A Comparative Analysis of the New -3(-n) - 1 Remer Conjecture and a Proof of the 3n + 1 Collatz Conjecture

This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.

Fast Weighted Bit Flipping Algorithm for Higher-Speed Decoding of Low-Density Parity-Check Codes

Because of the speed limitation of the conventional bit-selection strategy in the exi- sting weighted bit flipping algorithms, a high- speed Low-Density Parity-Check （LDPC） dec- oder cannot be realised. To solve this problem, we propose a fast weighted bit flipping algo- rithm. Specifically, based on the identically dis- tributed error bits, a parallel bit-selection met- hod is proposed to reduce the selection delay of the flipped bits. The delay analysis demon- strates that, the decoding speed of LDPC codes can be significantly improved by the proposed algorithm. Furthermore, simulation results ver- ify the validity of the proposed algorithm.

Treatment of perforated giant gastric ulcer in an emergency setting

AIM:To study and assess clinical outcomes of various modes of treatment for perforated giant gastric ulcer in an emergency setting.METHODS:From May 2010 to February 2013,20cases of perforated giant gastric ulcer(>2 cm)were operated on in an emergency setting.All the patients presented with features of peritonitis and were resuscitated aggressively before taking for surgery.In the first4 cases,primary closure was done after taking a biopsy and among these,the 3rdcase also underwent partial distal gastrectomy and gastrojejunostomy and the 4th case underwent a radical subtotal gastrectomy with D2 lymphadenectomy and gastrojejunostomy for malignancy.All the remaining 16 cases underwent partial distal gastrectomy and gastrojejunostomy.RESULTS:Among the first 4 cases,2 had an uneventful recovery and were discharged on the 6thpostoperative day.The 3rdand 4thpatients developed gastricfistula,leading to prolonged hospitalization.For the 3rd patient,conservative management was tried for 1 wk,followed by partial distal gastrectomy and gastrojejunostomy,and he was discharged on the 20thday after admission,while the 4thpatient underwent a radical subtotal gastrectomy with D2 lymphadenectomy and gastrojejunostomy.Postoperatively,he developed adult respiratory distress syndrome,multiorgan dysfunction syndrome and expired on the 3rdpostoperative day of the second surgery.All the remaining 16 patients underwent partial distal gastrectomy and gastrojejunostomy and recovered well.Among these,4 of them were malignant and the remaining were benign ulcers.All had an uneventful recovery.The percentage of malignancy in our series was 30%(6 out of 20 cases).In our study,86%had an uneventful recovery,complications were seen in about 10%,and mortality was about 5%.CONCLUSION:In giant gastric ulcer,the chances of malignancy and leak after primary closure are high.So,we feel that partial distal gastrectomy and gastrojejunostomy is better.