Effects of silane grafting and water crosslinking reactions on crystallizations, melting behaviors, and dynamic mechanical properties of the LDPE/LLDPE blends are investigated using DSC and DMA. From DSC data, cocrystallization of LDPE and LLDPE does not occur, but cocrosslinking of these two polymers is evidenced at the experimental temperature of 100°C, a temperature lower than melting temperatures of both polymers. The water crosslinking reactions of the LLDPE‐rich blends enable development of a new phase having a melting endotherm in between that of LDPE and LLDPE. From the thermal fractionation data, interaction between LDPE and LLDPE is observed, and compatibilization of the blends can be achieved by the crosslinking reactions. From DMA data, the storage moduli of the blends are not found to be consistent with their degrees of crosslinking. The storage moduli of the blends are not simply determined by the degree of crosslinking but determined by very complicated but unclear factors. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 1808–1816, 2001

Water crosslinking reactions of LDPE, PP, LLDPE, and the LDPE/PP and LDPE/LLDPE blends are investigated. Degrees of crosslinking of these samples are quantitatively compared and discussed in detail in terms of crosslinking ability, phaseseparation behavior, molecular weight (or viscosity), morphology of the constituents in blends, or in the pure state. It is found that PP gives negligible crosslinking reactions in the pure state and in blends with LDPE. LDPE and LLDPE are both capable of giving considerable degrees of crosslinking, with LLDPE giving a higher degree of crosslinking than LDPE at all conditions studied. Degrees of crosslinking of the LDPE/ LLDPE blends are not linearly but are zigzagly related to the compositions of the blends with the LDPE/LLDPE ϭ 50/50 blend giving a relatively high degree of crosslinking at 100, 120, and 140°C for a certain time except the condition at 140°C for 12 h compared with the LDPE/LLDPE ϭ 75/25 and 25/75 blends.

Effects of silane grafting and water crosslinking reactions on crystallizations, melting behaviors, and dynamic mechanical properties of the LDPE/LLDPE blends are investigated using DSC and DMA. From DSC data, cocrystallization of LDPE and LLDPE does not occur, but cocrosslinking of these two polymers is evidenced at the experimental temperature of 100°C, a temperature lower than melting temperatures of both polymers. The water crosslinking reactions of the LLDPE-rich blends enable development of a new phase having a melting endotherm in between that of LDPE and LLDPE. From the thermal fractionation data, interaction between LDPE and LLDPE is observed, and compatibilization of the blends can be achieved by the crosslinking reactions. From DMA data, the storage moduli of the blends are not found to be consistent with their degrees of crosslinking. The storage moduli of the blends are not simply determined by the degree of crosslinking but determined by very complicated but unclear factors.

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The hypercube family Q n is one of the most well-known interconnection networks in parallel computers. With Q n , dual-cube networks, denoted by DC n , was introduced and shown to be a (n + 1)-regular, vertex symmetric graph with some fault-tolerant Hamiltonian properties. In addition, DC n 's are shown to be superior to Q n 's in many aspects. In this article, we will prove that the n-dimensional dual-cube DC n contains n + 1 mutually independent Hamiltonian cycles for n ≥ 2. More specifically, let v i ∈ V (DC n ) for 0 ≤ i ≤ |V (DC n )| − 1 and let v 0 , v 1 , . . . , v |V (DC n )|−1 , v 0 be a Hamiltonian cycle of DC n . We prove that DC n contains n +1 Hamiltonian cycles of the form v 0 , v k 1 , . . . , v k |V (DC n )|−1 , v 0 for 0 ≤ k ≤ n, in which v k i = v k i whenever k = k . The result is optimal since each vertex of DC n has only n + 1 neighbors.