A direct proof of uniqueness of square-root of a positive semi-definite tensor

Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields, especially for its square-root. Uniqueness of the square-root of a positive semi-definite tensor is proven in this paper without resorting to the notion of eigenvalues, eigenvectors and the spectral decomposition of the second-order symmetric tensor.

THE PRIMAL-DUAL POTENTIAL REDUCTION ALGORITHM FOR POSITIVE SEMI-DEFINITE PROGRAMMING

In this paper we introduce a primal-dual potential reduction algorithm for positive semi-definite programming. Using the symetric preserving scalings for both primal and dual interior matrices, we can construct an algorithm which is very similar to the primal-dual potential reduction algorithm of Huang and Kortanek [6] for linear programming. The complexity of the algorithm is either O(nlog(X0 · S0/ε) or O(nlog(X0· S0/ε) depends on the value of ρ in the primal-dual potential function, where X0 and S0 is the initial interior matrices of the positive semi-definite programming.

Positive health:An integrated quantitative approach in patients with chronic gastrointestinal and hepato-pancreatico-biliary disorders

BACKGROUND The concept of positive health(PH)supports an integrated approach for patients by taking into account six dimensions of health.This approach is especially relevant for patients with chronic disorders.Chronic gastrointestinal and hepatopancreatico-biliary(GI-HPB)disorders are among the top-6 of the most prevalent chronically affected organ systems.The impact of chronic GI-HPB disorders on individuals may be disproportionally high because:(1)The affected organ system frequently contributes to a malnourished state;and(2)persons with chronic GIHPB disorders are often younger than persons with chronic diseases in other organ systems.AIM To describe and quantify the dimensions of PH in patients with chronic GI-HPB disorders.METHODS Prospective,observational questionnaire study performed between 2019 and 2021 in 235 patients with a chronic GIHPB disorder attending the Outpatient Department of the Maastricht University Medical Center.Validated questionnaires and data from patient files were used to quantify the six dimensions of PH.Internal consistency was tested with McDonald’s Omega.Zero-order Pearson correlations and t-tests were used to assess associations and differences.A P value<0.05 was considered significant.RESULTS The GI-HPB patients scored significantly worse in all dimensions of PH compared to control data or norm scores from the general population.Regarding quality of life,participation and daily functioning,GI-HPB patients scored in the same range as patients with chronic disorders in other organ systems,but depressive symptoms(in 35%)and malnutrition(in 45%)were more frequent in patients with chronic GI-HPB disorders.Intercorrelation scores between the six dimensions were only very weak to weak,forcing us to quantify each domain separately.CONCLUSION All six dimensions of PH are impaired in the GI-HPB patients.Malnutrition and depressive symptoms are more prevalent compared to patients with chronic disorders in other organ systems.

Predictive value of positive lymph node ratio in patients with locally advanced gastric remnant cancer

BACKGROUND Traditional lymph node stage(N stage)has limitations in advanced gastric remnant cancer(GRC)patients;therefore,establishing a new predictive stage is necessary.AIM To explore the predictive value of positive lymph node ratio(LNR)according to clinicopathological characteristics and prognosis of locally advanced GRC.METHODS Seventy-four patients who underwent radical gastrectomy and lymphadenectomy for locally advanced GRC were retrospectively reviewed.The relationship between LNR and clinicopathological characteristics was analyzed.The survival analysis was performed using Kaplan-Meier survival curves and Cox regression model.RESULTS Number of metastatic LNs,tumor diameter,depth of tumor invasion,Borrmann type,serum tumor biomarkers,and tumor-node-metastasis(TNM)stage were correlated with LNR stage and N stage.Univariate analysis revealed that the factors affecting survival included tumor diameter,anemia,serum tumor biomarkers,vascular or neural invasion,combined resection,LNR stage,N stage,and TNM stage(all P<0.05).The median survival time for those with LNR0,LNR1,LNR2 and LNR3 stage were 61,31,23 and 17 mo,respectively,and the differences were significant(P=0.000).Anemia,tumor biomarkers and LNR stage were independent prognostic factors for survival in multivariable analysis(all P<0.05).CONCLUSION The new LNR stage is uniquely based on number of metastatic LNs,with significant prognostic value for locally advanced GRC,and could better differentiate overall survival,compared with N stage.

Reviewing Stability Criteria for Positive Homogeneous Systems and Adding One for Discrete-Time Cases with Degree Less Than One

The article synthesizes and presents the results regarding the stability of positive homogeneous systems that have been researched and published in recent years. Next, we provide a sufficient condition for global exponential stability in the case of discrete-time positive homogeneous systems with an order less than one with time-varying delays.

Impact of web-based positive psychological intervention on emotions,psychological capital,and quality of life in gastric cancer patients on chemotherapy

BACKGROUND Gastric cancer is a malignant digestive tract tumor that originates from the epithelium of the gastric mucosa and occurs in the gastric antrum,particularly in the lower curvature of the stomach.AIM To evaluate the impact of a positive web-based psychological intervention on emotions,psychological capital,and quality of survival in gastric cancer patients on chemotherapy.METHODS From January 2020 to October 2023,121 cases of gastric cancer patients on chemotherapy admitted to our hospital were collected and divided into a control group(n=60)and an observation group(n=61)according to the admission order.They were given either conventional nursing care alone and conventional nursing care combined with web-based positive psychological interventions,respectively.The two groups were compared in terms of negative emotions,psychological capital,degree of cancer-caused fatigue,and quality of survival.RESULTS After intervention,the number of patients in the observation group who had negative feelings toward chemotherapy treatment was significantly lower than that of the control group(P<0.05);the Positive Psychological Capital Questionnaire score was considerably higher than that of the control group(P<0.05);the degree of cancer-caused fatigue was significantly lower than that of the control group(P<0.05);and the Quality of Life Scale for Cancer Patients(QLQ-30)score was significantly higher than that of the control group(P<0.05).CONCLUSION Implementing a web-based positive psychological intervention for gastric cancer chemotherapy patients can effectively improve negative emotions,enhance psychological capital,and improve the quality of survival.

Health risk assessment of trace metal(loid)s in agricultural soils based on Monte Carlo simulation coupled with positive matrix factorization model in Chongqing, southwest China

This study aimed to investigate the pollution characteristics, source apportionment, and health risks associated with trace metal(loid)s(TMs) in the major agricultural producing areas in Chongqing, China. We analyzed the source apportionment and assessed the health risk of TMs in agricultural soils by using positive matrix factorization(PMF) model and health risk assessment(HRA) model based on Monte Carlo simulation. Meanwhile, we combined PMF and HRA models to explore the health risks of TMs in agricultural soils by different pollution sources to determine the priority control factors. Results showed that the average contents of cadmium(Cd), arsenic (As), lead(Pb), chromium(Cr), copper(Cu), nickel(Ni), and zinc(Zn) in the soil were found to be 0.26, 5.93, 27.14, 61.32, 23.81, 32.45, and 78.65 mg/kg, respectively. Spatial analysis and source apportionment analysis revealed that urban and industrial sources, agricultural sources, and natural sources accounted for 33.0%, 27.7%, and 39.3% of TM accumulation in the soil, respectively. In the HRA model based on Monte Carlo simulation, noncarcinogenic risks were deemed negligible(hazard index <1), the carcinogenic risks were at acceptable level(10^(-6)<total carcinogenic risk ≤ 10^(-4)), with higher risks observed for children compared to adults. The relationship between TMs, their sources, and health risks indicated that urban and industrial sources were primarily associated with As, contributing to 75.1% of carcinogenic risks and 55.7% of non-carcinogenic risks, making them the primary control factors. Meanwhile, agricultural sources were primarily linked to Cd and Pb, contributing to 13.1% of carcinogenic risks and 21.8% of non-carcinogenic risks, designating them as secondary control factors.

Effects of pulmonary surfactant combined with noninvasive positive pressure ventilation in neonates with respiratory distress syndrome

BACKGROUND Neonatal respiratory distress syndrome(NRDS)is one of the most common diseases in neonatal intensive care units,with an incidence rate of about 7%among infants.Additionally,it is a leading cause of neonatal death in hospitals in China.The main mechanism of the disease is hypoxemia and hypercapnia caused by lack of surfactant AIM To explore the effect of pulmonary surfactant(PS)combined with noninvasive positive pressure ventilation on keratin-14(KRT-14)and endothelin-1(ET-1)levels in peripheral blood and the effectiveness in treating NRDS.METHODS Altogether 137 neonates with respiratory distress syndrome treated in our hospital from April 2019 to July 2021 were included.Of these,64 control cases were treated with noninvasive positive pressure ventilation and 73 observation cases were treated with PS combined with noninvasive positive pressure ventilation.The expression of KRT-14 and ET-1 in the two groups was compared.The deaths,complications,and PaO_(2),PaCO_(2),and PaO_(2)/FiO_(2)blood gas indexes in the two groups were compared.Receiver operating characteristic curve(ROC)analysis was used to determine the diagnostic value of KRT-14 and ET-1 in the treatment of NRDS.RESULTS The observation group had a significantly higher effectiveness rate than the control group.There was no significant difference between the two groups in terms of neonatal mortality and adverse reactions,such as bronchial dysplasia,cyanosis,and shortness of breath.After treatment,the levels of PaO_(2)and PaO_(2)/FiO_(2)in both groups were significantly higher than before treatment,while the level of PaCO_(2)was significantly lower.After treatment,the observation group had significantly higher levels of PaO_(2)and PaO_(2)/FiO_(2)than the control group,while PaCO_(2)was notably lower in the observation group.After treatment,the KRT-14 and ET-1 levels in both groups were significantly decreased compared with the pre-treatment levels.The observation group had a reduction of KRT-14 and ET-1 levels than the control group.ROC curve analysis showed that the area under the curve(AUC)of KRT-14 was 0.791,and the AUC of ET-1 was 0.816.CONCLUSION Combining PS with noninvasive positive pressure ventilation significantly improved the effectiveness of NRDS therapy.KRT-14 and ET-1 levels may have potential as therapeutic and diagnostic indicators.

False Positive HIV “Combo” Screening Test in a Hemodialysis Patient in Saudi Arabia: A Case Report and Review of the Literature

Introduction: HIV screening tests are routinely conducted on dialysis patients as the constant exposure of their blood during the dialysis process makes them a reasonable risk for blood-borne infections. However, in low prevalence settings, where HIV rates are <0.1% of the population, false positive results are more likely. This results in apprehension in the dialysis unit as breaches in infectious disease protocols could be presumed. This is illustrated in the case report below. Case Summary: A 62-year-old male Saudi end-stage kidney disease patient secondary to DM nephropathy began dialysis a year before presentation in a hemodialysis center in Saudi Arabia. Routine screening tests done at the start of dialysis revealed negative Hepatitis C, HIV 1 and 2 screening but a positive Hepatitis B surface antigen screen. The patient went for holiday dialysis at another facility and had a routine fourth-generation HIV test done which was positive. A confirmatory HIV PCR test was negative. Conclusion: This case highlights the need for caution in interpreting highly sensitive and specific HIV screening tests in a low-prevalence setting. Routine screening beyond the national recommendation may not be necessary in low-prevalence areas.

A Review of Research on Second Language Acquisition from a Positive Psychology Perspective

This paper reviews the research on second language acquisition from the perspective of positive psychology.First,it introduces the background and purpose of the study and discusses the significance of the application of positive psychology in the field of language acquisition.Then,the basic theories of positive psychology,including the core concepts and principles of positive psychology,are summarized.Subsequently,the theory of second language acquisition is defined and outlined,including the definition,characteristics,and related developmental theories of second language acquisition.On this basis,the study of second language acquisition from the perspective of positive psychology is discussed in detail.By combing and synthesizing the literature,this paper summarizes the current situation and trend of second language acquisition research under the perspective of positive psychology and puts forward some future research directions and suggestions.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

The Impact of Positive Psychological Intervention on English Teaching

This study aims to explore the application of positive psychological intervention in English teaching and its impact on students’learning.Through literature review,empirical research,and case analysis,this paper deeply analyzes the positive effect of positive psychological intervention on students’learning motivation,attitude,and performance,and puts forward specific suggestions for the implementation of positive psychological intervention in teaching practice.

A Discussion on Chinese Family Education from the Perspective of Positive Psychology

In modern society,positive psychology has gained increasing attention as an important branch of psychology.This paper explores some issues and educational strategies in modern family education from the perspective of positive psychology.Firstly,the paper introduces the origin and basic concepts of positive psychology.Secondly,the current situation and problems of Chinese family education are analyzed.Lastly,a series of strategies applicable to family education based on the principles of positive psychology are proposed.These strategies include establishing a positive family education environment,cultivating children’s positive psychological qualities,adopting positive educational approaches and methods,paying attention to children’s individual differences and diverse development,fostering children’s positive emotional experiences and expression abilities,as well as enhancing children’s social adaptability.By implementing these strategies,family education can better promote children’s holistic development,improve their mental health and well-being,and lay a solid foundation for their future.

Exploration of the Integration of Positive Emotions and Flow Experience in STEAM Education

STEAM(science,technology,engineering,arts,and mathematics)education aims to cultivate innovative talents with multidimensional literacy through interdisciplinary integration and innovative practice.However,lack of student motivation has emerged as a key factor hindering its effectiveness.This study explores the integrated application of positive emotions and flow experience in STEAM education from the perspective of positive psychology.It systematically explains how these factors enhance learning motivation and promote knowledge internalization,proposing feasible pathways for instructional design,resource provision,environment creation,and team building.The study provides theoretical insights and practical guidance for transforming STEAM education in the new era.

The relationship between the distribution of HBcAg in liver cells and the pathological manifestations of the liver in 429 HBeAg-positive chronic HBV-infected individuals

Background:The natural history of chronic HBV infection is typically characterized by four stages:the immune tolerance period,the immune clearance period,the immune control period,and the immune escape period.These stages are associated with the distribution of HBcAg in liver cells;however,this relationship remains a topic of broad debate within the field of liver disease.To objectively and quantitatively measure the intracellular distribution of HBcAg,this paper aims to design a method referred to as the“layered evaluation method”and to examine its validation.Methods:The distribution of HBcAg in liver cells is assessed using Image Pro Plus image processing software,along with calculations of cytoplasmic and nuclear positive staining rates.Results:The findings indicate that the highest proportion of patients exhibited a positive cytoplasmic expression rate ranging from 0-2.5%.More than 40% of the total sample was categorized within the 0-2.5% positive nuclear expression range.The HBcAg cytoplasmic positive staining rates were classified into five levels:a cytoplasmic HBcAg positive staining rate of less than 0.05% is designated as level 0,indicating negative expression;a staining rate between 0.05% and 5% is classified as level 1;a rate from 5% to less than 10% is classified as level 2;a rate from 10% to less than 20% is classified as level 3;and a nuclear positivity rate exceeding 20% is classified as level 4.Conclusion:The inflammatory activity grade in these patients was positively correlated with the cytoplasmic distribution of HBcAg.Furthermore,the nuclear distribution rate of HBcAg was significantly higher in the G3 group compared to the other groups.

Analysis of the Effect of Non-Invasive Positive Pressure Ventilation in Emergency Treatment of Severe Bronchial Asthma with Respiratory Failure

Objective:This study aims to evaluate the clinical efficacy of non-invasive positive pressure ventilation(NIPPV)in patients with severe bronchial asthma combined with respiratory failure.Methods:90 patients with severe bronchial asthma combined with respiratory failure between September 2022 and December 2023 were selected for the study and randomly divided into the experimental group(NIPPV-assisted treatment)and the control group.The differences between the two groups were compared in terms of total effective rate of treatment,days of clinical symptom disappearance,days of hospitalization,lung function indexes,incidence of adverse reactions,and quality of life.Results:Patients in the experimental group had a significantly higher total effective rate of treatment(97.78%)than the control group(75.56%).In terms of pulmonary function indexes,patients in the experimental group showed significant improvement after treatment,especially the increase in forced expiratory volume and forced vital capacity,while these improvements were not as obvious in the control group.In addition,the incidence of adverse reactions was significantly lower in the experimental group than in the control group,suggesting that the application of NIPPV is relatively safe.Quality of life assessment also showed that patients in the experimental group had significantly better quality of life than the control group after treatment.Conclusion:This study demonstrated the effectiveness of NIPPV as an adjunctive treatment for severe bronchial asthma combined with respiratory failure.NIPPV can improve lung function,reduce the incidence of adverse effects,increase the overall effectiveness of the treatment,and contribute to the improvement of patients'quality of life.Therefore,NIPPV should be regarded as an effective and safe treatment in clinical management,especially in patients with severe bronchial asthma combined with respiratory failure,where its application has potential clinical significance.

The Prevalence of Overweight/Obesity and Related Comorbidities among HIV-Positive and HIV-Negative Patients Attending the Same Clinics in Gaborone, Botswana

Context: Antiretroviral therapy (ART) helps restore the health status of people living with HIV (PLHIV). Likewise, it increases the risk of overweight/obesity and related comorbidities among the recipients. In countries like Botswana where ±84% of PLHIV is on ART, the paucity of data comparing overweight/obesity between HIV-positive on ART and HIV-negative patients may impede clinical and policy decision-making. This study sought to estimate and compare: i) the prevalence of overweight/obesity between HIV-positive on ART and HIV-negative patients;ii) the prevalence of hypertension (HTN), diabetes mellitus (DM)/coronary heart disease (CHD) between HIV-positive patients on ART and HIV-negative patients attending same outpatient departments of general clinics in Gaborone, Botswana. Patients and Methods: Five hundred eighty-one (581) outpatients were recruited in four major clinics of Gaborone, Botswana, between June and July 2019;294 or 51% of them were HIV-negative and 287 or 49% were HIV-positive on ART. The prevalence of overweight/obesity and of HTN and DM/CHD were calculated and examined using stratified analysis. Subgroups were compared using Chi-square analysis with Yates correction or Fisher exact test and t-student test for continuous data. Results: Major findings after stratification of the study population by HIV status were: i) the prevalence of all categories of (BMI), including overweight/obesity, were comparable between HIV-negative-patients and HIV-positive. In fact, there were 24 (8.0%) cases of underweight among HIV-negative-Patients and 15(5%) cases among HIV-positive patients, p = 0.2;145 (49%) HIV-negative-patients and 128 (45%) HIV-positive, p = 0.07 cases of normal weight;72 (25%) HIV-negative-patients and 87 (30%) HIV-positive, p = 0.08, were overweight;53 (18%) HIV-negative-patients and 57 (20%) HIV-positive, p = 0.12, were obese;125 (43%) HIV-negative patients and 144 (50%) HIV-positive, p=0.06 were overweight/obese;ii) the prevalence of HTN and DM/CHD among HIV-positive-patients were significantly lower (p < 0.05) compared to HIV-negative patients: There were 32 (10.9%) cases of HTN among HIV-negative patients compared to 18 (6.3%) cases of HTN among HIV-positive patients, p = 0.001;32 (11%) cases of DM/CHD HIV-negative patients compared to 4 (1.4%) cases of DM/CHD among HIV-positive patients, p = 0.001. Conclusion: the prevalence of overweight/obesity observed between HIV-negative and HIV-positive patients may suggest that the two groups shared the same exposure factors. That HTN and DM/CHD prevalence was lower among HIV-positive compared to HIV-negative patients, is possibly due to interplay factors of ART, HIV or the host population. Further studies are, however, recommended for clarifications.

ON THE GENERALIZED DETERIORATED POSITIVE SEMI-DEFINITE AND SKEW-HERMITIAN SPLITTING PRECONDITIONER

For nonsymmetric saddle point problems,Huang et al.in [Numer.Algor.75 (2017), pp.1161-1191]established a generalized variant of the deteriorated positive semi-definite and skew-Hermitian splitting (GVDPSS)preconditioner to expedite the convergence speed of the Krylov subspace iteration methods like the GMRES method.In this paper,some new convergence properties as well as some new numerical results are presented to validate the theoretical results.

A Positive Influence Maximization Algorithm in Signed Social Networks

The influence maximization(IM)problem aims to find a set of seed nodes that maximizes the spread of their influence in a social network.The positive influence maximization(PIM)problem is an extension of the IM problem,which consider the polar relation of nodes in signed social networks so that the positive influence of seeds can be the most widely spread.To solve the PIM problem,this paper proposes the polar and decay related independent cascade(IC-PD)model to simulate the influence propagation of nodes and the decay of information during the influence propagation in signed social networks.To overcome the low efficiency of the greedy based algorithm,this paper defines the polar reverse reachable(PRR)set and devises a signed reverse influence sampling(SRIS)algorithm.The algorithm utilizes the ICPD model as well as the PRR set to select seeds.There are two phases in SRIS.One is the sampling phase,which utilizes the IC-PD model to generate the PRR set and a binary search algorithm to calculate the number of needed PRR sets.The other is the node selection phase,which uses a greedy coverage algorithm to select optimal seeds.Finally,Experiments on three real-world polar social network datasets demonstrate that SRIS outperforms the baseline algorithms in effectiveness.Especially on the Slashdot dataset,SRIS achieves 24.7% higher performance than the best-performing compared algorithm under the weighted cascade model when the seed set size is 25.

Research on the Generation Path of Heuristic Teaching Language Based on Positive Psychology Theory

As the essence of traditional Chinese educational thought,heuristic teaching has gradually enriched and devel-oped its ideas through the continuous efforts of educational researchers of the past dynasties.In front-line teach-ing,heuristic teaching,as a teaching principle that can help teachers and students to interact and learn,undoubtedly plays an important role in students’acquisition of knowledge and scientific thinking activities.But teachers’understanding of heuristic teaching is not the same.In actual teaching,there are obvious gaps in language ability among different teachers.This research aims to enrich the heuristic teaching theory based on the perspective of psychology,and provide a certain theoretical basis for teacher training.Through the research and analysis of the generation path of the heuristic teaching language,this paper helps more teachers realize the advantages of the heuristic teaching language,improve their own heuristic teaching language level,and provide reference for the scientific teaching evaluation standard.We apply the heuristic instruction language approach proposed in this study and apply it to real classrooms.In the application,it can be clearly found that the students’thinking and participation have been strengthened,and the teaching effect has been significantly improved com-pared with the past,which indicates that the heuristic teaching language generation path in this study has certain practical application value.