Normal edge-colorings of cubic graphs

A normal $k$-edge-coloring of a cubic graph is an edge-coloring with $k$ colors having the additional property that when looking at the set of colors assigned to any edge $e$ and the four edges adjacent it, we have either exactly five distinct colors or exactly three distinct colors. We denote by $\chi'_{N}(G)$ the smallest $k$, for which $G$ admits a normal $k$-edge-coloring. Normal $k$-edge-colorings were introduced by Jaeger in order to study his well-known Petersen Coloring Conjecture. More precisely, it is known that proving $\chi'_{N}(G)\leq 5$ for every bridgeless cubic graph is equivalent to proving Petersen Coloring Conjecture and then, among others, Cycle Double Cover Conjecture and Berge-Fulkerson Conjecture. Considering the larger class of all simple cubic graphs (not necessarily bridgeless), some interesting questions naturally arise. For instance, there exist simple cubic graphs, not bridgeless, with $\chi'_{N}(G)=7$. On the other hand, the known best general upper bound for $\chi'_{N}(G)$ was $9$. Here, we improve it by proving that $\chi'_{N}(G)\leq7$ for any simple cubic graph $G$, which is best possible. We obtain this result by proving the existence of specific no-where zero $\mathbb{Z}_2^2$-flows in $4$-edge-connected graphs.Comment: 17 pages, 6 figure

Nurses\u27 Alumnae Association Bulletin, April 1955

Alumnae Notes Annual Giving Committee Reports Digest of Alumnae Meetings Graduation Awards - 1954 Legal Aspects of Nursing Marriages Necrology New Arrivals Physical Advances at Jefferson President\u27s Message School of Nursing Report The Challenge of Neurosurgical Nursin

WSC-07: Evolving the Web Services Challenge

Service-oriented architecture (SOA) is an evolving architectural paradigm where businesses can expose their capabilities as modular, network-accessible software services. By decomposing capabilities into modular services, organizations can share their offerings at multiple levels of granularity while also creating unique access points for their peer organizations. The true impact of SOA will be realized when 3rd party organizations can obtain a variety of services, on-demand, and create higher-order composite business processes. The Web Services Challenge (WSC) is a forum where academic and industry researchers can share experiences of developing tools that automate the integration of web services. In the third year (i.e. WSC-07) of the Web Services Challenge, software platforms will address several new composition challenges. Requests and results will be transmitted within SOAP messages. In addition, semantic representations will be both represented in the eXtensible Markup Language (XML) and in the Web Ontology Language (OWL). Finally, composite processes will have both sequential and concurrent branches

Post-injection normal closure of fractures as a mechanism for induced seismicity

Understanding the controlling mechanisms underlying injection-induced seismicity is important for optimizing reservoir productivity and addressing seismicity-related concerns related to hydraulic stimulation in Enhanced Geothermal Systems. Hydraulic stimulation enhances permeability through elevated pressures, which cause normal deformations, and the shear slip of pre-existing fractures. Previous experiments indicate that fracture deformation in the normal direction reverses as the pressure decreases, e.g., at the end of stimulation. We hypothesize that this normal closure of fractures enhances pressure propagation away from the injection region and significantly increases the potential for post-injection seismicity. To test this hypothesis, hydraulic stimulation is modeled by numerically coupling fracture deformation, pressure diffusion and stress alterations for a synthetic geothermal reservoir in which the flow and mechanics are strongly affected by a complex three-dimensional fracture network. The role of the normal closure of fractures is verified by comparing simulations conducted with and without the normal closure effect

Effects of infrequent dried distillers grain supplementation on spring-calving cow performance

Feed and supplement costs and the expenses associated with delivery of winter supplements account for a large proportion of the total operating expenditures for cow-calf producers. Cattle grazing low-quality dormant native range (<6% crude protein) typically are unable to consume sufficient protein from the forage base, which limits microbial activity and forage digestion. Supplemental protein often is required to maintain cow body weight and body condition score during the last trimester of pregnancy. Low cow body condition scores at calving are common and may negatively affect lactation, rebreeding rates, and calf weaning weight. Failure to maintain proper nutritional status during this period severely affects short-term cow performance, reduces overall herd productivity, and limits profit potential. The most effective means of supplying supplemental protein to cows consuming dormant native range is to provide a small amount of high-protein feedstuff (>30% crude protein). Dried distillers grains with solubles (DDGS) are a by-product of the ethanol refining process. Distillers grains supply the recommended 30% crude protein level, are readily available, and often are favorably priced compared with more traditional feedstuffs. With the rising costs of inputs in today’s cow-calf sector, reducing cost is necessary to maintain viability of the national cowherd. Reducing the frequency of supplementation results in less labor and fuel use, effectively reducing input costs; however, this is viable only as long as cow performance is maintained at acceptable levels. Therefore, the objective of this study was to examine the effects of infrequent supplementation of dried distillers grains with solubles on cow body weight and body condition score

Damage-cluster distributions and size effect on strength in compressive failure

We investigate compressive failure of heterogeneous materials on the basis of a continuous progressive damage model. The model explicitely accounts for tensile and shear local damage and reproduces the main features of compressive failure of brittle materials like rocks or ice. We show that the size distribution of damage-clusters, as well as the evolution of an order parameter, the size of the largest damage-cluster, argue for a critical interpretation of fracture. The compressive failure strength follows a normal distribution with a very small size effect on the mean strength, in good agreement with experiments

Condensation of Hard Spheres Under Gravity

Starting from Enskog equation of hard spheres of mass m and diameter D under the gravity g, we first derive the exact equation of motion for the equilibrium density profile at a temperature T and examine its solutions via the gradient expansion. The solutions exist only when \beta\mu \le \mu_o \approx 21.756 in 2 dimensions and \mu_o\approx 15.299 in 3 dimensions, where \mu is the dimensionless initial layer thickness and \beta=mgD/T. When this inequality breaks down, a fraction of particles condense from the bottom up to the Fermi surface.Comment: 9 pages, one figur