We prove a relationship between the Cleaning problem and the Balanced Vertex– Ordering problem, namely that the minimum total imbalance of a graph equals twice the brush number of a graph. This equality has consequences for both problems. On one hand, it allows us to prove the NP-completeness of the Cleaning problem, which was conjectured by Messinger et al. [7]. On the other hand, it also enab...

Linear depolarization ratios in clean air ranges were measured with POLIS-6 at 355 and 532 nm. The mean deviation from the theoretical values, including the rotational Raman lines within the filter bandwidths, amounts to 0.0005 at 355 nm and to 0.0012 at 532 nm. The mean uncertainty of the measured linear depolarization ratio of clean air is about 0.0005 at 355 nm and about 0.0006 at 532 nm.

let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

Using path integral Monte Carlo we have calculated exchange frequencies as electrons undergo ring exchanges in a "clean" 2D Wigner crystal as a function of density. The results show agreement with WKB calculations at very low density, but show a more rapid increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2D (3)He. Using the res...

the zero-divisor graph of a commutative ring r with respect to nilpotent elements is a simple undirected graph $gamma_n^*(r)$ with vertex set z_n(r)*, and two vertices x and y are adjacent if and only if xy is nilpotent and xy is nonzero, where z_n(r)={x in r: xy is nilpotent, for some y in r^*}. in this paper, we investigate the basic properties of $gamma_n^*(r)$. we discuss when it will be eu...

We study the kernel and cokernel of the Frobenius map on the p-typical Witt vectors of a commutative ring, not necessarily of characteristic p. We give many equivalent conditions to surjectivity of the Frobenus map on both finite and infinite length Witt vectors. In particular, surjectivity on finite Witt vectors turns out to be stable under certain integral extensions; this provides a clean fo...

The photochemistry of three 9-(dihydroxyphenyl)anthracenes 6-8 was studied in neat CH(3)CN and selected organic solvents, to investigate excited state intramolecular proton transfer (ESIPT) from the phenol to the anthracene moiety. In D(2)O-CH(3)CN mixtures, the observed deuterium exchange of 6-8 is consistent with water-mediated (formal) ESIPT process from the ortho phenolic OH to the 10'-posi...

We present an experimental as well as theoretical study of kink motion in one-dimensional arrays of Josephson junctions connected in parallel by superconducting wires. The boundaries are closed to form a ring, and the waveform and stability of an isolated circulating kink is discussed. Two one-dimensional rings can be coupled which provides an interesting and clean platform to study interaction...

Imaging simulations have been carried out with a version of the spiral zoom array presented in Conway(2000) (Memo 283). Two test images were used, one based on a VLA image of Cygnus A and another based on an OVRO CO map of M51. Both snapshot and long track CLEAN simulations were carried out. The results were compared with those obtained for a single ring array with similar resolution. The singl...