Blow-up criteria for Boussinesq system and MHD system and Landau-Lifshitz equations in a bounded domain

In this paper, we prove some blow-up criteria for the 3D Boussinesq system with zero heat conductivity and MHD system and Landau-Lifshitz equations in a bounded domain.Comment: 20 page

ON THE EXISTENCE AND UNIQUENESS OF A LIMIT CYCLE FOR A LIENARD SYSTEM WITH A DISCONTINUITY LINE

In this paper, we investigate the existence and uniqueness of crossing limit cycle for a planar nonlinear Lienard system which is discontinuous along a straight line (called a discontinuity line). By using the Poincare mapping method and some analysis techniques, a criterion for the existence, uniqueness and stability of a crossing limit cycle in the discontinuous differential system is established. An application to Schnakenberg model of an autocatalytic chemical reaction is given to illustrate the effectiveness of our result. We also consider a class of discontinuous piecewise linear differential systems and give a necessary condition of the existence of crossing limit cycle, which can be used to prove the non-existence of crossing limit cycle

Case report: Bilateral carotid body tumors with a concomitant skull-base paraganglioma

BackgroundBilateral carotid body tumors with a concomitant skull-base paraganglioma are extremely rare, of which only one case has been reported in the literature to date.Case presentationWe present the case of a 35-year-old male with 1 year of hypertension and high levels of dopamine and 3-methoxytyramine. Magnetic resonance imaging (MRI) scans demonstrated three separate masses at the left middle cranial fossa floor and bilateral carotid bifurcation. Genetic testing showed succinate dehydrogenase complex subunit D mutation. The patient underwent the resection of the left skull base mass. Histopathology and immunohistochemistry confirmed the presence of a skull-base paraganglioma.ConclusionsSuccinate dehydrogenase complex subunit D mutation-associated bilateral carotid body tumors with a concomitant skull-base paraganglioma accompanied by abnormal dopamine and hypertension are extremely rare, which not only provides ideas for considering the association of gene mutations, biochemical abnormalities and clinical symptoms but also provides an expanded diagnostic spectrum for paraganglioma in atypical locations

Profiles of cyclin B and cdc2 during ovarian and embryonic development in <em>Exopalaemon carinicauda</em>

Mitosis-promoting factor (MPF) is a complex formed by cyclin B (cyclin B) and cyclin-dependent kinase (cdc2). To investigate the role of MPF in the reproduction of Exopalaemon carinicauda, we cloned its full-length cDNA of the Ec-cyclin B and Ec-cdc2 genes. We analyzed their molecular characteristics and expression profiles during ovarian and embryonic development. The results showed that the Ec-cyclin B gene was 1194 bp long and encoded a 397 amino acid (aa) long protein. However, Ec-cdc2 was 900 bp long, which encoded 299 aa with a conserved cyclin binding motif PSTAIRE. The phylogenetic tree analysis showed that Ec-cyclin B had the highest homology with the cyclin B of Macrobrachium rosenbergii (81.06%). In comparison, Ec-cdc2 had the highest homology with the cdc2 of E. modestus (96.80%). Ec-cyclin B showed the highest expression in the ovary, whereas Ec-cdc2 was the highest in the hepatopancreas, followed by the ovary. In the five stages of ovarian development, Ec-cyclin B and Ec-cdc2 expression levels reach the highest at stage Ⅴ(p < 0.05). Overall, the expression of these two genes first increased and then decreased at different embryonic developmental stages. Therefore, these findings suggested that cyclin B and cdc2 played an essential role in the ovarian and embryonic development of E. carinicauda