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41.
本文针对第二类端点奇异Fredholm积分方程构造基于分数阶Taylor展开的退化核方法,设计了两种计算格式,一是在全区间上使用分数阶Taylor展开式近似核函数,二是在包含奇点的小区间上采用分数阶插值,在剩余区间上采用分段二次多项式插值逼近核函数.讨论了两种退化核方法收敛的条件,并给出了混合插值法的收敛阶估计.数值算例表明对于非光滑核函数分数阶退化核方法有着良好的计算效果,且混合二次插值法比全区间上的分数阶退化核方法有着更广泛的适用范围. 相似文献
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Fabrizio Colombo Samuele Mongodi Marco Peloso Stefano Pinton 《Mathematical Methods in the Applied Sciences》2019,42(5):1662-1686
Let e?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory. 相似文献
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Yan‐Ping Zhang Yue Li Guan‐Cheng Xu Jin‐Yu Li Hua‐Ying Luo Jin‐Yao Li Li Zhang Dian‐Zeng Jia 《应用有机金属化学》2019,33(3)
Two new complexes, namely [Cu6L6] ( 1 ) and [Zn(HL)2] ( 2 ) (H2L = N‐(1‐phenyl‐3‐methyl‐4‐propenylidene‐5‐pyrazolone)‐2‐furancarboxylic acid hydrazide), have been synthesized and characterized. Single crystal X‐ray analysis indicates that complex 1 has a hexanuclear structure and complex 2 exhibits a mononuclear structure. The DNA/bovine serum albumin (BSA) binding properties of complexes 1 and 2 were investigated by absorption spectroscopy and fluorescence quenching. Both complexes could effectively intercalate to DNA with calculated quenching constants of 2.6 × 105 and 1.25 × 105 M?1, respectively. The quenching mechanism of the intrinsic fluorescence of BSA by the complexes was found to be a static one. The cytotoxicities of 1 and 2 were investigated in two human tumor cell lines, human esophageal cancer cells (Eca‐109) and cervical cancer cells (HeLa). Complex 1 exhibits higher antitumor activity than 2 . Furthermore, 1 can inhibit HeLa cells by inducing apoptosis and G0/G1 phase cell cycle arrest. All results demonstrate that 1 and 2 both have DNA/BSA binding capacity and antitumor activity. 相似文献
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Tae Hee Kim Hyun Mo Lee Hee Soo Park Sung Dong Kim Su Jin Kwon Atsushi Tahara Hideo Nagashima Bun Yeoul Lee 《应用有机金属化学》2019,33(4)
The original Sasol catalytic system for ethylene tetramerization is composed of a Cr source, a PNP ligand, and MAO (methylaluminoxane). The use of expensive MAO in excess has been a critical concern in commercial operation. Many efforts have been made to replace MAO with non‐coordinating anions (e.g., [B(C6F5)4]?); however, most of such attempts were unsuccessful. Herein, an extremely active catalytic system that avoids the use of MAO is presented. The successive addition of two equivalent [H(OEt2)2]+[B(C6F5)4]? and one equivalent CrCl3(THF)3 to (acac)AlEt2 and subsequent treatment with a PNP ligand [CH3(CH2)16]2C(H)N(PPh2)2 ( 1 ) yielded a complex presumably formulated as [ 1 ‐CrAl (acac)Cl3(THF)]2+[B(C6F5)4]?2, which exhibited high activity when combined with iBu3Al (1120 kg/g‐Cr/h; ~4 times that of the original Sasol system composed of Cr (acac)3, iPrN(PPh2)2, and MAO). Via the introduction of bulky trialkylsilyl substituents such as –SiMe3, –Si(nBu)3, or –SiMe2(CH2)7CH3 at the para‐position of phenyl groups in 1 (i.e., by using [CH3(CH2)16]2C(H)N[P(C6H4‐p‐SiR3)2]2 instead of 1 ), the activities were dramatically improved, i.e., tripled (2960–3340 kg/g‐Cr/h; more than 10 times that of the original Sasol system). The generation of significantly less PE (<0.2 wt%) even at a high temperature is another advantage achieved by the introduction of bulky trialkylsilyl substituents. NMR studies and DFT calculations suggest that increase of the steric bulkiness on the alkyl‐N and P‐aryl moieties restrict the free rotation around (alkyl)N–P (aryl) bonds, which may cause the generation of more robust active species in higher proportion, leading to extremely high activity along with the generation of a smaller amount of PE. 相似文献
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Transient transition behaviors of fractional-order simplest chaotic circuit with bi-stable locally-active memristor and its ARM-based implementation 下载免费PDF全文
Zong-Li Yang 《中国物理 B》2021,30(12):120515-120515
This paper proposes a fractional-order simplest chaotic system using a bi-stable locally-active memristor. The characteristics of the memristor and transient transition behaviors of the proposed system are analyzed, and this circuit is implemented digitally using ARM-based MCU. Firstly, the mathematical model of the memristor is designed, which is nonvolatile, locally-active and bi-stable. Secondly, the asymptotical stability of the fractional-order memristive chaotic system is investigated and some sufficient conditions of the stability are obtained. Thirdly, complex dynamics of the novel system are analyzed using phase diagram, Lyapunov exponential spectrum, bifurcation diagram, basin of attractor, and coexisting bifurcation, coexisting attractors are observed. All of these results indicate that this simple system contains the abundant dynamic characteristics. Moreover, transient transition behaviors of the system are analyzed, and it is found that the behaviors of transient chaotic and transient period transition alternately occur. Finally, the hardware implementation of the fractional-order bi-stable locally-active memristive chaotic system using ARM-based STM32F750 is carried out to verify the numerical simulation results. 相似文献
49.
On the (N+1)-dimensional local fractional reduced differential transform method and its applications
Jian-Gen Liu Xiao-Jun Yang Yi-Ying Feng Ping Cui 《Mathematical Methods in the Applied Sciences》2020,43(15):8856-8866
In this paper, we generalize the (N+1)-dimensional local fractional reduced differential transform method (LFRDTM) within the local fractional derivative sense. First, we show some new properties, lemmas, theorems and corollariesfor the (N+1)-dimensional LFRDTM. Second, these new properties, lemmas and theorems can be proved immediately after. Thirdly, we used two examples to state that this approach is efficient and simple to find numerical solutions to higher dimensional local fractional partial differential equations. Finally, we can be seen that this work can be looked as an extension of the prior work. 相似文献
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设(χ,d,μ)是一个同时满足上双倍条件和几何双倍条件的非齐度量测度空间,对于引进的一类非齐度量测度空间上的Morrey-Herz空间,利用非齐度量测度空间的特征,证明了广义分数次积分算子及其交换子在非齐度量测度空间上MorreyHerz空间的有界性. 相似文献