On eight solvable systems of difference equations in terms of generalized Padovan sequences

WOS:000741090800016In this study we show that the systems of difference equations x(n+1) = f(-1)(af(p(n-1)) - bf (q(n-2))), y(n+1) =f(-1)(af(r(n-1)) + bf(s(n-2))), for n is an element of N-0, where the sequences p(n), q(n) , r(n) and s(n) are some of the sequences x(n) and y(n), f : D-f -> R is a "1 - 1" continuous function on its domain D-f subset of R, initial values x(-j), y(-j), j is an element of {0,1, 2}, are arbitrary real numbers in D-f and the parameters a,b are arbitrary complex numbers, with b not equal 0, can be explicitly solved in terms of generalized Padovan sequences. Some analytical examples are given to demonstrate the theoretical results

Solutions formulas for some general systems of difference equations

WOS:000741090800004In this paper, we give explicit formulas of the solutions of the two general systems of difference equations x(n+1 )= f(-1) (ag(y(n)) + bf (x(n-1)) + cg(y(n-2)) + df (x(n-3))) , y(n+1)= g(-1) (af (x(n)) + b(g)(y(n-1)) + cf (x(n-2)) + dg(y(n-3))) , and x(n+1) = f(-1) (a+b/g(y(n)) + c/ g(y(n))f(x(n-1)) + d/g(y(n))f(x(n-1))g(y(n-2))), y(n+1) = g(-1) (a+b/f(x(n)) + c/ f(x(n))g(y(n-1)) + d/f(x(n))g(y(n-1))f(x(n-2))), where n is an element of N-0, f, g : D -> R are "1 - 1" continuous functions on D subset of R, the initial values x(-i), y(-i), i = 0,1,2,3 are arbitrary real numbers in D and the parameters a, b, c and d are arbitrary real numbers. Our results considerably extend some existing results in the literature

Noradrenergic-dependent functions are associated with age-related locus coeruleus signal intensity differences

Abstract: The locus coeruleus (LC), the origin of noradrenergic modulation of cognitive and behavioral function, may play an important role healthy ageing and in neurodegenerative conditions. We investigated the functional significance of age-related differences in mean normalized LC signal intensity values (LC-CR) in magnetization-transfer (MT) images from the Cambridge Centre for Ageing and Neuroscience (Cam-CAN) cohort - an open-access, population-based dataset. Using structural equation modelling, we tested the pre-registered hypothesis that putatively noradrenergic (NA)-dependent functions would be more strongly associated with LC-CR in older versus younger adults. A unidimensional model (within which LC-CR related to a single factor representing all cognitive and behavioral measures) was a better fit with the data than the a priori two-factor model (within which LC-CR related to separate NA-dependent and NA-independent factors). Our findings support the concept that age-related reduction of LC structural integrity is associated with impaired cognitive and behavioral function