The k-Derivation Acting as a k-Endomorphism and as an Anti-k-Endomorphism on Semiprime Nobusawa Gamma Ring

On Jordan generalized k-derivations of semiprime Γ_N-Rings

Endomorphism Spectrums and Endomorphism Types of Graphs

In this paper, the endomorphisms, the half-strong endomorphisms, the locally strong endomorphisms, the quasi-strong endomorphisms, the strong endomorphisms and the automorphisms of a join of cycle n C and a vertex y are investigated. Some enumerative problems concerning these graphs are solved. In particular, the endomorphism spectrums and the endomorphism types of these graphs are given. It ha...

Reemergence of the maxi K+ as a K+ secretory channel.

37881–37887. 10. Walter SJ, Shirley DG, Folkerd EJ, Unwin RJ. Effects of the potassium channel blocker barium on sodium and potassium transport in the rat loop of Henle in vivo. Exp Physiol 2001; 86: 469–474. 11. Biner HL, Arpin-Bott MP, Loffing J et al. Human cortical distal nephron: distribution of electrolyte and water transport pathways. J Am Soc Nephrol 2002; 13: 836–847. 12. Salomonsson M...

The centralizer of an element in an endomorphism ring

We prove that the centralizer Cφ ⊆ HomR(M,M) of a nilpotent endomorphism φ of a finitely generated semisimple left R-module RM (over an arbitrary ring R) is the homomorphic image of the opposite of a certain Z(R)-subalgebra of the full m×m matrix algebra Mm×m(R[t]), where m is the dimension (composition length) of ker(φ). If R is a finite dimensional division ring over its central subfield Z(R)...

Unique k-SAT is as Hard as k-SAT

In this work we show that Unique k-SAT is as hard as k-SAT for every k ∈ N. This settles a conjecture by Calabro, Impagliazzo, Kabanets and Paturi [4]. To provide an affirmative answer to this conjecture, we develop a randomness optimal construction of Isolation Lemma for k-SAT.