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Aijun Yang,Weigao Ge 한국수학교육학회 2009 純粹 및 應用數學 Vol.16 No.2
This paper deals with the existence of positive solutions for a kind of multi-point nonlinear fractional differential boundary value problem at resonance. Our main approach is different from the ones existed and our main ingredient is the Leggett-Williams norm-type theorem for coincidences due to O'Regan and Zima. The most interesting point is the acquisition of positive solutions for fractional differential boundary value problem at resonance. And an example is constructed to show that our result here is valid.
Yang, Aijun,Wang, Helin The Korean Society for Computational and Applied M 2012 Journal of applied mathematics & informatics Vol.30 No.1
We consider the fourth-order differential equation with one-dimensional $p$-Laplacian (${\phi}_p(x^{\prime\prime}(t)))^{\prime\prime}=f(t,x(t),x^{\prime}(t),x^{\prime\prime}(t)$) a.e. $t{\in}[0,1]$, subject to the boundary conditions $x^{\prime\prime}}(0)=0$, $({\phi}_p(x^{\prime\prime}(t)))^{\prime}{\mid}_{t=0}=0$, $x(0)={\sum}_{i=1}^n{\mu}_ix({\xi}_i)$, $x(t)=x(1-t)$, $t{\in}[0,1]$, where ${\phi}_p(s)={\mid}s{\mid}^{p-2}s$, $p$ > 1, 0 < ${\xi}_1$ < ${\xi}_2$ < ${\cdots}$ < ${\xi}_n$ < $\frac{1}{2}$, ${\mu}_i{\in}\mathbb{R}$, $i=1$, 2, ${\cdots}$, $n$, ${\sum}_{i=1}^n{\mu}_i=1$ and $f:[0,1]{\times}\mathbb{R}^3{\rightarrow}\mathbb{R}$ is a $L^1$-Carath$\acute{e}$odory function with $f(t,u,v,w)=f(1-t,u,-v,w)$ for $(t,u,v,w){\in}[0,1]{\times}\mathbb{R}^3$. We obtain the existence of at least one nonconstant symmetric solution by applying an extension of Mawhin's continuation theorem due to Ge. Furthermore, an example is given to illustrate the results.
Aijun Yang,Helin Wang 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.1
We consider the fourth-order differential equation with one-dimensional p-Laplacian [수식] subject to the boundary conditions [수식] is a L1-Caratheodory function with [수식]. We obtain the existence of at least one nonconstant symmetric solution by applying an extension of Mawhin's continuation theorem due to Ge. Furthermore, an example is given to illustrate the results.
Aijun Yang,Weigao Ge 한국수학교육학회 2008 純粹 및 應用數學 Vol.15 No.4
In this paper, we study the self-adjoint second order boundary value problem with integral boundary conditions: (p(t)x0(t))0 + f(t; x(t)) = 0; t 2 (0; 1); x0(0) = 0; x(1) = Z 1 0 x(s)g(s)ds: A new result on the existence of positive solutions is obtained. The interesting points are: the ¯rst, we employ a new tool{ the recent Leggett-Williams norm-type theorem for coincidences; the second, the boundary value problem is involved in integral condition; the third, the solutions obtained are positive.
Yi Yang,Min Li,Aijun Tang,Yayun Liu,Zhen Li,Shaohai Fu 한국섬유공학회 2020 Fibers and polymers Vol.21 No.8
Conventional colored latex particles have poor solvent resistance due to the absence of chemical bonds betweenthe dye and polymer component, resulting in staining and greatly restricting its application. In this research, the disperse dyewas chemically bonded to the polymer to prepare covalent and solvent-resistance colored latex particles. Firstly, C.I. DisperseRed 60, as a common disperse dye in industry, was modified by acryloyl chloride (amidation reaction) for the purpose ofintroducing the C=C bonds. The structure of modified C.I. Disperse Red 60 was confirmed by 1HNMR, FTIR and elementalanalysis and its spectral property was also evaluated. Then the covalent colored latex particles were synthesized via miniemulsioncopolymerization of styrene (St) and ethyl acrylate (EA) in presence of modified C.I. Disperse Red 60 monomer. Results of FTIR, TG, DSC and TEM indicated that the covalent colored latex particles were successfully prepared. By usingUV-spectroscopy, the solvent resistance of the colored latex membranes in petroleum ether, hexane, cyclohexane, and ethanolwas monitored, respectively. Slight change of the absorption was detected for 10 days, which verified the excellent solventresistance of covalent colored latex membranes. Finally, the prepared colored latex particles were applied on cotton printingin the absence of binder. The results showed that the colored latex particles printed fabric had superior rubbing fastness andsoft hand feel.
OSCILLATION AND NONOSCILLATION OF HIGHER-ORDER DIFFERENCE EQUATIONS WITH NONLINEAR NEUTRAL TERMS
Zhenguo Zhang,Aijun Yang,Congna Di 한국수학교육학회 2007 純粹 및 應用數學 Vol.14 No.2
In this paper, the oscilation and existence of nonoscilatory solutions of odd order difference equations with nonlinear neutral terms are studied respec-tively. Some new criteria are established. Furthermore, some examples are given to illustrate the advance of our results.
Zhang, Zhenguo,Yang, Aijun,Di, Congna 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.25 No.1
In this paper, the existence of bounded positive solution of the second-order nonlinear neutral differential equations are studied. Some new sufficient conditions are given. Furthermore, examples given show that the results here are almost sharp.
Bionic natural small molecule co-assemblies towards targeted and synergistic Chemo/PDT/CDT
Shiyao Fu,Mingao Wang,Bin Li,Xu Li,Jianjun Cheng,Haitian Zhao,Hua Zhang,Aijun Dong,Weihong Lu,Xin Yang 한국생체재료학회 2023 생체재료학회지 Vol.27 No.00
Background Multi-component nano-delivery systems based on chemotherapy (chemo)- photodynamic therapy (PDT)- chemodynamic therapy (CDT) have gained increased attention as a promising strategy to improve clinical outcomes in cancer treatment. However, there remains a challenge in developing biodegradable, biocompatible, less toxic, yet highly efficient multicomponent nanobased drug delivery systems (DDS). Here, our study presents the screening and development of a novel DDS based on co-assemblies natural small molecule (NSMs). These molecules (oleanolic acid, and betulinic acid) are combined with photosensitizers Chlorine6 (Ce6) and Cu2+ that are encapsulated by tumor cell membranes. This nanocarrier encapsulated in tumor cell membranes achieved good tumor targeting and a significant improvement in tumor accumulation. Methods A reprecipitation method was used to prepare the co-assembled nanocarrier, followed by the introduction of Cu2 + into the DDS (OABACe6 NPs). Then, by wrapping the surface of NPs with the cell membranes of 4T1 which is a kind of mouse breast cancer cells (CM@OABACe6/Cu NPs). and analysis of its structure and size distribution with UV– Vis, XPS, FT-IR, SEM, TEM, and DLS. The synergistic effects of in vitro chemotherapy, CDT and PDT and targeting were also validated by cellular and animal studies. Results It was shown that CM@OABACe6/Cu NPs achieved good tumor targeting and a significant improvement in tumor accumulation. In the composite nano-assembly, the NSMs work together with the Ce6 to provide effective and safe chemo and PDT. Moreover, the effect of reduced PDT due to the depletion of reactive oxygen species (ROS) by excess glutathione (GSH) in the tumor can be counteracted when Cu2 + is introduced. More importantly, it also confers CDT through a Fenton-like catalytic reaction with H2O overexpressed at the tumor site. Conclusions By constructing CM@OABACe6/Cu NPs with homologous targeting, we create a triple synergistic platform for cancer therapy using PDT, chemo, and CDT. We propose here a novel combinatorial strategy for designing more naturally co-assembled small molecules, especially for the development of multifunctional synergistic therapies that utilize NSMs.