This paper investigates the roles of partial correlation and conditional correlation as measures of the conditional independence of two random variables. It first establishes a sufficient condition for the coincidence of the partial correlation with the conditional correlation. The condition is satisfied not only for multivariate normal but also for elliptical, multivariate hypergeometric, multivariate negative hypergeometric, multinomial and Dirichlet distributions. Such families of distributions are characterized by a semigroup property as a parametric family of distributions. A necessary and sufficient condition for the coincidence of the partial covariance with the conditional covariance is also derived. However, a known family of multivariate distributions which satisfies this condition cannot be found, except for the multivariate normal. The paper also shows that conditional independence has no close ties with zero partial correlation except in the case of the multivariate normal distribution; it has rather close ties to the zero conditional correlation. It shows that the equivalence between zero conditional covariance and conditional independence for normal variables is retained by any monotone transformation of each variable. The results suggest that care must be taken when using such correlations as measures of conditional independence unless the joint distribution is known to be normal. Otherwise a new concept of conditional independence may need to be introduced in place of conditional independence through zero conditional correlation or other statistics.

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A highly adherent Cu-Ni-P film was successfully grown on a UV-irradiated liquid-crystal-polymer ͑LCP͒ film. Irradiation from a UV light under an atmospheric condition created hydrophilic nanometer-scale roughness on the LCP film surface by introducing hydrophilic groups on the surface. The high adhesion strength of more than 0.8 kN/m was obtained because of the anchoring effect of the nanometer-scale roughness developed at the interface between the deposited metal and the LCP film. Copper circuit patterns formed on the LCP film showed satisfactory performance for various reliability tests. Fine circuit formation and selective plating facilitated by UV irradiation could lead to a manufacturing approach for the next generation of flexible-printed-circuit technology.Flexible printed circuits ͑FPCs͒ are widely used for fabricating compact electronic devices, such as cellular phones and digital cameras. Materials used for FPC boards must meet several requirements, including low weight, high heat resistance, flexibility, and size stability. However, the rapid advancement of electronic devices in recent years has imposed additional requirements for scaling down the circuit packaging and for yielding a higher speed of the signal propagation for better performance. 1-3 To improve the signal propagation of the conductor on the FPC board, it is necessary to consider the skin effect. The skin effect is the phenomenon in which high frequency electric current tends to travel at/near the conductor surface. The current flow region, measured as a skin depth, decreases with increasing frequency. If the conductor/substrate interface is rough, the signal propagation speed is retarded because of a large transmission loss due to the electron scattering at the interface. Therefore, the interface between the conductor and the substrate has to be as smooth as possible for high speed signal propagation.One of the leading materials used for the FPC board is a polyimide ͑PI͒ film, which has high heat resistance and flexibility. However, the adhesion strength between a PI film substrate and a conductor layer often deteriorates because the PI film tends to have a high rate of water absorption and a low capacity as a gas barrier after heat-treatment. A liquid-crystal-polymer ͑LCP͒ film is emerging as a promising FPC material because of its low water absorption, high gas barrier, and excellent electrical properties in the high frequency region when compared to the properties of the PI film. By use of conventional procedures, such as a pretreatment with a concentrated alkaline solution and dry processes, however, it has been difficult to achieve good adhesion strength between the LCP substrate and a deposited metal layer. 4 Conventional pretreatment methods that use a strong oxidizing agent usually roughen the substrate surface and create micrometer-scale roughness, which improves the adhesion strength. Because micrometer-scale roughness is still too large, an approach to reduce the substrate roughness has been anticipated for some time.Our grou...