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Fn+1
"... ABSTRACT. Below we give some exercises on linear difference equations with constant coefficients. These problems are taken from [MTB]. 1. EXERCISES Exercise 1.1 (Recurrence Relations). Let α0,..., αk−1 be fixed integers and consider the recurrence relation of order k xn+k = αk−1xn+k−1 + αk−2xn+k−2 ..."
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, this determines the values of c1,..., ck. Investigate the cases where the characteristic polynomial has repeated roots. For more on recursive relations, see [GKP], §7.3.
logFn, ∞ = h Notice that
"... The purpose of this note is to present in simple manner one of my main results in [1], which unfortunately was obscured by the generality and length of that paper. Let (Xn)∞n=1 be a stationary and ergodic process on a finite alphabet. For i ≤ j the block of symbols from i to j in the sequence (Xn) i ..."
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) is denoted Xji = XiXi+1... Xj. The first recurrence time of the initial nblock is the first time the block Xn1 repeats in the sample X
Staphylococcus aureus Keratinocyte Invasion Is Dependent upon Multiple HighAffinity Fibronectin Binding Repeats within FnBPA
"... Staphylococcus aureus is a commensal organism and a frequent cause of skin and soft tissue infections, which can progress to serious invasive disease. This bacterium uses its fibronectin binding proteins (FnBPs) to invade host cells and it has been hypothesised that this provides a protected niche f ..."
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from host antimicrobial defences, allows access to deeper tissues and provides a reservoir for persistent or recurring infections. FnBPs contain multiple tandem fibronectinbinding repeats (FnBRs) which bind fibronectin with varying affinity but it is unclear what selects for this configuration. Since
•o#o# THE FIBONACCI SEQUENCE Fn MODULO Lm
, 1981
"... This paper is concerned with determining the length of the period of a Fibonacci series after reducing it by a modulus m. Some of the results established by Wall (see [1]) are used. We investigate further the length of the period. The Fibonacci sequence is defined with the conditions f0=a9f1= $ and ..."
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= $ and fn + i ~ fn + / f ° r n ^ '! • ^ e will refer to the two special sequences when a = 0, 3 = 1 and a = 23 $ = 1 as (Fn) and (Ln), respectively. (Ln) is often called the Lucas sequence. The Fibonacci sequence 0, 1, 1, 25 3, 5S 8,... reduced modulo 3 is 0, 1, 1, 2, 05 2, 2, 1, 0,1, 1, 2, &apos
GRAPHS WITHOUT REPEATED CYCLE LENGTHS
, 2003
"... In 1975, P. Erdös proposed the problem of determining the maximum number f(n) of edges in a graph of n vertices in which any two cycles are of different lengths. In this paper, it is proved that f(n) ≥ n + 36t for t = 1260r + 169 (r ≥ 1) and n ≥ 540t2 + 175811 2 t + 7989 ..."
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In 1975, P. Erdös proposed the problem of determining the maximum number f(n) of edges in a graph of n vertices in which any two cycles are of different lengths. In this paper, it is proved that f(n) ≥ n + 36t for t = 1260r + 169 (r ≥ 1) and n ≥ 540t2 + 175811 2 t + 7989
Repeated Compositions of Analytic Maps
"... Abstract. Given a sequence fj of analytic maps of the open unit disc D into itself, we consider conditions that guarantee that the sequence f1 ± ¢ ¢ ¢ ± fn of compositions converges uniformly on D to a constant. The proofs are given entirely in terms of two and threedimensional hyperbolic geome ..."
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Abstract. Given a sequence fj of analytic maps of the open unit disc D into itself, we consider conditions that guarantee that the sequence f1 ± ¢ ¢ ¢ ± fn of compositions converges uniformly on D to a constant. The proofs are given entirely in terms of two and threedimensional hyperbolic
Staphylococcus aureus Host Cell Invasion and Virulence in Sepsis is Facilitated by the Multiple Repeats within FnBPA. PLoS Pathog. 6(6): e1000964
, 2010
"... Entry of Staphylococcus aureus into the bloodstream can lead to metastatic abscess formation and infective endocarditis. Crucial to the development of both these conditions is the interaction of S. aureus with endothelial cells. In vivo and in vitro studies have shown that the staphylococcal invasin ..."
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invasin FnBPA triggers bacterial invasion of endothelial cells via a process that involves fibronectin (Fn) bridging to a 5b 1 integrins. The Fnbinding region of FnBPA usually contains 11 nonidentical repeats (FnBRs) with differing affinities for Fn, which facilitate the binding of multiple Fn molecules
Altered rate of fibronectin matrix assembly by deletion of the first type III repeats
 J. Cell Biol
, 1996
"... Abstract. The assembly of fibronectin (FN) into a fibrillar matrix is a complex stepwise process that involves binding to integrin receptors as well as interactions between FN molecules. To follow the progression of matrix formation and determine the stages during which specific domains function, we ..."
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, we have developed cell lines that lack an endogenous FN matrix but will form fibrils when provided with exogenous FN. Recombinant FNs (recFN) containing deletions of either the RGD cellbinding sequence (RGD) or the first type III repeats (FNAIIII_7) including the IIIx FN binding site were generated
On locally repeated values of certain arithmetic functions, I
, 1985
"... Let v(n) denote the number of distinct prime factors of n. We show that the equation n + v(n) = m + v(m) has many solutions with n #M. We also show that if v is replaced by an arbitrary, integervalued function f with certain properties assumed about its average order, then the equation n +f(n) =m+ ..."
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Let v(n) denote the number of distinct prime factors of n. We show that the equation n + v(n) = m + v(m) has many solutions with n #M. We also show that if v is replaced by an arbitrary, integervalued function f with certain properties assumed about its average order, then the equation n +f(n) =m
Retrograde renegades and the Pascal connection: Repeating decimals represented by . . .
, 1989
"... Repeating decimals show a surprisingly rich variety of number sequence patterns when their repetends are viewed in retrograde fashion, reading from the rightmost digit of the repeating cycle towards the left. They contain geometric sequences as well as Fibonacci numbers generated by an application o ..."
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of Pascal*s triangle. Further, fractions whose repetends end with successive terms of Fnm, m = 1, 2,..., occurring in repeating blocks of k digits, are completely characterized, as well as fractions ending with Fnm+p or Lnm+p, where Fn is the n th
Results 1  10
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128