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On Explicit Determinants of the RFMLR and RLMFL Circulant Matrices Involving Certain Famous Numbers
"... Abstract: The row firstminuslast right (RFMLR) circulant matrices and the row lastminusfirst left (RLMFL) circulant matrices are two special pattern matrices. By using the inverse factorization of polynomial, we give the explicit determinants of the two pattern matrices involving Fibonacci, Luc ..."
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Cited by 1 (1 self)
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Abstract: The row firstminuslast right (RFMLR) circulant matrices and the row lastminusfirst left (RLMFL) circulant matrices are two special pattern matrices. By using the inverse factorization of polynomial, we give the explicit determinants of the two pattern matrices involving Fibonacci, Lucas, Pell and PellLucas sequences in terms of finite many terms of these sequences.
An Introduction to the Kalman Filter
 UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL
, 1995
"... In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discretedata linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area o ..."
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Cited by 1146 (13 self)
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In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discretedata linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area
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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. Schnorr's protocol can also be broken, but a larger number of erroneous executions is needed. Keywords: Hardware faults, Cryptanalysis, RSA, FiatShamir, Schnorr, Public key systems, Identification protocols. 1 Introduction Direct attacks on the famous RSA cryptosystem seem to require that one factor
The Power of Convex Relaxation: NearOptimal Matrix Completion
, 2009
"... This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix Prize and other similar questions in collaborative filtering. In ..."
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Cited by 359 (7 self)
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This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix Prize and other similar questions in collaborative filtering
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
The Catalan numbers are the famous sequence
"... Dedicated to my friend Dennis Stanton Abstract. L. Shapiro found an elegant formula for the selfconvolution of the even subscrtipted terms in the Catalan sequence. This paper provides a natural qanalog of Shapiro’s formula together with three proofs, one of which ..."
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Dedicated to my friend Dennis Stanton Abstract. L. Shapiro found an elegant formula for the selfconvolution of the even subscrtipted terms in the Catalan sequence. This paper provides a natural qanalog of Shapiro’s formula together with three proofs, one of which
3D Sound for Virtual Reality and Multimedia
, 2000
"... This paper gives HRTF magnitude data in numerical form for 43 frequencies between 0.212 kHz, the average of 12 studies representing 100 different subjects. However, no phase data is included in the tables; group delay simulation would need to be included in order to account for ITD. In 3D sound ..."
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Cited by 290 (5 self)
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applications intended for many users, we want might want to use HRTFs that represent the common features of a number of individuals. But another approach might be to use the features of a person who has desirable HRTFs, based on some criteria. (One can sense a future 3D sound system where the pinnae
Bethe Ansatz for Quantum Strings
, 2004
"... We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS5×S 5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed allloop gauge theory asymptotic Bethe ansatz by add ..."
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Cited by 281 (16 self)
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. Secondly, we explain how to derive the 1/J energy corrections of Mimpurity BMN states, provide explicit, general formulae for both distinct and confluent mode numbers, and compare to asymptotic gauge theory. In the special cases M = 2, 3 we reproduce the results of direct quantization of Callan et al
Famous trails to Paul Erdős
 MATHEMATICAL INTELLIGENCER
, 1999
"... The notion of Erdős number has floated around the mathematical research community for more than thirty years, as a way to quantify the common knowledge that mathematical and scientific research has become a very collaborative process in the twentieth century, not an activity engaged in solely by ..."
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Cited by 24 (0 self)
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The notion of Erdős number has floated around the mathematical research community for more than thirty years, as a way to quantify the common knowledge that mathematical and scientific research has become a very collaborative process in the twentieth century, not an activity engaged in solely
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