Evaluating Model Effectiveness for Soil Infiltration Attribute: Comparison of Green-Ampt, Horton and Modified Green-Ampt Infiltration Models

Soil infiltration is a very important concept in hydrology as well as irrigation, which plays a vital role in estimating surface runoff and groundwater recharge. It is a complicated process that varies with numerous factors. Accurate estimation of soil infiltration is required for future irrigation, and many other purposes. To estimate the infiltration process, there are numerous models. The majority of them have some presumptions, a unique calculation method, and some limitations. The purpose of the paper was to assess the model’s performance for a similar hypothetical scenario involving soil infiltration. It compared the infiltration rate, runoff rate, and incremental infiltration versus time for three different infiltration models: the Green-Ampt model (GA), the Horton model and the Modified Green-Ampt (MGA) model. A spreadsheet was used to calculate the Horton model, and HYDROL-INF (V 5.03) was used to simulate the other two models. Among those three models, the MGA model outperformed those three models, while the GA model produced greater infiltration rate than rainfall, which was insensible. The study showed that the MGA model, which provides useful infiltration predictions, outperformed the other two infiltration models. Since the Horton model does not consider ponding conditions, it is only applicable when the effective rainfall intensity exceeds the final infiltration capacity. Moreover, the GA model’s initial infiltration rate is irrational because it disregards the intensity of the rainfall. The results of this study will assist in selecting the most accurate method for estimating soil infiltration for agricultural purposes.

A dual-RPA based lateral flow strip for sensitive,on-site detection of CP4-EPSPS and Cry1Ab/Ac genes in genetically modified crops

Traditional transgenic detection methods require high test conditions and struggle to be both sensitive and efficient.In this study,a one-tube dual recombinase polymerase amplification(RPA)reaction system for CP4-EPSPS and Cry1Ab/Ac was proposed and combined with a lateral flow immunochromatographic assay,named“Dual-RPA-LFD”,to visualize the dual detection of genetically modified(GM)crops.In which,the herbicide tolerance gene CP4-EPSPS and the insect resistance gene Cry1Ab/Ac were selected as targets taking into account the current status of the most widespread application of insect resistance and herbicide tolerance traits and their stacked traits.Gradient diluted plasmids,transgenic standards,and actual samples were used as templates to conduct sensitivity,specificity,and practicality assays,respectively.The constructed method achieved the visual detection of plasmid at levels as low as 100 copies,demonstrating its high sensitivity.In addition,good applicability to transgenic samples was observed,with no cross-interference between two test lines and no influence from other genes.In conclusion,this strategy achieved the expected purpose of simultaneous detection of the two popular targets in GM crops within 20 min at 37°C in a rapid,equipmentfree field manner,providing a new alternative for rapid screening for transgenic assays in the field.

Effect of Modified Biochar with Organic Fertiliser on the Growth and Development of Chinese Rose

In order to reduce the waste of resources and environmental pollution caused by excessive application of chemical fertilizers, improve the utilization rate of fertilizers, and promote the large-scale and high-quality development of the Chinese rose industry. In this experiment, corn stover biochar, phosphoric acid modified biochar and organic fertilizer were used as test materials, and the effects of mixed application of modified biochar and organic fertilizer on the growth and development of Chinese rose as well as soil physicochemical properties were investigated by using the method of pot planting test. The results showed that modified biochar with organic fertilizer had the most significant effect on the enhancement of soil pH, organic matter content and soil carbon-to-nitrogen ratio. After 120 d of planting, modified biochar with organic fertilizer had the most significant effect on the enhancement of plant height and crown width of Chinese rose;both organic fertilizer and modified biochar with organic fertilizer significantly increased the chlorophyll content of Chinese rose. The number of flowers and the number of branches were the highest in the modified biochar with organic fertilizer treatment. In conclusion, the application of modified biochar with organic fertilizer can better improve the soil pH, and increase the soil organic matter content and carbon-to-nitrogen ratio to change the biological traits of Chinese rose. The results of this study provide a theoretical basis for the reduction of chemical fertilizers and the resource utilization of agricultural wastes and guarantee the sustainable development of the cut flower industry.

Multi-soliton solutions, breather-like and bound-state solitons for complex modified Korteweg–de Vries equation in optical fibers

Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained through the Hirota method and symbolic computation. Breather-like and bound-state solitons are constructed in which the signs of the imaginary parts of the complex wave numbers and the initial separations of the two parallel solitons are important factors for the interaction patterns. The periodic structures and position-induced phase shift of some solutions are introduced.

Fatigue Resistance of RCA Modified Asphalt Based on Dielectric Properties

In order to study the anti-fatigue performance of RCA modified asphalt (RMA),the performance of RMA and 90#matrix asphalt with different modifier content were measured by asphalt penetration,ductility,softening point,Brookfield viscosity,rheological index,infrared spectrum and dielectric constant test.This paper discusses the changes of asphalt basic indexes,fatigue properties and asphalt components based on dielectric properties under different modifier contents,and analyzes the grey correlation degree between components and asphalt pavement performance indexes.The results show that the optimum content of RCA modifier is 16.7%of the asphalt quality according to the penetration,ductility,softening point,Brockfield viscosity,viscosity temperature curve and fatigue life.In the phase angle-strain curve,there is disorder in the latter part of the curve.According to the strain (ε_(d)) corresponding to the disorder point,a new fatigue failure criterion is proposed and proved.Based on the new asphalt fatigue failure criterion,the fatigue prediction model of asphalt mixture is improved,and the fatigue life predicted by the improved fatigue model is compared with the fatigue life obtained by four-point bending fatigue test.The results show that the proposed new asphalt fatigue failure criterion is reasonable,and the fatigue life predicted by the improved asphalt mixture fatigue prediction model is accurate.The research method of classifying asphalt components based on dielectric properties is simple and effective,and the components have a high correlation with the road performance of base asphalt and modified asphalt.

Modified Xiaoyao powder for postpartum depression:A systematic review and meta-analysis

Objective:To evaluate the effectiveness and safety of modified Xiaoyao powder for postpartum depression(PPD)by conducting a systematic review of randomized controlled trials(RCTs).Methods:The Chinese National Knowledge Infrastructure Databases(CNKI),the Chinese Scientific Journals Database(VIP),Wanfang,Google Scholar,the SinoMed,Embase,Cochrane Library,and PubMed databases were searched from their inception to April 25,2023.The Cochrane Risk of Bias tool was used to assess the quality of the trials.We applied the risk ratio to present dichotomous data and the mean difference to present continuous data.Data with similar characteristics were pooled for meta-analysis and heterogeneity was assessed using I2.Results:This review included 35 trials involving 2848 participants.The quality of the included studies was low(unclear randomization processes and insufficient reporting of blinding).Participants treated with modified Xiaoyao powder plus Western medicine showed lower Hamilton Depression Scale(HAMD)depression score than those who used Western medicine alone(mean difference=-2.15;95%confidence interval:-2.52 to 1.78;P<.00001),and higher effective rate(relative risk=1.19;95%confidence interval:1.15 to 1.24;P<.00001),When comparing modified Xiaoyao alone with Western medicine,the HAMD depression score remained low,however,the efficacy rate was higher in the modified Xiaoyao group.Regarding adverse events,the modified Xiaoyao group reported weight gain,nausea,and diarrhea,but no severe adverse events were reported.Conclusion:Modified Xiaoyao may help relieve depression in PPD when used alone or in combination with Western medicine,with minor side effects.Therefore,future high-quality,large-sample size RCTs are warranted.

Preparation of Modified UiO-66 Catalyst and Its Catalytic Performance for NH_(3)-SCR Denitration

Zirconium-based metal-organic framework UiO-66 was successfully prepared by solvothermal method,and UiO-66 was modified by adding regulators such as formic acid,acetic acid,and hydrochloric acid.The NH_(3)-SCR reactivity of the samples was evaluated by the denitration activity evaluation system,and the UiO-66 and the regulator-modified UiO-66 were characterized by XRD,SEM,BET,FTIR,TG,NH_(3)-TPD,etc.,the effects of regulator types on the structure and properties of UiO-66 were investigated.The experimental results show that,after adding the modifier,the morphology of UiO-66 changes from irregular quadrilateral with serious agglomeration to particles with regular crystal shape and good dispersibility,and the crystal morphology of the catalyst is improved.In addition,after adding the modifier,UiO-66 has a larger specific surface area and stronger surface acidity,which optimizes the catalytic performance of UiO-66.The catalytic performance test results of NH_(3)-SCR show that the low-temperature activity of UiO-66 is poor,and it only shows a certain catalytic activity at higher temperatures.The catalytic activity of UiO-66 was significantly improved after adding the regulator.Among them,the UiO-66-HCl modified with hydrochloric acid had the best catalytic activity,and the denitration rate reached 70%when the denitration temperature was 380℃.

A Modified Iterative Learning Control Approach for the Active Suppression of Rotor Vibration Induced by Coupled Unbalance and Misalignment

This paper proposes a modified iterative learning control(MILC)periodical feedback-feedforward algorithm to reduce the vibration of a rotor caused by coupled unbalance and parallel misalignment.The control of the vibration of the rotor is provided by an active magnetic actuator(AMA).The iterative gain of the MILC algorithm here presented has a self-adjustment based on the magnitude of the vibration.Notch filters are adopted to extract the synchronous(1×Ω)and twice rotational frequency(2×Ω)components of the rotor vibration.Both the notch frequency of the filter and the size of feedforward storage used during the experiment have a real-time adaptation to the rotational speed.The method proposed in this work can provide effective suppression of the vibration of the rotor in case of sudden changes or fluctuations of the rotor speed.Simulations and experiments using the MILC algorithm proposed here are carried out and give evidence to the feasibility and robustness of the technique proposed.

Modified intratympanic steroid therapy for sudden sensorineural hearing loss via tympanic tube and gelfoam as a salvage treatment

Background: Sudden sensorineural hearing loss(SSNHL) is a prevalent emergency in ear, nose, and throat practice. Previous studies have demonstrated that intratympanic steroid therapy(IST) can serve as a salvage treatment for SSNHL after the failure of systemic steroid therapy(SST).Objective: This study aimed to analyze the efficacy of modified IST involving the insertion of a tympanic tube and gelfoam as a salvage treatment for patients with SSNHL, and to explore its associated factors.Methods: Totally, 74 patients who were aged 22–81 years with SSNHL were enrolled and allocated to either the control group(n = 25) or the treatment group(n = 49) based on their treatment modalities. All patients received SST lasting for at least 7 days. Subsequently, patients in the treatment group, after SST failure, underwent IST twice a week for 2–6 weeks, while the control group did not. Efficacy was assessed by the improvement in pure tone average at the affected frequency at the beginning and end of IST.Results: Hearing improvement in all patients after IST in the treatment group was 9.71 ± 14.84 dB, with significant improvement at affected frequencies(250-8000 Hz) compared with the control group(P < 0.05). The findings indicated the duration from the onset of SSNHL to the beginning of IST as an independent factor for pure tone average improvement after treatment(P = 0.002), whereas age, duration of SST, and time of IST were not(P > 0.05).Conclusion: The modified IST was demonstrated to be a safe and effective method as a salvage treatment for SSNHL. This study explored the efficacy of a modified IST approach, incorporating the utilization of tympanic tubes and gelfoam as key components. The findings underscore the advantages of gelfoam as a strategic drug carrier placed in the round window niche. By minimizing drug loss, extending action time, and increasing perilymph concentration, gelfoam enhances the therapeutic impact of IST, contributing to improved hearing outcomes in patients with SSNHL.

Clinical efficacy of modified Kamikawa anastomosis in patients with laparoscopic proximal gastrectomy

BACKGROUND With the increasing incidence of proximal gastric cancer,laparoscopic proximal gastrectomy has been applied.However,reflux esophagitis often occurs after traditional esophagogastric anastomosis.In order to solve this problem,several methods of digestive tract reconstruction have emerged,but the most satisfying method remains to be discussed.Therefore,we modified traditional Kamikawa anastomosis to investigate the appropriate digestive tract reconstruction in laparo-scopic proximal gastrectomy.All the patients were successfully operated on without conversion to laparotomy.The duration of operation and digestive tract reconstruction were 203.500(150-224)min and 87.500(73-111)min,respectively.The intraoperative amount of bleeding was 20.500 mL±0.696 mL.The time of postoperative first flatus,the first postoperative fluid intake,and the postoperative length of stay were 2(1-3)d,4(3-5)d,and 9(8-10)d,respectively.All the patients were followed up for 12-23 months.The body mass index at 6 and 12 months after surgery were 22.577 kg/m2±3.098 kg/m2 and 22.594 kg/m2±3.207 kg/m2,respectively.The nutrition risk screening 2002 score,the patient-generated subjective global assessment score,and the gastroesophageal reflux disease scale score were good at 6 and 12 months after surgery.Reflux esophagitis and anastomotic stenosis were not observed in any of the patients during their 12-month postoperative gastroscopy or upper gastrointestinal tract visits.All the patients exhibited no tumor recurrence or metastasis.CONCLUSION The modified Kamikawa anastomosis is safe and feasible for laparoscopic proximal gastrectomy and has good antireflux effects and nutritional status.

Arterial Duct Stenting Versus Modified Blalock-Taussig Shunt in Patient with Ductal-Dependent Pulmonary Circulation: Systematic Review & Meta-Analysis

Objective:Patients with ductal-dependent pulmonary circulation require alternative bloodflow to provide and maintain adequate oxygenation.Modified Blalock-Taussig Shunt(MBTS)has been the standard for providing such a result.Currently,less invasive methods such as Arterial Duct(AD)stenting have been performed as alter-natives.This study aims to compare the outcome of AD stenting and MBTS.Method:Systematic research was performed in online databases using the PRISMA protocol.The outcomes measured were 30-day mortality,com-plication,unplanned intervention,oxygen saturation,duration of hospital,and ICU length of stay.Any compara-tive study provided with full text is included.The outcome of each study was analyzed using a trandom effects model with relative risk and mean difference as the effect size.Bias risk assessment was conducted using the New-castle-Ottawa Scale.All analyses were performed using Review Manager 5.4.1.Result:A total of 11 studies with 3154 samples included in this study.There is no significant difference in 30-day mortality between the two groups(p-value=0.10).However,there is significantly less complication(RR 0.53[0.35,0.82];p-value=0.004)and unplanned intervention(RR 0.59[0.38,0.92];p-value=0.02)in the AD stent group.Comparison of the Nakata index showed no significant difference(p-value=0.88).Post-operative oxygen saturation was measured signifi-cantly higher in the AD stenting(MD 1.80[0.85,2.74];p-value=0.0002).However,AD stent group shows sig-nificantly lower long-term oxygen saturation(MD-8.43[-14.38,-2.48];p-value=0.005).Both hospital and ICU length of stay was significantly shorter in the AD stent group(MD-8.30[-11.13,-5.48];p-value<0.00001;MD-5.09[-7.79,-2.38];p-value=0.0002).Conclusion:AD stenting provides comparable outcomes relative to MBTS as it provides less complication and unplanned intervention and higher post-procedural O2 saturation.However,MBTS proved its superiority in maintaining higher long-term oxygen saturation and still became the preferred option to manage complex cases where stenting is either challenging or unsuccessful.

Modified Black Widow Optimization-Based Enhanced Threshold Energy Detection Technique for Spectrum Sensing in Cognitive Radio Networks

This study develops an Enhanced Threshold Based Energy Detection approach(ETBED)for spectrum sensing in a cognitive radio network.The threshold identification method is implemented in the received signal at the secondary user based on the square law.The proposed method is implemented with the signal transmission of multiple outputs-orthogonal frequency division multiplexing.Additionally,the proposed method is considered the dynamic detection threshold adjustments and energy identification spectrum sensing technique in cognitive radio systems.In the dynamic threshold,the signal ratio-based threshold is fixed.The threshold is computed by considering the Modified Black Widow Optimization Algorithm(MBWO).So,the proposed methodology is a combination of dynamic threshold detection and MBWO.The general threshold-based detection technique has different limitations such as the inability optimal signal threshold for determining the presence of the primary user signal.These limitations undermine the sensing accuracy of the energy identification technique.Hence,the ETBED technique is developed to enhance the energy efficiency of cognitive radio networks.The projected approach is executed and analyzed with performance and comparison analysis.The proposed method is contrasted with the conventional techniques of theWhale Optimization Algorithm(WOA)and GreyWolf Optimization(GWO).It indicated superior results,achieving a high average throughput of 2.2 Mbps and an energy efficiency of 3.8,outperforming conventional techniques.

Bound-Preserving Discontinuous Galerkin Methods with Modified Patankar Time Integrations for Chemical Reacting Flows

In this paper,we develop bound-preserving discontinuous Galerkin(DG)methods for chemical reactive flows.There are several difficulties in constructing suitable numerical schemes.First of all,the density and internal energy are positive,and the mass fraction of each species is between 0 and 1.Second,due to the rapid reaction rate,the system may contain stiff sources,and the strong-stability-preserving explicit Runge-Kutta method may result in limited time-step sizes.To obtain physically relevant numerical approximations,we apply the bound-preserving technique to the DG methods.Though traditional positivity-preserving techniques can successfully yield positive density,internal energy,and mass fractions,they may not enforce the upper bound 1 of the mass fractions.To solve this problem,we need to(i)make sure the numerical fluxes in the equations of the mass fractions are consistent with that in the equation of the density;(ii)choose conservative time integrations,such that the summation of the mass fractions is preserved.With the above two conditions,the positive mass fractions have summation 1,and then,they are all between 0 and 1.For time discretization,we apply the modified Runge-Kutta/multi-step Patankar methods,which are explicit for the flux while implicit for the source.Such methods can handle stiff sources with relatively large time steps,preserve the positivity of the target variables,and keep the summation of the mass fractions to be 1.Finally,it is not straightforward to combine the bound-preserving DG methods and the Patankar time integrations.The positivity-preserving technique for DG methods requires positive numerical approximations at the cell interfaces,while Patankar methods can keep the positivity of the pre-selected point values of the target variables.To match the degree of freedom,we use polynomials on rectangular meshes for problems in two space dimensions.To evolve in time,we first read the polynomials at the Gaussian points.Then,suitable slope limiters can be applied to enforce the positivity of the solutions at those points,which can be preserved by the Patankar methods,leading to positive updated numerical cell averages.In addition,we use another slope limiter to get positive solutions used for the bound-preserving technique for the flux.Numerical examples are given to demonstrate the good performance of the proposed schemes.

Quintessence anisotropic stellar models in quadratic and Born-Infeld modified teleparallel Rastall gravity

This study aims to discuss anisotropic solutions that are spherically symmetric in the quintessence field,which describe compact stellar objects in the modified Rastall teleparallel theory of gravity.To achieve this goal,the Krori and Barua arrangement for spherically symmetric components of the line element is incorporated.We explore the field equations by selecting appropriate off-diagonal tetrad fields.Born-Infeld function of torsion f(T)=β√λT+1-1 and power law form h(T)=δTn are used.The Born-Infeld gravity was the first modified teleparallel gravity to discuss inflation.We use the linear equation of state pr=ξρto separate the quintessence density.After obtaining the field equations,we investigate different physical parameters that demonstrate the stability and physical acceptability of the stellar models.We use observational data,such as the mass and radius of the compact star candidates PSRJ 1416-2230,Cen X-3,&4U 1820-30,to ensure the physical plausibility of our findings.

Localization in modified polar representation: hybrid measurements and closed-form solution

Classical localization methods use Cartesian or Polar coordinates, which require a priori range information to determine whether to estimate position or to only find bearings. The modified polar representation (MPR) unifies near-field and farfield models, alleviating the thresholding effect. Current localization methods in MPR based on the angle of arrival (AOA) and time difference of arrival (TDOA) measurements resort to semidefinite relaxation (SDR) and Gauss-Newton iteration, which are computationally complex and face the possible diverge problem. This paper formulates a pseudo linear equation between the measurements and the unknown MPR position,which leads to a closed-form solution for the hybrid TDOA-AOA localization problem, namely hybrid constrained optimization(HCO). HCO attains Cramér-Rao bound (CRB)-level accuracy for mild Gaussian noise. Compared with the existing closed-form solutions for the hybrid TDOA-AOA case, HCO provides comparable performance to the hybrid generalized trust region subproblem (HGTRS) solution and is better than the hybrid successive unconstrained minimization (HSUM) solution in large noise region. Its computational complexity is lower than that of HGTRS. Simulations validate the performance of HCO achieves the CRB that the maximum likelihood estimator (MLE) attains if the noise is small, but the MLE deviates from CRB earlier.

Adsorption Effect of Phosphate Modified Grape Branch Biochar on Cd2

Two major problems facing agriculture at present are soil pollution and the disposal of solid wastes generated during plant growth. The method of preparing biochar from solid wastes produced by plants is a means of maximizing the use of resources to combat the problem of soil pollution. In this study, we did not choose straw in the traditional sense but the waste branches from grape pruning, which has higher lignin cellulose, as the raw material. The biochar derived from grape branches pyrolyzed at 300˚C for two hours was utilized as a raw material to prepare modified biochar with varying concentrations of phosphoric acid. The adsorption performance and mechanism of Cd2 were explored through experiments involving different concentrations, addition amounts, reaction times, kinetic analyses, and isothermal adsorption tests. The findings indicated that the optimal adsorption of Cd2 occurred with a 20% phosphoric acid concentration, achieving the highest adsorption rate of 84.62%. At a dosage of 10 g/L, the maximum adsorption capacity reached 7.02 mg/g. The adsorption kinetics and isothermal adsorption of Cd2 on biochar modified with 0.2% phosphoric acid (0.2 PB) closely followed the pseudo-first-order kinetics model (R2 > 0.98) and the Freundlich model (R2 > 0.97), respectively. This suggests that the adsorption process involves both physical and chemical mechanisms. SEM and FTIR analyses revealed that phosphoric acid modification primarily increased the biochar’s specific surface area and enhanced certain original functional groups. The adsorption process predominantly involved rapid ion diffusion and chemical adsorption, as confirmed by kinetic analysis and isothermal adsorption model analysis. In summary, the adsorption efficiency of 0.2 PB significantly improved, showing potential and feasibility for heavy metal remediation in soil. This supports the environmentally friendly concept of “treating waste with waste”.

Analysis of quality-related proteins in golden pompano(Trachinotus ovatus)fillets with modified atmosphere packaging under superchilling storage

Here,we aimed to study the changes in proteome of golden pompano fillets during post-mortem storage.Tandem mass tags(TMT)-labeled quantitative proteomic strategy was applied to investigate the relationships between protein changes and quality characteristics of modified atmosphere packaging(MAP)fillets during superchilling(-3°C)storage.Scanning electron microscopy was used to show that the muscle histology microstructure of fillets was damaged to varying degrees,and low-field nuclear magnetic resonance was used to find that the immobilized water and free water in the muscle of fillets changed significantly.Total sulfhydryl content,TCA-soluble peptides and Ca2+-ATPase activity also showed that the fillet protein had a deterioration by oxidation and denaturation.The Fresh(FS),MAP,and air packaging(AP)groups were set.Total of 150 proteins were identified as differential abundant proteins(DAPs)in MAP/FS,while 209 DAPs were in AP/FS group.The KEGG pathway analysis indicated that most DAPs were involved in binding proteins and protein turnover.Correlation analysis found that 52 DAPs were correlated with quality traits.Among them,8 highly correlated DAPs are expected to be used as potential quality markers for protein oxidation and water-holding capacity.These results provide a further understanding of the muscle deterioration mechanism of packaging golden pompano fillets during superchilling.

Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

A Modified Lagrange Method for Solving Convex Quadratic Optimization Problems

In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.

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.