A polyhelix is continuous space curve with continuous Frenet frame that consists of a sequence of connected helical segments. The main result of this paper is that given n points in space, there exist infinitely many polyhelices passing through these points. These curves are by construction continuous with continuous derivatives and are completely specified by 3n numbers, i.e., the initial posi...

Let E n = {[τ ]a = (τ (a1) 1 , . . . , τ (an) n )|τ ∈ Sn, 1 ≤ ai ≤ r} be the set of all signed permutations on the symbols 1, 2, . . . , n with signs 1, 2, . . . , r. We prove, for every 2-letter signed pattern [τ ]a, that the number of [τ ]a-avoiding signed permutations in E n is given by the formula n ∑ j=0 j!(r−1) ( n j 2 . Also we prove that there are only one Wilf class for r = 1, four Wil...

Recently, a mechanism for relaxing a large cosmological constant (CC) has been proposed [1], which transforms any initial vacuum energy density of arbitrary sign and magnitude into a harmless quantity without fine-tuning. The setup is implemented in the ΛXCDM framework, and it yields a reasonable cosmological background evolution similar to the ΛCDM model with a fine-tuned CC. In this work we a...

We report observations of SMC X-1 in three new high-intensity states with ROSAT HRI in December 1995, May 1997, and March 1998 in which pulsations with a period of 0.70769 (± 0.00006) s, 0.70706 (± 0.00001) s, and 0.706707 (± 0.00001) s respectively were detected. Combining the pulse periods from observations with ROSAT PSPC in high-intensity states in October 1991 and March 1998, respectively,...

We study a problem concerning parabolic induction in certain p-adic unitary groups. More precisely, for $E/F$ quadratic extension of fields the associated group $G=\mathrm{U}(n,n)$ contains subgroup $P$ with Levi component $L$ isomorphic to $\mathrm{GL}_n(E)$. Let $\pi$ be an irreducible supercuspidal representation depth zero. use Hecke algebra methods determine when parabolically induced $\io...