Jaśkowski’s logic D2 was formulated with the help of the modal logic S5, [8]–[10]. It was shown (see [12], [16]) that to define D2 one could use normal modal logics weaker than S5. In the present paper we indicate a certain regular modal logic which also defines D2. This logic is the weakest regular modal logic defining D2.

Most receptor-like protein tyrosine phosphatases (RPTPs) contain two conserved phosphatase domains (D1 and D2) in their intracellular region. The carboxy-terminal D2 domain has little or no catalytic activity. The crystal structure of the tandem D1 and D2 domains of the human RPTP LAR revealed that the tertiary structures of the LAR D1 and D2 domains are very similar to each other, with the exc...

For nonnegative integers d1, d2, and L(d1, d2)-labeling of a graph G, is a function f : V(G) 3 {0, 1, 2, . . .} such that f(u) f(v) di whenever the distance between u and v is i in G, for i 1, 2. The L(d1, d2)-number of G, d1,d2(G) is the smallest k such that there exists an L(d1, d2)-labeling with the largest label k. These labelings have an application to a computer code assignment problem. T...

Let d1 and d2 be discriminants of distinct quadratic imaginary orders and let J(d1, d2) denote the product of differences of CM j-invariants with discriminants d1 and d2. In 1985, Gross and Zagier gave an elegant formula for the factorization of the integer J(d1, d2) in the case that d1 and d2 are relatively prime and discriminants of maximal orders. We generalize their methods and give a compl...

BACKGROUND We have previously reported associations between frontal D2/3 receptor binding potential positive symptoms and cognitive deficits in antipsychotic-naïve schizophrenia patients. Here, we examined the effect of dopamine D2/3 receptor blockade on cognition. Additionally, we explored the relation between frontal D2/3 receptor availability and treatment effect on positive symptoms. METH...

Narcolepsy is a sleep disorder characterized by abnormal manifestations of rapid-eye-movement (REM) sleep and excessive daytime sleepiness. Using a canine model of the disease, we found that central D2 antagonists suppressed cataplexy, a form of REM-sleep atonia occurring in narcolepsy, whereas this symptom was aggravated by D2 agonists. The effect on cataplexy was stereospecific for the S(-) e...

BACKGROUND Dopamine receptor 2 agonists (D2-ags) inhibit vascular endothelial growth factor (VEGF) secretion in luteinized granulosa cells (LGCs) both in vitro and in vivo. However, the mechanism of D2 regulation of the VEGF/VEGF Receptor 2 (VEGFR-2) pathway remains to be elucidated. We sought to determine the effects of D2 signaling on VEGF transcription and translation in LGCs, with the expec...

Under normal conditions the brain maintains a delicate balance between inputs of reward seeking controlled by neurons containing the D1-like family of dopamine receptors and inputs of aversion coming from neurons containing the D2-like family of dopamine receptors. Cocaine is able to subvert these balanced inputs by altering the cell signaling of these two pathways such that D1 reward seeking p...