Results on entire solutions for a degenerate critical elliptic equation with anisotropic coefficients

In this paper, we study the following degenerate critical elliptic equations with anisotropic coefficients $$-div(|x_{N}|^{2\alpha}\nabla u)=K(x)|x_{N}|^{\alpha\cdot 2^{*}(s)-s}|u|^{2^{*}(s)-2}u {in} \mathbb{R}^{N}$$ where $x=(x_{1},...,x_{N})\in\mathbb{R}^{N},$ $N\geq 3,$ $\alpha>1/2,$ $0\leq s\leq 2$ and $2^{*}(s)=2(N-s)/(N-2).$ Some basic properties of the degenerate elliptic operator $-div(|x_{N}|^{2\alpha}\nabla u)$ are investigated and some regularity, symmetry and uniqueness results for entire solutions of this equation are obtained. We also get some variational identities for solutions of this equation. As a consequence, we obtain some nonexistence results for solutions of this equation.Comment: 29 page

High-Frequency Electrooptic Fabry-Perot Modulators

Electrooptic modulators built from GaAs/AlxGa1-xAs Fabry-Perot cavities operating up to 6.5 GHz are reported. The measured frequency response agrees well with the one predicted using an equivalent circuit model derived from high-speed electrical measurements. The parasitic capacitances have been reduced to approximately 30 fF by fabricating the devices on semi-insulating GaAs substrates and integrating them with on-wafer bound pads which have dimensions compatible with microwave coplanar probes

Knockout of Epstein-Barr Virus BPLF1 Retards B-Cell Transformation and Lymphoma Formation in Humanized Mice

ABSTRACT BPLF1 of Epstein-Barr virus (EBV) is classified as a late lytic cycle protein but is also found in the viral tegument, suggesting its potential involvement at both initial and late stages of viral infection. BPLF1 possesses both deubiquitinating and deneddylating activity located in its N-terminal domain and is involved in processes that affect viral infectivity, viral DNA replication, DNA repair, and immune evasion. A recently constructed EBV BPLF1-knockout (KO) virus was used in conjunction with a humanized mouse model that can be infected with EBV, enabling the first characterization of BPLF1 function in vivo . Results demonstrate that the BPLF1-knockout virus is approximately 90% less infectious than wild-type (WT) virus. Transformation of human B cells, a hallmark of EBV infection, was delayed and reduced with BPLF1-knockout virus. Humanized mice infected with EBV BPLF1-knockout virus showed less weight loss and survived longer than mice infected with equivalent infectious units of WT virus. Additionally, splenic tumors formed in 100% of mice infected with WT EBV but in only 25% of mice infected with BPLF1-KO virus. Morphological features of spleens containing tumors were similar to those in EBV-induced posttransplant lymphoproliferative disease (PTLD) and were almost identical to cases seen in human diffuse large B-cell lymphoma. The presence of EBV genomes was detected in all mice that developed tumors. The results implicate BPLF1 in human B-cell transformation and tumor formation in humanized mice. IMPORTANCE Epstein-Barr virus infects approximately 90% of the world’s population and is the causative agent of infectious mononucleosis. EBV also causes aggressive lymphomas in individuals with acquired and innate immune disorders and is strongly associated with diffuse large B-cell lymphomas, classical Hodgkin lymphoma, Burkitt lymphoma, and nasopharyngeal carcinoma (NPC). Typically, EBV initially infects epithelial cells in the oropharynx, followed by a lifelong persistent latent infection in B-cells, which may develop into lymphomas in immunocompromised individuals. This work is the first of its kind in evaluating the effects of EBV’s BPLF1 in terms of pathogenesis and lymphomagenesis in humanized mice and implicates BPLF1 in B-cell transformation and tumor development. Currently, there is no efficacious treatment for EBV, and therapeutic targeting of BPLF1 may lead to a new path to treatment for immunocompromised individuals or transplant recipients infected with EBV

Fixed point theorems for the sum of three classes of mixed monotone operators and applications

In this paper we develop various new fixed point theorems for a class of operator equations with three general mixed monotone operators, namely A(x,x)+B(x,x)+C(x,x)=x on ordered Banach spaces, where A, B, C are the mixed monotone operators. A is such that for any t∈(0,1), there exists φ(t)∈(t,1] such that for all x,y∈P, A(tx,t−1y)≥φ(t)A(x,y); B is hypo-homogeneous, i.e. B satisfies that for any t∈(0,1), x,y∈P, B(tx,t−1y)≥tB(x,y); C is concave-convex, i.e. C satisfies that for fixed y, C(⋅,y):P→P is concave; for fixed x, C(x,⋅): P→P is convex. Also we study the solution of the nonlinear eigenvalue equation A(x,x)+B(x,x)+C(x,x)=λx and discuss its dependency to the parameter. Our work extends many existing results in the field of study. As an application, we utilize the results obtained in this paper for the operator equation to study the existence and uniqueness of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions

Iterative positive solutions for singular nonlinear fractional differential equation with integral boundary conditions

In this article, we study the existence of iterative positive solutions for a class of singular nonlinear fractional differential equations with Riemann-Stieltjes integral boundary conditions, where the nonlinear term may be singular both for time and space variables. By using the properties of the Green function and the fixed point theorem of mixed monotone operators in cones we obtain some results on the existence and uniqueness of positive solutions. We also construct successively some sequences for approximating the unique solution. Our results include the multipoint boundary problems and integral boundary problems as special cases, and we also extend and improve many known results including singular and non-singular cases

SOD2 polymorphisms: unmasking the effect of polymorphism on splicing

BACKGROUND: The SOD2 gene encodes an antioxidant enzyme, mitochondrial superoxide dismutase. SOD2 polymorphisms are of interest because of their potential roles in the modulation of free radical-mediated macromolecular damage during aging. RESULTS: We identified a new splice variant of SOD2 in human lymphoblastoid cell lines (LCLs). The alternatively spliced product was originally detected by exon trapping of a minigene in order to examine the consequences of an intronic polymorphism found upstream of exon 4 (nucleotide 8136, 10T vs 9T). Examination of the transcripts derived from the endogenous loci in five LCLs with or without the intron 3 polymorphism revealed low levels of an in-frame deletion of exon 4 that were different from those detected by the exon trap assay. This suggested that exon trapping of the minigene unmasked the effect of the 10T vs 9T polymorphism on the splicing of the adjacent exon. We also determined the frequencies of single nucleotide polymorphisms in a sample of US African-Americans and non-African-Americans ages 65 years and older who participated in the 1999 wave of the National Long Term Care Survey (NLTCS). Particularly striking differences between African-Americans and non-African-Americans were found for the frequencies of genotypes at the 10T/9T intron 3 polymorphism. CONCLUSION: Exon trapping can unmask in vitro splicing differences caused by a 10T/9T intron 3 polymorphism. Given the recent evidence that SOD2 is in a region on chromosome 6 linked to susceptibility to hypertension, it will be of interest to investigate possible associations of this polymorphism with cardiovascular disorders

The Impact of Hydrogen Bonding on Amide 1H Chemical Shift Anisotropy Studied by Cross-Correlated Relaxation and Liquid Crystal NMR Spectroscopy

Site-specific (1)H chemical shift anisotropy (CSA) tensors have been derived for the well-ordered backbone amide moieties in the B3 domain of protein G (GB3). Experimental input data include residual chemical shift anisotropy (RCSA), measured in six mutants that align differently relative to the static magnetic field when dissolved in a liquid crystalline Pf1 suspension, and cross-correlated relaxation rates between the (1)H(N) CSA tensor and either the (1)H-(15)N, the (1)H-(13)C', or the (1)H-(13)C(alpha) dipolar interactions. Analyses with the assumption that the (1)H(N) CSA tensor is symmetric with respect to the peptide plane (three-parameter fit) or without this premise (five-parameter fit) yield very similar results, confirming the robustness of the experimental input data, and that, to a good approximation, one of the principal components orients orthogonal to the peptide plane. (1)H(N) CSA tensors are found to deviate strongly from axial symmetry, with the most shielded tensor component roughly parallel to the N-H vector, and the least shielded component orthogonal to the peptide plane. DFT calculations on pairs of N-methyl acetamide and acetamide in H-bonded geometries taken from the GB3 X-ray structure correlate with experimental data and indicate that H-bonding effects dominate variations in the (1)H(N) CSA. Using experimentally derived (1)H(N) CSA tensors, the optimal relaxation interference effect needed for narrowest (1)H(N) TROSY line widths is found at similar to 1200 MHz

Iterative algorithm and estimation of solution for a fractional order differential equation

In this paper, we establish an iterative algorithm and estimation of solutions for a fractional turbulent flow model in a porous medium under a suitable growth condition. Our main tool is the monotone iterative technique

Regulation of IL-2 gene expression by Siva and FOXP3 in human T cells

<p>Abstract</p> <p>Background</p> <p>Severe autoinflammatory diseases are associated with mutations in the <it>Foxp3 </it>locus in both mice and humans. <it>Foxp3 </it>is required for the development, function, and maintenance of regulatory T cells (T_regs), a subset of CD4 cells that suppress T cell activation and inflammatory processes. <it>Siva </it>is a pro-apoptotic gene that is expressed across a range of tissues, including CD4 T cells. Siva interacts with three tumor necrosis factor receptor (TNFR) family members that are constitutively expressed on T_regcells: CD27, GITR, and OX40.</p> <p>Results</p> <p>Here we report a biophysical interaction between FOXP3 and Siva. We mapped the interaction domains to Siva's C-terminus and to a central region of FOXP3. We showed that <it>Siva </it>repressed IL-2 induction by suppressing <it>IL-2 </it>promoter activity during T cell activation. Siva-1's repressive effect on <it>IL-2 </it>gene expression appears to be mediated by inhibition of NFkappaB, whereas FOXP3 repressed both NFkappaB and NFAT activity.</p> <p>Conclusions</p> <p>In summary, our data suggest that both <it>FOXP3 </it>and <it>Siva </it>function as negative regulators of IL-2 gene expression in T_regcells, via suppression of NFAT by <it>FOXP3 </it>and of NFkappaB by both <it>FOXP3 </it>and <it>Siva</it>. Our work contributes evidence for <it>Siva's </it>role as a T cell signalling mediator in addition to its known pro-apoptotic function. Though further investigations are needed, evidence for the biophysical interaction between FOXP3 and Siva invites the possibility that Siva may be important for proper T_regcell function.</p