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We prove inequalities on non-integer powers of products of generalized matrices functions on the sum of positive semi-definite matrices. For example, for any real number, positive semi-definite matrices,, and generalized matrix functionssuch as the determinant and permanent, etc., we have A general scheme is introduced to prove more general inequalities involvingmpositive semi-definite matrices forthat extend the results of other authors. [ABSTRACT FROM PUBLISHER]

The main purpose of this work is to present a better bound than the recent result given by Zhang [Linear Multilinear Algebra. 2015;63:2511–2517]. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, The Weighted Moore-Penrose of intuitionistic fuzzy matrices and weighted left (right) cancelable intuitionistic fuzzy matrices were defined. Finally we derive the equivalent condition for the existence of the Weighted Moore-Penrose and give an algorithm for computing the Weighted Moore-Penrose of Intuitionistic Fuzzy Matrices. [Copyright &y& Elsevier]

The purpose of this study was to investigate the effects of propofol anesthesia combined with remifentanil on inflammation, stress response, and immune function in children undergoing tonsil and adenoid surgery. For this aim,  126 children admitted to our hospital for elective temperature-controlled radio-frequency of tonsils and adenoids from October 2020 to September 2021 were randomly divided into an observation group (n=63) and a control group (n=63). The observation group was anesthetized with propofol in combination with remifentanil, while the control group underwent propofol combined with ketamine. The mean arterial pressure (MAP), heart rate, serum C-reactive protein (CRP), interleukin-6 (IL-6), tumour necrosis factor-α (TNF-α), epinephrine, cortisol (Cor), CD3+ T lymphocytes, CD4+ helper T lymphocytes, CD8+ suppressor T lymphocytes and CD4+/CD8+ ratio were compared between the two groups before induction of anaesthesia (T1), upon intubation (T2), at the beginning of surgery (T3), at the end of surgery (T4) and 5 min after extubation (T5). -(TNF-α). The recovery time from anaesthesia and adverse reactions after extubation were observed in the two groups. Results showed that the MAP and heart rate in both groups increased significantly at T2 compared to T1, but the observation group had lower values than the control group after the maintenance of anaesthesia (P<0.05). Serum CRP, IL-6 and TNF-α levels increased with time in both groups, and the increase was considered significant (P<0.05). In addition, serum epinephrine and Cor levels gradually rose from T1 to T4 in both groups, and then decreased at T5. The difference was statistically significant (P<0.05) between any two-time points. CRP, IL-6, TNF-α, epinephrine and Cor in the observation group were significantly lower than those in the control group from T3 to T5 (P<0.05). CD3+, CD4+ and CD4+/CD8+ ratio decreased whereas CD8+ went up in both groups at T4 and T5, and which were considered statistically significant when compared with data from T1 to T3 (P<0.05). However, CD3+, CD4+, CD8+ and CD4+/CD8+ ratios did not differ statistically significantly between the two groups at each time point (P>0.05). In the observation group, the time to recovery of spontaneous respiration, the time to resumption of limb movements and the span from discontinuation of anaesthetic to extubation were all significantly shorter than those in the control group, and the incidence of agitation during the awakening period was lower than that in the control group (P<0.05). Then propofol combined with remifentanil is more effective in inflammation, stress response and immune function in anesthetizing children undergoing tonsil and adenoid surgery. The observation group presented more stable hemodynamics, lower levels of inflammation and stress reactions, rapid awakening and fewer adverse effects, so the combination therapy was worthy of clinical promotion in pediatric surgery requiring general anesthesia.