Existing algorithms for isolating real solutions of zero-dimensional polynomial systems do not compute the multiplicities of the solutions. In this paper, we define in a natural way the multiplicity of solutions of zero-dimensional triangular polynomial systems and prove that our definition is equivalent to the classical definition of local (intersection) multiplicity. Then we present an effective and complete algorithm for isolating real solutions with multiplicities of zero-dimensional triangular polynomial systems using our definition. The algorithm is based on interval arithmetic and square-free factorization of polynomials with real algebraic coefficients. The computational results on some examples from the literature are presented.
ObjectiveThe aim of this study was to describe a novel surgical technique of endoscopic percutaneous repair in pediatric patients with type 1, type 2 and type 3 laryngeal cleft (LC).MethodsA retrospective study involving 12 patients with LC was performed at a tertiary pediatric hospital between February 2021 and June 2022. Endoscopic percutaneous repair was performed in all the patients. Information such as demographics, comorbidities, history of tracheostomy and the open approach for the repair, type of cleft and complications were analyzed.ResultsTwelve patients were diagnosed with LC. The median age of the patients at the time of surgery was 8.50 months (interquartile range, 49.50 months). Seven patients had tracheomalacia, four patients had subglottic stenosis, three patients had laryngomalacia. No surgical complications occurred in the 10 patients who underwent the primary procedure. For two patients who underwent a secondary procedure, endoscopic percutaneous repair failed again to heal the cleft. During the follow-up period after surgery, none of the patients had stridor, recurrent pneumonia, feeding difficulties, or dyspnea. Follow-up modified barium swallow postoperatively demonstrated no aspiration in 10 patients. Only the 2 patients with a secondary procedure had intermittent cough while taking large gulps of water. The cure rate of endoscopic percutaneous repairer was 83.3% (95% confidence interval: 73.9%–92.8%).ConclusionEndoscopic percutaneous repair should be considered as an alternative to the open transcervical approach and the traditional endoscopic approach for type 1, type 2 and type 3 LC.
Purpose
To evaluate the feasibility and clarify the appropriate indications for extubation immediately after single-stage laryngotracheal reconstruction (SS-LTR) in pediatric subglottic stenosis (SGS).
Methods
A retrospective study was performed from July 2017 to July 2022. All patients underwent SS-LTR with anterior costal cartilage graft. Information such as demographics, comorbidities, history of intubation or tracheostomy, Classification and grading of airway stenosis, the operation-specific decannulation rate and overall decannulation rate were analyzed.
Results
Twenty-two patients with simple SGS were identified. The median age at SS-LTR was 19 months (IQR = 18.5 months). Fourteen patients (63.6%) were intubated prior to the presentation of symptoms. Fourteen patients (63.6%) required preoperative tracheostomy to maintain a secure airway. Eight patients (36.4%) had congenital SGS, 10 patients (45.5%) had acquired SGS, and 4 patients (18.2%) had mixed SGS. Three patients had Grade II stenosis. Nineteen patients had Grade III stenosis. Comorbidities were found in 10 patients (45.5%). Major comorbidities were pneumonia. Congenital airway anomalies were found in 6 patients (27.3%). After anesthesia, all 22 patients were successfully extubated and returned to the general ward. Twenty patients had a satisfactory airway after SS-LTR. Two patients required reintubation or tracheostomy after operation. Operation-specific decannulation rate was 90.9%. The overall decannulation rate is 100%.
Conclusion
SS-LTR with anterior costal cartilage graft is an effective method to treat simple SGS ranging from Grades I to III in children. Extubation immediately after surgery is safe and feasible.
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