The existence of mild solutions for non-autonomous evolution equations with nonlocal conditions in Banach space is studied in this article. We obtained the existence of at least one mild solution to the evolution equa...The existence of mild solutions for non-autonomous evolution equations with nonlocal conditions in Banach space is studied in this article. We obtained the existence of at least one mild solution to the evolution equations by using Krasnoselskii’s fixed point theorem as well as the theory of the evolution family. The interest of this paper is that any assumptions are not imposed on the nonlocal terms and Green’s functions and a new alternative method is applied to prove the existence of mild solutions. The results obtained in this paper may improve some related conclusions on this topic. An example is given as an application of the results.展开更多
In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differen...In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differential equation are obtained by Banach and Krasnoselakii fixed point theorems, and sufficient conditions for the existence and uniqueness of the solution are also developed. In addition, the Hyers-Ulam stability of the solution is considered. At last, an example is given to illustrate the main results.展开更多
A rapid and reproducible method has been developed for the simultaneous quantification of dopamine (DA), norepinephrine (NE), and serotonin (5-HT) in rat brain microdialysates. Derivatization was processed through red...A rapid and reproducible method has been developed for the simultaneous quantification of dopamine (DA), norepinephrine (NE), and serotonin (5-HT) in rat brain microdialysates. Derivatization was processed through reductive amination with butyraldehyde and sodium cyanoborohydride at 60℃ for 80 min incubation. Dibutylated monoamine neurotransmitters (MANTs) were directly analyzed with ultra-high-performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS). The chromatographic run time was shorter (2.1 min/sample) than previous studies [15] [18] [20]. Good linearity (R2 > 0.99) was obtained for DA, NE and 5-HT in the range of 25 - 5000 pg/mL, 5 - 1000 pg/mL and 2.5 - 500 pg/mL, respectively. Acceptable precision (CV, 8.5% - 13.4%) as well as accuracy (recovery, 94.1% - 106.8%) could be acquired by analysis of six batches of quality control samples (QCs) at four different concentrations, which demonstrated the reliability and reproducibility of current method. This method was successfully applied to the simultaneous determination of DA, NE and 5-HT in rat brain microdialysates, where basal levels as well as elevated levels after dosing with amphetamine (AMPH) were quantified for all three MANTs. This study provides a simple and rapid way to analyze MANTs in the biofluid in the future.展开更多
文摘The existence of mild solutions for non-autonomous evolution equations with nonlocal conditions in Banach space is studied in this article. We obtained the existence of at least one mild solution to the evolution equations by using Krasnoselskii’s fixed point theorem as well as the theory of the evolution family. The interest of this paper is that any assumptions are not imposed on the nonlocal terms and Green’s functions and a new alternative method is applied to prove the existence of mild solutions. The results obtained in this paper may improve some related conclusions on this topic. An example is given as an application of the results.
文摘In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differential equation are obtained by Banach and Krasnoselakii fixed point theorems, and sufficient conditions for the existence and uniqueness of the solution are also developed. In addition, the Hyers-Ulam stability of the solution is considered. At last, an example is given to illustrate the main results.
文摘A rapid and reproducible method has been developed for the simultaneous quantification of dopamine (DA), norepinephrine (NE), and serotonin (5-HT) in rat brain microdialysates. Derivatization was processed through reductive amination with butyraldehyde and sodium cyanoborohydride at 60℃ for 80 min incubation. Dibutylated monoamine neurotransmitters (MANTs) were directly analyzed with ultra-high-performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS). The chromatographic run time was shorter (2.1 min/sample) than previous studies [15] [18] [20]. Good linearity (R2 > 0.99) was obtained for DA, NE and 5-HT in the range of 25 - 5000 pg/mL, 5 - 1000 pg/mL and 2.5 - 500 pg/mL, respectively. Acceptable precision (CV, 8.5% - 13.4%) as well as accuracy (recovery, 94.1% - 106.8%) could be acquired by analysis of six batches of quality control samples (QCs) at four different concentrations, which demonstrated the reliability and reproducibility of current method. This method was successfully applied to the simultaneous determination of DA, NE and 5-HT in rat brain microdialysates, where basal levels as well as elevated levels after dosing with amphetamine (AMPH) were quantified for all three MANTs. This study provides a simple and rapid way to analyze MANTs in the biofluid in the future.
