We find a sufficient condition to establish that certain abelian groups are not CI-groups with respect to ternary relational structures, and then show that the groups Z3×Z2, Z7×Z2, and Z5 ×Z2 satisfy this condition. Then we completely determine which groups Z2 ×Zp, p a prime, are CI-groups with respect to color binary and ternary relational structures. Finally, we show that Z2 is not a CI-group...

A binary linear code C is a Z2-double cyclic code if the set of coordinates can be partitioned into two subsets such that any cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be identified as submodules of the Z2[x]-module Z2[x]/(x r −1)×Z2[x]/(x − 1). We determine the structure of Z2-double cyclic codes giving the generator polynomials of these codes. ...

The paper studies the following question: Given a ring R, when does the zero-divisor graph (R) have a regular endomorphism monoid? We prove if R contains at least one nontrivial idempotent, then (R) has a regular endomorphism monoid if and only if R is isomorphic to one of the following rings: Z2 × Z2 × Z2; Z2 × Z4; Z2 × (Z2[x]/(x)); F1 × F2, where F1, F2 are fields. In addition, we determine a...

Worker Preferences Firm Preferences w1 : [f1] f2 f3 f4 f5 f6 f7 f8 f1 : [w1] w2 w3 w4 w5 w6 w7 w8 w2 : f1 [f2] f3 f4 f5 f6 f7 f8 f2 : w1 [w2] w3 w4 w5 w6 w7 w8 w3 : f1 f2 [f3] f4 f5 f6 f7 f8 f3 : w1 w2 [w3] w4 w5 w6 w7 w8 w4 : f1 f2 f3 [f4] f5 f6 f7 f8 f4 : w1 w2 w3 [w4] w5 w6 w7 w8 w5 : f1 f2 f3 f4 [f5] f6 f7 f8 f5 : w1 w2 w3 w4 [w5] w6 w7 w8 w6 : f1 f2 f3 f4 f5 [f6] f7 f8 f6 : w1 w2 w3 w4 w5 ...

The main theorem of this paper states that ifM is a closed orientable hyperbolic 3-manifold of volume at most 3.08, then the dimension of H1(M ;Z2) is at most 7, and that it is at most 6 unless M is “strange.” To say that a closed, orientable 3-manifold M , for which H1(M ;Z2) has dimension 7, is strange means that the Z2-vector space H1(M ;Z2) has a 2-dimensional subspace X such that for every...

Whether the host's immune response genes influence the severity of hepatitis C virus (HCV) liver disease is controversial. Human leukocyte antigen (HLA) class II alleles were analyzed in 233 HCV RNA-positive patients with chronic active hepatitis (197 patients with Knodell index of fibrosis F0-F3 and 36 patients with index of F4). The 2 groups did not differ by sex, duration of infection, mode ...

We write P for the polynomial algebra in one variable over finite field Z2 and P⊗t=Z2[x1,…,xt] its t-fold tensor product with itself. grade P⊗t by assigning degree 1 to each generator. are interested determining a minimal set of generators ring invariants (P⊗t)Gt as module Steenrod ring, A2. Here Gt is subgroup general linear group GL(t,Z2). An equivalent problem find monomial basis space “unhi...