In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/（N-2） is the critical Sobolev exponent, 2 【 q 【 2 , 0≤μ 【 μˉ=（N-2）2<sub>4</sub> , a（x）, k（x） ∈ C（...In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/（N-2） is the critical Sobolev exponent, 2 【 q 【 2 , 0≤μ 【 μˉ=（N-2）2<sub>4</sub> , a（x）, k（x） ∈ C（RN ）. Through a compactness analysis of the functional corresponding to the problems , we obtain the existence of positive solutions for this problem under certain assumptions on a（x） and k（x）.展开更多
By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for...By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for a class of first order differential equation. As applications of the main results, two examples are given at the end of this paper.展开更多
Background:Positive regulatory domain-containing 16(PRDM16)plays a key role in brown adipose transcription,but its function in cancer is unclear.Our research to investigate the potential roles of PRDM16 across multipl...Background:Positive regulatory domain-containing 16(PRDM16)plays a key role in brown adipose transcription,but its function in cancer is unclear.Our research to investigate the potential roles of PRDM16 across multiple types of cancer by pan cancer analyses.Methods:UALCAN and TIMER2 database were utilized to evaluate PRDM16 expression in cancer patients.Gene Expression Profiling Interactive Analysis was employed to analyze the overall survival and disease-free survival across all The Cancer Genome Atlas Program tumors.Using the cBioPortal tool,we analyzed the mutation features of PRDM16 for the The Cancer Genome Atlas Program tumors,then utilized the Encyclopedia of RNA Interactomes database to predict the miRNA-mRNA relationships associated with the PRDM16 for all tumors.Results:The expression level of PRDM16 in the tumor tissues is lower than that in the normal tissues.Interesting,the high expression of PRDM16 has a positive effect on the prognosis of kidney clear cell carcinoma and lung adenocarcinoma,but not conducive to the prognosis of most cancers.In multiple cancer types,the expression of PRDM16 was significantly positively correlated with immune infiltration of cancer-associated fibroblasts.Kyoto Encyclopedia of Genes and Genomes and Gene Ontology analysis indicated that PRDM16 may be related to transcriptional misregulation pathway in cancer.We identified potential miRNAs that play regulatory roles of PRDM16 in kidney clear cell carcinoma and lung adenocarcinoma.Conclusion:PRDM16 is expressed in different cancers,it can be used as a biomarker for prognosis of pan-cancer and is associated with immune infiltration.展开更多
Applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains, subject to Dirichle...Applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains, subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.展开更多
Flavin-containing monooxygenase (FMO), like cytochrome P450 (CYP), is a monooxygenase that uses the reducing equivalents of NADPH to reduce one atom of molecular oxygen to water, while the other atom is used to oxidiz...Flavin-containing monooxygenase (FMO), like cytochrome P450 (CYP), is a monooxygenase that uses the reducing equivalents of NADPH to reduce one atom of molecular oxygen to water, while the other atom is used to oxidize the substrate. Recently, it was shown that some CYP isoforms have been subject to positive selection. However, it is unknown whether the highly conserved phase I detoxification enzyme, FMO, has undergone similar positive Darwinian selection. We used maximum-likelihood models of codon substitution, evolutionary fingerprinting, and cross species comparison to investigate the occurrence of adaptive evolution in FMO sequences. We used recent genomic data from a range of species, including vertebrates and invertebrates. We present the evidence for the occurrence of adaptive evolution in mammalian FMO 3, 4, 5, and fugu FMOs but not in mammalian FMO 1, FMO 2, frog FMOs, other fish FMOs and invertebrate FMOs. The sites under adaptive evolution were significantly associated with the insertion domain in mammalian FMO 5. We identified specific amino acid sites in FMOs 3–5 that are likely targets for selection based on the patterns of parallel amino acid change. The most likely role of adaptive evolution is the repair of mutations that permitted optimal NADP+ binding and improved catalytic efficiency. The occurrence of positive selection during the evolution of phase I detoxification enzymes such as FMOs 3–5 and fugu FMO suggests the occurrence of both high selection pressure acting on species within their unique habitats and significant changes in intensity and direction (forms of xenobiotics and drugs) resulting from changes in microhabitat and food.展开更多
We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analys...We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analysis is rather subtle and it is inadequate to apply the powerful theory of monotone dynamical systems. By using the method of super-sub solutions, combined with the careful analysis of the kernel function in the nonlocal term, we prove nonexistence, existence and uniqueness of positive steady states of the model.Moreover, due to the mature individuals do not diffuse, the solution semiflow to the model is not compact. To overcome the difficulty of non-compactness in describing the global asymptotic stability of the unique positive steady state, we first establish an appropriate comparison principle. With the help of the comparison principle,we can employ the theory of dissipative systems to obtain the global asymptotic stability of the unique positive steady state. The main results are illustrated with the nonlocal Nicholson's blowflies equation and the nonlocal Mackey-Glass equation.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.10631030, 10871075)the PhD Specialized Grant of the Ministry of Education of China (Grant No. 20060511001)the Natural Science Foundation of Guangdong Province, China (Grant No. 9451064201003736)
文摘In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/（N-2） is the critical Sobolev exponent, 2 【 q 【 2 , 0≤μ 【 μˉ=（N-2）2<sub>4</sub> , a（x）, k（x） ∈ C（RN ）. Through a compactness analysis of the functional corresponding to the problems , we obtain the existence of positive solutions for this problem under certain assumptions on a（x） and k（x）.
基金Supported by the National Natural Science Foundation of China(No.10671167)the Natural Science Foundation of Liaocheng University(31805)
文摘By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for a class of first order differential equation. As applications of the main results, two examples are given at the end of this paper.
基金This study was financially supported by the Young Teachers Support Program of Hubei University of Chinese Medicine(2021ZZX025)Hubei Province College Students’innovation and entrepreneurship training program(S202210507018).
文摘Background:Positive regulatory domain-containing 16(PRDM16)plays a key role in brown adipose transcription,but its function in cancer is unclear.Our research to investigate the potential roles of PRDM16 across multiple types of cancer by pan cancer analyses.Methods:UALCAN and TIMER2 database were utilized to evaluate PRDM16 expression in cancer patients.Gene Expression Profiling Interactive Analysis was employed to analyze the overall survival and disease-free survival across all The Cancer Genome Atlas Program tumors.Using the cBioPortal tool,we analyzed the mutation features of PRDM16 for the The Cancer Genome Atlas Program tumors,then utilized the Encyclopedia of RNA Interactomes database to predict the miRNA-mRNA relationships associated with the PRDM16 for all tumors.Results:The expression level of PRDM16 in the tumor tissues is lower than that in the normal tissues.Interesting,the high expression of PRDM16 has a positive effect on the prognosis of kidney clear cell carcinoma and lung adenocarcinoma,but not conducive to the prognosis of most cancers.In multiple cancer types,the expression of PRDM16 was significantly positively correlated with immune infiltration of cancer-associated fibroblasts.Kyoto Encyclopedia of Genes and Genomes and Gene Ontology analysis indicated that PRDM16 may be related to transcriptional misregulation pathway in cancer.We identified potential miRNAs that play regulatory roles of PRDM16 in kidney clear cell carcinoma and lung adenocarcinoma.Conclusion:PRDM16 is expressed in different cancers,it can be used as a biomarker for prognosis of pan-cancer and is associated with immune infiltration.
文摘Applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains, subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.
基金supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China (2008ZX10005-004)Educational Commission of Liaoning Province of China (2009A120)China Postdoctoral Science Foundation (20080440019 and 200902069)
文摘Flavin-containing monooxygenase (FMO), like cytochrome P450 (CYP), is a monooxygenase that uses the reducing equivalents of NADPH to reduce one atom of molecular oxygen to water, while the other atom is used to oxidize the substrate. Recently, it was shown that some CYP isoforms have been subject to positive selection. However, it is unknown whether the highly conserved phase I detoxification enzyme, FMO, has undergone similar positive Darwinian selection. We used maximum-likelihood models of codon substitution, evolutionary fingerprinting, and cross species comparison to investigate the occurrence of adaptive evolution in FMO sequences. We used recent genomic data from a range of species, including vertebrates and invertebrates. We present the evidence for the occurrence of adaptive evolution in mammalian FMO 3, 4, 5, and fugu FMOs but not in mammalian FMO 1, FMO 2, frog FMOs, other fish FMOs and invertebrate FMOs. The sites under adaptive evolution were significantly associated with the insertion domain in mammalian FMO 5. We identified specific amino acid sites in FMOs 3–5 that are likely targets for selection based on the patterns of parallel amino acid change. The most likely role of adaptive evolution is the repair of mutations that permitted optimal NADP+ binding and improved catalytic efficiency. The occurrence of positive selection during the evolution of phase I detoxification enzymes such as FMOs 3–5 and fugu FMO suggests the occurrence of both high selection pressure acting on species within their unique habitats and significant changes in intensity and direction (forms of xenobiotics and drugs) resulting from changes in microhabitat and food.
基金supported by National Natural Science Foundation of China(Grant Nos.11031002 and 11371107)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20124410110001)
文摘We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analysis is rather subtle and it is inadequate to apply the powerful theory of monotone dynamical systems. By using the method of super-sub solutions, combined with the careful analysis of the kernel function in the nonlocal term, we prove nonexistence, existence and uniqueness of positive steady states of the model.Moreover, due to the mature individuals do not diffuse, the solution semiflow to the model is not compact. To overcome the difficulty of non-compactness in describing the global asymptotic stability of the unique positive steady state, we first establish an appropriate comparison principle. With the help of the comparison principle,we can employ the theory of dissipative systems to obtain the global asymptotic stability of the unique positive steady state. The main results are illustrated with the nonlocal Nicholson's blowflies equation and the nonlocal Mackey-Glass equation.
