The Leavitt path algebra of a graph

For any row-finite graph $E$ and any field $K$ we construct the {\its Leavitt path algebra} $L(E)$ having coefficients in $K$. When $K$ is the field of complex numbers, then $L(E)$ is the algebraic analog of the Cuntz Krieger algebra $C^*(E)$ described in [8]. The matrix rings $M_n(K)$ and the Leavitt algebras L(1,n) appear as algebras of the form $L(E)$ for various graphs $E$. In our main result, we give necessary and sufficient conditions on $E$ which imply that $L(E)$ is simple

Purely infinite simple Leavitt path algebras

We give necessary and sufficient conditions on a row-finite graph E so that the Leavitt path algebra L(E) is purely infinite simple. This result provides the algebraic analog to the corresponding result for the Cuntz-Krieger C$^*$-algebra C$^*$(E) given in [7]

Commutator Leavitt path algebras

For any field K and directed graph E, we completely describe the elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E),L_K(E)]. We then use this result to classify all Leavitt path algebras L_K(E) that satisfy L_K(E)=[L_K(E),L_K(E)]. We also show that these Leavitt path algebras have the additional (unusual) property that all their Lie ideals are (ring-theoretic) ideals, and construct examples of such rings with various ideal structures.Comment: 24 page

Snow parameters from Nimbus-6 electrically scanned microwave radiometer

Two sites in Canada were selected for detailed analysis of the ESMR-6/ snow relationships. Data were analyzed for February 1976 for site 1 and January, February and March 1976 for site 2. Snowpack water equivalents were less than 4.5 inches for site 1 and, depending on the month, were between 2.9 and 14.5 inches for site 2. A statistically significant relationship was found between ESMR-6 measurements and snowpack water equivalents for the Site 2 February and March data. Associated analysis findings presented are the effects of random measurement errors, snow site physiolography, and weather conditions on the ESMR-6/snow relationship

"Capital Intensity and U.S. Country Population Growth during the Late Nineteenth Century"

The United States witnessed substantial growth in manufacturing and urban populations during the last half of the nineteenth century. To date, no convincing evidence has been presented to explain the shift in population to urban areas. We find evidence that capital intensity, particularly new capital in the form of steam horsepower, played a significant role in drawing labor into counties and by inference into urban areas. This provides support for the hypothesis that the locational decisions of manufacturers and their placement of capital in urban areas fueled urban growth in the nineteenth century.urbanization, capital intensity, regional population growth, technological change

Circles Minimize most Knot Energies

We define a new class of knot energies (known as renormalization energies) and prove that a broad class of these energies are uniquely minimized by the round circle. Most of O'Hara's knot energies belong to this class. This proves two conjectures of O'Hara and of Freedman, He, and Wang. We also find energies not minimized by a round circle. The proof is based on a theorem of G. Luko on average chord lengths of closed curves.Comment: 15 pages with 3 figures. See also http://www.math.sc.edu/~howard

Orudis in the management of osteo-arthritis of the knee

A controlled double-blind crossover trial of Orudis, a nonsteroid anti-inflammatory drug, has been car.ried out in 98 patients with osteo-arthritis of the knee. The new preparation was tested against placebo (27 patients), paracetamol (42 patients) and acetylsalicylic acid (29 patients). It showed statistically significant superiority over placebo (P<0,05). Compared with paracetamol, the over-all results showed a marked trend in favour of Orudis, though this did not reach statistical significance (0,1>P>0,05). On the principal criteria for assessment there was no significant difference between Orudis and high-dosage salicylate (P<0,05); most of the patients, however, favoured the former.S. Afr. Med. J. 48, 1526 (1974)