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An Algebraic Proof of the Associative Law of Elliptic Curves

Advances in Pure Mathematics 2017年第12期7卷 649-659页

作者： Kazuyuki Fujii hiroshi oike International College of Arts and Sciences Yokohama City University Yokohama Japan Takado Yamagata Japan

In this paper we revisit the addition of elliptic curves and give an algebraic proof to the associative law by use of MATHEMATICA. The existing proofs of the associative law are rather complicated and hard to understand for beginners. An ‘‘elementary” proof to it based on algebra has not been given as far as we know. Undergraduates or non-experts can master the addition of elliptic curves through this paper. After mastering it they should challenge the elliptic curve cryptography.

关键词： Elliptic Curve Addition Associative Law MATHEMATICA Elliptic Curve Cryptography

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Shadow free texture acquisition of a large scale scene for city modeling

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重庆邮电学院学报（自然科学版） 2004年第5期16卷 121-128页

作者： Thanda Oo oike Jiro MIYAMOTO Mitsunori KAWASAKI hiroshi OHSAWA Yutaka Department of Information and Computer Science Faculty of Engineering Saitama UniversityJapanDepartment of Information and Computer Science Faculty of Engineering Saitama UniversityJapanDepartment of Information and Computer Science Faculty of Engineering Saitama UniversityJapanDepartment of Information and Computer Science Faculty of Engineering Saitama UniversityJapanDepartment of Information and Computer Science Faculty of Engineering Saitama UniversityJapan

Texture acquisition of a large scale scene is one of the critical research areas in computer vision and can be used in other application areas such as computer graphics (CG), the intelligent transportation system (ITS) and the 3D geographic information system (GIS). Moreover, to acquire texture without noise (e.g., a shadow, an obstacle body) is vital for such work. Although obstacles can be removed by using 3D geometric data, shadow elimination is still a difficult problem and strongly required for the CG and ITS community, especially for city modeling and simulation purposes. In this paper, we propose an automatic multiple image fusion technique and an efficient and simple shadow removing technique to retrieve high quality texture images of an urban area. The image fusion can be efficiently achieved by epipolar plane image (EPI) analysis, and the shadow elimination can be successfully carried out by an illumination independent color clustering technique. The strength of this algorithm is that we can successfully fuse multiple images and eliminate shadows from the fused single image, especially in low dynamic range images, which have proven difficult using previous techniques.

关键词：场景阴影计算机图象平面图象建模

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Osteoinduction and Osteoconduction with Porous Beta-Tricalcium Phosphate Implanted after Fibular Resection in Humans

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Journal of Biomaterials and Nanobiotechnology 2019年第3期10卷 159-173页

作者： Takashi Ariizumi Hiroyuki Kawashima hiroshi Hatano Tetsuro Yamagishi Naoki oike Taro Sasaki Hajime Umezu Yongjun Xu Naoto Endo Akira Ogose Division of Orthopedic Surgery Niigata University Graduate School of Medical and Dental Sciences Niigata Japan Department of Orthopedic Surgery Niigata Cancer Center Hospital Niigata Japan Division of Pathology Niigata University Hospital Niigata Japan Department of Orthopedic Surgery Harbin Medical University Hospital Harbin China Department of Orthopedic Surgery Uonuma Kikan Hospital Niigata Japan

Osteoinductive properties of β-TCP remain unknown in humans. It is important to improve the bone grafts which have been the standard treatment for bone defect due to their biocompatibility and bone-healing properties. The purpose of this study was to radiologically clarify the bone forming property of β-TCP by evaluating the replacement of β-TCP by newly formed bone in the defect after fibular resection and to examine the histological features of a β-TCP specimen three months after grafting. Radiographs of 17 patients who underwent β-TCP grafting were evaluated. Osteoinductive and osteoconductive properties were assessed by examining bone formation from the remnant fibula, periosteum, and β-TCP alone. In one case, β-TCP was removed later because of postoperative complications and was evaluated histologically. Twenty two of 34 sites between the remnant fibula and β-TCP had achieved good bone regeneration. Five of 14 sites between the periosteum and β-TCP had achieved good bone regeneration. We found immature but evident bone formation in three cases with no osseous and periosteal sites. Histological analysis revealed bone formation on the outer macropore surface of β-TCP. Some blood vessels formed in the macropores expressed CD31 and CD34, while a few lymphatic vessels expressed CD34 and podoplanin. Thus, the osteoinductive ability of β-TCP alone was demonstrated in humans radiographically for the first time. The histological morphology of β-TCP was demonstrated at an early stage after grafting in humans.

关键词： Osteoinduction Osteoconduction Beta-Tricalcium Phosphate Bioactive

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