Let k be an imaginary quadratic number field with Ck,2, the 2-Sylow subgroup of its ideal class group Ck, of rank 4. We show that k has infinite 2-class field tower for particular families of fields k, according to the 4-rank of Ck, the Kronecker symbols of the primes dividing the discriminant ∆k of k, and the number of negative prime discriminants dividing ∆k. In particular we show that if the...

We prove that the dimension of the 1-nullity distributionN(1) on a closed Sasakianmanifold M of rank l is at least equal to 2l−1 provided thatM has an isolated closed characteristic. The result is then used to provide some examples ofK-contact manifolds which are not Sasakian. On a closed, 2n+ 1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension o...

Let M be a tropical matrix (k + x) × (k + x ′) for some k, x , x ′ ∈ N − {0} with tropical rank k. We show that Kapranov rank is k too if x and x ′ are not too big; namely if we are in one of the following cases: a) k ≥ 6 and x , x ′ ≤ 2 b) k = 4, 5, x ≤ 2 and x ′ ≤ 3 (or obviuosly the converse, that is x ≤ 3 and x ′ ≤ 2) c) k = 3 and either x , x ′ ≤ 3 or x ≤ 2 and x ′ ≤ 4 (or obviuosly the co...

We introduce a novel adaptive digital beamforming algorithm for application in cellular CDMA communications systems. A Noniterative Rank-one Signal Subspace eigenstruc-ture Update (NR1SSU) algorithm enables low-complexity re-cursive processing of beamforming weights. A PN chip-level IS-95 CDMA reference model 3] has been used to test the beamforming algorithm via simulation. Our results show th...