NOTES ON FINITE LINEAR PROJECTIVE PLANES 1. Projective
... if there exist one-to-one, onto maps σ : P → Q and τ : L → K such that p ∈ ` if and only if σ(p) ∈ τ (`). The multiplicative identity element 1 has played no role so far. Define a pre-double loop to be an algebra R = hR, +, ·, 0, i satisfying the remaining properties 1–8 of Lemma 7. A coordinatizing ...
... if there exist one-to-one, onto maps σ : P → Q and τ : L → K such that p ∈ ` if and only if σ(p) ∈ τ (`). The multiplicative identity element 1 has played no role so far. Define a pre-double loop to be an algebra R = hR, +, ·, 0, i satisfying the remaining properties 1–8 of Lemma 7. A coordinatizing ...
The generalized order-k Fibonacci–Pell sequence by matrix methods
... where Fn2 is the usual Fibonacci number. Indeed, we generalize the following relation involving the usual Fibonacci numbers [24] Fn+m = Fm+1 Fn + Fm Fn−1 . For later use, we give the following lemma. Lemma 4. Let uin be the generalized order-k F–P number. Then for 2 i k − 1, uin+1 = u1n + ui+1 n ...
... where Fn2 is the usual Fibonacci number. Indeed, we generalize the following relation involving the usual Fibonacci numbers [24] Fn+m = Fm+1 Fn + Fm Fn−1 . For later use, we give the following lemma. Lemma 4. Let uin be the generalized order-k F–P number. Then for 2 i k − 1, uin+1 = u1n + ui+1 n ...
Algebra for Digital Communication
... same way for both f and g, so we’ll do it only for f . The application is well-defined since : f ([x + 4y]4 ) = [9(x + 4y)]12 = [9x]12 + [36y]12 = [9x]12 . Moreover, it is clearly additive by construction, and multiplicative since : f ([x]4 )f ([y]4 ) = [9x]12 [9y]12 = [9]12 [9xy]12 = [9xy]12 = f ([ ...
... same way for both f and g, so we’ll do it only for f . The application is well-defined since : f ([x + 4y]4 ) = [9(x + 4y)]12 = [9x]12 + [36y]12 = [9x]12 . Moreover, it is clearly additive by construction, and multiplicative since : f ([x]4 )f ([y]4 ) = [9x]12 [9y]12 = [9]12 [9xy]12 = [9xy]12 = f ([ ...
