منابع مشابه
A Theorem concerning Six Points
1. Introduction and statement of results. "Let three points be specified on a line. Then one of the points is in the interior of the line segment joining the other two, and one of the points is exterior to the line segment joining the other two." This elementary statement concerning the ordering of three points on a line is capable of various extensions. Thus, e.g., it is easy to prove the foll...
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The proposed theorem in this paper is indicative of a kind of duality in the propagation of waves in the dual media of and in the spherical structures. Independent of wave frequency, the number of layers, their thickness, and the type of polarization, this theorem holds true in case of any change in any of these conditions. Theorem: Consider a plane wave incident on a multilayered spheric...
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By system we mean a multi-set whose elements are unordered but may occur repeatedly. FollowingŠ. Znám [8] we use a(n) to denote the residue class { x ∈ Z : x ≡ a (mod n) }. For a system (1) A = {a i (n i)} k i=1 of residue classes, the n i are called its moduli. Definition. An integer T is said to be a covering period of (1) if it is a period of the characteristic function of the set k i=1 a i ...
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Both theorems, (I) and the stronger (II), although they are very simple in their statements, have been conjectured to require Fourier analysis for their proofs; see, e.g., p. 396 of Billingsley [2] for the first and p. 49 of Billingsley [1] for the second part. This note gives probabilistic proofs of the two theorems and thus answers this conjecture to the negative. The main argument of the pro...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1978
ISSN: 0022-0396
DOI: 10.1016/0022-0396(78)90004-9