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*BRIEFING* *NOTES*

, 2010

"... Policy recommendations Biofuel cultivation worldwide continues to increase in intensity and extent despite a lack of empirical data on the sustainability impacts. This briefing note reflects on two case studies from sub-Saharan Africa outlining the current context of the cultivation of the inedible, ..."

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Policy recommendations Biofuel cultivation worldwide continues to increase in intensity and extent despite a lack of empirical data on the sustainability impacts. This

*briefing**note*reflects on two case studies from sub-Saharan Africa outlining the current context of the cultivation of the inedible###
*BRIEF* *NOTES*

"... by virtue of the celebrated "isoperimetric inequality " (which states that the area enclosed by a planar, simple, closed curve of fixed length, is a maximum when the perimeter is a circle). If z ' & 0, then the projected curve xi + yj, 0 < f < 2ir, is closed, but need not b ..."

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by virtue of the celebrated "isoperimetric inequality " (which states that the area enclosed by a planar, simple, closed curve of fixed length, is a maximum when the perimeter is a circle). If z ' & 0, then the projected curve xi + yj, 0 < f < 2ir, is closed, but need not be simple, and its length is less than L. Consequently, the isoperimetric inequality is not directly applicable. Nonetheless, we can establish (14) in a manner similar to Hurwicz's proof of the isoperimetric inequality (cf. Courant and Hilbert (1953)). In view of equations (5) and (13), it follows that 0 l(.x')2+(y')2+(z')2-xy'+x'y]dt. (15) Under the conditions imposed upon p (cf., Section 2), we have the Fourier series representations

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*BRIEF* *NOTES*

"... by virtue of the celebrated "isoperimetric inequality " (which states that the area enclosed by a planar, simple, closed curve of fixed length, is a maximum when the perimeter is a circle). If z ' & 0, then the projected curve xi + yj, 0 < f < 2ir, is closed, but need not b ..."

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by virtue of the celebrated "isoperimetric inequality " (which states that the area enclosed by a planar, simple, closed curve of fixed length, is a maximum when the perimeter is a circle). If z ' & 0, then the projected curve xi + yj, 0 < f < 2ir, is closed, but need not be simple, and its length is less than L. Consequently, the isoperimetric inequality is not directly applicable. Nonetheless, we can establish (14) in a manner similar to Hurwicz's proof of the isoperimetric inequality (cf. Courant and Hilbert (1953)). In view of equations (5) and (13), it follows that 0 l(.x')2+(y')2+(z')2-xy'+x'y]dt. (15) Under the conditions imposed upon p (cf., Section 2), we have the Fourier series representations

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*BRIEF* *NOTES*

"... powder gun launched the 0.078-kg rods shown in Fig. 3 to in-cident velocities between 210-700 m/s. The rods were encased in two-piece, serrated, plastic sabots. Pusher plates were 15.7-mm-dia., 6.35-mm-long, titanium discs, and the ob-turator was made from the same material as the sabot. The sabot f ..."

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powder gun launched the 0.078-kg rods shown in Fig. 3 to in-cident velocities between 210-700 m/s. The rods were encased in two-piece, serrated, plastic sabots. Pusher plates were 15.7-mm-dia., 6.35-mm-long, titanium discs, and the ob-turator was made from the same material as the sabot. The sabot fit snugly in the gun barrel, while the slightly oversized obturator was forced into the barrel so as to provide a gas seal. Centrifugal force and air drag stripped the sabot, pusher plate, and obturator from the rod prior to impact. Incident velocity was determined within one-percent ac-curacy by the penetrator interrupting two continuously monitored laser beams, and incident yaw was measured with an orthogonal pair of flash x-rays. Two pairs of orthogonal, flash x-rays determined residual velocity within two-percent accuracy. Incident yaw angles were less than one degree, and

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*BRIEF* *NOTES*

"... leads to a loss of spatial correlation as well. Thus, our con-jectures are confirmed for this example. A final remark concerning the higher modes that were not retained in the numerical analysis may be made. In the nu-merical analysis, one only need retain those terms of 0(1) in amplitude, i.e., tho ..."

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leads to a loss of spatial correlation as well. Thus, our con-jectures are confirmed for this example. A final remark concerning the higher modes that were not retained in the numerical analysis may be made. In the nu-merical analysis, one only need retain those terms of 0(1) in amplitude, i.e., those physical modal amplitudes that are of the order of the plate thickness. Once the time histories and power spectra of these order-one modes are determined, the response in the higher modes, whose amplitudes by definition are in the linear response range, may be determined by standard linear vibration theory where now the higher linear modes are driven by the numerically determined lower nonlinear, chaotic modes. Further, over a given bandwidth of frequency in which many linear mode resonances lie, the classical, linear random vibration theory result may be well approximated by asymp-

###
*BRIEF* *NOTES*

"... leads to a loss of spatial correlation as well. Thus, our con-jectures are confirmed for this example. A final remark concerning the higher modes that were not retained in the numerical analysis may be made. In the nu-merical analysis, one only need retain those terms of 0(1) in amplitude, i.e., tho ..."

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leads to a loss of spatial correlation as well. Thus, our con-jectures are confirmed for this example. A final remark concerning the higher modes that were not retained in the numerical analysis may be made. In the nu-merical analysis, one only need retain those terms of 0(1) in amplitude, i.e., those physical modal amplitudes that are of the order of the plate thickness. Once the time histories and power spectra of these order-one modes are determined, the response in the higher modes, whose amplitudes by definition are in the linear response range, may be determined by standard linear vibration theory where now the higher linear modes are driven by the numerically determined lower nonlinear, chaotic modes. Further, over a given bandwidth of frequency in which many linear mode resonances lie, the classical, linear random vibration theory result may be well approximated by asymp-

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*BRIEF* *NOTES*

, 2003

"... Radiation hybrid mapping of three skeletal muscle genes (CKM, ECH1 and TNNT1) to porcine chromosome 6 ..."

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Radiation hybrid mapping of three skeletal muscle genes (CKM, ECH1 and TNNT1) to porcine chromosome 6

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*Brief* *Notes*

"... At the present state of the art, it is appropriate to reexamine the relevance of the data and theory on the contribution of the deposits of osmium compounds in tissues fixed in Os04 to the contrast observed in electron micrographs of sections of such tissues. It is the purpose of this communication ..."

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to

*note*briefly the interrelationship of a number of crucial observations and opinions on this point. It is generally agreed (e.g. see reference 1) that the osmium deposited in tissues probably exists in the form of mixed lower osmium oxides and/or hydroxides and metallo-organic compounds. These may have###
*BRIEF* *NOTES*

"... of the most undesirable factors in bridge expolitation. Indeed, spans of bridges similar to the Mianus bridge are often rested on four-hinge supports designed primarily for longitudinal loading. Any substantial lateral load will inevitably cause dangerous horizontal shearing and bending reactions i ..."

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N (considered in the foregoing) braking with the deceleration a = 2.5 m/sec 2 would develop the repulsive force R = 70 kN instead of 8 kN obtained from (8)!

*Note*, that the deceleration a = 2.5 m/sec 2 means that the truck has to stop completely from the speed V = 25 km/h over the distance ^ = 10 m