Perioperative acute pain management in pediatric patients is essential to reduce complications. Adenoidectomy-Tonsillectomy are surgical procedures requiring pain control, and risk minimization for postoperative bleeding, nausea, and vomiting. Despite their known secondary effects, the use of opioid analgesics remains preponderant in pediatric perioperative management. We present an updated review on perioperative pain management in children and describe the development and implementation of a multimodal analgesia protocol aimed to improve patients’ pain management while consistently reducing opioids use. Information from relevant articles was summarized, then compared to our clinical needs. Learnings were used to create and implement a multimodal analgesia protocol to be used in patients 3-9 years-old undergoing adenoidectomy/tonsillectomy. Analgesic strategies have emerged to reduce or avoid the use of opioids. Among these strategies, combining different non-opioid analgesics (Ibuprofen, Paracetamol, Metamizole) has been shown to be an effective and safe pharmacological strategy when implemented as part of postoperative multimodal analgesia protocols. Significant evidence associating the use of NSAIDs with a bigger risk of postoperative bleeding does not exist. Multimodal and preventive analgesia has shown to provide significantly more effective analgesia than some opioid regimens. Ibuprofen offers highly effective analgesia for postoperative pain, particularly when combined with acetaminophen.

At present paper, we aim to study the long-time behavior of a stochastic semi-linear degenerate parabolic equation on bounded or unbounded domain and driven by a nonlinear noise and defined. Since the theory of pathwise random dynamical systems can not be applied directly to the equation with nonlinear noise, first, we establish the existence of weak pullback mean random attractors for the equation by applying the theory of mean-square random dynamical systems; then, we prove the existence of (pathwise) pullback random attractors for the Wong-Zakai approximate system of the equation. In addition, we establish the upper semicontinuity of pullback random attractors for the Wong-Zakai approximate system of the equation under consideration driven by a linear multiplicative noise.

This paper presents the symmetries of differential equations associated with one-variable and Bivariate Hermite polynomials by proposing a representation of Lie algebra for these differential operators. Applying the Baker-Campbell-Hausdorff formula to these algebras, results in new relations and generating functions in one-variable and Bivariate Hermite polynomials. A general form of representation for other orthogonal polynomials such as Laguerre polynomials is introduced.

The present paper introduces a method of basis transformation of vector fields that is specifically applicable to polynomials space and differential equations with certain polynomials solutions such as Hermite, Laguerre and Legendre polynomials. The method based on separated transformation of vector space basis by a set of operators that are equivalent to the formal basis transformation and connected to it by linear combination with projection operators. Applying the Forbenius covariants yields a general method that incorporates the Rodrigues formula as a special case in polynomial space. Using the Lie algebra modules, specifically , on polynomial space results in isomorphic algebras whose Cartan sub-algebras are Hermite, Laguerre and Legendre differential operators. Commutation relations of these algebras and Baker-Campbell-Hausdorff formula gives new formulas for special polynomials