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This is a paper in whiuch several famous theorems are poven by using ths same method. There formula due to Marston Morse which I think is exceptional. Vector Fields and Famous Theorems
"... What do I mean? Look at the example of Newton’s Law of Gravitation. Here is a mathematical statement of great simplicity which implies logically vast number of phenomena of incredible variety. For example, Galileo’s observation that objects of different weights fall to the Earth with the same accele ..."
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What do I mean? Look at the example of Newton’s Law of Gravitation. Here is a mathematical statement of great simplicity which implies logically vast number of phenomena of incredible variety. For example, Galileo’s observation that objects of different weights fall to the Earth with the same acceleration, or Kepler’s laws governing the motion
Multicommodity maxflow mincut theorems and their use in designing approximation algorithms
 J. ACM
, 1999
"... In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied by ..."
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Cited by 357 (6 self)
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by the mincut. The result (which is existentially optimal) establishes an important analogue of the famous 1commodity maxflow mincut theorem for problems with multiple commodities. The result also has substantial applications to the field of approximation algorithms. For example, we use the flow result
On the Importance of Checking Cryptographic Protocols for Faults
, 1997
"... We present a theoretical model for breaking various cryptographic schemes by taking advantage of random hardware faults. We show how to attack certain implementations of RSA and Rabin signatures. An implementation of RSA based on the Chinese Remainder Theorem can be broken using a single erroneous s ..."
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Cited by 405 (6 self)
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We present a theoretical model for breaking various cryptographic schemes by taking advantage of random hardware faults. We show how to attack certain implementations of RSA and Rabin signatures. An implementation of RSA based on the Chinese Remainder Theorem can be broken using a single erroneous
Polynomial time algorithms for multicast network code construction
 IEEE TRANS. ON INFO. THY
, 2005
"... The famous maxflow mincut theorem states that a source node can send information through a network ( ) to a sink node at a rate determined by the mincut separating and. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediat ..."
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Cited by 316 (29 self)
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The famous maxflow mincut theorem states that a source node can send information through a network ( ) to a sink node at a rate determined by the mincut separating and. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided
ON A GENERALIZATION OF THE STONEWEIERSTRASS THEOREM
"... Abstract. A categorical version of the famous theorem of Stone and Weierstrass is formulated and studied in detail. Several applications and examples are given. ..."
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Cited by 5 (1 self)
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Abstract. A categorical version of the famous theorem of Stone and Weierstrass is formulated and studied in detail. Several applications and examples are given.
1 GENERALIZATIONS OF THE THEOREM OF CEVA AND THEIR APPLICATIONS
"... In these paragraphs one presents three generalizations of the famous theorem of Ceva, which states: “If in a triangle ABC one draws the concurrent straight lines ..."
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In these paragraphs one presents three generalizations of the famous theorem of Ceva, which states: “If in a triangle ABC one draws the concurrent straight lines
Fourier Analysis and Szemerédi's Theorem
, 1998
"... . The famous theorem of Szemer'edi asserts that for every positive integer k and every positive real number ffi ? 0 there is a positive integer N such that every subset of f1 ..."
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Cited by 9 (0 self)
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. The famous theorem of Szemer'edi asserts that for every positive integer k and every positive real number ffi ? 0 there is a positive integer N such that every subset of f1
ON A GENERALIZATION OF THE BINOMIAL THEOREM
, 1996
"... The elementary binomial theorem is arguably one of the oldest and perhaps most wellknown result in mathematics. This famous theorem, which was known to Chinese mathematicians from as early as the thirteenth century, has been subject since that time to a number of generalizations, one of which is at ..."
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The elementary binomial theorem is arguably one of the oldest and perhaps most wellknown result in mathematics. This famous theorem, which was known to Chinese mathematicians from as early as the thirteenth century, has been subject since that time to a number of generalizations, one of which
An extension of Lucas’ theorem
 Proc. Amer. Math. Soc
"... Abstract. Let p be a prime. A famous theorem of Lucas states that ( mp+s) ≡ ( np+t m) ( s) (mod p) ifm, n, s, t are nonnegative integers with s, t < p. Inthispaper n t we aim to prove a similar result for generalized binomial coefficients defined in terms of second order recurrent sequences with ..."
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Cited by 26 (16 self)
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Abstract. Let p be a prime. A famous theorem of Lucas states that ( mp+s) ≡ ( np+t m) ( s) (mod p) ifm, n, s, t are nonnegative integers with s, t < p. Inthispaper n t we aim to prove a similar result for generalized binomial coefficients defined in terms of second order recurrent sequences
Results 1  10
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