An Approximation Algorithm for Two-Edge-Connected Subgraph Problem via Triangle-free Two-Edge-Cover

The $2$-Edge-Connected Spanning Subgraph problem (2-ECSS) is one of the most fundamental and well-studied problems in the context of network design. In the problem, we are given an undirected graph $G$, and the objective is to find a $2$-edge-connected spanning subgraph $H$ of $G$ with the minimum number of edges. For this problem, a lot of approximation algorithms have been proposed in the literature. In particular, very recently, Garg, Grandoni, and Ameli gave an approximation algorithm for 2-ECSS with factor $1.326$, which was the best approximation ratio. In this paper, we give a $(1.3+\varepsilon)$-approximation algorithm for 2-ECSS, where $\varepsilon$ is an arbitrary positive fixed constant, which improves the previously known best approximation ratio. In our algorithm, we compute a minimum triangle-free $2$-edge-cover in $G$ with the aid of the algorithm for finding a maximum triangle-free $2$-matching given by Hartvigsen. Then, with the obtained triangle-free $2$-edge-cover, we apply the arguments by Garg, Grandoni, and Ameli

A Transposition Flap Reconstruction after Resection of a Soft-Tissue Sarcoma in the Buttock

Introduction: Large defects following resection in the gluteal region are challenging. Of note, there are a limited number of fairly morbid options for reconstruction. Case Report: A 65-year-old female presented with complaints of an enlarging mass in the left buttock over the past several months. A high-grade sarcoma was diagnosed based on a biopsy. The final diagnosis was an undifferentiated pleomorphic sarcoma based on the resected tumor. An 11-cm tumor with surrounding tissues, including the great gluteal muscle, was resected, which resulted in a 17-cm full thickness defect. The defect was reconstructed with a transposition flap elevated from the lateral thorax. A transposition flap can cover large buttock defects without sacrificing other muscles. Conclusion: Moreover, a transposition flap is esthetically acceptable because most of the operative scar is within the buttock area. A transposition flap reconstruction is one of the several options for large defects after soft-tissue sarcoma resection in the buttock

Thoracoabdominal flap reconstruction after resection of superficial soft-tissue sarcomas in the chest wall

The thoracoabdominal flap is a rotation flap, and is well known for reconstruction of defects following resections for breast cancer, but the flap is not well known for reconstructing defects following resections of soft-tissue sarcomas involving the chest wall. Here we present two patients with superficial chest wall sarcomas consisting of a dermatofibrosarcoma protuberans in a 42-year-old man and a recurrent myxofibrosarcoma in a 76-year-old man. The tumors were resected with the surrounding tissue. The defect was reconstructed with a thoracoabdominal flap elevated from the ipsilateral thorax (medially-based flap). Neither case developed necrosis of the flap or reduced shoulder range of motion. The chest wall presents few options for a donor vessel. The thoracoabdominal flap has an axial blood supply and does not require a microsurgical procedure. A thoracoabdominal flap is a suitable reconstruction option for a defect after the resection of a superficial soft-tissue sarcoma in the chest wall

RF Conductivity and Surface Impedance of a Superconductor Taking into Account the Complex Superconducting gap Energy

AbstractThe Mattis-Bardeen theory for the anomalous skin effect in the superconductors has been extended taking the complex gap energy into account and the surface impedance of superconductors has been calculated using the extended Mattis-Bardeen theory. It is found that the surface resistance of the superconductor increases with increasing magnitude of the imaginary part of the gap energy. It is demonstrated that the calculated surface resistance for a NbN film quantitatively agrees with the measured one. Itis also found that temperature dependence of Q values of super conducting resonators is well describedby those calculated by the extended Mattis-Bardeen equation

Multifidus muscle retracted and preserved in resection of malignant bone tumor in the sacral ala

Resection of malignant tumors in the posterior pelvis requires multidirectional approaches for the resection and the subsequent spine-pelvic fixation. The multifidus muscle can be scarified during the operation. This is a case report of a 44-year-old male with a secondary chondrosarcoma arising from an osteochondroma in the sacral ala. Recurrence occurred 11 months after the initial operation, and the resected tissue from the recurrence was diagnosed as a chondrosarcoma. In both operations, the multifidus muscle was elevated from its distal attachment to provide an adequate view of the tumor resection and insertion of spine-pelvic instrumentation. An adequate view by elevation of the multifidus muscle is useful for a safe operation. A preserved multifidus muscle covering the instrumentation may reduce the risk of infection. The elevation and preservation of the multifidus muscle is an easy and simple method that contributes to successful resection of a malignant tumor of the pelvis

Singular behavior of the macroscopic quantities in the free molecular gas

Steady behavior of the free molecular gas is studied with a special interest in the behavior around a convex body. Two types of singular behavior are shown to occur at the level of the macroscopic quantities. Their occurrence and the strength of singularity are discussed in detail both numerically and analytically. A universal law behind them is revealed by the consideration of the local geometry of the boundary