Research on the independence polynomial of graphs has been very active.However,the computational complexity of determining independence polynomials for general graphs remains NP-hard.Letα(G)be the independence number...Research on the independence polynomial of graphs has been very active.However,the computational complexity of determining independence polynomials for general graphs remains NP-hard.Letα(G)be the independence number of G and i(G;k)be the number of independent sets of order k in G,then the independence polynomial is defined as I(G;x)=∑_(k=0)^(α(G))i(G;k)x^(k),i(G;0)=1.In this paper,by utilizing the transfer matrix,we obtain an analytical expression for I(CGn;x)of mono-cylindrical grid graphs CGn and present a crucial proof of it.Moreover,we also explore the Merrifield-Simmons index and other properties of CGn.展开更多
The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Ho- soya index of a graph is defined as the total number of the match- ings of the graph. In this pap...The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Ho- soya index of a graph is defined as the total number of the match- ings of the graph. In this paper, the definition of a class of po- lygonal chains is given, ordering of the polygonal chains with respect to Merrifield-Simmons index and Hosoya index are ob- tained, and their extremal graphs with respect to these two topo- logical indices are determined.展开更多
In this paper, we give the ordering of single-corner hexagonal chains with respect to Merrifield-Simmons index. At the same time, the hexagonal chain with the second largest Merrifield-Simmons index is also determined.
The Gabes aquifer system,located in southeastern Tunisia,is a crucial resource for supporting local socio-economic activities.Due to its dual porosity structure,is particularly vulnerable to pollution.This study aims ...The Gabes aquifer system,located in southeastern Tunisia,is a crucial resource for supporting local socio-economic activities.Due to its dual porosity structure,is particularly vulnerable to pollution.This study aims to develop a hybrid model that combines the Fracture Aquifer Index(FAI)with the conventional GOD(Groundwater occurrence,Overall lithology,Depth to water table)method,to assess groundwater vulnerability in fractured aquifer.To develop the hybrid model,the classical GOD method was integrated with FAI to produce a single composite index.Each parameter within both GOD and FAI was scored,and a final index was calculated to delineate vulnerable areas.The results show that the study area can be classified into four vulnerability levels:Very low,low,moderate,and high,indicating that approximately 8%of the area exhibits very low vulnerability,29%has low vulnerability,25%falls into the moderate category,and 38%is considered highly vulnerable.The FAI-GOD model further incorporates fracture network characteristics.This refinement reduces the classification to three vulnerability classes:Low,medium,and high.The outcomes demonstrate that 46%of the area is highly vulnerable due to a dense concentration of fractures,while 17%represents an intermediate zone characterized by either shallow or deeper fractures.In contrast,37%corresponds to areas with lightly fractured rock,where the impact on vulnerability is minimal.Multivariate statistical analysis was employed using Principal Components Analysis(PCA)and Hierarchical Cluster Analysis(HCA)on 24 samples across six variables.The first three components account for over 76%of the total variance,reinforcing the significance of fracture dynamics in classifying vulnerability levels.The FAI-GOD model removes the very-low-vulnerability class and expands the spatial extent of low-and high-vulnerability zones,reflecting the dominant influence of fracture networks on aquifer sensitivity.While both indices use a five-class system,FAI-GOD redistributes vulnerability by eliminating very-low-vulnerability areas and amplifying low/high categories,highlighting the critical role of fractures.A strong correlation(R2=0.94)between the GOD and FAI-GOD indices,demonstrated through second-order polynomial regression,confirms the robustness of the FAI-GOD model in accurately predicting vulnerability to pollution.This model provides a useful framework for assessing the vulnerability of complex aquifers and serves as a decision-making tool for groundwater managers in similar areas.展开更多
This commentary critically appraises the study by Li et al which pioneered the exploration of the triglyceride-glucose(TyG)index as a prognostic marker in hepatitis B virus-related advanced hepatocellular carcinoma pa...This commentary critically appraises the study by Li et al which pioneered the exploration of the triglyceride-glucose(TyG)index as a prognostic marker in hepatitis B virus-related advanced hepatocellular carcinoma patients undergoing combined camrelizumab and lenvatinib therapy.While we acknowledge the study’s clinical relevance in proposing an easily accessible metabolic biomarker,we delve into the mechanistic plausibility linking insulin resistance to immunotherapy response and angiogenic inhibition.We further critically examine the methodological limitations,including the retrospective design,the populationspecific TyG cut-off value,and unaddressed metabolic confounders.We highlight the imperative for future research to validate its utility across diverse etiologies and treatment settings,and to unravel the underlying immunometabolic pathways.展开更多
BACKGROUND Timely and accurate evaluation of mental disorders in adolescents using appropriate mental health literacy assessment tools is essential for improving their mental health literacy levels.AIM To develop an e...BACKGROUND Timely and accurate evaluation of mental disorders in adolescents using appropriate mental health literacy assessment tools is essential for improving their mental health literacy levels.AIM To develop an evaluation index system for the mental health literacy of adolescent patients with mental disorders,providing a scientific,comprehensive,and reliable tool for the monitoring and intervention of mental health literacy of such patients.METHODS From December 2022 to June 2023,the evaluation index system for mental health literacy of adolescents with mental disorders was developed through literature reviews,semi-structured interviews,expert letter consultations,and the analytic hierarchy process.Based on this index system,a self-assessment questionnaire was compiled and administered to 305 adolescents with mental disorders to test the reliability and validity of the index system.RESULTS The final evaluation index system for mental health literacy of adolescents with mental disorders included 4 first-level indicators,10 second-level indicators,and 52 third-level indicators.The overall Cronbach’sαcoefficient of the index system was 0.957,with a partial reliability of 0.826 and a content validity index of 0.975.The cumulative variance contribution rate of 10 common factors was 66.491%.The correlation coefficients between each dimension and the total questionnaire ranged from 0.672 to 0.724,while the correlation coefficients in each dimension ranged from 0.389 to 0.705.CONCLUSION The evaluation index system for mental health literacy of adolescents with mental disorders,developed in this study,demonstrated notable reliability and validity,making it a valuable tool for evaluating mental health literacy in this population.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.U20A20228)Huzhou Science and Technology Plan Project(Grant No.2022YZ53).
文摘Research on the independence polynomial of graphs has been very active.However,the computational complexity of determining independence polynomials for general graphs remains NP-hard.Letα(G)be the independence number of G and i(G;k)be the number of independent sets of order k in G,then the independence polynomial is defined as I(G;x)=∑_(k=0)^(α(G))i(G;k)x^(k),i(G;0)=1.In this paper,by utilizing the transfer matrix,we obtain an analytical expression for I(CGn;x)of mono-cylindrical grid graphs CGn and present a crucial proof of it.Moreover,we also explore the Merrifield-Simmons index and other properties of CGn.
基金Supported by the National Natural Science Foundation of China(11161041)Innovative Team Subsidize of Northwest University for Nationalitiesthe Fundamental Research Funds for the Central Universities(31920140059)
文摘The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Ho- soya index of a graph is defined as the total number of the match- ings of the graph. In this paper, the definition of a class of po- lygonal chains is given, ordering of the polygonal chains with respect to Merrifield-Simmons index and Hosoya index are ob- tained, and their extremal graphs with respect to these two topo- logical indices are determined.
基金This research was supported by Fujian Education Committee Foundation.
文摘In this paper, we give the ordering of single-corner hexagonal chains with respect to Merrifield-Simmons index. At the same time, the hexagonal chain with the second largest Merrifield-Simmons index is also determined.
文摘The Gabes aquifer system,located in southeastern Tunisia,is a crucial resource for supporting local socio-economic activities.Due to its dual porosity structure,is particularly vulnerable to pollution.This study aims to develop a hybrid model that combines the Fracture Aquifer Index(FAI)with the conventional GOD(Groundwater occurrence,Overall lithology,Depth to water table)method,to assess groundwater vulnerability in fractured aquifer.To develop the hybrid model,the classical GOD method was integrated with FAI to produce a single composite index.Each parameter within both GOD and FAI was scored,and a final index was calculated to delineate vulnerable areas.The results show that the study area can be classified into four vulnerability levels:Very low,low,moderate,and high,indicating that approximately 8%of the area exhibits very low vulnerability,29%has low vulnerability,25%falls into the moderate category,and 38%is considered highly vulnerable.The FAI-GOD model further incorporates fracture network characteristics.This refinement reduces the classification to three vulnerability classes:Low,medium,and high.The outcomes demonstrate that 46%of the area is highly vulnerable due to a dense concentration of fractures,while 17%represents an intermediate zone characterized by either shallow or deeper fractures.In contrast,37%corresponds to areas with lightly fractured rock,where the impact on vulnerability is minimal.Multivariate statistical analysis was employed using Principal Components Analysis(PCA)and Hierarchical Cluster Analysis(HCA)on 24 samples across six variables.The first three components account for over 76%of the total variance,reinforcing the significance of fracture dynamics in classifying vulnerability levels.The FAI-GOD model removes the very-low-vulnerability class and expands the spatial extent of low-and high-vulnerability zones,reflecting the dominant influence of fracture networks on aquifer sensitivity.While both indices use a five-class system,FAI-GOD redistributes vulnerability by eliminating very-low-vulnerability areas and amplifying low/high categories,highlighting the critical role of fractures.A strong correlation(R2=0.94)between the GOD and FAI-GOD indices,demonstrated through second-order polynomial regression,confirms the robustness of the FAI-GOD model in accurately predicting vulnerability to pollution.This model provides a useful framework for assessing the vulnerability of complex aquifers and serves as a decision-making tool for groundwater managers in similar areas.
文摘This commentary critically appraises the study by Li et al which pioneered the exploration of the triglyceride-glucose(TyG)index as a prognostic marker in hepatitis B virus-related advanced hepatocellular carcinoma patients undergoing combined camrelizumab and lenvatinib therapy.While we acknowledge the study’s clinical relevance in proposing an easily accessible metabolic biomarker,we delve into the mechanistic plausibility linking insulin resistance to immunotherapy response and angiogenic inhibition.We further critically examine the methodological limitations,including the retrospective design,the populationspecific TyG cut-off value,and unaddressed metabolic confounders.We highlight the imperative for future research to validate its utility across diverse etiologies and treatment settings,and to unravel the underlying immunometabolic pathways.
基金Supported by Inter Disciplinary Direction Cultivation Project of Hunan University of Chinese Medicine,No.2025JC01032025 Hunan Province Science and Technology Innovation Plan Project,No.2025RC9012+2 种基金2022"Unveiling and Leading"Project of Discipline Construction at Hunan University of Chinese Medicine,No.22JBZ044Changsha Municipal Natural Science Foundation,No.kq2402174Hunan Provincial Science Popularization Fund Project,No.2025ZK4223.
文摘BACKGROUND Timely and accurate evaluation of mental disorders in adolescents using appropriate mental health literacy assessment tools is essential for improving their mental health literacy levels.AIM To develop an evaluation index system for the mental health literacy of adolescent patients with mental disorders,providing a scientific,comprehensive,and reliable tool for the monitoring and intervention of mental health literacy of such patients.METHODS From December 2022 to June 2023,the evaluation index system for mental health literacy of adolescents with mental disorders was developed through literature reviews,semi-structured interviews,expert letter consultations,and the analytic hierarchy process.Based on this index system,a self-assessment questionnaire was compiled and administered to 305 adolescents with mental disorders to test the reliability and validity of the index system.RESULTS The final evaluation index system for mental health literacy of adolescents with mental disorders included 4 first-level indicators,10 second-level indicators,and 52 third-level indicators.The overall Cronbach’sαcoefficient of the index system was 0.957,with a partial reliability of 0.826 and a content validity index of 0.975.The cumulative variance contribution rate of 10 common factors was 66.491%.The correlation coefficients between each dimension and the total questionnaire ranged from 0.672 to 0.724,while the correlation coefficients in each dimension ranged from 0.389 to 0.705.CONCLUSION The evaluation index system for mental health literacy of adolescents with mental disorders,developed in this study,demonstrated notable reliability and validity,making it a valuable tool for evaluating mental health literacy in this population.
