Let UZ(n) be the minimal rank of n-universal Z-lattices, by which we mean positive definite Z-lattices which represent all positive Z-lattices of rank n. It is a well known fact that UZ(n) = n + 3 for 1 ≤ n ≤ 5. In this paper, we determine UZ(n) and find all n-universal lattices of rank UZ(n) for 6 ≤ n ≤ 8.

Elif Kazancı1, Hüseyin Gülen2, Ayşe Erbay3, Canan Vergin4 1Clinics of Pediatric Hematology Oncology, Dr. Behçet Uz Children’s Hospital, İzmir, Turkey 2Department of Pediatric Hematology, Faculty of Pediatric, Celal Bayar University, Manisa, Turkey 3Clinics of Pediatric Hematology Oncology, Dr. Behçet Uz Children’s Hospital, İzmir, Turkey 4Clinics of Pediatric Hematology Oncology, Dr. Behçet Uz ...

Linear codes are considered over the ring Z 4 + uZ 4 , a non-chain extension of Z 4. Lee weights, Gray maps for these codes are defined and MacWilliams identities for the complete, symmetrized and Lee weight enumer-ators are proved. Two projections from Z 4 + uZ 4 to the rings Z 4 and F 2 + uF 2 are considered and self-dual codes over Z 4 +uZ 4 are studied in connection with these projections. ...

Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 + u)-constacyclic codes over Z 4 + uZ 4 of any length are studied. A new Gray map between Z 4 + uZ 4 and Z 4 (4) is defined. By means of this map, it is shown that the Z 4 Gray image of a (1 + u)-constacyclic code of length n over ...

Fifty-six male patients with pulmonary emphysema and normal serum alpha 1-antitrypsin were followed for a minimum period of three years (range 3-13 yr) to observe the effects of the radiological distribution of emphysema on the annual rate of change of lung function indices. The subjects were placed in three categories--upper zone (UZ), lower zone (LZ), and generalised (G). The influence of smo...

Let Uz be the universal norm distribution and M a fixed power of prime p, by using the double complex method employed by Anderson, we study the universal Kolyvagin recursion occurred in the canonical basis in the cohomology group H(Gz ,Uz/MUz). We furthermore show that the universal Kolyvagin recursion implies the Kolyvagin recursion in the theory of Euler systems. One certainly hopes this coul...

We present echelle spectroscopy of the close pre-main-sequence binary star systems DQ Tau and UZ Tau-E. Over a 16 day time interval we acquired 14 nights of spectra for DQ Tau and 12 nights of spectra for UZ Tau-E. This represents the entire phase of DQ Tau, and 63 percent of the phase of UZ Tau-E. As expected, photospheric lines such as Li I λ6707 clearly split into two components as the prima...