At z = 0, we have:[A1(t,0)B1(t,0)]=J0 [A0(t,0)B0(t,0)], J0=[r0(+)r0(?)r0(?)r0(+)]with r0(��)=12(��1/��0����0/��1). Similarly, at z = L:[A2(t,L)B2(t,L)]=J1 [A1(t,L)B1(t,L)], J1=[r1(+)r1(?)r1(?)r1(+)]with r1(��)=12(��2/��1����1/��2). We can write these relations in terms of the apply for it functions aj, bj as:[a1(t)b1(t)]=J0 [f(t)b0(t)], [a2(t)0]=J1 [a1(t?L /c1)b1(t+L /c1)]which can be solved to get the reflected and transmitted waves. The situation is more complicated than in the case of a single interface, because of the time delays ��L/c1. A convenient and Inhibitors,Modulators,Libraries general way to handle these delays is by going to the frequency domain, so that the time shifts are replaced by phase factors.

The Fourier transforms of the modes are defined by:a^j (��)=��aj (t)ei��tdt, b^j (��)=��aj (t)ei��tdtThey satisfy the interface conditions:[a^1(��)b^1(��)]=J0 Inhibitors,Modulators,Libraries [f^(��)b^0(��)], [a^2(��)0]=J1 [a^1(��)ei��Lc1b^1(��)e?i��Lc1](14)where Inhibitors,Modulators,Libraries we have used the identity:��a1(t?L / c1) ei��tdt=��a1(s) ei��(s+Lc1)ds=a^1(��) ei��Lc1Introducing Inhibitors,Modulators,Libraries the frequency-dependent matrix:J^1(��)=[r1(+) ei��Lc1r1(?) e?i��Lc1r1(?) ei��Lc1r1(+) e?i��Lc1]The second equation of (14) can be written as:[a^2(��)0]=J^1(��)[a^1(��)b^1(��)](15)The syplectic matrix ?1(��) is a propagator in the frequency domain. It propagates the right- and left-going modes from the right side of the interface 0 to the right side of the interface 1, and it depends on the layer thickness L. Finally, combining the first equation of (14) and (15), we obtain the relation:[a^2(��)0]=K^0(��)[f^(��)b^0(��)](16)where the frequency-dependent syplectic matrix:K^0(��)=J^1(��)J0=[U^(��)V^(��)��V^(��)U^(��)��]is the overall propagator of the slab.

Equation (16) shows that 0(��) propagates the right- and left-going modes from the left side of the interface 0 to the right side of the interface 1. We find explicitly:U^(��)=r0(+)r1(+)ei��Lc1+r0(?)r1(?)e?i��Lc1V^(��)=r0(+)r1(?)ei��Lc1+r0(?)r1(+)e?i��Lc1By AV-951 solving equation (16), whose unknowns are a2 (��) and 0 (��) and using the expressions of rj(��), we obtain:b^0(��)=?^(��)f^(��), a^2(��)=?^(��)f^(��)where the frequency-dependent reflection and transmission coefficients are:?^(��)=?V^(��)U^(��)��=R1e2i��Lc1+R01+R0R1e2i��Lc1(17)?^(��)=1U^(��)��=T0T1ei��Lc11+R0R1e2i��Lc1(18)using that |?(��)|2 ? |(��)|2 = 1.
The IEEE 802.15.

4 standard (which describes the Physical Layer and Medium Access Control [1]) and ZigBee [2] jointly specify a protocol http://www.selleckchem.com/products/U0126.html stack for the development of short-range and low power communications for Wireless Personal Area Networks (WPANs). This stack is aimed at providing networking architectures for low-cost wireless embedded devices with consumption and bandwidth limitations. In particular the basic framework of IEEE 802.15.4 permits up to 10-meter communications with a transfer rate of 250 kbps, although this parameter can be decreased even more (down to 20 Kbps in the 868/915 MHz band) to enable a lower power consumption in the ZigBee nodes. IEEE 802.15.