منابع مشابه
A note on orthogonal similitude groups
Let V be a vector space over the field F such that charðF Þ 61⁄4 2, and let V have a symmetric nondegenerate bilinear form. Let GOðV Þ be the orthogonal similitude group for this symmetric form, with similitude character . We prove that if g 2 GOðV Þ with ðgÞ 1⁄4 , then g 1⁄4 t1t2 where t1 is an orthogonal involution, and t2 is such that t 2 2 1⁄4 I and ðt2Þ 1⁄4 . As an application, we obtain a...
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In the past Euler has shown considerable interest in specific cases of similarity in which one figure is constructed from another in some way (consider, e.g., E-129, Opera Omnia I.27 130-180 Investigatio curvarum quae evolutae sui similes producant, in which the objects of study are planar curves which are similar to their own evolutes). In the current work, he considers any two similar figur...
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In concept learning, inductive techniques perform a global approximation to the target concept. Instead, lazy learning techniques use local approximations to form an implicit global approximation of the target concept. In this paper we present C-LID, a lazy learning technique that uses LID for generating local approximations to the target concept. LID generates local approximations in the form ...
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The concepts of Similitude, Dimensional Analysis and Theory of Models are presented and used in this chapter. They constitute important theoretical tools that allow scientists from many different areas to go further on their studies prior to actual experiments or using small scale models. The applications discussed herein are focused on thermal sciences (Heat Transfer and Fluid Mechanics). Usin...
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This note provides a few comments on the conditions required for similitude between velocity and electric field in electroosmotic flows. The velocity fields of certain electroosmotic flows with relatively thin electric double layers (EDLs) are known to be irrotational in regions outside of the EDL. Under restricted conditions, the velocity field, V , can be expressed in terms of the electric fi...
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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 1947
ISSN: 0033-569X,1552-4485
DOI: 10.1090/qam/20904