The left-to-right and right-to-left iterative languages are previously unnoticed subclasses of the regular languages of infinite size that are identifiable in the limit from positive data. Essentially, these language classes are the ones obtained by merging final states in a prefix tree and initial states in a suffix tree of the observed sample, respectively. Strikingly, these classes are also ...

For G = n , 1 / 2 $$ G={G}_{n,1/2} the Erd?s–Renyi random graph, let X {X}_n be variable representing number of distinct partitions V ( ) V(G) into sets A … q {A}_1,\dots, {A}_q so that degree each vertex in [ i ] G\left[{A}_i\right] is divisible by for all ? i\in \left[q\right] . We prove if ? 3 q\ge odd then ? d Po ! {X}_n\overset{d}{\to \limits}\mathrm{Po}\left(1/q!\right) and 4 even \limits...

We bound the second eigenvalue of random d $$ -regular graphs, for a wide range degrees , using novel approach based on Fourier analysis. Let G n {G}_{n,d} be uniform graph vertices, and λ ( ) \lambda \left({G}_{n,d}\right) its largest by absolute value. For some constant c > 0 c>0 any degree with log 10 ≪ ≤ {\log}^{10}n\ll d\le cn we show that = 2 + o 1 − / \left({G}_{n,d}\right)=\left(2+o(1)\...

The objective of this study was to determine the chronology of changes in blood pressure in renalhypertension induced by solid plexiglass clips in rats. Saw blades with the thickness of 0.21-0.22 mm wereused to make clips sized 4 × 2 × 2 mm from a piece of 2-mm thick plexiglass. Rats were subjected to shamoperation or left renal arterial clipping, and 1, 2, 3 and 4 weeks later blood pressure, a...

It is well known that if a function from set A to set B has a right inverse then the function is a surjection and the right inverse is an injection. For finite sets, the number of functions, injections, and surjections can also be counted. Relations generalize functions: do similar results exist for relations? This paper proves several new results concerning binary relations. For finite sets, w...