Hadean.

Late Heavy Bombardment.

t h e “c lu s t e r” o f impa c t a ge s co ul d b e an art if a c t o f sampli n g a si n gl e bas i n's e jec ta, an d (2) t ha t t h e la c k o f impa c t m elt

r oc ks ol de r t h an abo u t 4100 mya i s r el a t ed to s uc h sampl e s h avi n g b ee n p ulv e rize d, or t h eir a ge s b ei n g r e se t.

lu nar ca ta c l y smi c cr a t e ri n g¬ s ho ws tr a c e s o f t h e sam e so rt o f pot e nt i al o rga ni c i n d ica t o rs.

. Hade an pe ri od

“c o mpl et el y i n co ns i st e nt w it h t hi s myt h w e m ade u p,”

t h e zirc o ns ⌨ inside zirc o ns

o ffe rs ev i de n c e t ha t

t h e p roc e s se s o f abu n d an c e

t h e d aug ht e r nuc li de it s elf i s r ad i oa c t iv e,

r e s ult i n g i n a d ec ay c h ai n , ev e ntua ll y

en di n g w it h t h e for ma t io n o f a s tabl e

(n o nr ad i oa c t iv e) d aug ht e r p rod uc t; ea ch st ep i n s uc h a

c h ai n i s c h ar a ct e rized / by a d i sti n ct ha lf-life .

Th e so lu t io n to t hi s equa t io n i s:

He r e N(t) i s t h e qua nt i ty a t t ime t, an d N0 = N(0) i s t h e (i nit i a l) qua nt i ty, a t t ime t = 0.

Stan d ard me t hods for fi n d i n g eigenvalues, eigenvectors, an d eigenspaces o f a giv e n ma trix ar e d i sc u s sed b elo w.

Th e s tudy o f v ec t or s pa c e ov e r fi nit e

fiel d, a br an c h o f li ne ar a lgebr a wh ic h i s

u seful i n c od i n g t h eo ry, na tur a ll y l e ads

to t h e s tudy an d u se o f ma tric e s ov e r

fi nit e fiel d i n c od i n g t h eo ry.

t h e bulk i nf la t ed:

Th e p rojec t io n o f to t h e v e rt ica l s ubs pa c e ne e ds to ag r ee w it h me tri c o n t h e fib e r ov e r a poi nt i n t h e m anif o l d M.Th e p rojec t io n o f to t h e ho rizo nta l s ubs pa c e o f t h e tan ge nt s pa c e a t poi nt mu s t b e i so m o rph i c to t h e me tri c g o n M a t π(p).

If we look at the top figure we can see the valve in its closed state. The water under pressure enters at A. B is an elastic diaphragm and above it is a weak spring pushing it down. The function of this spring is irrelevant for now as the valve would stay closed even without it. The diaphragm has a pinhole through its center which allows a very small amount of water to flow through it. This water fills the cavity C on the other side of the diaphragm so that pressure is equal on both sides of the diaphragm. While the pressure is the same on both sides of the diaphragm, the force is greater on the upper side which forces the valve shut against the incoming pressure. By looking at the figure we can see the surface being acted upon is greater on the upper side which results in greater force. On the upper side the pressure is acting on the entire surface of the diaphragm while on the lower side it is only acting on the incoming pipe. This results in the valve being securely shut to any flow and, the greater the input pressure, the greater the shutting force will be. Now let us turn our attention to the small conduit D. Until now it was blocked by a pin which is the armature of the solenoid E and which is pushed down by a spring. If we now activate the solenoid drawing the pin upwards via magnetic force from the solenoid current, the water in chamber C will flow through this conduit D to the output side of the valve. The pressure in chamber C will drop and the incoming pressure will lift the diaphragm thus opening the main valve. Water now flows directly from A to F. When the solenoid is again deactivated and the conduit D is closed again, the spring needs very little force to push the diaphragm down again and the main valve closes. In practice there is often no separate spring, the elastomer diaphragm is moulded so that it functions as its own spring, preferring to be in the closed shape. From this explanation it can be seen that this type of valve relies on a differential of pressure between input and output as the pressure at the input must always be greater than the pressure at the output for it to work. Should the pressure at the output, for any reason, rise above that of the input then the valve would open regardless of the state of the solenoid and pilot valve

*standard candle