Each biological system possesses a widely unrecognized buffer system to maintain acid-base balance to a specific pH. The skin pH is crucial for physiological skin function. In aged or diseased skin, pH increase is obs...Each biological system possesses a widely unrecognized buffer system to maintain acid-base balance to a specific pH. The skin pH is crucial for physiological skin function. In aged or diseased skin, pH increase is observed and may negatively affect skin health. Skin care products with a pH that is slightly more acidic than the average normal skin pH and have an adequate buffering capacity, are considered beneficial for the skin. However, the buffer capacity of these products also plays an important role. In the present study, a possible normalization or acidification of skin surface pH and influence on skin hydration and skin barrier function was assessed via application of buffered skin care products that are formulated with pH ≤ 4.5. 48 subjects aged above 50 were treated with three different skin care products (Vitamin C Spheres, Collagen Spray, and Collagen Mask) and skin surface pH, skin hydration and barrier integrity were assessed before treatment start and after 4 weeks. The results show that after 4-week treatment with Vitamin C, the skin pH is acidified. Treatment with Collagen Spray and Collagen Mask showed maintenance of a physiological skin pH. Subgroup analysis of subjects that had a higher than average skin pH at study start demonstrated that all three tested skin care products were able to acidify the skin surface. In addition, skin hydration was also increased for two of the three tested products, whereas skin barrier is not significantly changed. This demonstrates that buffered skin care products formulated to a pH ≤ 4.5 are able to acidify and maintain physiological skin pH and may contribute to a physiological skin function.展开更多
Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonst...Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonstrated. We present a theorem and its proof that confirms the possibility to obtain the finite process and imposes the requirement for the matrix of SLAE. This matrix must be unipotent, i.e. all its eigenvalues to be equal to 1. An example of transformation of SLAE given analytically to the form with a unipotent matrix is presented. It is shown that splitting the unipotent matrix into identity and nilpotent ones results in Cramer’s analytical formulas in a finite number of iterations.展开更多
THE spread of the novel coronavirus nearly brought the Chinese economy to a standstill in January 2020 as the country focused on combatting the epidemic.As part of the containment measures,the sevenday Spring Festival...THE spread of the novel coronavirus nearly brought the Chinese economy to a standstill in January 2020 as the country focused on combatting the epidemic.As part of the containment measures,the sevenday Spring Festival holiday beginning on January 24 was also extended,leaving urban factories closed when thousands of migrant workers were kept at home.展开更多
文摘Each biological system possesses a widely unrecognized buffer system to maintain acid-base balance to a specific pH. The skin pH is crucial for physiological skin function. In aged or diseased skin, pH increase is observed and may negatively affect skin health. Skin care products with a pH that is slightly more acidic than the average normal skin pH and have an adequate buffering capacity, are considered beneficial for the skin. However, the buffer capacity of these products also plays an important role. In the present study, a possible normalization or acidification of skin surface pH and influence on skin hydration and skin barrier function was assessed via application of buffered skin care products that are formulated with pH ≤ 4.5. 48 subjects aged above 50 were treated with three different skin care products (Vitamin C Spheres, Collagen Spray, and Collagen Mask) and skin surface pH, skin hydration and barrier integrity were assessed before treatment start and after 4 weeks. The results show that after 4-week treatment with Vitamin C, the skin pH is acidified. Treatment with Collagen Spray and Collagen Mask showed maintenance of a physiological skin pH. Subgroup analysis of subjects that had a higher than average skin pH at study start demonstrated that all three tested skin care products were able to acidify the skin surface. In addition, skin hydration was also increased for two of the three tested products, whereas skin barrier is not significantly changed. This demonstrates that buffered skin care products formulated to a pH ≤ 4.5 are able to acidify and maintain physiological skin pH and may contribute to a physiological skin function.
文摘Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonstrated. We present a theorem and its proof that confirms the possibility to obtain the finite process and imposes the requirement for the matrix of SLAE. This matrix must be unipotent, i.e. all its eigenvalues to be equal to 1. An example of transformation of SLAE given analytically to the form with a unipotent matrix is presented. It is shown that splitting the unipotent matrix into identity and nilpotent ones results in Cramer’s analytical formulas in a finite number of iterations.
文摘THE spread of the novel coronavirus nearly brought the Chinese economy to a standstill in January 2020 as the country focused on combatting the epidemic.As part of the containment measures,the sevenday Spring Festival holiday beginning on January 24 was also extended,leaving urban factories closed when thousands of migrant workers were kept at home.
