5 . (b) Applying the product rule, we have ((1 + 4x)e−4x)′ = (1 + 4x)′e−4x + (1 + 4x)(e−4x)′ = 4e−4x + (1 + 4x)e−4x(−4x)′ = 4e−4x + (1 + 4x)e−4x(−4) = 4e−4x − 4e−4x − 16xe−4x = −16xe−4x. (c) [(sec(x) + tan(x))3]′ = 3(sec(x) + tan(x))(sec(x) + tan(x))′ = 3(sec(x) + tan(x))(sec(x) tan(x) + sec(x)) = 3(sec(x) + tan(x)) · sec(x) · (sec(x) + sec(x)) = 3 sec(x)(sec(x) + tan(x)). (d)(x cos(x)− 6x sin(...

6 = 2(cos( (π+2kπ) 6 ) + i sin( (π+2kπ) 6 )) where k = 0, 1, 2, · · · , 5. Let rk = 2(cos( (π+2kπ) 6 ) + i sin( (π+2kπ) 6 )) where k = 0, 1, 2, · · · , 5. Therefore r0 = 2(cos( π 6 )+i sin( 6 )) = √ 3+i, r1 = 2(cos( π 2 )+i sin( 2 )) = 2i, r2 = 2(cos( 5π 6 )+ i sin( 6 )) = − √ 3 + i, r3 = 2(cos( 7π 6 ) + i sin( 6 )) = − √ 3 − i, r4 = 2(cos( 2 ) + i sin( 2 )) = −2i and r5 = 2(cos( 6 ) + i sin( 1...

6 = 2(cos( (π+2kπ) 6 ) + i sin( (π+2kπ) 6 )) where k = 0, 1, 2, · · · , 5. Let rk = 2(cos( (π+2kπ) 6 ) + i sin( (π+2kπ) 6 )) where k = 0, 1, 2, · · · , 5. Therefore r0 = 2(cos( π 6 )+i sin( 6 )) = √ 3+i, r1 = 2(cos( π 2 )+i sin( 2 )) = 2i, r2 = 2(cos( 5π 6 )+ i sin( 6 )) = − √ 3 + i, r3 = 2(cos( 7π 6 ) + i sin( 6 )) = − √ 3 − i, r4 = 2(cos( 2 ) + i sin( 2 )) = −2i and r5 = 2(cos( 6 ) + i sin( 1...

Because cone outer segments (COS) are now known to be continually renewed, I reexamined COS morphogenesis in retinas of Xenopus tadpoles (prepared by standard histologic techniques and viewed by light and electron microscopy) to clarify how COS incorporate new membrane. I observed that developing COS underwent an unexpected shape change: they were always conical, but their taper (width divided ...

Some facts about sines and cosines: • cos(A+B) = cos(A) cos(B)− sin(A) sin(B) • sin(A+B) = sin(A) cos(B) + cos(A) sin(B) • Cosine is an even function: cos(−θ) = cos(θ) • Sine is an odd function: sin(−θ) = − sin(θ) • cos(ωt− π/2) = sin(ωt) • R cos(ωt + φ) = R sin(φ) cos(ωt) + R cos(φ) sin(ωt), and any wave form can be written as a linear combination of sines and cosines. Similarly, A sin(ωt) +B ...

The most recent results from the B-factories on the time-dependent CP asymmetries measured in B 0-decays mediated by b → c¯ cs quark-transitions are reviewed. The Standard Model interpretation of the results in terms of the parameter sin 2β leads to a four-fold ambiguity on the unitarity triangle β which can be reduced to a twofold ambiguity by measuring the sign of the parameter cos 2β. The re...

The most recent results from the B-factories on the time-dependent CP asymmetries measured in B -decays mediated by b → cc̄s quark-transitions are reviewed. The Standard Model interpretation of the results in terms of the parameter sin 2β leads to a four-fold ambiguity on the unitarity triangle β which can be reduced to a two-fold ambiguity by measuring the sign of the parameter cos 2β. The resu...

BACKGROUND Core outcome sets (COS) can enhance the relevance of research by ensuring that outcomes of importance to health service users and other people making choices about health care in a particular topic area are measured routinely. Over 200 COS to date have been developed, but the clarity of these reports is suboptimal. COS studies will not achieve their goal if reports of COS are not com...

The electro-active third component (BID)-incorporated PM6-B10-based organic solar cell shows a high performance (PCE = 17.2%) and mechanical stretchability (COS avg 11.4%), outperforming the PM6-based device 15.8%, COS 2.0%).

The nematic-to-isotropic orientational phase transition, or equivalently the RP 2 model, is considered in two dimensions and the question of the nature of the phase transition is addressed. Using powerful conformal techniques adapted to the investigation of critical properties of two-dimensional scale-invariant systems, we report strong evidences for a transition governed by topological defects...