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    ABSTRACT: The topographical Wiener index is calculated for two-dimensional graphs describing porous arrays, including bee honeycomb. For tiling in the plane, we model hexagonal, triangular, and square arrays and compare with topological formulas for the Wiener index derived from the distance matrix. The normalized Wiener indices of C4, T13, and O(4), for hexagonal, triangular, and square arrays are 0.993, 0.995, and 0.985, respectively, indicating that the arrays have smaller bond lengths near the center of the array, since these contribute more to the Wiener index. The normalized Perron root (the first eigenvalue, λ 1), calculated from distance/distance matrices describes an order parameter, f = l1/n{\phi=\lambda_1/n} , where f = 1{\phi= 1} for a linear graph and n is the order of the matrix. This parameter correlates with the convexity of the tessellations. The distributions of the normalized distances for nearest neighbor coordinates are determined from the porous arrays. The distributions range from normal to skewed to multimodal depending on the array. These results introduce some new calculations for 2D graphs of porous arrays. KeywordsTopographical Wiener index-Porous arrays-Distance matrix-Order parameter
    Journal of Mathematical Chemistry 01/2010; 47(3):1145-1153. DOI:10.1007/s10910-009-9651-0
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    ABSTRACT: Hospitalized infants are often exposed to many painful procedures as a result of their illness or disease process. Untreated or poorly treated pain can have deleterious effects on normal nociceptive pain development as well as future development of pain pathways. Mechanical vibration has been found to be efficacious in adult and pediatric populations for the relief of mild-to-moderate acute and chronic pain. However, little is known about the efficacy of this intervention in the neonatal population. The purpose of this study was to test the hypothesis that mechanical vibration would be efficacious in the relief of pain associated with heel sticks in neonates. Heel sticks are one of the most common painful procedures during neonatal hospitalization. A random-sequencing crossover design was used with infants acting as their own controls. Newborn infants of 35 weeks' gestation or greater (N = 20) met the inclusion criteria for the study. Pain during heel stick was measured with the Neonatal Infant Pain Scale. The Neonatal Infant Pain Scale is a nonintrusive tool with extensive evidence of its reliability and validity in the neonatal population, when used by trained observers. Mechanical vibration produced an analgesic effect for infants who had previously experienced painful heel sticks that approached statistical significance. The apparent limitations of mechanical vibration as analgesia may be due to the concurrent use of sucrose and pacifier, the effects of order (ie, habituation), or type II error. Because vibration produced the predicted positive effect in some circumstances, further investigation in larger samples within a randomized clinical trial is warranted.
    The Journal of perinatal & neonatal nursing 01/2010; 24(3):274-83. DOI:10.1097/JPN.0b013e3181ea7350
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    ABSTRACT: This study was conducted to determine the effects of 5 different finger rest positions: opposite arch, standard intraoral, basic extraoral, cross arch, and finger on finger on the muscle activity of 4 forearm muscles (extensor carpi radialis longus, flexor carpi ulnaris, biceps brachii, and pronator teres) during a simulated periodontal scaling experience. A convenience sample of 32 consenting senior dental hygiene students who met inclusion criteria participated. Using a 4 x 5 counter-balanced research design, each participant used a Gracey 11/12 curet to scale one cc of artificial calculus from first permanent molar typodont teeth (#3,14,19,30). Five different typodonts were set up for each participant with fulcrums randomly assigned for use on each typodont. While scaling, the participant's muscle activity was measured by surface electromyography. Two-way analysis of variance with repeated measures was used to determine if significant differences existed in the amount of muscle activity generated with each fulcrum. Results revealed no statistically significant interaction effect between area of the mouth scaled, muscle activity, and fulcrum used. Similar muscle activity was produced throughout the mouth regardless of the fulcrum used. The upper right quadrant produced the most muscle activity (p= 0.0101) and the lower left quadrant produced the least (p=< .0001). When comparing the overall muscle activity generated with each fulcrum, only the cross arch fulcrum when compared to the opposite fulcrum produced statistically significant results (p=0.0110). Based on the results, similar muscle activity is produced when using any of the 5 fulcrums in each quadrant of the mouth. Clinicians appear to experience minimal ergonomic advantage in terms of fulcrums used and area of the mouth scaled during a simulated scaling experience.
    Journal of dental hygiene: JDH / American Dental Hygienists' Association 02/2008; 82(4):34.

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