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Percutaneous angioscopy, using high resolution fiberoptic imaging, allows direct and two-dimensional visualization of the vascular interior, thereby enabling macroscopic pathological diagnosis. Percutaneous angioscopy has revealed that the vascular luminal surface exhibits various colors and morphologies characteristic of different vascular diseases. This imaging technique is used for evaluation of the severity of vascular diseases, staging of atherosclerosis, analysis of thrombus composition, evaluation of interventional and surgical therapies, and for guidance of intravascular interventions such as angioplasty, venous valvuloplasty and aortic stentgrafting. Recently, dye-image angioscopy has been used clinically for analyses of thrombus composition, endothelial damage and plaque composition. Intravascular microscopy was also developed for cellular imaging of vascular disease. Furthermore, fluorescent angioscopy was developed for molecular imaging of substances comprising atherosclerotic plaques. In this article, we describe the history of the development of angioscopy, angioscopic systems and techniques, angioscopic changes associated with vascular diseases, angioscope-guided intravascular therapies, and evaluation of intravascular and surgical therapies. Angioscopic pictures, except those of the coronary arteries, have rarely been published in the literature, so we have included many representative angioscopic pictures obtained by the authors in this article.
It is given in Weil and Rosenlicht (, p. 15) that (resp. 2) for all non-negative integers m and n with m≠n if c is any even (resp. odd) integer. In the present paper we generalize this. Our purpose is to give other integral sequences such that G.C.D.(ym,yn)=1 for all positive integers m and n with m≠n. Roughly speaking we show the following 1) and 2). 1) There are infinitely many polynomial sequences such that G.C.D.(fm(a),fn(a))=1 for all positive integers