dynamic Analysis of a Predator-Prey Model with Holling-II Functional Response

A predator-prey model with linear capture term Holling-II functional response was studied by using differential equation theory. The existence and the stabilities of non-negative equilibrium points of the model were discussed. The results show that under certain limited conditions, these two groups can maintain a balanced position, which provides a theoretical reference for relevant departments to make decisions on ecological protection.

Functional Sustainability of a Flight Dynamics Control System for Stable Hovering Flight of an Unmanned Aerial Vehicle(UAV),such as in Agricultural Applications:Mathematical Modeling and Simulation

The simulation of a control system for the longitudinal axis of the rotary or fixed-wing unmanned aerial vehicles(UAVs)is demonstrated in this study.The control unit includes design considerations of two controllers to provide robust stability,tracking of the proposed linear dynamics,an adequate set of proportional-integral-derivative(PID)controller gains,and a minimal cost function.The PID control and linear quadratic regulator(LQR)with or without full-state-observer were evaluated.An optimal control system is assumed to provide fast rise and settling time,minimize overshoot,and eliminate the steady-state error.The effectiveness of this approach was verified by a linear model of the UAV aircraft in the semi-dynamic simulation platform of Matlab/Simulink,in which the open-loop system was assessed in terms of flight robustness and reference tracking.The experimental results show that the proposed controllers effectively improve the configuration of the control system of the plant,maintain the sustainability of the dynamic flight model stability,and diminish the flight controller errors.The LQR provides robust stability,but it is not optimal in the transient phase of particular plant output.The PID control system can adjust the controller’s gains for optimal hovering(or stable slow flight)and is especially useful for the tracking system.Finally,comparing aircraft stability using PID and LQR controllers shows that the latter has less overshoot and a shorter settling time;in addition,all proposed controllers can be practically deployed as one UAV’s system,which can be handled as an exemplary model of the UAV flight management system.

Generalized functional model of maximum and minimum detectable deformation gradient for PALSAR interferometry

Empirical functional models for the maximum and minimum detectable deformation gradient of PALSAR interferometry were established based on coherence and discrete look numbers. Then, a least square regression method was used to fit the model coefficients and thus obtain the generalized functional models for both coherence and look numbers. The experimental results with ALOS PALSAR data of Wenchuan earthquake of China show that the new model works well for judging whether the deformation gradient can be detected by the D-InSAR technology or not. The results can help researchers to choose PALSAR data and to configure processing parameters, and also benefit the interpretation of the measured surface deformation.

Evaluation of the water conservation function in the Ili River Delta of Central Asia based on the InVEST model

The Ili River Delta(IRD)is an ecological security barrier for the Lake Balkhash and an important water conservation area in Central Asia.In this study,we selected the IRD as a typical research area,and simulated the water yield and water conservation from 1975 to 2020 using the water yield module of the Integrated Valuation of Ecosystem Services and Tradeoffs(InVEST)model.We further analyzed the temporal and spatial variations in the water yield and water conservation in the IRD from 1975 to 2020,and investigated the main driving factors(precipitation,potential evapotranspiration,land use/land cover change,and inflow from the Ili River)of the water conservation variation based on the linear regression,piecewise linear regression,and Pearson's correlation coefficient analyses.The results indicated that from 1975 to 2020,the water yield and water conservation in the IRD showed a decreasing trend,and the spatial distribution pattern was"high in the east and low in the west";overall,the water conservation of all land use types decreased slightly.The water conservation volume of grassland was the most reduced,although the area of grassland increased owing to the increased inflow from the Ili River.At the same time,the increased inflow has led to the expansion of wetland areas,the improvement of vegetation growth,and the increase of regional evapotranspiration,thus resulting in an overall reduction in the water conservation.The water conservation depth and precipitation had similar spatial distribution patterns;the change in climate factors was the main reason for the decline in the water conservation function in the delta.The reservoir in the upper reaches of the IRD regulated runoff into the Lake Balkhash,promoted vegetation restoration,and had a positive effect on the water conservation;however,this positive effect cannot offset the negative effect of enhanced evapotranspiration.These results provide a reference for the rational allocation of water resources and ecosystem protection in the IRD.

The pig as a preclinical traumatic brain injury model:current models,functional outcome measures,and translational detection strategies

Traumatic brain injury(TBI) is a major contributor of long-term disability and a leading cause of death worldwide. A series of secondary injury cascades can contribute to cell death, tissue loss, and ultimately to the development of functional impairments. However, there are currently no effective therapeutic interventions that improve brain outcomes following TBI. As a result, a number of experimental TBI models have been developed to recapitulate TBI injury mechanisms and to test the efficacy of potential therapeutics. The pig model has recently come to the forefront as the pig brain is closer in size, structure, and composition to the human brain compared to traditional rodent models, making it an ideal large animal model to study TBI pathophysiology and functional outcomes. This review will focus on the shared characteristics between humans and pigs that make them ideal for modeling TBI and will review the three most common pig TBI models–the diffuse axonal injury, the controlled cortical impact, and the fluid percussion models. It will also review current advances in functional outcome assessment measures and other non-invasive, translational TBI detection and measurement tools like biomarker analysis and magnetic resonance imaging. The use of pigs as TBI models and the continued development and improvement of translational assessment modalities have made significant contributions to unraveling the complex cascade of TBI sequela and provide an important means to study potential clinically relevant therapeutic interventions.

Predictive functional control based on fuzzy T-S model for HVAC systems temperature control

In heating, ventilating and air-conditioning （HVAC） systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno （T-S） fuzzy model was proposed to control HVAC systems. The T-S fuzzy model of stabilized controlled process was obtained using the least squares method, then on the basis of global linear predictive model from T-S fuzzy model, the process was controlled by the predictive functional controller. Especially the feedback regulation part was developed to compensate uncertainties of fuzzy predictive model. Finally simulation test results in HVAC systems control applications showed that the proposed fuzzy model predictive functional control improves tracking effect and robustness. Compared with the conventional PID controller, this control strategy has the advantages of less overshoot and shorter setting time, etc.

Functional Integrals and Excitation Energy in Three-Band Hubbard Model

The normal and anomalous Green＇s functions of antiferromagnetie state in three-band Hubbard model are studied by using functional integrals and temperature Green＇s function method. The equations of energy spectrum are derived. In addition, excitation energy of Fermi fields are calculated under long wave approximation.

Functional Integrals and Collective Excitations in Boson-Fermion Model

In this paper, collective excitations in the boson-fermion model are investigated by means of functional integration method. The equations of energy gap and excitation spectrum are derived. Moreover, the Bose energy spectrum of zero wave vector Fermi fields is also calculated.

Functional Integrals and Free Energy in sine-Gordon-Thirring Model with Impurity Coupling

The free energy at low temperature in 1D sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon-Thirring model, free energy is obtained from perturbation expansion of functional determinant. Moreover, the free energy of massive model is calculated by use of an auxiliary Bose field method.

Functional Integrals and Variational-Cumulant Expansion in sine-Gordon-Thirring Model

The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strongcoupling range of fcrmion systems.