We study bosonic tau functions in relation with the charged free bosonic fields.It is proved that up to a constant the only tau function in the Fock space M is the vacuum vector,and some tau functions are given in the...We study bosonic tau functions in relation with the charged free bosonic fields.It is proved that up to a constant the only tau function in the Fock space M is the vacuum vector,and some tau functions are given in the completion M by using Schur functions.We also give a new proof of Borchardt’s identity and obtain several q-series identities by using the boson-boson correspondence.展开更多
OBJECTIVE Lychee seed,a famous traditional Chinese medicine,recently were reported to improve the learning and memory abilities in mice.However,it is still unclear whether lychee seed saponins(LSS)can improve the cogn...OBJECTIVE Lychee seed,a famous traditional Chinese medicine,recently were reported to improve the learning and memory abilities in mice.However,it is still unclear whether lychee seed saponins(LSS)can improve the cognitive function and associated mechanisms.METHODS In present studies,we established the Alzheimer disease(AD)model by injecting Aβ25-35 into the lateral ventricle of rats.Then the spatial learning and memory abilities of LSS-treated rats were evaluated with the Morris water maze,meanwhile the protein expressions of AKT,GSK3β and Tau in the hippocampal neuron were analyzed by immunohistochemistry and Western blotting.RESULTS The results showed LSS can improve the cognitive functions of AD rats through shortening the escape latency,increasing the number across the platform,platform quadrant dwell time and the percentage of the total distance run platform quadrant.The protein expression of AKT was significantly up-regulated and that of GSK3β and Tau were decreased remarkably in the hippocampal CA1 area.CONCLUSION Our study is the first to show that LSS significantly improve the cognitive function and prevent hippocampal neuronal injury of the rats with AD by activation of the PI3K/AKT/GSK3βsignaling pathway,suggesting LSS may be developed into the nutrient supplement for the treatment of AD.展开更多
There are few numerical techniques available to solve the Bagley-Torvik equation which occurs considerably frequently in various offshoots of applied mathematics and mechanics. In this paper, we show that Chelyshkov-t...There are few numerical techniques available to solve the Bagley-Torvik equation which occurs considerably frequently in various offshoots of applied mathematics and mechanics. In this paper, we show that Chelyshkov-tau method is a very effective tool in numerically solving this equation. To show the accuracy and the efficiency of the method, several problems are implemented and the comparisons are given with other methods existing in the recent literature. The results of numerical tests confirm that Chelyshkov-tau method is superior to other existing ones and is highly accurate.展开更多
Tau,left ventricular diastolic time constant,is the most established index to describe left ventricular diastolic function.Tau has been commonly derived only as an invasive measurement in the catheter lab,where it is ...Tau,left ventricular diastolic time constant,is the most established index to describe left ventricular diastolic function.Tau has been commonly derived only as an invasive measurement in the catheter lab,where it is inconvenient,expensive and time consuming.In 1992,a non-invasive formula was proposed in Harvard to calculate Tau in an Echo lab.[1]Five years later,it was clinically corroborated by Scalia,et al.[2]Unfortunately,we think this method is incorrect.On top of the bold assumptions used in the mathematical deduction process,[3]there are logical flaws in the Harvard formula.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11531004)the Simons Foundation(Grant No.523868)。
文摘We study bosonic tau functions in relation with the charged free bosonic fields.It is proved that up to a constant the only tau function in the Fock space M is the vacuum vector,and some tau functions are given in the completion M by using Schur functions.We also give a new proof of Borchardt’s identity and obtain several q-series identities by using the boson-boson correspondence.
基金supported by Science and Technology Planning Project of Sichuan Province(2008SZ0050,14JC0798)Educational Commission of Sichuan Province(10ZA035,15ZA0155)+1 种基金Science and Technology Program of Luzhou(2015-S-43,2016LZXNYD-T03)Key Development Program of Southwest Medical University(2010ZD-010)
文摘OBJECTIVE Lychee seed,a famous traditional Chinese medicine,recently were reported to improve the learning and memory abilities in mice.However,it is still unclear whether lychee seed saponins(LSS)can improve the cognitive function and associated mechanisms.METHODS In present studies,we established the Alzheimer disease(AD)model by injecting Aβ25-35 into the lateral ventricle of rats.Then the spatial learning and memory abilities of LSS-treated rats were evaluated with the Morris water maze,meanwhile the protein expressions of AKT,GSK3β and Tau in the hippocampal neuron were analyzed by immunohistochemistry and Western blotting.RESULTS The results showed LSS can improve the cognitive functions of AD rats through shortening the escape latency,increasing the number across the platform,platform quadrant dwell time and the percentage of the total distance run platform quadrant.The protein expression of AKT was significantly up-regulated and that of GSK3β and Tau were decreased remarkably in the hippocampal CA1 area.CONCLUSION Our study is the first to show that LSS significantly improve the cognitive function and prevent hippocampal neuronal injury of the rats with AD by activation of the PI3K/AKT/GSK3βsignaling pathway,suggesting LSS may be developed into the nutrient supplement for the treatment of AD.
文摘There are few numerical techniques available to solve the Bagley-Torvik equation which occurs considerably frequently in various offshoots of applied mathematics and mechanics. In this paper, we show that Chelyshkov-tau method is a very effective tool in numerically solving this equation. To show the accuracy and the efficiency of the method, several problems are implemented and the comparisons are given with other methods existing in the recent literature. The results of numerical tests confirm that Chelyshkov-tau method is superior to other existing ones and is highly accurate.
文摘Tau,left ventricular diastolic time constant,is the most established index to describe left ventricular diastolic function.Tau has been commonly derived only as an invasive measurement in the catheter lab,where it is inconvenient,expensive and time consuming.In 1992,a non-invasive formula was proposed in Harvard to calculate Tau in an Echo lab.[1]Five years later,it was clinically corroborated by Scalia,et al.[2]Unfortunately,we think this method is incorrect.On top of the bold assumptions used in the mathematical deduction process,[3]there are logical flaws in the Harvard formula.
