Bulletin of the Iranian Mathematical Society, 2020
Using the genus theory introduced by Krasnoselskii and a variant of the mountain pass theorem due... more Using the genus theory introduced by Krasnoselskii and a variant of the mountain pass theorem due to Rabinowitz [24], we study the existence of solutions for the following Kirchhoff type problem: M | u| p dx | u| p−2 u =λ|u| p * * −2 u+a(x)|u| p−2 u+ f (x, u), x ∈ , u = ∂u ∂ν = 0, x ∈ ∂ , where is a bounded domain in R N (N ≥ 3) with C 2 boundary, 1 < p < N 2 , p * * = N p N −2 p is the critical exponent, is the Laplace operator and ∂u ∂ν is the outer normal derivative, λ is a positive parameter, M : [0, +∞) → R and f : × R → R are continuous functions, and a ∈ L ∞ () is a weight function. Keywords Kirchhoff type problems • p-Biharmonic operators • Critical exponents • Indefinite weight • Variational methods Mathematics Subject Classification 47A75 • 35B38 • 35P30 Communicated by Mohammad B. Asadi.
Boletim da Sociedade Paranaense de Matemática, 2022
In this paper, we are interested in a class of bi-nonlocal problems with nonlinear Neumann bounda... more In this paper, we are interested in a class of bi-nonlocal problems with nonlinear Neumann boundary conditions and sublinear terms at infinity. Using $(S_+)$ mapping theory and variational methods, we establish the existence of at least two non-trivial weak solutions for the problem provied that the parameters are large enough. Our result complements and improves some previous ones for the superlinear case when the Ambrosetti-Rabinowitz type conditions are imposed on the nonlinearities.
In this paper, we consider a class of Kirchhoff type systems involving critical exponents in boun... more In this paper, we consider a class of Kirchhoff type systems involving critical exponents in bounded domains. Under appropriate conditions on the nonlinearities, we prove the existence and asymptotic behavior of positive solutions for the problem by using truncation argument combined with the mountain pass theorem and a variant of concentration compactness principle related to critical elliptic systems in [19].
ABSTRACT Changes in the activity of the cell wall hydrolases – polygalacturonase (EC 3.2.1.15), p... more ABSTRACT Changes in the activity of the cell wall hydrolases – polygalacturonase (EC 3.2.1.15), pectinesterase (EC 3.2.1.11) and β-galactosidase (EC 3.2.1.23) – have been investigated following wounding of tomato fruit pericarp tissue (Lycopersicon esculentum cv. Ailsa Craig). In ripening fruit wounding appears to arrest the further synthesis of polygalacturonase. β-Galactosidase synthesis may also have been arrested in ripening fruit. The level of pectinesterase declined over the first 24 h following harvest, and since this was apparent in both wounded and unwounded tissue may be related to a harvest, rather than a wounding effect. There was a recovery of activity in intact fruit by 48 h after harvest but this seems to be impaired in wounded tissue. In the case of pectinesterase, this observation was extended to examine the changes in isoform profile and it appeared that the decline of this enzyme may be associated with the reduction of one specific isoform — PE2. In contrast to ripening fruit, wounding of fruit at the fully ripe stage appears to have no significant effects on the activities of any of these three enzymes.
Mobile genetic elements that reside in gene-dense genomes face the problem of avoiding devastatin... more Mobile genetic elements that reside in gene-dense genomes face the problem of avoiding devastating insertional mutagenesis of genes in their host cell genomes. To meet this challenge, some Saccharomyces cerevisiae long terminal repeat (LTR) retrotransposons have evolved targeted integration at safe sites in the immediate vicinity of tRNA genes. Integration of yeast Ty3 is mediated by interactions of retrotransposon protein with the tRNA gene-specific transcription factor IIIB (TFIIIB). In the genome of the social amoeba Dictyostelium discoideum, the non-LTR retrotransposon TRE5-A integrates ϳ48 bp upstream of tRNA genes, yet little is known about how the retrotransposon identifies integration sites. Here, we show direct protein interactions of the TRE5-A ORF1 protein with subunits of TFIIIB, suggesting that ORF1p is a component of the TRE5-A preintegration complex that determines integration sites. Our results demonstrate that evolution has put forth similar solutions to prevent damage of diverse, compact genomes by different classes of mobile elements.
Boletim da Sociedade Paranaense de Matemática, 2011
We consider elliptic equations of p-Laplacian type with the nonlinear boundary condition of the f... more We consider elliptic equations of p-Laplacian type with the nonlinear boundary condition of the form −∆pu + |u| p−2 u = λf 1 (u) + µg 1 (u) in Ω, |∇u| p−2 ∂u ∂n = λf 2 (u) + µg 2 (u) in ∂Ω, where Ω ⊂ R N (N ≧ 3) is a bounded domain with smooth boundary ∂Ω, ∂ ∂n is the outer unit normal derivative, λ, µ are parameters. The functions f i , i = 1, 2, are assumed to be (p − 1)-sublinear while g i , i = 1, 2, are (p − 1)-assymptotically linear at infinity. Using variational techniques, an existence result is given.
Proceedings of the National Academy of Sciences, 2013
Significance Macrophages are central regulators of the immune response during infection and wound... more Significance Macrophages are central regulators of the immune response during infection and wound healing, and their behavior is largely thought to be regulated by soluble factors in the microenvironment. Here, we find that adhesive cues are also critical for regulating the proinflammatory vs. prohealing state of these cells. We use engineered cell culture substrates to control cell shape and find that elongation of cells promotes a prohealing phenotype. Moreover, we identify key molecular pathways that are responsible for transducing physical cues to the biochemical cues that govern this response. Together, these studies suggest an important role for cell shape in regulating macrophage function.
ABSTRACT This article investigates a class of anisotropic elliptic equations with non-standard gr... more ABSTRACT This article investigates a class of anisotropic elliptic equations with non-standard growth conditions {−∑i=1N∂xi(|∂xiu|pi(x)−2∂xiu)=f(x,u)in Ω,u=0on ∂Ω, Ω⊂RNΩ⊂RN N≥3N≥3 ∂Ω∂Ω pipi i=1,2,…,Ni=1,2,…,N Ω¯ 1&lt;pi(x)&lt;N1&lt;pi(x)&lt;N
In the compact Dictyostelium discoideum genome, non-long terminal repeat (non-LTR) retrotransposo... more In the compact Dictyostelium discoideum genome, non-long terminal repeat (non-LTR) retrotransposons known as TREs avoid accidental integration-mediated gene disruption by targeting the vicinity of tRNA genes. In this study we provide the first evidence that proteins of a non-LTR retrotransposon interact with a target-specific transcription factor to direct its integration. We applied an in vivo selection system that allows for the isolation of natural TRE5-A integrations into a known genomic location upstream of tRNA genes. TRE5-A frequently modified the integration site in a way characteristic of other non-LTR retrotransposons by adding nontemplated extra nucleotides and generating small and extended target site deletions. Mutations within the B-box promoter of the targeted tRNA genes interfered with both the in vitro binding of RNA polymerase III transcription factor TFIIIC and the ability of TRE5-A to target these genes. An isolated B box was sufficient to enhance TRE5-A integrat...
Bulletin of the Iranian Mathematical Society, 2020
Using the genus theory introduced by Krasnoselskii and a variant of the mountain pass theorem due... more Using the genus theory introduced by Krasnoselskii and a variant of the mountain pass theorem due to Rabinowitz [24], we study the existence of solutions for the following Kirchhoff type problem: M | u| p dx | u| p−2 u =λ|u| p * * −2 u+a(x)|u| p−2 u+ f (x, u), x ∈ , u = ∂u ∂ν = 0, x ∈ ∂ , where is a bounded domain in R N (N ≥ 3) with C 2 boundary, 1 < p < N 2 , p * * = N p N −2 p is the critical exponent, is the Laplace operator and ∂u ∂ν is the outer normal derivative, λ is a positive parameter, M : [0, +∞) → R and f : × R → R are continuous functions, and a ∈ L ∞ () is a weight function. Keywords Kirchhoff type problems • p-Biharmonic operators • Critical exponents • Indefinite weight • Variational methods Mathematics Subject Classification 47A75 • 35B38 • 35P30 Communicated by Mohammad B. Asadi.
Boletim da Sociedade Paranaense de Matemática, 2022
In this paper, we are interested in a class of bi-nonlocal problems with nonlinear Neumann bounda... more In this paper, we are interested in a class of bi-nonlocal problems with nonlinear Neumann boundary conditions and sublinear terms at infinity. Using $(S_+)$ mapping theory and variational methods, we establish the existence of at least two non-trivial weak solutions for the problem provied that the parameters are large enough. Our result complements and improves some previous ones for the superlinear case when the Ambrosetti-Rabinowitz type conditions are imposed on the nonlinearities.
In this paper, we consider a class of Kirchhoff type systems involving critical exponents in boun... more In this paper, we consider a class of Kirchhoff type systems involving critical exponents in bounded domains. Under appropriate conditions on the nonlinearities, we prove the existence and asymptotic behavior of positive solutions for the problem by using truncation argument combined with the mountain pass theorem and a variant of concentration compactness principle related to critical elliptic systems in [19].
ABSTRACT Changes in the activity of the cell wall hydrolases – polygalacturonase (EC 3.2.1.15), p... more ABSTRACT Changes in the activity of the cell wall hydrolases – polygalacturonase (EC 3.2.1.15), pectinesterase (EC 3.2.1.11) and β-galactosidase (EC 3.2.1.23) – have been investigated following wounding of tomato fruit pericarp tissue (Lycopersicon esculentum cv. Ailsa Craig). In ripening fruit wounding appears to arrest the further synthesis of polygalacturonase. β-Galactosidase synthesis may also have been arrested in ripening fruit. The level of pectinesterase declined over the first 24 h following harvest, and since this was apparent in both wounded and unwounded tissue may be related to a harvest, rather than a wounding effect. There was a recovery of activity in intact fruit by 48 h after harvest but this seems to be impaired in wounded tissue. In the case of pectinesterase, this observation was extended to examine the changes in isoform profile and it appeared that the decline of this enzyme may be associated with the reduction of one specific isoform — PE2. In contrast to ripening fruit, wounding of fruit at the fully ripe stage appears to have no significant effects on the activities of any of these three enzymes.
Mobile genetic elements that reside in gene-dense genomes face the problem of avoiding devastatin... more Mobile genetic elements that reside in gene-dense genomes face the problem of avoiding devastating insertional mutagenesis of genes in their host cell genomes. To meet this challenge, some Saccharomyces cerevisiae long terminal repeat (LTR) retrotransposons have evolved targeted integration at safe sites in the immediate vicinity of tRNA genes. Integration of yeast Ty3 is mediated by interactions of retrotransposon protein with the tRNA gene-specific transcription factor IIIB (TFIIIB). In the genome of the social amoeba Dictyostelium discoideum, the non-LTR retrotransposon TRE5-A integrates ϳ48 bp upstream of tRNA genes, yet little is known about how the retrotransposon identifies integration sites. Here, we show direct protein interactions of the TRE5-A ORF1 protein with subunits of TFIIIB, suggesting that ORF1p is a component of the TRE5-A preintegration complex that determines integration sites. Our results demonstrate that evolution has put forth similar solutions to prevent damage of diverse, compact genomes by different classes of mobile elements.
Boletim da Sociedade Paranaense de Matemática, 2011
We consider elliptic equations of p-Laplacian type with the nonlinear boundary condition of the f... more We consider elliptic equations of p-Laplacian type with the nonlinear boundary condition of the form −∆pu + |u| p−2 u = λf 1 (u) + µg 1 (u) in Ω, |∇u| p−2 ∂u ∂n = λf 2 (u) + µg 2 (u) in ∂Ω, where Ω ⊂ R N (N ≧ 3) is a bounded domain with smooth boundary ∂Ω, ∂ ∂n is the outer unit normal derivative, λ, µ are parameters. The functions f i , i = 1, 2, are assumed to be (p − 1)-sublinear while g i , i = 1, 2, are (p − 1)-assymptotically linear at infinity. Using variational techniques, an existence result is given.
Proceedings of the National Academy of Sciences, 2013
Significance Macrophages are central regulators of the immune response during infection and wound... more Significance Macrophages are central regulators of the immune response during infection and wound healing, and their behavior is largely thought to be regulated by soluble factors in the microenvironment. Here, we find that adhesive cues are also critical for regulating the proinflammatory vs. prohealing state of these cells. We use engineered cell culture substrates to control cell shape and find that elongation of cells promotes a prohealing phenotype. Moreover, we identify key molecular pathways that are responsible for transducing physical cues to the biochemical cues that govern this response. Together, these studies suggest an important role for cell shape in regulating macrophage function.
ABSTRACT This article investigates a class of anisotropic elliptic equations with non-standard gr... more ABSTRACT This article investigates a class of anisotropic elliptic equations with non-standard growth conditions {−∑i=1N∂xi(|∂xiu|pi(x)−2∂xiu)=f(x,u)in Ω,u=0on ∂Ω, Ω⊂RNΩ⊂RN N≥3N≥3 ∂Ω∂Ω pipi i=1,2,…,Ni=1,2,…,N Ω¯ 1&lt;pi(x)&lt;N1&lt;pi(x)&lt;N
In the compact Dictyostelium discoideum genome, non-long terminal repeat (non-LTR) retrotransposo... more In the compact Dictyostelium discoideum genome, non-long terminal repeat (non-LTR) retrotransposons known as TREs avoid accidental integration-mediated gene disruption by targeting the vicinity of tRNA genes. In this study we provide the first evidence that proteins of a non-LTR retrotransposon interact with a target-specific transcription factor to direct its integration. We applied an in vivo selection system that allows for the isolation of natural TRE5-A integrations into a known genomic location upstream of tRNA genes. TRE5-A frequently modified the integration site in a way characteristic of other non-LTR retrotransposons by adding nontemplated extra nucleotides and generating small and extended target site deletions. Mutations within the B-box promoter of the targeted tRNA genes interfered with both the in vitro binding of RNA polymerase III transcription factor TFIIIC and the ability of TRE5-A to target these genes. An isolated B box was sufficient to enhance TRE5-A integrat...
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