On improving trapezoidal and triangular approximations of fuzzy numbers

AbstractRecently, various researchers have proved that the approximations of fuzzy numbers may fail to be fuzzy numbers, such as the trapezoidal approximations of fuzzy numbers. In this paper, we show by an example that the weighted triangular approximation of fuzzy numbers, proposed by Zeng and Li, may lead to the same result. For filling the gap, improvements of trapezoidal and triangular approximations are proposed. The formulas for computing the two improved approximations are provided. Some properties of the two improved approximations are also proved

Therapeutic Effect of Yi-Chi-Tsung-Ming-Tang on Amyloid β

Alzheimer's disease (AD) is an irreversible neurodegenerative disorder characterized by amyloid accumulation, neuronal death, and cognitive impairments. Yi-Chi-Tsung-Ming-Tang (YCTMT) is a traditional Chinese medicine and has never been used to enhance cognitive function and treat neurodegenerative disorders such as senile dementia. Whether YCTMT has a beneficial role in improving learning and memory in AD patients remains unclear. The present study showed that oral administration of YCTMT ameliorated amyloid-β- (Aβ1−40) injection-induced learning and memory impairments in rats, examined using passive avoidance and Morris water-maze tests. Immunostaining and Western Blot results showed that continuous Aβ1−40 infusion caused amyloid accumulation and decreased acetylcholine level in hippocampus. Oral administration of medium and high dose of YCTMT 7 days after the Aβ1−40 infusion decreased amyloid accumulation area and reversed acetylcholine decline in the Aβ1−40-injected hippocampus, suggesting that YCTMT might inhibit Aβ plague accumulation and rescue reduced acetylcholine expression. This study has provided evidence on the beneficial role of YCTMT in ameliorating amyloid-induced AD-like symptom, indicating that YCTMT may offer an alternative strategy for treating AD

Nil Polynomials of Prime Rings

AbstractAssume thatRis a prime ring without nonzero nil one-sided ideals and thatf(x1,…,xd) is a polynomial in the noncommuting variablesx1,…,xdand with the coefficients in the extended centroidCofR. If for allr1,…,rd∈R, there exists an integern=n(r1,…,rd)≥1, depending onr1,…,rd∈R, such thatf(r1,…,rd)n=0, then eitherf(r1,…,rd)=0 for allr1,…,rd∈RorRis a finite matrix ring over a finite field

Therapeutic Effect of Yi-Chi-Tsung-Ming-Tang on Amyloid β1−40-Induced Alzheimer's Disease-Like Phenotype via an Increase of Acetylcholine and Decrease of Amyloid β

Alzheimer's disease (AD) is an irreversible neurodegenerative disorder characterized by amyloid accumulation, neuronal death, and cognitive impairments. Yi-Chi-Tsung-Ming-Tang (YCTMT) is a traditional Chinese medicine and has never been used to enhance cognitive function and treat neurodegenerative disorders such as senile dementia. Whether YCTMT has a beneficial role in improving learning and memory in AD patients remains unclear. The present study showed that oral administration of YCTMT ameliorated amyloid-β- (Aβ1−40) injection-induced learning and memory impairments in rats, examined using passive avoidance and Morris water-maze tests. Immunostaining and Western Blot results showed that continuous Aβ1−40 infusion caused amyloid accumulation and decreased acetylcholine level in hippocampus. Oral administration of medium and high dose of YCTMT 7 days after the Aβ1−40 infusion decreased amyloid accumulation area and reversed acetylcholine decline in the Aβ1−40-injected hippocampus, suggesting that YCTMT might inhibit Aβ plague accumulation and rescue reduced acetylcholine expression. This study has provided evidence on the beneficial role of YCTMT in ameliorating amyloid-induced AD-like symptom, indicating that YCTMT may offer an alternative strategy for treating AD