In the paper, Guo–Krasnoselskii’s fixed point theorem is adapted to study the existence of positive solutions to a class of boundary value problems for higher order differential equations with delay. The sufficient conditions, which assure that the equation has one positive solution or two positive solutions, are derived. These conclusions generalize some existing ones.
In this paper, by using a fixed-point theorem in cones to study the boundary value problem for a class of quadratic mixed type of delay differential equations with eigenvalue, the sufficient condition of existence of their solutions is derived. The main results in this paper are the generalization and improvement of those existing ones.
In this paper, we study the chaotic dynamics of a Variable-Order Fractional Financial System (VOFFS). The Variable-Order Fractional Derivative (VOFD) is defined in Caputo type. A necessary condition for occurrence of chaos in VOFFS is obtained. Numerical experiments on the dynamics of the VOFFS with various conditions are given. Based on them, it is shown that the VOFFS has complex dynamical behavior, and the occurrence of chaos depends on the choice of order function. Furthermore, the chaos synchronization of the VOFFS is studied via active control method. Numerical simulations demonstrate that the active control method is effective and simple for synchronizing the VOFFSs with commensurate or incommensurate order functions.
Axinastatin 3 as a potential anticancer agent was synthesized by chemical methods. In an electrospray ion-trap mass spectrometer, using one stage of tandem mass spectrometry (MS/MS), the linear peptide intermediate was sequenced via the complementarities of y and b ions. Then, using multistep MS/MS (to MS6), the cyclic peptide was sequenced through sequentially removing one amino acid residue in each stage of MS/MS. The difference of the fragmentation mechanisms and the sequencing approaches between them is discussed.
Two heptapeptides have been prepared by Fmoc methodology using Wang resin as solid support. For attachment of the first amino acid, several coupling systems were evaluated, and DIC/DMAP system could give yields of >99% and low levels of racemization. The selection of scavenger combination to deprotect side chains revealed that H2O/p-cresol was good at scavenging trityl and 1,2-ethanedithiol was highly efficient for scavenging t-butyl. Through shortening the preactivation time to 5 min, the racemization which occurred during formation of amide bonds coupled by HBTU was minimized. The crude peptides were characterized by RP-HPLC and MS, and sequenced by MS/MS to acquire reliable amino acid sequence information.
The existence of positive periodic solutions for a class of second order impulsive differential equations is studied. By using fixed point theorem in cone, new existence results of positive periodic solutions are obtained without assuming the existence of positive periodic solutions of the corresponding continuous equation.
As an important plateau cereal crop, hulless barley is the principal food for the Tibetan people in China. ADP-glucose pyrophosphorylase (AGPase) is considered as the key enzyme for starch biosynthesis in plants. In this study, cDNAs encoding the small subunit (SSU I) and large subunit (LSU I) of AGPase were isolated from hulless barley. The results showed that SSU I and LSU I were 1438 and 1786 bp in length with a complete open reading frame (ORF) of 1419 and 1572 bp. The ORF-encoded polypeptides of 472 and 523 amino acids were having calculated molecular masses of 52.01 and 58.23 kDa, and the pI values were 5.59 and 6.30. In addition, phylogenetic analysis showed that SSU I and LSU I had the same phylogenetic trends with some species. Furthermore, expression levels in different growth periods and tissues of two hulless barley varieties were analyzed by quantitative reverse transcription-polymerase chain reaction. Gene expression levels of SSU I and LSU I were consistent with the total starch accumulation rate in endosperm. In conclusion, our data confirmed that SSU I and LSU I played an important role in hulless barley starch synthesis.
STGC3 is a novel candidate tumor suppressor gene that was found to be associated with nasopharyngeal carcinoma (NPC) via the cDNA cloning and RACE processes. The biological function of the STGC3 protein and its expression level in nasopharyngeal carcinoma remain unknown. This study aimed to evaluate the STGC3 protein expression level in NPC and to investigate the inhibitory function of STGC3 as a candidate tumor suppressor gene. We assessed the expression of the STGC3 protein in NPC biopsies and normal control specimens via Western blot and immunohistochemical analysis. The expression of STGC3 as induced by doxycycline (Dox) via a tetracycline (Tet)-regulated system in human nasopharyngeal carcinoma cell line CNE2 was also established, and the effect of STGC3 restoration on the biological behavior of CNE2 was observed. A reduced level of STGC3 expression (0.978 ± 0.213 versus 0.324 ± 0.185, P < 0.05) was detected in NPC versus normal nasopharyngeal tissue by Western blot assay. Immunohistochemical assays for STGC3 detected positive staining in the nuclei and cytoplasm of epithelial cells, and the positive expression rate in NPC, 8 of 21 (38%), was lower than that in normal nasopharynx samples, 16 of 22 (72%). After STGC3 expression was restored, the growth capacity and clone formation potential of CNE2 cells in soft agar were significantly suppressed, and the cell percentage in G0/G1 phase increased, while the percentage of cells entering the S and G2 phases decreased. This indicates that an abnormality in STGC3 expression is associated with nasopharyngeal carcinogenesis and that it may play an important role in controlling cell growth and regulating the cell cycle.