Supersonic flow onto a solid wedge

We consider the problem of 2D supersonic flow onto a solid wedge, or equivalently in a concave corner formed by two solid walls. For mild corners, there are two possible steady state solutions, one with a strong and one with a weak shock emanating from the corner. The weak shock is observed in supersonic flights. A long-standing natural conjecture is that the strong shock is unstable in some sense. We resolve this issue by showing that a sharp wedge will eventually produce weak shocks at the tip when accelerated to a supersonic speed. More precisely we prove that for upstream state as initial data in the entire domain, the time-dependent solution is self-similar, with a weak shock at the tip of the wedge. We construct analytic solutions for self-similar potential flow, both isothermal and isentropic with arbitrary $\gamma\geq 1$. In the process of constructing the self-similar solution, we develop a large number of theoretical tools for these elliptic regions. These tools allow us to establish large-data results rather than a small perturbation. We show that the wave pattern persists as long as the weak shock is supersonic-supersonic; when this is no longer true, numerics show a physical change of behaviour. In addition we obtain rather detailed information about the elliptic region, including analyticity as well as bounds for velocity components and shock tangents.Comment: 105 pages; 22 figure

The permafrost carbon inventory on the Tibetan Plateau : a new evaluation using deep sediment cores

Acknowledgements We are grateful for Dr. Jens Strauss and the other two anonymous reviewers for their insightful comments on an earlier version of this MS, and appreciate members of the IBCAS Sampling Campaign Teams for their assistance in field investigation. This work was supported by the National Basic Research Program of China on Global Change (2014CB954001 and 2015CB954201), National Natural Science Foundation of China (31322011 and 41371213), and the Thousand Young Talents Program.Peer reviewedPostprin

A nonhomogeneous boundary value problem in mass transfer theory

We prove a uniqueness result of solutions for a system of PDEs of Monge-Kantorovich type arising in problems of mass transfer theory. The results are obtained under very mild regularity assumptions both on the reference set $\Omega\subset\mathbf{R}^n$, and on the (possibly asymmetric) norm defined in $\Omega$. In the special case when $\Omega$ is endowed with the Euclidean metric, our results provide a complete description of the stationary solutions to the tray table problem in granular matter theory.Comment: 22 pages, 2 figure

Critical points for nondifferentiable functions in presence of splitting

AbstractA classical critical point theorem in presence of splitting established by Brézis–Nirenberg is extended to functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. The obtained result is then exploited to prove a multiplicity theorem for a family of elliptic variational–hemivariational eigenvalue problems

Exclusion of a major role for the PTEN tumour-suppressor gene in breast carcinomas

PTEN is a novel tumour-suppressor gene located on chromosomal band 10q23.3. This region displays frequent loss of heterozygosity (LOH) in a variety of human neoplasms including breast carcinomas. The detection of PTEN mutations in Cowden disease and in breast carcinoma cell lines suggests that PTEN may be involved in mammary carcinogenesis. We here report a mutational analysis of tumour specimens from 103 primary breast carcinomas and constitutive DNA from 25 breast cancer families. The entire coding region of PTEN was screened by single-strand conformation polymorphism (SSCP) analysis and direct sequencing using intron-based primers. No germline mutations could be identified in the breast cancer families and only one sporadic carcinoma carried a PTEN mutation at one allele. In addition, all sporadic tumours were analysed for homozygous deletions by differential polymerase chain reaction (PCR) and for allelic loss using the microsatellite markers D10S215, D10S564 and D10S573. No homozygous deletions were detected and only 10 out of 94 informative tumours showed allelic loss in the PTEN region. These results suggest that PTEN does not play a major role in breast cancer formation. 1999 Cancer Research Campaig

High-resolution genome-wide allelotype analysis identifies loss of chromosome 14q as a recurrent genetic alteration in astrocytic tumours

Diffusely infiltrative astrocytic tumours are the most common neoplasms in the human brain. To localise putative tumour suppressor loci that are involved in low-grade astrocytomas, we performed high-resolution genome-wide allelotype analysis on 17 fibrillary astrocytomas. Non-random allelic losses were identified on chromosomal arms 10p (29%), 10q (29%), 14q (35%), 17p (53%), and 19q (29%), with their respective common regions of deletions delineated at 10p14-15.1, 10q25.1-qter, 14q212.2-qer, 17p11.2-pter and 19q12-13.4. These results suggest that alterations of these chromosomal regions play important roles in the development of astrocytoma. We also allelotyped 21 de novo glioblastoma multiforme with an aim to unveil genetic changes that are common to both types of astrocytic tumours. Non-random allelic losses were identified on 9p (67%), 10p (62%), 10q (76%), 13q (60%), 14q (50%), and 17p (65%). Allelic losses of 10p, 10q, 14q and 17p were common genetic alterations detectable in both fibrillary astrocytomas and glioblastoma multiforme. In addition, two common regions of deletions on chromosome 14 were mapped to 14q22.3-32.1 and 14q32.1-qter, suggesting the presence of two putative tumour suppressor genes. In conclusion, our comprehensive allelotype analysis has unveiled several critical tumour suppressor loci that are involved in the development of fibrillary astrocytomas and glioblastoma multiforme. Although these two types of brain tumours are believed to evolve from different genetic pathways, they do share some common genetic changes. Our results indicate that deletions of chromosome 14q is a recurrent genetic event in the development of astrocytoma and highlight the subchromosomal regions on this chromosome that are likely to contain putative tumour suppressor genes involved in the oncogenesis of astrocytic tumours