Application of the theory of linear algebra on mathematical modeling practice

The application level of mathematics in each science discipline signs the level of development of this science. With the advancement of science and technology, especially the rapid development of computer technology, mathematics has permeated from natural scientific technology to agricultural construction, from economic activities to all areas of social life. Generally, when the actual problem requires us to provide quantitative results of analysis, forecasting, decision making, control and other aspects for real object under study, we are often inseparable from the application of mathematics. Mathematical modeling is the key to this process, whose purpose is to make mathematics applied to social and social services, and using mathematics to solve practical problems is through mathematical models. When using mathematical methods to solve some practical problems, we usually first transfer practical problems into mathematical language, and then abstract them into a mathematical model.

A Study on the Work Process-Based Practical Training Model for Basic Nursing Skills in Vocational Colleges

Objective:To explore and analyze the work process-based practical training teaching model for basic nursing skills in vocational colleges and its implementation effects.Methods:A total of 82 nursing students from our school were selected for the study,which was conducted from April 2023 to April 2024.Using a random number table method,the students were divided into an observation group and a control group,each with 41 students.The control group received conventional practical training teaching,while the observation group followed the work process-based practical training model for basic nursing skills.The assessment scores and teaching satisfaction of the two groups were compared.Results:The comparison of assessment scores showed that the observation group performed significantly better than the control group(P<0.05).The comparison of teaching satisfaction also indicated that the observation group had significantly higher satisfaction than the control group(P<0.05).Conclusion:The work process-based practical training teaching model for basic nursing skills in vocational colleges can improve students’assessment scores and enhance teaching satisfaction,demonstrating its value for wider application.

Effects of the information–knowledge–attitude–practice nursing model combined with predictability intervention on patients with cerebrovascular disease

BACKGROUND Cerebrovascular disease(CVD)poses a serious threat to human health and safety.Thus,developing a reasonable exercise program plays an important role in the long-term recovery and prognosis for patients with CVD.Studies have shown that predictive nursing can improve the quality of care and that the information–knowledge–attitude–practice(IKAP)nursing model has a positive impact on patients who suffered a stroke.Few studies have combined these two nursing models to treat CVD.AIM To explore the effect of the IKAP nursing model combined with predictive nursing on the Fugl–Meyer motor function(FMA)score,Barthel index score,and disease knowledge mastery rate in patients with CVD.METHODS A total of 140 patients with CVD treated at our hospital between December 2019 and September 2021 were randomly divided into two groups,with 70 patients in each.The control group received routine nursing,while the observation group received the IKAP nursing model combined with predictive nursing.Both groups were observed for self-care ability,motor function,and disease knowledge mastery rate after one month of nursing.RESULTS There was no clear difference between the Barthel index and FMA scores of the two groups before nursing(P>0.05);however,their scores increased after nursing.This increase was more apparent in the observation group,and the difference was statistically significant(P<0.05).The rates of disease knowledge mastery,timely medication,appropriate exercise,and reasonable diet were significantly higher in the observation group than in the control group(P<0.05).The satisfaction rate in the observation group(97.14%)was significantly higher than that in the control group(81.43%;P<0.05).CONCLUSION The IKAP nursing model,combined with predictive nursing,is more effective than routine nursing in the care of patients with CVD,and it can significantly improve the Barthel index and FMA scores with better knowledge acquisition,as well as produce high satisfaction in patients.Moreover,they can be widely used in the clinical setting.

The development and evaluation of a nurse anaesthesia model for practice in South Africa

Objective This article aimed to present a developed model for nurse anaesthesia practice in South Africa and then to evaluate the model by national and international anaesthetist experts.Methods For the model development,a theory-generative research design was used as guided by Chinn&Kramer.The study included four steps to develop and evaluate the model:step one,concept analysis;step two,placing the concepts into relationships;step three,description and critical reflection of the model;step four,evaluation of the model.For evaluation of the model,data were collected using individual,in-depth interviews.Four South African medical specialist anaesthesiologists and four international nurse anaesthetists were interviewed.Transcribed interviews were analyzed using Tesch’s eight steps of thematic data analysis.Results The model was described in four phases:relationship phase,working phase,termination phase,and independent phase.The model shows a development process of a student nurse anaesthetist by a nurse anaesthetist facilitator to the mastery of the scope of practice of a nurse anaesthetist.Two themes(six categories)emerged through thematic analysis:the model and guidelines for implementation were found to be appropriate(model and guidelines for implementation are important because of the need for nurse anaesthetist,the model is applicable because it is described as comprehensive,the relationship phase was found to be important and the interdependence between disciplines is imperative,the affirmation that mastery has to be attained by nurse anaesthetists due to the complexity of services rendered),anticipated limitations to the South African nurse anaesthetist(the need to identify complex patients and limitations on the setting and refer to higher level of care,limitations due to red tape).Conclusions This model provides fertile soil to inform and outline the education(curriculum)and practice(scope of practice)and research for nurse anaesthesia practice in South Africa.

Connotation and Realization of Ningxia Agricultural Organization:Practice Induction and Model Reference

Through a large number of literature studies and field survey,from the perspective of small farmers’integration into agricultural modernization,this paper innovatively divided the current integration mode of national agricultural organizations into five main types:leading enterprises,leading new agricultural business entities,cooperative financial institutions,embedded scientific research institutes,and financial poverty alleviation and assistance.It found that Ningxia region can gradually carry out horizontal integration and extension in the process of promoting the vertical integration and extension of agricultural industry value chain,and try to explore the possibility of new integration mode such as"modern agricultural cloud service public platform+leading enterprises+farmers"in Ningxia,in order to bridge the gaps in agricultural organization policies through the pilot,because the village plans to plan the development of the industry,adapt to the local conditions to strengthen the village collective economy,and continuously improve the degree of farmers’organization.

Showcasing modeling strategies in the ESOL writing class： Blending rhetorical fluency with grammatical accuracy

This paper argues for an overt innovational shift in praxis, as well as classroom configuration in the ESOL writing class by calling for a move away from the current foci on process-based pedagogies for newcomer populations, to an explicit teaching of modeling strategies with concomitant practice opportunities provided in the ESOL writing class. It is argued that explicit, sequenced instruction in the domains of rhetorical structure as well as grammatical accuracy provide ESOL （English for Speakers of Other Languages） learners in the emerging stages of language learning with a more concrete grasp of meaning, structure and grammar in rhetorical construction. The modeling strategies proposed in the paper focus on a simultaneous building of rhetorical fluency and grammatical accuracy via spotlighted and sequenced strategies which afford learners practice in smaller chunks of composition including but not limited to thesis statement writing, varied paragraph organization, multiple modes of exposition, and grammatical complexity all in a bid to generate rhetorical depth and grammatical detail in writing. In short, both form and function need to be explicitly taught in the ESOL writing class with adequate opportunities provided for rhetorical practice. Using a meticulous blend of meaningful, authentic and purposeful tasks combined with one-on-one instruction which incorporates a variety of visual and rhetorical modeling strategies, emerging writers, it is argued a move from controlled to automatic writing fluency within a short time span. The pedagogy proposed in the current paper spotlights the specific learner, rather than the writing process and entails a move away from traditional, teacher-fronted classrooms to targeted, workshop-centered configurations which permit for one-on-one conferencing in the ESOL writing class. The visually rendered modeling strategies proposed in this paper argue for writing instruction for ESOL students which is learner responsive, relevant and practical.

Theory and Practice of Learning Organization ——Investigation and Thinking for the Management Committee of the Baotou Rare Earth High-tech Area

Nowadays, many countries and regions use the human resources development as the major approach in holding the initiative in competition. The Baotou Rare Earth High-tech Area implements the strategies for revitalizing the area through establishing science and education learning organization and developing the entire learning in Management Committee. In accordance with the fundamental of mathematics ＂The arithmetical mean is equal to or larger than its geometric mean to any positive real number＂, it submits ＂the theoretical model of proportional development advantage of the same element in the same level＂ in order to solve ＂the problem that a few people behind in the department block the development of the High-tech Area＂, realize every member＇s common progress and each department＇s proportional development, and finally make the effect of Rare Earth High-tech maximum by strengthening team cooperation and producing a multiplier effect.

Development, assessment and implementation of integrated stormwater management plan: a case study in Shanghai

An innovative stormwater master plan based on low impact development LID is proposed.Unlike the traditional urban drainage plan this plan employs a sustainable stormwater management approach in communities utilizing LID practices to reduce runoff and pollution load. An integrated hydraulic model which combines the traditional drainage sewer system with LID practices is adopted to assess the master plan.Through a long-term continuous simulation for 20 years the results reveal that the runoff volume will be reduced by over 80% following full implementation of this plan. Combining with the local conditions technical guidelines are established to provide assistance in implementing the stormwater master plan. Bioretention facilities for three main roads are constructed and other areas of development are being implemented sequentially under the guidance of the plan. This project provides an alternative method of stormwater management through the implementation of LID and it acts as a good example for other developing districts in China.

Practical Model of Sea Ice Thickness of Bohai Sea Based on MODIS Data

Sea ice thickness is one of the most important input parameters in the studies on sea ice disaster prevention and mitigation. It is also the most important content in remote sensing monitoring of sea ice. In this study, a practical model of sea ice thickness(PMSIT) was proposed based on the Moderate Resolution Imaging Spectroradiometer(MODIS) data. In the proposed model, the MODIS data of the first band were used to estimate sea ice thickness and the difference between the second-band reflectance and the fifth-band reflectance in the MODIS data was calculated to obtain the difference attenuation index(DAI) of each pixel. The obtained DAI was used to estimate the integrated attenuation coefficient of the first band of the MODIS at the pixel level. Then the model was used to estimate sea ice thickness in the Bohai Sea with the MODIS data and then validated with the actual sea ice survey data. The validation results showed that the proposed model and corresponding parameterization scheme could largely avoid the estimation error of sea ice thickness caused by the spatial and temporal heterogeneity of sea ice extinction and allowed the error of 18.7% compared with the measured sea ice thickness.

Machine learning predicts portal vein thrombosis after splenectomy in patients with portal hypertension: Comparative analysis of three practical models

BACKGROUND For patients with portal hypertension(PH),portal vein thrombosis(PVT)is a fatal complication after splenectomy.Postoperative platelet elevation is considered the foremost reason for PVT.However,the value of postoperative platelet elevation rate(PPER)in predicting PVT has never been studied.AIM To investigate the predictive value of PPER for PVT and establish PPER-based prediction models to early identify individuals at high risk of PVT after splenectomy.METHODS We retrospectively reviewed 483 patients with PH related to hepatitis B virus who underwent splenectomy between July 2011 and September 2018,and they were randomized into either a training(n=338)or a validation(n=145)cohort.The generalized linear(GL)method,least absolute shrinkage and selection operator(LASSO),and random forest(RF)were used to construct models.The receiver operating characteristic curves(ROC),calibration curve,decision curve analysis(DCA),and clinical impact curve(CIC)were used to evaluate the robustness and clinical practicability of the GL model(GLM),LASSO model(LSM),and RF model(RFM).RESULTS Multivariate analysis exhibited that the first and third days for PPER(PPER1,PPER3)were strongly associated with PVT[odds ratio(OR):1.78,95%confidence interval(CI):1.24-2.62,P=0.002;OR:1.43,95%CI:1.16-1.77,P<0.001,respectively].The areas under the ROC curves of the GLM,LSM,and RFM in the training cohort were 0.83(95%CI:0.79-0.88),0.84(95%CI:0.79-0.88),and 0.84(95%CI:0.79-0.88),respectively;and were 0.77(95%CI:0.69-0.85),0.83(95%CI:0.76-0.90),and 0.78(95%CI:0.70-0.85)in the validation cohort,respectively.The calibration curves showed satisfactory agreement between prediction by models and actual observation.DCA and CIC indicated that all models conferred high clinical net benefits.CONCLUSION PPER1 and PPER3 are effective indicators for postoperative prediction of PVT.We have successfully developed PPER-based practical models to accurately predict PVT,which would conveniently help clinicians rapidly differentiate individuals at high risk of PVT,and thus guide the adoption of timely interventions.

Inclusive Multiple Models(IMM)for predicting groundwater levels and treating heterogeneity

An explicit model management framework is introduced for predictive Groundwater Levels(GWL),particularly suitable to Observation Wells(OWs)with sparse and possibly heterogeneous data.The framework implements Multiple Models(MM)under the architecture of organising them at levels,as follows:(i)Level 0:treat heterogeneity in the data,e.g.Self-Organised Mapping(SOM)to classify the OWs;and decide on model structure,e.g.formulate a grey box model to predict GWLs.(ii)Level 1:construct MMs,e.g.two Fuzzy Logic(FL)and one Neurofuzzy(NF)models.(iii)Level 2:formulate strategies to combine the MM at Level 1,for which the paper uses Artificial Neural Networks(Strategy 1)and simple averaging(Strategy 2).Whilst the above model management strategy is novel,a critical view is presented,according to which modelling practices are:Inclusive Multiple Modelling(IMM)practices contrasted with existing practices,branded by the paper as Exclusionary Multiple Modelling(EMM).Scientific thinking over IMMs is captured as a framework with four dimensions:Model Reuse(MR),Hierarchical Recursion(HR),Elastic Learning Environment(ELE)and Goal Orientation(GO)and these together make the acronym of RHEO.Therefore,IMM-RHEO is piloted in the aquifer of Tabriz Plain with sparse and possibly heterogeneous data.The results provide some evidence that(i)IMM at two levels improves on the accuracy of individual models;and(ii)model combinations in IMM practices bring‘model-learning’into fashion for learning with the goal to explain baseline conditions and impacts of subsequent management changes.

Effect of KAP Intervention Model on Resilience and Cancer-related Fatigue in Patients with Colorectal Cancer Undergoing Chemotherapy

Objective:To explore the effect of KAP intervention mode on resilience and cancer-related fatigue in patients with colorectal cancer undergoing chemotherapy.Methods:A prospective randomized trial was conducted.55 patients with colorectal cancer who received routine nursing from February 2018 to February 2019 were included in the control group,and 55 patients who received routine nursing+KAP intervention from March 2019 to March 2020 were included in the observation group.The scores of Resilience Scale and cancer-related fatigue scale(CFS)before and 6 months after intervention were compared between the two groups.Results:After 6 months of intervention,the score of resilience of the two groups was higher than that before intervention,and that of the observation group was higher than that of the control group,the difference was statistically significant(P<0.05);The CFS score of the two groups was lower than that before intervention,and that of the observation group was lower than that of the control group,the difference was statistically significant(P<0.05).Conclusion:KAP intervention model can improve the resilience of patients with colorectal cancer chemotherapy,reduce cancerrelated fatigue.

PRACTICAL AND PREDICTIVE MODELLING OF ORE DEPOSITS IN HYDROTHERMAL SYSTEMS

Over the pastfive years,we have been making efforts to develop a practical and predic- tive tool to exploreforgiantore deposits in hydrothermal systems. Towards this goal,a sig- nificant progress has been made towards a better understanding of the basic physical and chemical processes behind ore body formation and mineralization in hydrothermal systems. On the scientific developmentside,we have developed analytical solutions to answerthe fol- lowing scientific questions:(1) Can thepore- fluid pressure gradientbemaintained atthe val- ue of the lithostaticpressure gradientin the uppercrustof the Earth?and(2 ) Can convective pore- fluid flow take place in the uppercrustof the Earth ifthere is a fluid/mass leakage from the mantle to the upper crustof the Earth?On the modelling developmentside,we have developed numerical methods to model the following problems:(1) convective pore- fluid flow in two- dimensional hydrothermal systems;(2 ) coupled reactive pore- fluid flow and multiple species transport in porous media;(3) precipitation and dissolution of minerals and rock al- teration in the upper crust of the Earth;(4 ) double diffusion driven reactive flow transport in deformable fluid- saturated porous media with particular consideration of temperature- de- pendentchemical reaction rates;(5 ) pore- fluid flow patterns neargeological lenses in hydro- dynamic and hydrothermal systems;(6 ) dissipative structures for nonequilibrium chemical reactions in fluid- saturated porousmedia;(7) convectivepore- fluid flow and the related min- eralization in three- dimensional hydrothermal systems;(8) fluid- rock interaction problems associated with the rock alteration and metamorphic process in fluid- saturated hydrothermal/ sedimentary basins;and (9) various aspects of the fully coupled problem involving material deformation,pore- fluid flow,heattransferand species transport/ chemical reactionsin pore- fluid saturated porous rock masses. The above- mentioned work has significantly enriched our knowledge about the physical and chemical processes related to ore body formation and mineralization in the upper crustof the

Capacity Analysis for Dynamic Space Networks

To evaluate transmission rate of highly dynamic space networks,a new method for studying space network capacity is proposed in this paper. Using graph theory,network capacity is defined as the maximum amount of flows ground stations can receive per unit time. Combined with a hybrid constellation model,network capacity is calculated and further analyzed for practical cases. Simulation results show that network capacity will increase to different extents as link capacity,minimum ground elevation constraint and satellite onboard processing capability change. Considering the efficiency and reliability of communication networks,how to scientifically design satellite networks is also discussed.

Hope to be from model to practice——Words of the Editor-in-Chief

The article ＂3D palaeogeographic reconstructions of the Phanerozoic versus sea-level and Sr-ratio variations＂ contributed by Christian Verard, Cyril Hochard, Peter O. Baumgartner and Gerard M. Stampfli, is an academic thesis on global and mobile tectonopalaeogeography. The model proposed in this article makes it possible to reconstruct the surface features of topography since the Phanerozoic, i. e., the altitude above sea-level of oldland and the water depth ofpalaeoocean of＂anywhere on the globe and at any geological time＂. It is truly a significant creation.