In this paper, we investigate the first order neutral differential equation of Euler form with variable unbounded delay
where 0 ≤ c < 1, 0 < α < 1, 0 < βi < 1 and pi > 0 are constants, i=1,2,…,n. Some necessary and sufficient as well as explicit sufficient conditions for the oscillation of all solutions are established.
This paper is concerned with the existence of extreme solutions of nonlinear three-point boundary value problems for a class of first order impulsive functional differential equations. In the presence of a lower solution α and an upper solution β with the classical condition α ≤ β or the reversed ordering condition β ≤ α, some sufficient conditions for the existence of extreme solutions are obtained by using the method of upper and lower solutions coupled with the monotone iterative technique.
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.
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.
Two new lignan glycosides (1, 2) and four known lignan glycosides (3–6) have been isolated from the ethanolic extract of the stems of Viburnum melanocarpum through repeated column chromatography. Their structures including absolute configurations were confirmed by spectroscopic data [one-dimensional (1D) and two-dimensional (2D) nuclear magnetic resonance (NMR), high-resolution electrospray ionization mass spectra (HRESIMS), optical rotatory dispersion (ORD) and circular dichroism (CD)] and chemical methods. Additionally, the α-glucosidase inhibitory activity of these compounds was tested in vitro. Compound 1 exhibited the strongest inhibitory activity against α-glucosidase with a half-maximal inhibitory concentration (IC50) value of 10.3 μM.
Secreted proteins play important roles in many crucial biological processes, and can be new agents or targets for drug therapies. Here, we report on the isolation and characterization of a novel human non-classical secreted protein which is encoded by the hypothetical gene C19orf24 (chromosome 19 open reading frame 24). It has no signal peptide, but can still secrete extracellularly despite the presence of the inhibitor brefeldin A (BFA), proving its non-classical secreted protein status. Via subcellular localization using C19orf24 in vivo and transfected pEYFP-Golgi plasmid in Hela cells, C19orf24 was shown not to co-localize in the Golgi apparatus, which suggested that it secretes via a new and unknown pathway. Deglycosylation analysis with PNGase F verified that it has no N-glycosylation modification sites. Via the reverse transcription-PCR method, it was found to be expressed only in the human liver, and preferentially in normal tissue. In addition, C19orf24 was shown to be a recently evolved gene, found only in Homo sapiens and Pan troglodytes. By calculating its synonymous and non-synonymous substitution rate (d
N), we found that it experienced a purifying selection, which suggests that C19orf24 may have a special, irreplaceable biological function in the human organism.
A novel norneolignan glycoside (1), categorized as an unusual 7-noraryl-4′,7-epoxy-8,5′-neolignan glycoside, four new phenolic glycosides (2–5), and a known neolignan glycoside (6) have been isolated from the ethanolic extract of the stems of Viburnum fordiae Hance. Dried stems of V. fordiae were extracted with 95% ethanol, and the concentrated extract was portioned successively with petroleum ether, ethyl acetate and n-butanol. The n-butanol portion was subjected to the macroporous resin HPD-100, silica gel, octadecyl SiO2, MCI gel and Sephadex LH-20 columns to obtain six compounds. Their structures including absolute configurations were determined by spectroscopic data [1H and 13C nuclear magnetic resonance (NMR), total correlation spectroscopy (TOCSY), heteronuclear single quantum coherence (HSQC), heteronuclear multiple-bond correlation (HMBC) and optical rotatory dispersion (ORD)] and chemical methods.