Following Anders and Archer, we say that an unordered rooted labeled forest avoids the pattern σ∈Sk if in each tree, sequence of labels along shortest path from root to a vertex does not contain subsequence with same relative order as σ. For permutation σ∈Sk−2, construct bijection between n-vertex forests avoiding (σ)(k−1)k≔σ(1)⋯σ(k−2)(k−1)k (σ)k(k−1)≔σ(1)⋯σ(k−2)k(k−1), giving common generaliza...

In this article we examine four objections to the genetic modification of human beings: the freedom argument, the giftedness argument, the authenticity argument, and the uniqueness argument. We then demonstrate that each of these arguments against genetic modification assumes a strong version of genetic determinism. Since these strong deterministic assumptions are false, the arguments against g...

Let σ={σi:i∈I} be a partition of the set all prime numbers. A subgroup H finite group G is said to σ-subnormal in if can joined by chain subgroups H=H0⊆H1⊆⋯⊆Hn=G where, for every j=1,⋯,n, Hj−1 normal Hj or Hj/CoreHj(Hj−1) σi-group some i∈I. B soluble normalising Nσ-residual non-σ-subnormal G, where Nσ saturated formation σ-nilpotent groups. We show that normalises does not have section σ-residu...

In this paper, we introduce the property (h) on Banach lattices and present its characterization in terms of disjoint sequences. Then, an example is given to show that order-to-norm continuous operator may not be σ-order continuous. Suppose T:E→F order-bounded from Dedekind σ-complete lattice E into complete F. We prove T σ-order-to-norm if only both order weakly compact addition, can represent...