In this paper, it has been proved that for a Noetherian ring R and an automorphism σ of R, an associated prime ideal of R[x, σ] or R[x, x−1, σ] is the extension of its contraction to R and this contraction is the intersection of the orbit under σ of some associated prime ideal of R. The same statement is true for minimal prime ideals also. It has also been proved that for a Noetherian Q-algebra...

A deduction-based decision procedure for a fragment of mutual belief logic with quantified agent variables (MBQL) is presented. A language of MBQL contains variables and constants for agents. The language ofMBQL is convenient to describe properties of rational agents when the number of agents is not known in advance. The multi-modal logic KD45n extended with restricted occurrences of quantifier...

The involvement of muscarinic receptors in neurogenic responses of the ileum was studied in wild-type and muscarinic-receptor (M-receptor) knockout (KO) mice. Electrical field stimulation to the wild-type mouse ileum induced a biphasic response, a phasic and sustained contraction that was abolished by tetrodotoxin. The sustained contraction was prolonged for an extended period after the termina...