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New conditions for the reverse order laws for {1,3} and {1,4}-generalized inverses

In this note, the reverse order laws for {1, 3} and {1, 4}-generalized inverses of matrices are considered. New necessary and sufficient conditions for (AB){1, 3} ⊆ B{1, 3} · A{1, 3} and (AB){1, 4} ⊆ B{1, 4} ·A{1, 4} are presented.

MTHE 217 - Algebraic Structures with Applications

(a) First realize that [8] = [3] in Z5. Take different powers of [8] until we arrive at [8] = [1]. This will help us to significantly simplify [8]. [8] = [3] = [9] = [4]; [8] = [8][8] = [8][4] = [3][4] = [2]; [8] = [8][8] = [2][3] = [1]. Hence [8] = [1]. Now 391 = (97) · 4 + 3. Thus [8] = [8](97)·4+3 = [8](97)·4[8]3 = ([8])[8] = [1][8] = [8] = [2]. Therefore the remainder when 8 is divided by 5...

Pb ( Mg 1 / 3 Nb 2 / 3 ) O 3 ( PMN ) Relaxor : Dipole Glass or Nano - Domain Ferroelectric ?

Hybrid Bounds for Twists of Gl(3) L-functions

Let π be a Hecke-Maass cusp form for SL(3,Z) and χ = χ1χ2 a Dirichlet character with χi primitive modulo Mi. Suppose that M1, M2 are primes such that max{(M |t|)1/3+2δ/3,M2/5|t|−9/20,M1/2+2δ|t|−3/4+2δ}(M |t|)ε < M1 < min{(M |t|)2/5, (M |t|)1/2−8δ}(M |t|)−ε for any ε > 0, where M = M1M2, |t| ≥ 1 and 0 < δ < 1/52. Then we have L ( 1 2 + it, π ⊗ χ ) ≪π,ε (M |t|).

Quantum subgroups of the compact quantum group SU_-1(3)

We study the (compact) quantum subgroups of the compact quantum group SU−1(3): we show that any non-classical such quantum subgroup is a twist of a compact subgroup of SU(3) or is isomorphic to a quantum subgroup of U−1(2).

Uropathogenic Escherichia Coli Genome ( strain D 3 ) and Comparative Analysis with Other 1 Uropathogenic and Nonpathogenic Strains 2 3 Brian

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