Minor Self-conjugate and Skewpositive Semidefinite Solutions to a System of Matrix Equations over Skew Fields

Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and sufficient conditions for the existence of and the expressions for the msc solutions and the ssd solutions are obtained for the system.

THE SYMMETRIC AND SYMMETRIC POSITIVE SEMIDEFINITE SOLUTIONS OF LINEAR MATRIX EQUATION——B^TXB = D ON LINEAR MANIFOLDS

This paper discusses the solutions of the linear matrix equation BT X B=Don some linear manifolds.Some necessary and sufficient conditions for the existenceof the solution and the expression of the general solution are given.And also someoptimal approximation solutions are discussed.

COMPUTING THE NEAREST BISYMMETRIC POSITIVE SEMIDEFINITE MATRIX UNDER THE SPECTRAL RESTRICTION

Let A and C denote real n × n matrices. Given real n-vectors x1,……… ,xm,m≤n,and a set of numbers (L)={λ1,λ2…λm}，We descrbe(Ⅰ)the set( ) of all real n × n bisymmetric positive seidefinite matrices A such that Axi is the "best"approximate to λixi, i = 1, 2,..., m in Frobenius norm and (Ⅱ) the Y in set ( )which minimize Frobenius norm of ||C - Y||.An existence theorem of the solutions for Problem Ⅰ and Problem Ⅱ is given andthe general expression of solutions for Problem Ⅰ is derived. Some sufficient conditionsunder which Problem Ⅰ and Problem Ⅱ have an explicit solution is provided. A numer-ical algorithm of the solution for Problem Ⅱ has been presented.

PROBLEM OF EQUALITIES IN EIGENVALUE INEQUALITIES FOR PRODUCTS OF POSITIVE SEMIDEFINITE HERMITIAN MATRICES

Let A∈Cm×n,set eigenvalues of matrix A with |λ1 （A）|≥|λ2（A）|≥…≥|λn（A）|,write A≥0 if A is a positive semidefinite Hermitian matrix, and denote∧k （A）=diag （λ1（A）,…,λk（A））,∧(（n-k）.（A）=diag (λk+1（A）,…,λn（A）)for any k=1, 2,...,n if A≥0. Denote all n order unitary matrices by Un×n.Problem of equalities to hold in eigenvalue inequalities for products of matrices

TWO-STAGE MULTISPLITTING OF SYMMETRIC POSITIVE SEMIDEFINITE MATRICES

Main resultsTheorem 1 Let A be symmetric positive semidefinite.Let (?) be a diagonally compen-sated reduced matrix of A and Let (?)=σI+(?)(σ】0) be a modiffication(Stieltjes) matrixof (?).Let the splitting (?)=M-(?) be regular and M=F-G be weak regular,where M andF are symmetric positive definite matrices.Then the resulting two-stage method corre-sponding to the diagonally compensated reduced splitting A=M-N and inner splitting M=F-G is convergent for any number μ≥1 of inner iterations.Furthermore,the

Generalized bipositive semidefinite solutions to a system of matrix equations

In this paper, a system of complex matrix equations was studied. Necessary and sufficient conditions for the existence and the expression of generalized bipositive semidefinite solution to the system were given. In addition, a criterion for a matrix to be generalized bipositive semidefinite was determined.

THE POSITIVE SEMIDEFINITE SOLUTION OF THE MATRIX EQUATION (A^TXA, B^TXB) = (C, D)

In this paper, we consider the positive semidefinite solution of the matrix equation (AT X A, BT X B) - (C, D). A necessary and sufficient condition for the existence of such solution is derived using the generalized singular value decomposition.The general forms of positive semidefinite solution are given.

Assessment of Liver Fibrosis in HBsAg-Negative and Anti HBc Positive Patients

Background: Surface antigen (HBsAg) is the mean marker of hepatitis B virus infection. During the course of the infection, some patients lose the HBsAg and only the presence of anti-HBc antibody indicates previous contact with the virus. Among these patients, some have detectable viral load (occult infection) but most without viral replication. There is no guideline regarding these patients. The aim of this study was to assess hepatic fibrosis in patients with only the hepatitis B virus contact marker “total anti-HBc”. Patients and methods: it was a descriptive and analytical cross-sectional study, conducted in three private hospitals from January to August 2022. Were included HBsAg-negative and HBc-positive patients, consulting in Gastroenterology departments. Noninvasive methods (APRI, FIB-4 and FIBROSCAN) were used to evaluate liver stiffness because of their easy accessibility and low-cost. The hepatic fibrosis was considered significant when the score determined by APRI, FIB-4 and FIBROSCAN® tests was respectively greater than 1.5;2.67 and 8 kPa corresponding to fibrosis level 2 (F2). Results: A total of 63 HBsAg-negative/total HBcAg-positive patients were included. The mean age was 49.9 ± 13.4 years. The male/female sex ratio was 1.78. Of the 63 patients, 19 had significant liver fibrosis (30.1%) among which 9 patients had HCC. The FIB-4 score outperformed the APRI score in assessing liver fibrosis, with a sensitivity of 84.2%, a specificity of 100% and a negative predictive value of 93.6%. In univariate analysis, there was a significant association between the occurrence of significant liver fibrosis and age over 40 years, dyslipidaemia, obesity, alcohol consumption, smoking, herbal medicine, negative anti-HBs immunological status and detectable viral load. Conclusion: Our study revealed a high prevalence of significant to severe hepatic fibrosis in anti-HBc positive patients. In most of the cases, the fibrosis was severe. Progression to HCC has also been possible. There is no consensus on the follow-up strategy for those patients. However, screening for hepatic fibrosis using noninvasive methods should be recommended for patients aged over 40 years, alcohol or herbal medicine users, patients with metabolic syndrome or occult hepatitis B. In HBsAg-negative/anti-HBc-positive patients, liver stiffness should be evaluated and if it is greater than F2, HCC screening should be started.

Embedding Perovskite in Polymer Matrix Achieved Positive Temperature Response with Inversed Temperature Crystallization

Organic perovskites are promising semiconductor materials for advanced photoelectric applications.Their fluorescence typically shows a negative temperature coefficient due to bandgap change and structural instability.In this study,a novel perovskite-based composite with positive sensitivity to temperature was designed and obtained based on its inverse temperature crystallization,demonstrating good flexibility and solution processability.The supercritical drying method was used to address the limitations of annealing drying in preparing high-performance perovskite.Optimizing the precursor composition proved to be an effective approach for achieving high fluorescence and structural integrity in the perovskite material.This perovskite-based composite exhibited a positive temperature sensitivity of 28.563%℃^(-1)for intensity change and excellent temperature cycling reversibility in the range of 25-40℃in an ambient environment.This made it suitable for use as a smart window with rapid response.Furthermore,the perovskite composite was found to offer temperature-sensing photoluminescence and flexible processability due to its components of perovskite-based compounds and polyethylene oxide.The organic precursor solvent could be a promising candidate for use as ink to print or write on various substrates for optoelectronic devices responding to temperature.

Amplifying colorectal cancer progression: impact of a PDIA4/SP1 positive feedback loop by circPDIA4 sponging miR-9-5p

Objective:Colorectal cancer(CRC)is a prevalent malignant tumor with a high fatality rate.CircPDIA4 has been shown to have a vital role in cancer development by acting as a facilitator.Nevertheless,the impact of the circPDIA4/miR-9-5p/SP1 axis on development of CRC has not been studied.Methods:Western blot,immunohistochemistry,and reverse transcription-quantitative polymerase chain reaction assays were used to analyze gene expression.The CCK-8 assay was used to assess cell growth.The Transwell assay was used to detect invasion and migration of cells.The luciferase reporter and RNA immunoprecipitation tests were used to determine if miR-9-5p and circPDIA4(or SP1)bind to one another.An in vivo assay was used to measure tumor growth.Results:It was shown that circPDIA4 expression was greater in CRC cell lines and tissues than healthy cell lines and tissues.CircPDIA4 knockdown prevented the invasion,migration,and proliferation of cells in CRC.Additionally,the combination of circPDIA4 and miR-9-5p was confirmed,as well as miR-9-5p binding to SP1.Rescue experiments also showed that the circPDIA4/miR-9-5p/SP1 axis accelerated the development of CRC.In addition,SP1 combined with the promoter region of circPDIA4 and induced circPDIA4 transcription.CircPDIA4 was shown to facilitate tumor growth in an in vivo assay.Conclusions:The circPDIA4/miR-9-5p/SP1 feedback loop was shown to aggravate CRC progression.This finding suggests that the ceRNA axis may be a promising biomarker for CRC patient treatment.

Observation and analysis of positive leader re-illumination in a 10 m ultra-high voltage transmission line gap under switching impulse voltages

The leader propagation is one of the most important stages in long air gap discharge.The mechanism behind leader re-illumination remains unclear.In high humidity conditions(20.0–30.1 g/m^(3)),we have conducted experiments of long sparks in a 10 m ultra-high voltage(UHV)transmission line gap under switching impulse voltages.The positive leaders predominantly propagate discontinuously,with almost no significantly continuous propagation occurring.The leader channels are intensely luminous and each elongation segment is straight,with streamers resembling the“branch type”which differs from the“diffuse type”streamers at the front of continuous propagation leaders.The distribution of the propagation velocities is highly random(3.7–18.4 cm/μs),and the average velocity(9.2 cm/μs)significantly exceeds that of continuous propagation(1.5–2.0 cm/μs).Analysis suggests that the current-velocity models suitable for continuous leader propagation do not align well with the experimental data in re-illumination mode.Based on the discharge current waveforms and optical images,it is speculated that the newly elongated leader in re-illumination mode does not evolve gradually from the stem(about 1 cm)but rather evolves overall from a thermal channel much longer than stem.

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.