4,215 research outputs found
Relaxation of Planar Graphs With d∆≥2 and No 4-Cycles
First, let a graph be a set of vertices (points) and a set of edges (lines) connecting these vertices. Further, let a planar graph be a graph that can be represented on the plane without any edges crossing. Define a (c1, c2,…ck)-coloring of graph G from G to {1,2,…k} such that for every i, 1≤ i ≤ k, G[Vi] has maximum degree at most ci, where G[Vi] represents the subgraph induced by the vertices colored with i. The Four Color Theorem by Appel and Haken (1973) states that all planar graphs are 4-colorable. The Bordeaux Conjecture (2003) postulates that planar graphs with no 5-cycles and without intersecting triangles is 3-colorable. Liu, Li and Yu (2014) proved that planar graphs without intersecting triangles and 5-cycles is (2,0,0) colorable. We prove that all planar graphs without 4-cycles and no less than two edges between triangles is also (2,0,0) colorable
Energy Conservation and Economic Analysis of Residential Refrigerators
A detailed computer model is developed to calculate energy flows and electricity use for residential refrigerators. Model equations are derived from application of the first law of thermodynamics, analysis of manufacturers\u27 literature, and related studies. The model is used to evaluate the energy (and associated initial cost) impacts of alternative designs to reduce refrigerator energy use.
Model results show that 56% of the total heat gain in a typical 0.45 m3 (16 ft3) top-freezer refrigerator is due to conduction through cabinet walls and doors. The remaining 44% is from door openings, heaters, fans, food, gasket area infiltration, and miscellaneous heat sources. Operation of the compressor to remove this heat and maintain the refrigerated spaces at constant temperatures accounts for 70% of the unit\u27s electricity use. The remainder is for operation of heaters and fans.
Several energy-saving design changes are examined using the energy model. These changes are: increased insulation thickness, improved insulation conductivity, removal of fan from cooled area, use of anti-sweat heater switch, improved compressor efficiency, increased condenser and evaporator surface areas, and elimination of the frost-free feature. Application of all these changes would reduce refrigerator electricity use 71% and increase initial cost 5%. Implementing all these changes except for elimination of the frost-free feature would reduce electricity use 52% and increase initial cost 19%. These results show that there are large opportunities for reducing refrigerator electricity use with only slight initial cost increases
Book Reviews/ Poems
Sterling Brown: Building the Black Aesthetic Tradition By Joanne V. Gabbin, Greenwood Press, Westport, Conn., 245 pp. Reviewed by Eugenia Collier
- …