On c‐Bhaskar Rao designs with block size 4

Several new families of c‐Bhaskar Rao designs with block size 4 are constructed. The necessary conditions for the existence of a c‐BRD (υ,4,λ) are that: (1)λ_min=?λ/3 ≤ c ≤ λ and (2a) c≡λ (mod 2), if υ > 4 or (2b) c≡ λ (mod 4), if υ = 4 or (2c) c≠ λ ? 2, if υ = 5. It is proved that these conditions are necessary, and are sufficient for most pairs of c and λ; in particular, they are sufficient whenever λ?c ≠ 2 for c > 0 and whenever c ? λ_min≠ 2 for c < 0. For c < 0, the necessary conditions are sufficient for υ> 101; for the classic Bhaskar Rao designs, i.e., c = 0, we show the necessary conditions are sufficient with the possible exception of 0‐BRD (υ,4,2)'s for υ≡ 4 (mod 6). © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 361–386, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10009     

Robust Dynamics and Control of a Partially Observed Markov Chain

In a seminal paper, Martin Clark (Communications Systems and Random Process Theory, Darlington, 1977, pp. 721–734, 1978) showed how the filtered dynamics giving the optimal estimate of a Markov chain observed in Gaussian noise can be expressed using an ordinary differential equation. These results offer substantial benefits in filtering and in control, often simplifying the analysis and an in some settings providing numerical benefits, see, for example Malcolm et al. (J. Appl. Math. Stoch. Anal., 2007, to appear). Clark’s method uses a gauge transformation and, in effect, solves the Wonham-Zakai equation using variation of constants. In this article, we consider the optimal control of a partially observed Markov chain. This problem is discussed in Elliott et al. (Hidden Markov Models Estimation and Control, Applications of Mathematics Series, vol. 29, 1995). The innovation in our results is that the robust dynamics of Clark are used to compute forward in time dynamics for a simplified adjoint process. A stochastic minimum principle is established.     

Ultrasonic analysis of edible fats and oils

Low intensity ultrasound is a powerful analytical technique for investigating the physico-chemical properties of many biological and non-biological materials. In this article its application for the characterization of edible fats and oils is assessed. Ultrasound can be used to determine the dynamic rheology and composition of oils, the oil content and droplet size of emulsions and the solid fat content of partially crystalline emulsions. It is capable of rapid and precise measurements, is non-destructive and non-invasive, can be used on-line or off-line and is relatively inexpensive. Ultrasonic techniques will therefore prove a useful addition to the existing analytical techniques used to characterize fats and oils.     

Solvation forces in asymmetrically charged electrolytes

Density functional theories of solvation forces in charged fluids which self-consistently include the effects of finitesized ions are extended to treat asymmetrically charged electrolytes. For a given electrolyte concentration both the electric potential and the solvation force between charged surfaces are seen to deviate from the results of the classical DLVO theory more markedly for asymmetrically charged electrolytes than for a 1 : 1 electrolyte.     

Treatment of Malignant Melanoma by High-Peak-Power 1064 nm Irradiation Followed by Photodynamic Therapy

Irradiation of B16 pigmented melanoma subcutaneously transplanted in C57 mice with a single 650 mj pulse (10 ns) of 1064 nm light from a Q-switched Nd: YAG laser caused instantaneous bleaching of the pigmented tissue. Visual and histological examination of the resulting gray-colored tumor revealed the breakdown of melanosomes with no detectable alteration of the normal and tumor-overlying skin. Histological examination of the irradiated tumor showed some degree of vascular damage; the depth of the photodamage was not affected by the successive delivery of three consecutive light pulses. The bleached tumor grew at a modestly slower rate but the high-peak-power (HPP) laser treatment did not affect the tumor concentration of a photodynamic sensitizer Si(IV)-naphthalocyanine (isoBO-SiNc) intravenously injected 24 h before Nd : YAG irradiation. Treatment of the B16 pigmented melanoma by photodynamic therapy (PDT: 1 mg/kg isoBO-SiNc, 300 mW/cm², 520 J/cm²) from a 774 nm diode laser immediately after the 1064 nm irradiation resulted in a 16 day delay of tumor regrowth, which was markedly longer than the delay (ca 6 days) obtained after PDT under identical conditions without the preirradia-tion. Thus, pretreatment of pigmented tumors with HPP 1064 nm light appears to enhance their susceptibility to conventional PDT. The tumor response was further enhanced by repeating the combined HPP/PDT treatment at an interval of 10 days (regrowth delay: 27 days), as well as by applying hyperthermia immediately after HPP/PDT (regrowth delay: ca 34 days).