Self-similar extinction for a diffusive Hamilton-Jacobi equation with critical absorption

International audienceThe behavior near the extinction time is identified for non-negative solutions to the diffusive Hamilton-Jacobi equation with critical gradient absorption ∂_t u − ∆_p u + |∇u|^{p−1} = 0 in (0, ∞) × R^N , and fast diffusion 2N/(N + 1) < p < 2. Given a non-negative and radially symmetric initial condition with a non-increasing profile which decays sufficiently fast as |x| → ∞, it is shown that the corresponding solution u to the above equation approaches a uniquely determined separate variable solution of the form U (t, x) = (T_e − t)^{1/(2−p)} f_* (|x|), (t, x) ∈ (0, T_e) × R^N , as t → T_e , where T_e denotes the finite extinction time of u. A cornerstone of the convergence proof is an underlying variational structure of the equation. Also, the selected profile f_* is the unique non-negative solution to a second order ordinary differential equation which decays exponentially at infinity. A complete classification of solutions to this equation is provided, thereby describing all separate variable solutions of the original equation. One important difficulty in the uniqueness proof is that no monotonicity argument seems to be available and it is overcome by the construction of an appropriate Pohozaev functional

Velocity profiles in a real vegetated channel

Most of the studies regarding vegetation effects on velocity profiles are based on laboratory experiments. The main focus of this paper is to show how the laboratory knowledge established for submerged vegetation applies to real-scale systems affected by vegetation growth (mainly Ranunculus fluitans). To do so, experiments are conducted at two gage stations of an operational irrigation system. The analysis of first- and second-order fluctuations of velocities is based on field measurements performed by micro-acoustic doppler velocimeter during 8 months, completed with flow measurement campaigns in different seasons. The Reynolds stresses are used to determine shear velocities and deflected plant heights. Then, the modified log–wake law (MLWL), initially derived from laboratory flume experiments, is applied with a unique parametrisation for the whole set of velocity profiles. The MLWL, along with a lateral distribution function, is used to calculate the discharge and to show the influence of vegetation height on the stage–discharge relationships

Angiotensin-2 receptors (AT1-R and AT2-R), new prognostic factors for renal clear-cell carcinoma?

International audienceBackground: The growth factor Angiotensin-2 signals through Angiotensin receptor type 1 (AT1-R) in a broad range of cell types and tumours and through the type-2 receptor (AT2-R) in a more restricted group of cell types. Although numerous forms of cancer have been shown to overexpress AT1-R, expression of AT1-R and AT2-R by human renal clear-cell carcinoma (RCCC) is not well understood. In this study, the expression of both angiotensin receptors was quantified in a retrospective series of RCCC and correlated with prognostic factors.Methods: Angiotensin receptor type 1 and AT2-R expressions were quantified on tumour tissues by immunohistochemistry (IHC), western blot and quantitative reverse transcriptase PCR (qRT–PCR). IHC results were correlated to Fuhrman's grade and patient progression-free survival (PFS).Results: A total of 84 RCCC were analysed. By IHC, AT1-R and AT2-R were expressed to a greater level in high-grade tumours (AT1-R: P<0.001, AT2-R: P<0.001). Univariate analysis showed a correlation between PFS and AT1-R or AT2-R expression (P=0.001). By multivariate analysis, only AT2-R expression correlated with PFS (HR 1.021, P=0.006) and cancer stage (P<0.001). By western blot, AT1-R and AT1-R were also found to be overexpressed in higher Fuhrman's grade (P<0.01 and P=0.001 respectively). By qRT–PCR, AT1-R but not AT2-R mRNA were downregulated (P=0.001 and P=0.118, respectively).Conclusion: Our results show that AT1-R and AT2-R proteins are overexpressed in the most aggressive forms of RCCC and that AT2-R expression correlates with PFS. AT1-R or AT2-R blockage could, therefore, offer novel directions for anti-RCCC therapy

Genomic profiling using array comparative genomic hybridization define distinct subtypes of diffuse large b-cell lymphoma: a review of the literature

Diffuse large B-cell lymphoma (DLBCL) is the most common type of non-Hodgkin Lymphoma comprising of greater than 30% of adult non-Hodgkin Lymphomas. DLBCL represents a diverse set of lymphomas, defined as diffuse proliferation of large B lymphoid cells. Numerous cytogenetic studies including karyotypes and fluorescent in situ hybridization (FISH), as well as morphological, biological, clinical, microarray and sequencing technologies have attempted to categorize DLBCL into morphological variants, molecular and immunophenotypic subgroups, as well as distinct disease entities. Despite such efforts, most lymphoma remains undistinguishable and falls into DLBCL, not otherwise specified (DLBCL-NOS). The advent of microarray-based studies (chromosome, RNA, gene expression, etc) has provided a plethora of high-resolution data that could potentially facilitate the finer classification of DLBCL. This review covers the microarray data currently published for DLBCL. We will focus on these types of data; 1) array based CGH; 2) classical CGH; and 3) gene expression profiling studies. The aims of this review were three-fold: (1) to catalog chromosome loci that are present in at least 20% or more of distinct DLBCL subtypes; a detailed list of gains and losses for different subtypes was generated in a table form to illustrate specific chromosome loci affected in selected subtypes; (2) to determine common and distinct copy number alterations among the different subtypes and based on this information, characteristic and similar chromosome loci for the different subtypes were depicted in two separate chromosome ideograms; and, (3) to list re-classified subtypes and those that remained indistinguishable after review of the microarray data. To the best of our knowledge, this is the first effort to compile and review available literatures on microarray analysis data and their practical utility in classifying DLBCL subtypes. Although conventional cytogenetic methods such as Karyotypes and FISH have played a major role in classification schemes of lymphomas, better classification models are clearly needed to further understanding the biology, disease outcome and therapeutic management of DLBCL. In summary, microarray data reviewed here can provide better subtype specific classifications models for DLBCL

Extinction of solutions of semilinear higher order parabolic equations with degenerate absorption potential

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Extinction in a finite time for solutions of a class of quasilinear parabolic equations

International audienceWe study the property of extinction in a finite time for nonnegative solutions of 1 q ∂ ∂ t ( u q ) − ∇ ( | ∇ u | p − 2 ∇ u ) + a ( x ) u λ = 0 for the Dirichlet Boundary Conditions when q > λ > 0, p ⩾ 1 + q, p ⩾ 2, a ( x ) ⩾ 0 and Ω a bounded domain of R N ( N ⩾ 1). We prove some necessary and sufficient conditions. The threshold is for power functions when p > 1 + q while finite time extinction occurs for very flat potentials a ( x ) when p = 1 + q

Extinction in a finite time for solutions of large classes of Parabolic Equations involving p-Laplacian

We study the property of extinction in a finite time for nonnegative solutions of 1/q ∂t (u q) − delta_p u + a(x)u^λ = 0 for the Dirichlet Boundary Conditions when q > λ > 0, p ≥ 1 + q, p ≥ 2, a(x) ≥ 0 and Ω ⊂ R^N a bounded domain of R^N (N ≥ 1). Necessary and sufficient conditions are provided with the help of a family of infimum. When p > 1 + q, the threshold is for power functions but for p = 1 + q, it happens extinction in a finite time for very flat functions

Extinction in a finite time for solutions of a class of quasilinear parabolic equations

We study the property of extinction in a finite time for nonnegative solutions of 1 q ∂ ∂ t ( u q ) - Δ ( | Δ u | p - 2 Δ u ) + a ( x ) u λ = 0 for the Dirichlet Boundary Conditions when q > λ > 0, p > 1 + q, p > 2, a ( x ) > 0 and ω a bounded domain of R N ( N > 1). We prove some necessary and sufficient conditions. The threshold is for power functions when p > 1 + q while finite time extinction occurs for very flat potentials a ( x ) when p = 1 + q. © 2022 - IOS Press. All rights reserved