A simple method for solving the Fredholm singular integro-differential equations with Cauchy kernel is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. The advantage of the approach lies in the fact that, on the one hand, by improving the definition of traditional inner product, the representation of new reproducing kernel function becomes simple and requirement for image space of operator is weakened comparing with traditional reproducing kernel method; on the other hand, the approximate solution and its derivatives converge uniformly to the exact solution and its derivatives. Some examples are displayed to demonstrate the validity and applicability of the proposed method. 相似文献
A novel 3D star-shaped acceptor based on triphenylamine as a core and diketopyrrolopyrrole as arms (S(TPA-DPP)) was synthesized. S(TPA-DPP) exhibited excellent thermal stability, strong absorption, and very high open-circuit voltage (1.18 V) in solution-processed organic solar cells based on P3HT:S(TPA-DPP). 相似文献
A new building block of benzo[1,2-b:4,5-b']difuran (BDF) was firstly designed and synthesized. The newly designed unit was applied for constructing a new photovoltaic low band gap polymer, PBDFDTBT, which exhibited promising power conversion efficiency of 5.0%. 相似文献
To understand the effects rendered on the relevant basic physical properties and device function by controlling the regiochemistry of the cyclopenta[1,2‐b:5,4‐b′]dithiophene‐fluorobenzo[c][1,2,5]thiadiazole polymer (hereafter referred to as the CDT‐FBT polymer), two polymers, the regiorandom polymer (RA) and regioregular version (RR), respectively, are synthesized and characterized. In addition, an efficient route for synthesizing a key monomer for RR using various synthesis scope and optimizing the reaction conditions is discussed. Although RA exhibits optical, electrochemical, and morphological properties similar to RR, it shows better field‐effect transistor (FET) performance. Surprisingly, by employing a capillarity‐mediated sandwich‐casting process on a nanogrooved substrate, an unprecedented mobility of 17.8 cm2 V?1 s?1 is obtained for RA‐based FETs; this mobility value is almost twofold greater than those of the corresponding RR‐based FETs. For the first time, this study challenges previously reported results in that high carrier mobility is related to the high degree of polymer order induced by the backbone regioregularity. 相似文献
A three-dimensional porous network graphene aerogel (GAs) with large specific area and excellent conductivity was loaded with β-cyclodextrin polymer (Pβ-CD) to serve as a support for immobilization of antibodies. A highly sensitive immunosensor for the cancer marker carbohydrate antigen 15–3 (CA15–3) was designed based on the use of Pβ-CD/GAs. The large specific area of GAs warrants high loading with antibodies, and their excellent electrical conductivity warrants strong electrical signals. Based on the synergistic effect of GAs and Pβ-CD, an immunoassay was designed that is making use of hexacyanoferrate as an electrochemical probe and having a pleasantly low working potential of 0.2 V (vs. SCE). Response is linear in the 0.1 mU mL?1 to 100 U mL?1 activity range, and the lower detection limit is 0.03 mU mL?1 (at S/N =?3). The immunoassay is stable, selective and reproducible. It was applied to the analysis of spiked samples, and results were satisfactory.
Graphical abstract Schematic of an electrochemical immunoassay for the carbohydrate antigen 15–3. It is based on the use of β-cyclodextrin polymer and a graphene aerogel.
