The most general planar transformations that map parabolas into parabolas
نویسندگان
چکیده
منابع مشابه
Arithmetic Discrete Parabolas
In the present paper, we propose a new definition of discrete parabolas, the so-called arithmetic discrete parabolas. We base our approach on a non-constant thickness function and characterized the 0connected and 1-connected parabolas in terms of thickness function. This results extend the well-known characterization of the κ-connectedness of arithmetic discrete lines, depending on the norm ‖ ·...
متن کاملOn the Archimedean Characterization of Parabolas
Archimedes knew that the area between a parabola and any chord AB on the parabola is four thirds of the area of triangle ∆ABP where P is the point on the parabola at which the tangent is parallel to AB. We consider whether this property (and similar ones) characterizes parabolas. We present five conditions which are necessary and sufficient for a strictly convex curve in the plane to be a parab...
متن کاملImproving Photoacoustic Inversion on Parabolas
Photoacoustic tomography (PAT) is a novel tomographic imaging paradigm that combines the benefits of ultrasound imaging and optical tomography [8]. When a semitransparent sample is illuminated with a short pulse of electromagnetic energy, then parts of the optical energy become absorbed which in turn induces an acoustic pressure wave inside the sample (see Figure 1.1). The induced acoustic pres...
متن کاملFitting parabolas in noisy images
A novel approach to fitting parabolas to scattered data is introduced by putting special emphasis on the robustness of the approach. The robust fit is achieved by not taking into account a proportion α of the “most outlying” observations, allowing the procedure to trim them off. The most outlying observations are self-determined by the data. Procrustes analysis techniques and a particular type ...
متن کاملA Bilinear Oscillatory Integral along Parabolas
We establish an L×L → L norm estimate for a bilinear oscillatory integral operator along parabolas incorporating oscillatory factors e −β .
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2009
ISSN: 1944-4176
DOI: 10.2140/involve.2009.2.79