The computer bus paths specifying operations and coordinating progress, including requests and acknowledgments. Some control travels from initiator to target and some returns. In the diagram, bus arbitration requests and grants are shown separately from transfer control to distinguish choosing an initiator from executing its bus transaction.^[ref]

The computer bus path carrying payload. A write sends data from the initiator to the target; a read returns data from the target. Owning the request path does not mean driving the data bus in both directions.^[ref]

The computer bus path identifying the destination or location of a bus transaction. An initiator supplies an address; decoding selects the intended target. Address width describes the available address encodings, whereas data bus width describes how many bits can be carried at once.^[ref]

In a channel whose transverse width $b(z)$ does not depend on downstream position, the wetted area is $A(h)={\int }_0^{h}b(z)dz$ and the integrated hydrostatic pressure force divided by density is $P(h)=g{\int }_0^h(h-z)b(z)dz$. With cross-sectionally uniform velocity, volume conservation and momentum conservation give the displayed shallow water equations. Since $P^{\prime }(h)=gA(h)$, the two characteristic speeds are $u\pm c$ with $c^2=gA/A^{\prime }$. For $b(z)=C{z}^p$, $c^2=gh/(p+1)$ and the Riemann invariants are $u\pm 2(p+1)c$.

A hydraulic jump connects shallow supercritical flow to deeper subcritical flow while conserving discharge and momentum and dissipating mechanical energy. Its Rankine-Hugoniot condition uses the channel's actual area and integrated hydrostatic pressure, which depend on cross-sectional geometry.

For cross-sectional area $S(x,h)$ and cross-sectionally uniform velocity, volume conservation gives $S_h(h_t+u{h}_x)+S{u}_x+u{S}_x=0$, while hydrostatic inviscid momentum gives $u_t+u{u}_x+g{h}_x=0$. Their characteristic speeds are $u\pm c$. With $D_{\pm }={\partial }_t+(u\pm c){\partial }_x$, the robust compatibility equation is $(g/c)D_{\pm }h\pm D_{\pm }u=-uc{S}_x/S$. Replacing $D_{\pm }h$ by $D_{\pm }c/c_h$ requires $c_x=0$ at fixed height; otherwise an explicit geometry term remains.

For a steady rectangular-channel flow with discharge $Q=bhu$, the shallow-water specific energy relative to the bed is $E=h+Q^2/(2g{b}^2{h}^2)$. At fixed discharge and width, $E_h=1-F^2$, where the Froude number satisfies $F^2=Q^2/(g{b}^2{h}^3)$. The minimum is $E_c=3h_c/2$, with $h_c=(Q^2/(g{b}^2){)}^{1/3}$. Without dissipation, $E+H$ is the conserved Bernoulli equation head for bed elevation $H$.

In a sectionally uniform flow, a volume source $Q_x$ per downstream length brings axial velocity $u_a$. Momentum conservation gives the displayed source correction, with $A$ the wetted area. The head derivative is $[h+H+u^2/(2g){]}_x=Q_x(u_a-u)/(gA)$. Removing fluid at the local velocity preserves the head in this approximation. Adding fluid at rest does not: its acceleration reduces that head. The volume source alone cannot specify the momentum exchange without a velocity assumption.

For an outgoing simple wave into water initially at rest at depth $H$, the incoming Riemann invariant is $u-2\sqrt{gh}=-2\sqrt{gH}$. Thus $\sqrt{gh}=\sqrt{gH}+u/2$ and the outgoing characteristic speed is $v=\sqrt{gH}+3u/2$. A boundary characteristic emitted at time $s$ is $x=v(s)(t-s)$. Its envelope satisfies $t=s+v/v^{\prime }$ and $x=v^2/v^{\prime }$. At a zero-velocity onset with positive acceleration, the leading-edge intersection is the displayed distance. Later characteristic curves can form a shock earlier elsewhere in a sufficiently strong waveform.

For a rectangular channel with stationary width $b(x)$ and constant reduced gravity $g^{\prime }$, volume conservation and momentum conservation give $h_t+u{h}_x+h{u}_x=-hu{b}^{\prime }/b$ and $u_t+u{u}_x+g^{\prime }{h}_x=0$. With $c=\sqrt{g^{\prime }h}$ the characteristic curves have speeds $u\pm c$. The combinations $u\pm 2c$ obey the displayed compatibility equations; they are Riemann invariants only when the width source term vanishes.

Oogenesis is development of female gametes; the unequal divisions of human meiosis produce polar bodies alongside the developing ovum.

In angiosperms, pollination transfers pollen from an anther to a stigma. Fertilization is a later fusion of gametes; seed development follows. Pollination may use animals, wind or water, so an insect visit is neither required for every flower nor sufficient evidence of fertilization.^[ref]

Fertilization is fusion of gametes. Fusion of two haploid gametes restores the diploid state in the inheritance model used for Mendelian segregation.

A gamete is a reproductive biological cell that can fuse with another gamete during fertilization. In the ordinary diploid inheritance model, a haploid gamete carries one copy at each genetic locus.

The Bateman equation gives the populations in a sequential radioactive decay chain. For a parent with population $N_1(0)$ and an initially absent daughter, distinct decay constants give $N_2(t)=N_1(0){\lambda }_1(e^{-{\lambda }_{1}t}-e^{-{\lambda }_{2}t})/({\lambda }_2-{\lambda }_1)$; the first population satisfies $N_1^{\prime }=-{\lambda }_1{N}_1$.

Cyclic adenosine monophosphate is a cyclic nucleotide made from ATP. It can serve as an intracellular second messenger, changing the activity of target proteins after a signal has been received. Different biological cells can respond differently because they contain different targets. ^[ref]