Abstract A blend of matrix summability and Euler summability transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties of this space and finally, some inclusion relations are presented.

ABSTRACT Purpose: Non - muscle - invasive bladder cancer (NMIBC) can recur despite transurethral resection (TURBT) and adjuvant intravesical therapy. Tobacco products excreted in the urine are hypothesized to cause tumor - promoting effects on urothelial cells through direct contact. We determined if moderate or severe lower urinary tract symptoms (LUTS) (defined as International Prostate Symptom Score [IPSS] ≥ 8) was associated with increased tumor recurrence. Materials and Methods: We retrospectively identified 70 consecutive men initially diagnosed with NMIBC at our institution from 2010 – 2016. Means were compared with independent T - test and proportions with chi - square analysis. Multivariate logistic regression was performed to determine independent predictors of recurrence. Results: The majority of patients had Ta disease (58.6%) followed by T1 (28.6%) and Tis (12.9%). Forty - one (58.6%) patients had moderate or severe LUTS upon presentation within 30 days of initial TURBT with mean IPSS of 13.2 vs. 5.2 in the control group (p < 0.01). Biopsy - proven tumor recurrence occurred in 24 (34.3%) patients at mean follow-up of 31.7 months. Mean time to recurrence was 14.6 months. Moderate or severe LUTS was an independent predictor of tumor recurrence (odds ratio [OR]: 19.1, 95% confidence interval [CI]: 2.86 – 127; p = 0.002). Voiding or storage symptoms based on the IPSS did not independently correlate with tumor recurrence (p = 0.08 and p = 0.31, respectively) although total mean IPSS score did (OR: 1.26, 95% CI: 1.07 – 1.47, p = 0.005). Conclusions: The presence of moderate or severe LUTS may be an important prognostic factor in NMIBC. Patients with significant urinary symptoms could be monitored more aggressively due to higher recurrence risk.

Abstract Objective: To compare the early and late outcomes of off-pump coronary artery bypass grafting and coronary artery bypass graft + mitral valve repair in elderly patients with moderate chronic ischemic mitral regurgitation. Methods: One hundred and fifty elderly (age > 70 years) patients with moderate chronic ischemic mitral regurgitation who underwent off-pump coronary artery bypass grafting (n=95) or coronary artery bypass graft + mitral valve repair (n=55) between January 2007 and December 2014 were studied. They were subdivided according to presence or absence of high operative risk. Peri-operative variables and early operative outcomes were retrospectively studied. Survival, mitral regurgitation grade, and functional outcomes were prospectively analysed. Results: Both groups were comparable in terms of age (P=0.23), sex (P=0.74), left ventricle ejection fraction (P=0.6) and preoperative functional class (P=0.52). The mean number of grafts for off-pump coronary artery bypass grafting group was 3.14 and coronary artery bypass graft + mitral valve repair was 3.21. Off-pump coronary artery bypass grafting group had statistically significant better early operative outcomes i.e perioperative blood transfusions, intraaortic balloon pump usage, arrhythmias, renal dysfunction, liver dysfunction, sepsis, mean hours of ventilation, intensive care unit stay and operative mortality. On a prospective follow up of 5±2.33 years (1-9 years), coronary artery bypass graft + mitral valve repair in low operative risk subgroup had better improvements in mitral regurgitation grade than off-pump coronary artery bypass grafting. Both groups had similar improvements in functional class and cumulative survival was also comparable (63.2% vs. 54.5%). Conclusion: Off-pump coronary artery bypass grafting is a safer alternative to coronary artery bypass graft + mitral valve repair with better early operative outcomes and comparable late survival and functional outcomes in elderly patients with moderate chronic ischemic mitral regurgitation, especially those with higher operative risk.

Abstract Objective: The study aimed to identify the factors affecting the prognosis of post myocardial infarction (MI) ventricular septal rupture (VSR) and to develop a protocol for its management. Methods: This was a single center, retrospective-prospective study (2009-2014), involving 55 patients with post MI VSR. The strengths of association between risk factors and prognosis were assessed using multivariate logistic regression analysis. The UNM Post MI VSR management and prognosis scoring systems (UPMS & UPPS) were developed. Results: Thirty-day mortality was 52.5% (35% in the last 3 years). Twenty-eight (70%) patients underwent concomitant coronary artery bypass grafting. Residual ventricular septal defect was found in 3 (7.5%) patients. The multivariate analysis showed low mean blood pressure with intra-aortic balloon pump (OR 11.43, P=0.001), higher EuroSCORE II (OR 7.47, P=0.006), higher Killip class (OR 27.95, P=0.00), and shorter intervals between MI and VSR (OR 7.90, P=0.005) as well as VSR and Surgery (OR 5.76, P=0.016) to be strong predictors of mortality. Concomitant coronary artery bypass grafting (P=0.17) and location (P=0.25) of VSR did not affect the outcome. Mean follow-up was 635.8±472.5 days and 17 out of 19 discharged patients were in NYHA class I-II. Conclusion: The UNM Post-MI VSR Scoring Systems (UPMS & UPPS) help in management and prognosis, respectively. They divide patients into 3 groups: 1) Immediate Surgery - Patients with scores of <25 require immediate surgery, preferably with extracorporeal membrane oxygenation support, and have poor prognosis; 2) Those with scores of 25-75 should be managed with "Optimal Delay" and they have intermediate outcomes; 3) Patients with scores of >75 can undergo Elective Repair and they are likely to have good outcomes.

Abstract OBJECTIVE: Myocardial protection is the most important in cardiac surgery. We compared our modified single-dose long-acting lignocaine-based blood cardioplegia with short-acting St Thomas 1 blood cardioplegia in patients undergoing single valve replacement. METHODS: A total of 110 patients who underwent single (aortic or mitral) valve replacement surgery were enrolled. Patients were divided in two groups based on the cardioplegia solution used. In group 1 (56 patients), long-acting lignocaine based-blood cardioplegia solution was administered as a single dose while in group 2 (54 patients), standard St Thomas IB (short-acting blood-based cardioplegia solution) was administered and repeated every 20 minutes. All the patients were compared for preoperative baseline parameters, intraoperative and all the postoperative parameters. RESULTS: We did not find any statistically significant difference in preoperative baseline parameters. Cardiopulmonary bypass time were 73.8±16.5 and 76.4±16.9 minutes (P=0.43) and cross clamp time were 58.9±10.3 and 66.3±11.2 minutes (P=0.23) in group 1 and group 2, respectively. Mean of maximum inotrope score was 6.3±2.52 and 6.1±2.13 (P=0.65) in group 1 and group 2, respectively. We also did not find any statistically significant difference in creatine-phosphokinase-MB (CPK-MB), Troponin-I levels, lactate level and cardiac functions postoperatively. CONCLUSION: This study proves the safety and efficacy of long-acting lignocaine-based single-dose blood cardioplegia compared to the standard short-acting multi-dose blood cardioplegia in patients requiring the single valve replacement. Further studies need to be undertaken to establish this non-inferiority in situations of complex cardiac procedures especially in compromised patients.

A transposição das grandes artérias com uma janela aortopulmonar é uma anomalia congênita rara. Descrevemos um caso de transposição das grandes artérias com janela aortopulmonar e múltiplos defeitos do septo ventricular em um menino de 5 meses submetido a tratamento cirúrgico com sucesso.

D-Transposition of great arteries with an aortopulmonary window is a rare congenital anomaly. We describe a case of D-Transposition of great arteries with an aortopulmonary window and multiple ventricular septal defects in a 5-month boy who underwent successful surgical repair.