Lassa Fever(LF)is a viral hemorrhagic illness transmitted via rodents and is endemic in West Africa,causing thousands of deaths annually.This study develops a dynamic model of Lassa virus transmission,capturing the pr...Lassa Fever(LF)is a viral hemorrhagic illness transmitted via rodents and is endemic in West Africa,causing thousands of deaths annually.This study develops a dynamic model of Lassa virus transmission,capturing the progression of the disease through susceptible,exposed,infected,and recovered populations.The focus is on simulating this model using the fractional Caputo derivative,allowing both qualitative and quantitative analyses of boundedness,positivity,and solution uniqueness.Fixed-point theory and Lipschitz conditions are employed to confirm the existence and uniqueness of solutions,while Lyapunov functions establish the global stability of both disease-free and endemic equilibria.The study further examines the role of the Caputo operator by solving the generalized power-law kernel via a two-step Lagrange polynomial method.This approach offers practical advantages in handling additional data points in integral forms,though Newton polynomial-based schemes are generally more accurate and can outperform Lagrange-based Adams-Bashforth methods.Graphical simulations validate the proposed numerical approach for different fractional orders(ν)and illustrate the influence of model parameters on disease dynamics.Results indicate that increasing the fractional order accelerates the decline of Lassa fever in both human and rodent populations.Moreover,fractional-order modeling provides more nuanced insights than traditional integer-order models,suggesting potential improvements for medical intervention strategies.The study demonstrates that carefully chosen fractional orders can optimize convergence and enhance the predictive capacity of Lassa fever models,offering a promising direction for future research in epidemiological modeling.展开更多
Background There is still limited data on predictive value of coronary computed tomography angiography(CCTA)–derived fractional flow reserve(CT-FFR) for long term outcomes. We examined the long-term prognostic value ...Background There is still limited data on predictive value of coronary computed tomography angiography(CCTA)–derived fractional flow reserve(CT-FFR) for long term outcomes. We examined the long-term prognostic value of CT-FFR combined with CCTA–defined atherosclerotic extent in diabetic patients with coronary artery disease(CAD).Methods A retrospective pooled analysis of individual patient data was performed. Deep-learning-based vessel-specific CTFFR was calculated. All patients enrolled were followed-up for at least 5 years. Predictive abilities for major adverse cardiac events(MACE) were compared among three models(model 1), constructed using clinical variables;model 2, model 1+CCTA–derived atherosclerotic extent(Leiden risk score);and model 3, model 2+CT-FFR.Results A total of 480 diabetic patients [median age, 61(55–66) years;52.9% men] were included. During a median follow-up time of 2197(2126–2355) days, 55 patients(11.5%) experienced MACE. In multivariate-adjusted Cox models, Leiden risk score(HR: 1.06;95% CI: 1.01–1.11;P = 0.013) and CT-FFR ≤ 0.80(HR: 6.54;95% CI: 3.18–13.45;P < 0.001) were the independent predictors. The discriminant ability was higher in model 2 than in model 1(C-index, 0.75 vs. 0.63;P < 0.001) and was further promoted by adding CT-FFR to model 3(C-index, 0.81 vs. 0.75;P = 0.002). Net reclassification improvement(NRI) was 0.19(P = 0.009) for model 2 beyond model 1. Of note, adding CT-FFR to model 3 also exhibited significantly improved reclassification compared with model 2(NRI = 0.14;P = 0.011).Conclusion In diabetic patients with CAD, CT-FFR provides robust and incremental prognostic information for predicting longterm outcomes. The combined model exhibits improved prediction abilities, which is beneficial for risk stratification.展开更多
Petroleum leakage is a major groundwater contamination source,with chemical composition of water soluble fractions(WSFs)from diverse oil sources significantly impacting groundwater quality and source identification.Th...Petroleum leakage is a major groundwater contamination source,with chemical composition of water soluble fractions(WSFs)from diverse oil sources significantly impacting groundwater quality and source identification.The aim of this study was to assess impact of 15 diverse oils on groundwater quality and environmental forensics based on oil-water equilibrium experiments.Our results indicate that contamination of groundwater by gasoline and naphtha is primarily attributed to volatile hydrocarbons,while pollution from diesel,kerosene,and crude oil is predominantly from non-hydrocarbons.Rapid determination of the extent of non-hydrocarbon pollution in WSFs was achieved through a new quantitative index.Gasoline and naphtha exhibited the highest groundwater contamination potential while kerosene and light crude oils were also likely to cause groundwater contamina-tion.Although volatile hydrocarbons in the WSFs of diesel and jet fuel do not easily exceed current regulatory standards,unregulated non-hydrocarbons may pose a more severe contamination risk to groundwater.Notably,the presence of significant benzene and toluene,hydrogenation and alkylation products(e.g.,C4-C5 alkylben-zenes,alkylindenes,alkyltetralins,and dihydro-indenes),cycloalkanes in WSFs can effectively be utilized for preliminary source identification of light distillates,middle distillates,and crude oils,respectively.展开更多
Insight into the carbon turnover in soil aggregates and density fractions is essential for reducing the uncertainty in estimating carbon pools on the Tibetan Plateau,and how they vary with land use type is unclear.In ...Insight into the carbon turnover in soil aggregates and density fractions is essential for reducing the uncertainty in estimating carbon pools on the Tibetan Plateau,and how they vary with land use type is unclear.In this study,the effect of land use type on carbon storage and fractionation was quantified based on organic carbon and its ^(13)C abundance at the microscale of soil aggregates and density fractions in Tibetan alpine ecosystems.The sequence of soil aggregate destruction in the land use types of plantation(13.1%)<shrubland(32.7%)<grassland(47.9%)<farmland(61.8%)shows that plantations strengthen the soil structure.Plantation land had a greater contribution of light fraction organic carbon(28.3%)but a lower contribution of mineral-associated organic carbon(40.6%)to the carbon stock compared to farmland(13.5 and 70.3%).Interestingly,plantation land enhanced the aggregational differentiation of organic carbon and ^(13)C in each density fraction,whereas no such phenomenon existed in the soil organic carbon.Carbon isotope analyses revealed that carbon transfer in the plantation land occurred from the light fraction in macroaggregates(–24.9‰)to the mineral-associated fraction in microaggregates(–19.9‰).When compared to the other three land use types,the low transferability of carbon in aggregates and density fractions in plantation land provides a stable carbon pool for the Tibetan Plateau.This study shows that plantations can mitigate global climate change by slowing carbon transfer and increasing carbon storage at the microscale of aggregates and density fractions in alpine regions.展开更多
Grifola frondosa(Maitake)is traditionally valued for its health benefits,with polysaccharides being key bioactive components.This paper investigates a specific subfraction,Fraction D(GFP-D),evaluating its clinical eff...Grifola frondosa(Maitake)is traditionally valued for its health benefits,with polysaccharides being key bioactive components.This paper investigates a specific subfraction,Fraction D(GFP-D),evaluating its clinical effects and mechanisms in immune enhancement,adjunctive anti-tumor activity,and regulation of glucose/lipid metabolism.Three clinical trials were conducted.In an immune study,120 healthy volunteers(CD4+T cell count 500–1000 cells/μL)received 150 mg/day GFP-D for 8 weeks,resulting in significant increases in CD4+T cells(from 632±95 to 812±108 cells/μL,28.5%increase,within the physiological activation range),CD4+/CD8+ratio,NK cell activity,IL-2,and IFN-γ(all P<0.001 vs.placebo).An anti-tumor study with 80 advanced cancer patients(stratified by age,tumor stage,and histotype)showed that adding 1000 mg/day GFP-D to chemotherapy improved objective response rate(52.5%vs.30.0%,P=0.036,95%CI:1.02–3.87),one-year progression-free survival(55.8%vs.33.3%,P=0.022),and preserved immune parameters versus chemotherapy alone.A metabolic study in 90 type 2 diabetes patients found that 400 mg/day GFP-D for 12 weeks significantly lowered fasting glucose,HbA1c,total cholesterol,triglycerides,and LDL-C,while raising HDL-C(from 1.0±0.2 to 1.2±0.2 mmol/L,20%increase,supported by increased AMPK phosphorylation).Mechanistically,immune enhancement involves macrophage/dendritic cell activation via Dectin-1/TLR4 receptors(confirmed by increased receptor expression and downstream signaling molecules),promoting cytokine-driven T/NK cell responses.Anti-tumor effects stem from immunomodulation,direct induction of cancer cell apoptosis(via mitochondrial/caspase pathways,verified by increased Bax/Bcl-2 ratio and caspase-3 activation),and angiogenesis inhibition by downregulating VEGF.Metabolic benefits are linked to AMPK pathway activation in liver/muscle(confirmed by increased p-AMPK/AMPK ratio),enhancing glucose uptake and inhibiting gluconeogenesis/lipogenesis,alongside modulation of gut microbiota(increased Bifidobacterium and Lactobacillus abundance).All trials reported no severe adverse events related to GFP-D;liver/kidney function parameters(ALT,AST,creatinine,urea nitrogen)remained within normal ranges throughout the intervention.Collectively,GFP-D emerges as a multi-functional bioactive agent with substantial therapeutic potential.展开更多
In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizh...In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizhong Zhou,Hongxia Liu and Yang Xu(2022).Then,an A_(α)-spectral condition is given to ensure that G is a fractional ID-[a,b]-factor-critical covered graph and an(a,b,k)-factor-critical graph,respectively.In fact,(a,b,k)-factor-critical graph is a graph which has an[a,b]-factor for k=0.Thus,these above results extend the results of Jia Wei and Shenggui Zhang(2023)and Ao Fan,Ruifang Liu and Guoyan Ao(2023)in some sense.展开更多
Developing a cost-effective and environmentally friendly process for the production of valuable chemicals from abundant herbal biomass receives great attentions in recent years.Herein,taking advantage of the“lignin f...Developing a cost-effective and environmentally friendly process for the production of valuable chemicals from abundant herbal biomass receives great attentions in recent years.Herein,taking advantage of the“lignin first”strategy,corn straw is converted to valuable chemicals including lignin monomers,furfural and 5-methoxymethylfurfural via a two steps process.The key of this research lies in the development of a green and low-cost catalytic process utilizing magnetic Raney Ni catalyst and high boiling point ethylene glycol.The utilization of neat ethylene glycol as the sole slovent under atmospheric conditions obviates the need for additional additives,thereby facilitating the entire process to be conducted in glass flasks and rendering it highly convenient for scaling up.In the initial step,depolymerization of corn straw lignin resulted in a monomer yield of 18.1 wt%.Subsequently,in a dimethyl carbonate system,the carbohydrate component underwent complete conversion in a one-pot process,yielding furfural and 5-methoxymethylfurfural as the primary products with an impressive yield of 47.7%.展开更多
Pitch produced by the lique-faction of coal was divided into two frac-tions:soluble in toluene(TS)and insol-uble in toluene but soluble in pyridine(TI-PS),and their differences in molecu-lar structure and oxidation ac...Pitch produced by the lique-faction of coal was divided into two frac-tions:soluble in toluene(TS)and insol-uble in toluene but soluble in pyridine(TI-PS),and their differences in molecu-lar structure and oxidation activity were studied.Several different carbon materi-als were produced from them by oxida-tion in air(350℃,300 mL/min)fol-lowed by carbonization(1000℃ in Ar),and the effect of the cross-linked structure on their structure and sodium storage properties was investigated.The results showed that the two pitch fractions were obviously different after the air oxidation.The TS fraction with a low degree of condensation and abundant side chains had a stronger oxidation activity and thus introduced more cross-linked oxygen-containing functional groups C(O)―O which prevented carbon layer rearrangement during the carbonization.As a result,a disordered hard carbon with more defects was formed,which improved the electrochemical performance.Therefore,the carbon materials derived from TS(O-TS-1000)had an obvious disordered structure and a larger layer spacing,giving them better sodium storage perform-ance than those derived from the TI-PS fraction(O-TI-PS-1000).The specific capacity of O-TS-1000 was about 250 mAh/g at 20 mA/g,which was 1.67 times higher than that of O-TI-PS-1000(150 mAh/g).展开更多
In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):104...In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].展开更多
文摘Lassa Fever(LF)is a viral hemorrhagic illness transmitted via rodents and is endemic in West Africa,causing thousands of deaths annually.This study develops a dynamic model of Lassa virus transmission,capturing the progression of the disease through susceptible,exposed,infected,and recovered populations.The focus is on simulating this model using the fractional Caputo derivative,allowing both qualitative and quantitative analyses of boundedness,positivity,and solution uniqueness.Fixed-point theory and Lipschitz conditions are employed to confirm the existence and uniqueness of solutions,while Lyapunov functions establish the global stability of both disease-free and endemic equilibria.The study further examines the role of the Caputo operator by solving the generalized power-law kernel via a two-step Lagrange polynomial method.This approach offers practical advantages in handling additional data points in integral forms,though Newton polynomial-based schemes are generally more accurate and can outperform Lagrange-based Adams-Bashforth methods.Graphical simulations validate the proposed numerical approach for different fractional orders(ν)and illustrate the influence of model parameters on disease dynamics.Results indicate that increasing the fractional order accelerates the decline of Lassa fever in both human and rodent populations.Moreover,fractional-order modeling provides more nuanced insights than traditional integer-order models,suggesting potential improvements for medical intervention strategies.The study demonstrates that carefully chosen fractional orders can optimize convergence and enhance the predictive capacity of Lassa fever models,offering a promising direction for future research in epidemiological modeling.
文摘Background There is still limited data on predictive value of coronary computed tomography angiography(CCTA)–derived fractional flow reserve(CT-FFR) for long term outcomes. We examined the long-term prognostic value of CT-FFR combined with CCTA–defined atherosclerotic extent in diabetic patients with coronary artery disease(CAD).Methods A retrospective pooled analysis of individual patient data was performed. Deep-learning-based vessel-specific CTFFR was calculated. All patients enrolled were followed-up for at least 5 years. Predictive abilities for major adverse cardiac events(MACE) were compared among three models(model 1), constructed using clinical variables;model 2, model 1+CCTA–derived atherosclerotic extent(Leiden risk score);and model 3, model 2+CT-FFR.Results A total of 480 diabetic patients [median age, 61(55–66) years;52.9% men] were included. During a median follow-up time of 2197(2126–2355) days, 55 patients(11.5%) experienced MACE. In multivariate-adjusted Cox models, Leiden risk score(HR: 1.06;95% CI: 1.01–1.11;P = 0.013) and CT-FFR ≤ 0.80(HR: 6.54;95% CI: 3.18–13.45;P < 0.001) were the independent predictors. The discriminant ability was higher in model 2 than in model 1(C-index, 0.75 vs. 0.63;P < 0.001) and was further promoted by adding CT-FFR to model 3(C-index, 0.81 vs. 0.75;P = 0.002). Net reclassification improvement(NRI) was 0.19(P = 0.009) for model 2 beyond model 1. Of note, adding CT-FFR to model 3 also exhibited significantly improved reclassification compared with model 2(NRI = 0.14;P = 0.011).Conclusion In diabetic patients with CAD, CT-FFR provides robust and incremental prognostic information for predicting longterm outcomes. The combined model exhibits improved prediction abilities, which is beneficial for risk stratification.
基金supported by the National Science Foundation of China(Nos.42177042,and 42477051)the National Key R&D Program of China(No.2023YFC3708700)the Science Foundation of China University of Petroleum-Beijing(No.2462022QNXZ006).
文摘Petroleum leakage is a major groundwater contamination source,with chemical composition of water soluble fractions(WSFs)from diverse oil sources significantly impacting groundwater quality and source identification.The aim of this study was to assess impact of 15 diverse oils on groundwater quality and environmental forensics based on oil-water equilibrium experiments.Our results indicate that contamination of groundwater by gasoline and naphtha is primarily attributed to volatile hydrocarbons,while pollution from diesel,kerosene,and crude oil is predominantly from non-hydrocarbons.Rapid determination of the extent of non-hydrocarbon pollution in WSFs was achieved through a new quantitative index.Gasoline and naphtha exhibited the highest groundwater contamination potential while kerosene and light crude oils were also likely to cause groundwater contamina-tion.Although volatile hydrocarbons in the WSFs of diesel and jet fuel do not easily exceed current regulatory standards,unregulated non-hydrocarbons may pose a more severe contamination risk to groundwater.Notably,the presence of significant benzene and toluene,hydrogenation and alkylation products(e.g.,C4-C5 alkylben-zenes,alkylindenes,alkyltetralins,and dihydro-indenes),cycloalkanes in WSFs can effectively be utilized for preliminary source identification of light distillates,middle distillates,and crude oils,respectively.
基金financially supported by the National Natural Science Foundation of China (42477044,32171648 and U23A2017)the Hubei Provincial Science and Technology Program,China (2025AFD451 and 2022CFB030)。
文摘Insight into the carbon turnover in soil aggregates and density fractions is essential for reducing the uncertainty in estimating carbon pools on the Tibetan Plateau,and how they vary with land use type is unclear.In this study,the effect of land use type on carbon storage and fractionation was quantified based on organic carbon and its ^(13)C abundance at the microscale of soil aggregates and density fractions in Tibetan alpine ecosystems.The sequence of soil aggregate destruction in the land use types of plantation(13.1%)<shrubland(32.7%)<grassland(47.9%)<farmland(61.8%)shows that plantations strengthen the soil structure.Plantation land had a greater contribution of light fraction organic carbon(28.3%)but a lower contribution of mineral-associated organic carbon(40.6%)to the carbon stock compared to farmland(13.5 and 70.3%).Interestingly,plantation land enhanced the aggregational differentiation of organic carbon and ^(13)C in each density fraction,whereas no such phenomenon existed in the soil organic carbon.Carbon isotope analyses revealed that carbon transfer in the plantation land occurred from the light fraction in macroaggregates(–24.9‰)to the mineral-associated fraction in microaggregates(–19.9‰).When compared to the other three land use types,the low transferability of carbon in aggregates and density fractions in plantation land provides a stable carbon pool for the Tibetan Plateau.This study shows that plantations can mitigate global climate change by slowing carbon transfer and increasing carbon storage at the microscale of aggregates and density fractions in alpine regions.
文摘Grifola frondosa(Maitake)is traditionally valued for its health benefits,with polysaccharides being key bioactive components.This paper investigates a specific subfraction,Fraction D(GFP-D),evaluating its clinical effects and mechanisms in immune enhancement,adjunctive anti-tumor activity,and regulation of glucose/lipid metabolism.Three clinical trials were conducted.In an immune study,120 healthy volunteers(CD4+T cell count 500–1000 cells/μL)received 150 mg/day GFP-D for 8 weeks,resulting in significant increases in CD4+T cells(from 632±95 to 812±108 cells/μL,28.5%increase,within the physiological activation range),CD4+/CD8+ratio,NK cell activity,IL-2,and IFN-γ(all P<0.001 vs.placebo).An anti-tumor study with 80 advanced cancer patients(stratified by age,tumor stage,and histotype)showed that adding 1000 mg/day GFP-D to chemotherapy improved objective response rate(52.5%vs.30.0%,P=0.036,95%CI:1.02–3.87),one-year progression-free survival(55.8%vs.33.3%,P=0.022),and preserved immune parameters versus chemotherapy alone.A metabolic study in 90 type 2 diabetes patients found that 400 mg/day GFP-D for 12 weeks significantly lowered fasting glucose,HbA1c,total cholesterol,triglycerides,and LDL-C,while raising HDL-C(from 1.0±0.2 to 1.2±0.2 mmol/L,20%increase,supported by increased AMPK phosphorylation).Mechanistically,immune enhancement involves macrophage/dendritic cell activation via Dectin-1/TLR4 receptors(confirmed by increased receptor expression and downstream signaling molecules),promoting cytokine-driven T/NK cell responses.Anti-tumor effects stem from immunomodulation,direct induction of cancer cell apoptosis(via mitochondrial/caspase pathways,verified by increased Bax/Bcl-2 ratio and caspase-3 activation),and angiogenesis inhibition by downregulating VEGF.Metabolic benefits are linked to AMPK pathway activation in liver/muscle(confirmed by increased p-AMPK/AMPK ratio),enhancing glucose uptake and inhibiting gluconeogenesis/lipogenesis,alongside modulation of gut microbiota(increased Bifidobacterium and Lactobacillus abundance).All trials reported no severe adverse events related to GFP-D;liver/kidney function parameters(ALT,AST,creatinine,urea nitrogen)remained within normal ranges throughout the intervention.Collectively,GFP-D emerges as a multi-functional bioactive agent with substantial therapeutic potential.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961041,12261055)the Key Project of Natural Science Foundation of Gansu Province(Grant No.24JRRA222)the Foundation for Innovative Fundamental Research Group Project of Gansu Province(Grant No.25JRRA805).
文摘In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizhong Zhou,Hongxia Liu and Yang Xu(2022).Then,an A_(α)-spectral condition is given to ensure that G is a fractional ID-[a,b]-factor-critical covered graph and an(a,b,k)-factor-critical graph,respectively.In fact,(a,b,k)-factor-critical graph is a graph which has an[a,b]-factor for k=0.Thus,these above results extend the results of Jia Wei and Shenggui Zhang(2023)and Ao Fan,Ruifang Liu and Guoyan Ao(2023)in some sense.
基金supported by the Fundamental Research Funds for the Central Universities(QNTD202302)National Natural Science Foundation of China(22378024)the Foreign expert program(G2022109001L).
文摘Developing a cost-effective and environmentally friendly process for the production of valuable chemicals from abundant herbal biomass receives great attentions in recent years.Herein,taking advantage of the“lignin first”strategy,corn straw is converted to valuable chemicals including lignin monomers,furfural and 5-methoxymethylfurfural via a two steps process.The key of this research lies in the development of a green and low-cost catalytic process utilizing magnetic Raney Ni catalyst and high boiling point ethylene glycol.The utilization of neat ethylene glycol as the sole slovent under atmospheric conditions obviates the need for additional additives,thereby facilitating the entire process to be conducted in glass flasks and rendering it highly convenient for scaling up.In the initial step,depolymerization of corn straw lignin resulted in a monomer yield of 18.1 wt%.Subsequently,in a dimethyl carbonate system,the carbohydrate component underwent complete conversion in a one-pot process,yielding furfural and 5-methoxymethylfurfural as the primary products with an impressive yield of 47.7%.
文摘Pitch produced by the lique-faction of coal was divided into two frac-tions:soluble in toluene(TS)and insol-uble in toluene but soluble in pyridine(TI-PS),and their differences in molecu-lar structure and oxidation activity were studied.Several different carbon materi-als were produced from them by oxida-tion in air(350℃,300 mL/min)fol-lowed by carbonization(1000℃ in Ar),and the effect of the cross-linked structure on their structure and sodium storage properties was investigated.The results showed that the two pitch fractions were obviously different after the air oxidation.The TS fraction with a low degree of condensation and abundant side chains had a stronger oxidation activity and thus introduced more cross-linked oxygen-containing functional groups C(O)―O which prevented carbon layer rearrangement during the carbonization.As a result,a disordered hard carbon with more defects was formed,which improved the electrochemical performance.Therefore,the carbon materials derived from TS(O-TS-1000)had an obvious disordered structure and a larger layer spacing,giving them better sodium storage perform-ance than those derived from the TI-PS fraction(O-TI-PS-1000).The specific capacity of O-TS-1000 was about 250 mAh/g at 20 mA/g,which was 1.67 times higher than that of O-TI-PS-1000(150 mAh/g).
基金Supported by NSFC(Nos.11661025,12161024)Natural Science Foundation of Guangxi(Nos.2020GXNSFAA159118,2021GXNSFAA196045)+2 种基金Guangxi Science and Technology Project(No.Guike AD20297006)Training Program for 1000 Young and Middle-aged Cadre Teachers in Universities of GuangxiNational College Student's Innovation and Entrepreneurship Training Program(No.202110595049)。
文摘In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].
