Ultrasonic techniques based on measurements of apparent backscatter may provide a useful means for diagnosing bone diseases such as osteoporosis. The term "apparent" means that the backscattered signals are not compensated for the frequency-dependent effects of attenuation and diffraction. We performed in vitro apparent backscatter measurements on 23 specimens of human cancellous bone prepared from the left and right femoral heads of seven donors. A mechanical scanning system was used to obtain backscattered signals from each specimen at several sites. Scans were performed using five different ultrasonic transducers with center frequencies of 1, 2.25, 5, 7.5, and 10 MHz. The -6 dB bandwidths of these transducers covered a frequency range of 0.6-15.0 MHz. The backscattered signals were analyzed to determine three ultrasonic parameters: apparent integrated backscatter (AIB), frequency slope of apparent backscatter (FSAB), and time slope of apparent backscatter (TSAB). Linear regression analysis was used to examine the correlation of these ultrasonic parameters with five measured physical characteristics of the specimens: mass density, X-ray bone mineral density, Young's modulus, yield strength, and ultimate strength. A total of 75 such correlations were examined (3 ultrasonic parameters x 5 specimen characteristics x 5 transducers). Good correlations were observed for AIB using the 5 MHz (r = 0.70 - 0.89) and 7.5 MHz (r = 0.75-0.93) transducers; for FSAB using the 2.25 MHz (r = 0.70 - 0.88), 5 MHz (r = 0.79 - 0.94), and 7.5 MHz (r = 0.80 - 0.92) transducers; and for TSAB using the 5 MHz (r = 0.68 - 0.89), 7.5 MHz (r = 0.75 - 0.89), and 10 MHz (r = 0.75 - 0.92) transducers.

If R is a supplementary semilattice sum of subrings Ra, a e Cl, then R is regular if and only if each Rat is regular. A ring is said to be regular, in the sense of von Neumann [6], if for each a e R there exists x e R such that axa=a. The concept of (supplementary) semilattice sum is defined in the previous article [8]. In this article, we prove that if R is a supplementary semilattice sum of subrings Rx, a e £2, then R is regular if and only if Rx is regular for every a e £2. We state, without proof, an application of this result to the regularity of semigroup rings. Throughout this paper D will denote a semigroup. Definitions of any concepts not defined herein will be found in [1] or [8]. We first prove the main theorem in the case when the semilattice has only two elements. Lemma 1. (i) If R = RX+Rß is a semilattice sum and Rx and Rß are regular then R is regular. (ii) If R = RX + Rß is a supplementary semilattice sum and R is regular then Rx and Rß are regular. Proof. Observe that in either case R is a semilattice sum of rings over {a, ß}. Hence either a/?=/?a=a or xß=ßa=ß. Suppose xß=ßo. = ß, then RxRß £ Rß, RßRx £ Rß and Rß is an ideal in R. By the Second Isomorphism Theorem, RJRxr\Rp^RIRfi. Since if R is any ring with ideal /, then R is regular if and only if Rjl and I are regular (cf. [3, Theorem 22]), Lemma 3 of [8] applies and (i) is proven. If R is a supplementary semilattice sum then Rx nRß=0 and so RX^RJRX nRß^R/Rß. Thus if R is regular, then so are Rß and RjRß and hence so is Rx. This proves (ii).

The interaction between a positively biased body traveling through an ionospheric space plasma has direct application to electrodynamic tether (EDT) systems. A 2‐D3v particle‐in‐cell model has been developed to study the plasma dynamics near a positively charged EDT system end‐body and their impact on the current collected. The results show that the azimuthal current structures observed during the reflight of the tethered satellite system (TSS‐1R) mission develop in the simulations and are found to enhance the current collected by the satellite by 67% when the magnetic field is ∼15° off of perpendicular to the orbital velocity. As the component of the magnetic field in the simulation's plane increases, the electrons are not able to easily cross the field lines causing plasma lobes to form in the +y and −y regions around the satellite. The lobes limit the current arriving at the satellite and also cause an enhanced wake to develop. A high satellite bias causes a stable bow shock structure to form in the ram region of the satellite, which limits the number of electrons entering the sheath region and thus limits the current collected. Electron‐neutral collisions are found to destabilize the bow shock structure, and its current limiting effects were negated. Analytical curve fits based on the simulations are presented in order to characterize the dependence of the current collected on the magnetic field's orientation, space plasma magnetization, and satellite potential. The variations in the collected current induced by space plasma environmental changes may introduce new instabilities in an EDT system's dynamics.

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