Model: Chandar/sv-subject-based-all-MiniLM-L6-v2
Author: Chandar
Pipeline: sentence-similarity
Library: sentence-transformers
Tags: sentence-transformers, safetensors, bert, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:1124250, loss:CoSENTLoss, arxiv:1908.10084, base_model:sentence-transformers/all-MiniLM-L6-v2, base_model:finetune:sentence-transformers/all-MiniLM-L6-v2, model-index, text-embeddings-inference, endpoints_compatible, region:us
Base models (finetune): id: sentence-transformers/all-MiniLM-L6-v2
Card metadata: tags: sentence-transformers, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:1124250, loss:CoSENTLoss
base_model: sentence-transformers/all-MiniLM-L6-v2
widget: source_sentence: with	the	origin	of	the	coal	formed	during	the	carboniferous	epoch,	two	or	three
considerations	suggest	themselves.
In	the	first	place,	the	great	phantom	of	geological	time	rises	before	the	student	of
this,	as	of	all	other,	fragments	of	the	history	of	our	earth—	springing
irrepressibly	out	of	the	facts,	like	the	Djin	from	the	jar	which	the	fishermen	so
incautiously	opened;	and	like	the	Djin	again,	being	vaporous,	shifting,	and
indefinable,	but	unmistakably	gigantic.	However	modest	the	bases	of	one's
calculation	may	be,	the	minimum	of	time	assignable	to	the	coal	period	remains
something	stupendous.
Principal	Dawson	is	the	last	person	likely	to	be	guilty	of	exaggeration	in	this
matter,	and	it	will	be	well	to	consider	what	he	has	to	say	about	it:—
"The	rate	of	accumulation	of	coal	was	very	slow.	The	climate	of	the	period,	in
the	northern	temperate	zone,	was	of	such	a	character	that	the	true	conifers	show
rings	of	growth,	not	larger,	nor	much	less	distinct,	than	those	of	many	of	their
modern	congeners.	The	
Sigillarioe
	and	
Calamites
	were	not,	as	often	supposed,
composed	wholly,	or	even	principally,	of	lax	and	soft	tissues,	or	necessarily
short-lived.	The	former	had,	it	is	true,	a	very	thick	inner	bark;	but	their	dense
woody	axis,	their	thick	and	nearly	imperishable	outer	bark,	and	their	scanty	and
rigid	foliage,	would	indicate	no	very	rapid	growth	or	decay.	In	the	case	of	the
Sigillarioe
,	the	variations	in	the	leaf-scars	in	different	parts	of	the	trunk,	the
intercalation	of	new	ridges	at	the	surface	representing	that	of	new	woody	wedges
in	the	axis,	the	transverse	marks	left	by	the	stages	of	upward	growth,	all	indicate
that	several	years	must	have	been	required	for	the	growth	of	stems	of	moderate
size.	The	enormous	roots	of	these	trees,	and	the	condition	of	the	coal-swamps,
must	have	exempted	them	from	the	danger	of	being	overthrown	by	violence.
They	probably	fell	in	successive	generations	from	natural	decay;	and	making
every	allowance	for	other	materials,	we	may	safely	assert	that	every	foot	of
thickness	of	pure	bituminous	coal	implies	the	quiet	growth	and	fall	of	at	least
fifty	generations	of	
Sigillarioe
,	and	therefore	an	undisturbed	condition	of	forest
growth	enduring	through	many	centuries.	Further,	there	is	evidence	that	an
immense	amount	of	loose	parenchymatous	tissue,	and	even	of	wood,	perished	by
decay,	and	we	do	not	know	to	what	extent	even	the	most	durable	tissues	may
have	disappeared	in	this	way;	so	that,	in	many	coal-seams,	we	may	have	only	a
very	small	part	of	the	vegetable	matter	produced."
Undoubtedly	the	force	of	these	reflections	is	not	diminished	when	the
sentences: Quantum Statistics 187
0
1
2
3
¯n
−2 −1 0123
α+βϵ
Figure 8.1: A comparison of the Bose-Einstein (solid curve), Maxwell-Boltzmann (dashed curve),
and Fermi-Dirac (dash-dotted curve) distributions.
Finally, the partition function of the gas is given by
ln Z =αN ±
∑
r
ln
(
1 ±e−α−βϵr
)
. (8.58)
Let us investigate the magnitude ofαin some important limiting cases. Consider, ﬁrst of all,
the case of a gas at a given temperature when its concentration is made suﬃciently low: that is,
when N is made suﬃciently small. The relation (8.57) can only be satisﬁed if each term in the
sum over states is made suﬃciently small; that is, if ¯nr ≪1o rα+βϵr ≫1 for all statesr.( S e e
Figure 8.1.)
Consider, next, the case of a gas made up of a ﬁxed number of particles when its temperature is
made suﬃciently large. That is, whenβis made suﬃciently small. In the sum in Equation (8.57),
the terms of appreciable magnitude are those for whichα+βϵr <1. (See Figure 8.1.) Thus, it
follows that asβ→0 an increasing number of terms with large values ofϵr contribute substantially
to this sum. In order to prevent the sum from exceedingN, the parameterαmust become large
enough that each term is made suﬃciently small: that is, it is again necessary that ¯nr ≪1o r
α+βϵr ≫1 for all statesr.
The previous discussion suggests that if theconcentration of an ideal gas is made suﬃciently
low, or the temperature is made suﬃciently high, thenαmust become so large that
exp(α+βϵr) ≫1 (8.59)
for allr. Equivalently, this means that the number of particles occupying each quantum state must
become so small that
¯nr ≪1 (8.60), myriads	as	to	stain	the	berg	and	the	pack	ice	wherever	they	were	washed	by	the
swell	of	the	sea;	and,	when	enclosed	in	the	congealing	surface	of	the	water,	they
imparted	to	the	brash	and	pancake	ice	a	pale	ochreous	colour.	In	the	open	ocean,
northward	of	the	frozen	zone,	this	order,	though	no	doubt	almost	universally
present,	generally	eludes	the	search	of	the	naturalist;	except	when	its	species	are
congregated	amongst	that	mucous	scum	which	is	sometimes	seen	floating	on	the
waves,	and	of	whose	real	nature	we	are	ignorant;	or	when	the	coloured	contents
of	the	marine	animals	who	feed	on	these	Algae	are	examined.	To	the	south,
however,	of	the	belt	of	ice	which	encircles	the	globe,	between	the	parallels	of
50°	and	70°	S.,	and	in	the	waters	comprised	between	that	belt	and	the	highest
latitude	ever	attained	by	man,	this	vegetation	is	very	conspicuous,	from	the
contrast	between	its	colour	and	the	white	snow	and	ice	in	which	it	is	imbedded.
Insomuch,	that	in	the	eightieth	degree,	all	the	surface	ice	carried	along	by	the
currents,	the	sides	of	every	berg	and	the	base	of	the	great	Victoria	Barrier	itself,
within	reach	of	the	swell,	were	tinged	brown,	as	if	the	polar	waters	were	charged
with	oxide	of	iron.
"As	the	majority	of	these	plants	consist	of	very	simple	vegetable	cells,	enclosed
in	indestructible	silex	(as	other	Algae	are	in	carbonate	of	lime),	it	is	obvious	that
the	death	and	decomposition	of	such	multitudes	must	form	sedimentary	deposits,
proportionate	in	their	extent	to	the	length	and	exposure	of	the	coast	against
which	they	are	washed,	in	thickness	to	the	power	of	such	agents	as	the	winds,
currents,	and	sea,	which	sweep	them	more	energetically	to	certain	positions,	and
in	purity,	to	the	depth	of	the	water	and	nature	of	the	bottom.	Hence	we	detected
their	remains	along	every	icebound	shore,	in	the	depths	of	the	adjacent	ocean,
between	80	and	400	fathoms.	Off	Victoria	Barrier	(a	perpendicular	wall	of	ice
between	one	and	two	hundred	feet	above	the	level	of	the	sea)	the	bottom	of	the
ocean	was	covered	with	a	stratum	of	pure	white	or	green	mud,	composed
principally	of	the	silicious	shells	of	the	
Diatomaceoe
.	These,	on	being	put	into
water,	rendered	it	cloudy	like	milk,	and	took	many	hours	to	subside.	In	the	very
deep	water	off	Victoria	and	Graham's	Land,	this	mud	was	particularly	pure	and
fine;	but	towards	the	shallow	shores	there	existed	a	greater	or	less	admixture	of
disintegrated	rock	and	sand;	so	that	the	organic	compounds	of	the	bottom
frequently	bore	but	a	small	proportion	to	the	inorganic."	…
"The	universal	existence	of	such	an	invisible	vegetation	as	that	of	the	Antarctic
Ocean,	is	a	truly	wonderful	fact,	and	the	more	from	its	not	being	accompanied
by	plants	of	a	high	order.	During	the	years	we	spent	there,	I	had	been
accustomed	to	regard	the	phenomena	of	life	as	differing	totally	from	what, The ‘Computational Unified Field Theory’ (CUFT):  
Harmonizing Quantum and Relativistic Models and Beyond 
 
537 
Tg : ∑oi{x,y,z}[USCF(n)] ≠ oj{(x+m),(y+m),(z+m)} [USCF(1...n)] /c x n{USCF’s}, 
such that:  
T: ∑oi{x,y,z}[USCF(n)] - oj{(x+m),(y+m),(z+m)} [USCF(1...n)] ≤ c x n{USCF’s}  
The temporal value of an event (or object) is computed based on the number of times that a 
given object or event has changed – relative to the speed of light (e.g., across a certain 
number of USCF's); However, the measurement of temporal changes (e.g., taking place at an 
object or event) differ significantly – when computed from the 'global' or 'local' perspectives: 
This is because from a 'global' perspective, the faster an object travels (e.g., relative to the 
speed of light) the less potential changes ar e exhibited in that object's or event's 
presentations (across the relevant series of USCF 's). In contrast, from a 'local' perspective, 
there is no change in the number of measured changes in the given object (e.g., as its 
velocity increases relative to the speed of light) – since the local (computational) perspective 
does not encompass globally measured changes in the object's displacement (relative to the 
speed of light)…  
Note also that we can begin appreciating the fact that from the CUFT’s (D2 USCF’s) 
computational perspective there seems to be inexorable (computational) interrelationships 
that exist between the eight computational prod ucts of the three postulated Computational 
Dimensions of ‘Framework’, ‘Consistency’ and ‘Locus’; Thus, for instance, we find that an 
acceleration in an object’s velocity increases the number of times that object is presented 
(e.g., 'globally' across a given number of USCF  frames) – which in tu rn also increases it 
‘mass’ (e.g., from the ‘global Locus’ computational perspective), and (inevitably) also 
decreases its (global) ‘temporal’ value (due to  the decreased number of instances that that 
object changes across those given number of fram es (e.g., globally- relative to the speed of 
light maximal change computational constraint)... Indeed, over and beyond the 
hypothesized capacity of the CUFT to replicate and account for all known relativistic and 
quantum empirical findings, its conceptually  higher-ordered ‘D2’ USCF’s emerging 
computational framework may point at the unification of all apparently “distinct” physical 
features of ‘space’, ‘time’, ‘energy’ and ‘mass’ (and ‘causality’) as well as a complete 
harmonization between the (apparently disparat e) quantum (microscopic) and relativistic 
(macroscopic) phenomena and laws; the apparent disparity between quantum (microscopic) 
and relativistic (macroscopic) phenomena and laws; 
Towards that end, we next consider the a pplicability of the CUFT to known quantum 
empirical findings: Specifically, we cons ider the CUFT’s account of the quantum 
(computational) complimentary properties of ‘space’ and ‘energy’ or ‘time’ and ‘mass’; of an 
alternative CUFT’s account of the “collapse” of the probability wave function; and of the 
‘quantum entanglement’ and ‘p article-wave duality’ subatomic phenomena; It is also 
hypothesized that these alternative CUFT’s th eoretical accounts may also pave the way for 
the (long-sought for) unification of quantum and relativistic models of physical reality. First, 
it is suggested that the quantum complimentary ‘physical’ features of ‘space’ and ‘energy’, 
‘time’ and ‘mass’ – may be due to a ‘computational exhaustiveness’ (or ‘complimentarity’) of 
each of the (two) levels of the Computational Dimension of ‘Framework’. It is hypothesized 
that both the ‘ frame’ and ‘object’ (‘D2-USCF’s’) computational perspectives are exhaustively 
comprised of their ‘consistent’ (e.g., ‘space’ and ‘energy’, or ‘mass’ and ‘time’ physical 
features, respectively): Thus, whether we chos e to examine the USCF’s (D2) computation of, source_sentence: with	the	origin	of	the	coal	formed	during	the	carboniferous	epoch,	two	or	three
considerations	suggest	themselves.
In	the	first	place,	the	great	phantom	of	geological	time	rises	before	the	student	of
this,	as	of	all	other,	fragments	of	the	history	of	our	earth—	springing
irrepressibly	out	of	the	facts,	like	the	Djin	from	the	jar	which	the	fishermen	so
incautiously	opened;	and	like	the	Djin	again,	being	vaporous,	shifting,	and
indefinable,	but	unmistakably	gigantic.	However	modest	the	bases	of	one's
calculation	may	be,	the	minimum	of	time	assignable	to	the	coal	period	remains
something	stupendous.
Principal	Dawson	is	the	last	person	likely	to	be	guilty	of	exaggeration	in	this
matter,	and	it	will	be	well	to	consider	what	he	has	to	say	about	it:—
"The	rate	of	accumulation	of	coal	was	very	slow.	The	climate	of	the	period,	in
the	northern	temperate	zone,	was	of	such	a	character	that	the	true	conifers	show
rings	of	growth,	not	larger,	nor	much	less	distinct,	than	those	of	many	of	their
modern	congeners.	The	
Sigillarioe
	and	
Calamites
	were	not,	as	often	supposed,
composed	wholly,	or	even	principally,	of	lax	and	soft	tissues,	or	necessarily
short-lived.	The	former	had,	it	is	true,	a	very	thick	inner	bark;	but	their	dense
woody	axis,	their	thick	and	nearly	imperishable	outer	bark,	and	their	scanty	and
rigid	foliage,	would	indicate	no	very	rapid	growth	or	decay.	In	the	case	of	the
Sigillarioe
,	the	variations	in	the	leaf-scars	in	different	parts	of	the	trunk,	the
intercalation	of	new	ridges	at	the	surface	representing	that	of	new	woody	wedges
in	the	axis,	the	transverse	marks	left	by	the	stages	of	upward	growth,	all	indicate
that	several	years	must	have	been	required	for	the	growth	of	stems	of	moderate
size.	The	enormous	roots	of	these	trees,	and	the	condition	of	the	coal-swamps,
must	have	exempted	them	from	the	danger	of	being	overthrown	by	violence.
They	probably	fell	in	successive	generations	from	natural	decay;	and	making
every	allowance	for	other	materials,	we	may	safely	assert	that	every	foot	of
thickness	of	pure	bituminous	coal	implies	the	quiet	growth	and	fall	of	at	least
fifty	generations	of	
Sigillarioe
,	and	therefore	an	undisturbed	condition	of	forest
growth	enduring	through	many	centuries.	Further,	there	is	evidence	that	an
immense	amount	of	loose	parenchymatous	tissue,	and	even	of	wood,	perished	by
decay,	and	we	do	not	know	to	what	extent	even	the	most	durable	tissues	may
have	disappeared	in	this	way;	so	that,	in	many	coal-seams,	we	may	have	only	a
very	small	part	of	the	vegetable	matter	produced."
Undoubtedly	the	force	of	these	reflections	is	not	diminished	when	the
sentences: multiplication	results	in	the	throwing	off	of	cells,	instead	of	resulting	in	the
formation	of	more	tissue.	Hence,	taking	an	average	view,	we	see	why	the	smaller
animals	so	soon	arrive	at	a	reproductive	age,	and	produce	large	and	frequent
broods;	and	why,	conversely,	increased	size	is	accompanied	by	retarded	and
diminished	fertility.
But,	as	above	implied,	it	is	not	so	much	to	the	bulk	of	the	body	as	a	whole,	as	to
the	bulk	of	the	nervous	system,	that	fertility	stands	related	amongst	the	higher
animals.	Probably,	indeed,	it	stands	thus	related	in	all	cases;	the	difference
simply	arising	from	the	fact,	that	whereas	in	the	lower	organisms,	where	the
nervous	system	is	not	concentrated,	its	bulk	varies	as	the	bulk	of	the	body,	in	the
higher	organisms	it	does	not	do	so.	Be	this	as	it	may,	however,	we	see	clearly
that,	amongst	the	vertebrata,	the	bodily	development	is	not	the	determining
circumstance.	In	a	fish,	a	reptile,	a	bird,	and	a	mammal	of	the	same	weight,	there
is	nothing	like	equality	of	fecundity.	Cattle	and	horses,	arriving	as	they	do	so
soon	at	a	reproductive	age,	are	much	more	prolific	than	the	human	race,	at	the
same	time	that	they	are	much	larger.	And	whilst,	again,	the	difference	in	size
between	the	elephant	and	man	is	far	greater,	their	respective	powers	of
multiplication	are	less	unlike.	Looking	in	these	cases	at	the	nervous	systems,
however,	we	find	no	such	discrepancy.	On	learning	that	the	average	ratio	of	the
brain	to	the	body	is—in	fishes,	1	to	5668;	in	reptiles,	1	to	1321;	in	birds,	1	to
212;	and	in	mammals,	1	to	186;
[99]
	their	different	degrees	of	fecundity	are
accounted	for.	Though	an	ox	will	outweigh	half-a-dozen	men,	yet	its	brain	and
spinal	cord	are	far	less	than	those	of	one	man;	and	though	in	bodily	development
the	elephant	so	immensely	exceeds	the	human	being,	yet	the	elephant's	cerebro-
spinal	system	is	only	thrice	the	size	attained	by	that	of	civilized	
men.
[100]
Unfortunately,	it	is	impossible	to	trace	throughout	the	animal	kingdom	this
inverse	relationship	between	the	nervous	and	reproductive	systems	with	any
accuracy.	Partly	from	the	fact	that,	in	each	case,	the	degree	of	fertility	depends
on	three	variable	elements—the	age	at	which	reproduction	begins,	the	number
produced	at	a	birth,	and	the	frequency	of	the	births;	partly	from	the	fact	that,	in
respect	to	most	animals,	these	data	are	not	satisfactorily	attainable,	and	that,
when	they	are	attainable,	they	are	vitiated	by	the	influence	of	domesticity;	and
partly	from	the	fact	that	no	precise	measurement	of	the	respective	nervous
systems	has	been	made,	we	are	unable	to	draw	any	but	general	and	somewhat
vague	comparisons.	These,	however,	as	far	as	they	go,	are	in	our	favour.
Ascending	from	beings	of	the	acrite	nerveless	type,	which	are	the	most	prolific
of	 all,	 through	 the	 various	 invertebrate	 sub-kingdoms,	 amongst	 which, 200 Chapter 7 Superposition of Quasi-Parallel Plane Waves
COMMENT: As the wave travels, the earlier part of the pulse oscillates
more slowly than the later part. This is called chirp, and it means
that the red frequencies get ahead of the blue ones since they experi-
ence a lower index. The instantaneous frequency is the effective local
frequency.
Exercises for 7.6 Generalized Context for Group Delay
P7.9 When the spectrum of a pulse is narrow compared to the resonant
spectral features of a material (like that depicted in Fig. 7.10), the re-
shaping delay (7.53) can be neglected. Show that the net delay in this
case (7.52) reduces to
lim
T →∞
∆tG (r) = ∂Rek
∂ω ·∆r
¯¯¯
¯
¯ω
HINT: The spectral intensity may be approximated asI (ω) = I0δ(ω− ¯ω).
P7.10 When the spectrum a pulse is very broad, the reshaping delay (7.53) is
negligible. Show that in this case the net delay reduces to
lim
T →0
∆tG (r) = ∆r
c
assuming k and ∆r are parallel. This implies that a sharply defined
signal cannot travel faster than c.
HINT: The real index of refractionn goes to unity far from resonance,
and the imaginary part κ goes to zero.
P7.11 Show that equation (7.49) can be written as
〈t〉 = −i
∞R
−∞
dω
h
∂
∂ωE (r,ω)
i
·E∗ (r,ω)
∞R
−∞
dωE (r,ω) ·E∗ (r,ω)
≡ T [E (r,ω)]
HINT: Parseval’ s theorem(7.21) can be used in the denominator. In
the numerator, substitute (7.18) for both fields, with ω and ω′ as the
dummy variables. Reorder integration to perform the time integral
first. The following trick is handy:
1
2π
∞R
−∞
t e−i (ω′−ω)t d t = −i ∂
∂ω
1
2π
∞R
−∞
e−i (ω′−ω)t d t = −i ∂
∂ωδ
¡
ω′ −ω
¢
.
P7.12 Use the result of P 7.11 to derive (7.51).
HINT: Compute
∆t = T [E (r0 +∆r,ω)] −T [E (r0,ω)]., any element of this algebra can be written as a sum of elements in normal order,
of the form
cl,m(a†
B)lam
B
with all annihilation operators aB on the right, for some complex constantscl,m.
As a vector space over C, Weyl(2, C) is infinite dimensional, with a basis
1, aB, a†
B, a2
B, a†
BaB, (a†
B)2, a3
B, a†
Ba2
B, (a†
B)2aB, (a†
B)3, . . .
This algebra is isomorphic to a more familiar one. Setting
a†
B = z, a B = d
dz
one sees that Weyl(2, C) can be identified with the algebra of polynomial coef-
ficient differential operators on functions of a complex variable z. As a complex
vector space, the algebra is infinite dimensional, with a basis of elements
zl dm
dzm
In our study of quantization by the Bargmann-Fock method, we saw that
the subset of such operators consisting of complex linear combinations of
1, z, d
dz , z 2, d2
dz2 , z d
dz
is closed under commutators, and is a representation of a Lie algebra of complex
dimension 6. This Lie algebra includes as subalgebras the Heisenberg Lie algebra
h3 ⊗ C (first three elements) and the Lie algebra sl(2, C) = sl(2, R) ⊗ C (last
three elements). Note that here we are allowing complex linear combinations,
so we are getting the complexification of the real six dimensional Lie algebra
that appeared in our study of quantization.
Since the aB and a†
B are defined in terms of P and Q, one could of course
also define the Weyl algebra as the one generated by 1, P, Q, with the Heisenberg
commutation relations, taking complex linear combinations of all products of
these operators.
28.1.2 One degree of freedom, fermionic case
Changing commutators to anticommutators, one gets a different algebra, the
Clifford algebra:
Definition (Complex Clifford algebra, one degree of freedom) . The complex
Clifford algebra in the one degree of freedom case is the algebra Cliff(2, C) gen-
erated by the elements 1, aF , a†
F , subject to the canonical anticommutation rela-
tions (CAR)
[aF , a†
F ]+ = 1, [aF , aF ]+ = [a†
F, a†
F]+ = 0
312, source_sentence: with	the	origin	of	the	coal	formed	during	the	carboniferous	epoch,	two	or	three
considerations	suggest	themselves.
In	the	first	place,	the	great	phantom	of	geological	time	rises	before	the	student	of
this,	as	of	all	other,	fragments	of	the	history	of	our	earth—	springing
irrepressibly	out	of	the	facts,	like	the	Djin	from	the	jar	which	the	fishermen	so
incautiously	opened;	and	like	the	Djin	again,	being	vaporous,	shifting,	and
indefinable,	but	unmistakably	gigantic.	However	modest	the	bases	of	one's
calculation	may	be,	the	minimum	of	time	assignable	to	the	coal	period	remains
something	stupendous.
Principal	Dawson	is	the	last	person	likely	to	be	guilty	of	exaggeration	in	this
matter,	and	it	will	be	well	to	consider	what	he	has	to	say	about	it:—
"The	rate	of	accumulation	of	coal	was	very	slow.	The	climate	of	the	period,	in
the	northern	temperate	zone,	was	of	such	a	character	that	the	true	conifers	show
rings	of	growth,	not	larger,	nor	much	less	distinct,	than	those	of	many	of	their
modern	congeners.	The	
Sigillarioe
	and	
Calamites
	were	not,	as	often	supposed,
composed	wholly,	or	even	principally,	of	lax	and	soft	tissues,	or	necessarily
short-lived.	The	former	had,	it	is	true,	a	very	thick	inner	bark;	but	their	dense
woody	axis,	their	thick	and	nearly	imperishable	outer	bark,	and	their	scanty	and
rigid	foliage,	would	indicate	no	very	rapid	growth	or	decay.	In	the	case	of	the
Sigillarioe
,	the	variations	in	the	leaf-scars	in	different	parts	of	the	trunk,	the
intercalation	of	new	ridges	at	the	surface	representing	that	of	new	woody	wedges
in	the	axis,	the	transverse	marks	left	by	the	stages	of	upward	growth,	all	indicate
that	several	years	must	have	been	required	for	the	growth	of	stems	of	moderate
size.	The	enormous	roots	of	these	trees,	and	the	condition	of	the	coal-swamps,
must	have	exempted	them	from	the	danger	of	being	overthrown	by	violence.
They	probably	fell	in	successive	generations	from	natural	decay;	and	making
every	allowance	for	other	materials,	we	may	safely	assert	that	every	foot	of
thickness	of	pure	bituminous	coal	implies	the	quiet	growth	and	fall	of	at	least
fifty	generations	of	
Sigillarioe
,	and	therefore	an	undisturbed	condition	of	forest
growth	enduring	through	many	centuries.	Further,	there	is	evidence	that	an
immense	amount	of	loose	parenchymatous	tissue,	and	even	of	wood,	perished	by
decay,	and	we	do	not	know	to	what	extent	even	the	most	durable	tissues	may
have	disappeared	in	this	way;	so	that,	in	many	coal-seams,	we	may	have	only	a
very	small	part	of	the	vegetable	matter	produced."
Undoubtedly	the	force	of	these	reflections	is	not	diminished	when	the
sentences: CHAPTER 
Moray Offshore Renewables Limited – Environmental Statement  
Telford, Stevenson and MacColl Offshore Wind Farms and Transmission Infrastructure 
 
Section 3 – Offshore Generating Station Impact Assessment 7-23 
7.1 
Decommissioning 
7.1.6.45 Effects of deco mmissioning activities will be comparable to those arising durin g the 
construction of the wind farms or where cables and other structures beneath the 
surface of the seabed are left in –situ, then effects will be much less .  Removal of 
turbine foundations and scour material will disturb seabed sediments for subsequent 
re–distribution over adjacent areas resulting in potential smothering effects as 
assessed above.  The dominant sediment habitats and co mmunities will be tolerant 
to these effects (as assessed) and the significance of related effects is expected to 
remain minor. 
7.1.6.46 Removal of the turbines will result in the removal of the epifaunal co mmunities 
attached to them .  A reduction in epibenthos to pre –construction conditions is 
therefore predicted .  Exposed seabed areas are expected to be rapidly 
re-colonised with full restitution of the habitats and biotopes expected within five 
years, subject to the condition of the seabed substrate and stability compa red to 
the baseline situation. 
7.1.6.47 Removal of turbines upon which sensitive and  / or protected species, such as the 
cold water coral Lophelia pertusa , have become attached would constitute a 
negative effect .  Current precedent for assessment in this regard includes the MV 
Hutton oil and gas platform deco mmissioning programme which regarded Lophelia 
pertusa as an opportunist suggesting that this is sufficient reason for it not to affect 
the decommissioning outcome of this facility (British Petroleum, 2006) .  With regard 
to the current development, statutory consultation will be required t o confirm 
requirements within the deco mmissioning p rogramme and to ensure that the 
potential for effects on protected species are properly assessed .  There are no 
records of Lophelia pertusa , or any other protected species likely to attach to the 
turbines, occurring within the vicinity of the proposed wind farms at Smith Bank 
although some records exist of its presence within the Southern Trench (see Chapter 
4.2: Benthic Ecology).  Furthermore, L. pertusa typically occurs at depths of greater 
than 150  m and is rarely found attached to hard substrata (Peckett, 2003) .  
Consequently, the likelihood of this species becoming established on the turbines 
within the three proposed wind farm sites is very low. 
Accidental Spillages of Chemicals 
7.1.6.48 Accidental spillages or release of chemicals such as grouting, fuel and oil during the 
construction, operation and deco mmissioning phases of the wind farms may 
potentially contaminate seabed sediments .  The severity of this effect on benthic 
ecology depends upon the quantities a nd nature of the spillage  / release, the 
dilution and dispersal properties of the receiving waters and the bio –availability of 
the contaminant to benthic species .  At this stage, the quantities and types of 
material which might conceivably enter the marine  environment in this way are not 
known and so scale and magnitude of effects are unquantifiable at present .  In the 
worst case scenario , the potential significance of an accidental spillage would be 
major.  Accidents are by definition unknown and the uncer tainty associated with 
this effect is therefore high., 212 BIOLOGYOFDEATH
inwhichtheenvironmentalforces(ofsub-lethalinten-
sity,ofcourse}chieflyactindeterminingdurationof
life,appearstolie~bychangingtherateofmetabolismof
theindividual.Furthermoreonewouldsuggest,ontMs
view,thatwhathereditydoesinrelationtodurationof
lifeischieflytodetermine,withinfairlynarrowlimits,
thetotalenergyoutputwhichtheindividualcanexhibit
initslifetime.Thislimitationisdirectlybroughtabout
presumablythroughtwogeneralfactors:viz,(a)the
kindorqualityofmaterialofwhichthisparticularvital
machineisbuilt,and(b)themannerinwhichtheparts
areputtogetherorassembled.Bothofthesefactors
are,ofcourse,expressionsoftheextentandcharacter
oftheprocessesoforganicevolutionwhichhavegiven
risetothisparticularspeciesaboutwhichwemaybe
talkinginaparticularinstance
Thereissomedirectexperimentalevidence,smallin
amounttobesure,butexactandpertinent,totheeffect
thatthedurationoflifeofananimalstandsininversere-
lationtothetotalamountofitsmetabolicactivity,orput
inotherwords,tothework,inthesenseoftheoretical
mechanics,thatitasamachinedoesduringitslife.
Slonakerkept4albinoratsincagesliketheoldfashioned
revolvingsquirrelcages,withaproperlycalibratedodo-
meterattachedtotheaxle,sothatthetotalamountof
runningwhichtheydidintheirwholelivescouldbe
recorded.TheresultswerethoseshowninTable26.
Itwillbeperceivedthattheamountofexercisetaken
bytheseratswasastonishinglylarge.Foraratto
run5,447milesinthecourseofitslifeisindeedare-
markableperformance.Nowthese4ratsattainedan
averageageatdeathof29.5months.Butthreecontrol
ratsconfinedinstationarycagessothattheycouldonly, 10.3 Fresnel Approximation 265
To approximate R in the exponent, we must proceed with caution. To this end
we expand (10.2) under the assumption z2 ≫ (x −x′)2 +(y − y′)2. Again, this is
consistent with the idea of restricting ourselves to relatively small angles. The
expansion of (10.2) is written as
R = z
s
1 + (x −x′)2 +
¡
y − y′¢2
z2
∼= z
"
1 +
¡
x −x′¢2 +
¡
y − y′¢2
2z2 +···
#
(exponent; Fresnel approximation) (10.12)
Substitution of (10.11) and (10.12) into the Huygens-Fresnel diffraction formula
(10.1) yields
E
¡
x, y, z
¢∼= −i ei kz ei k
2z (x2+y2)
λz
Ï
aperture
E
¡
x′, y′,0
¢
ei k
2z (x′2+y′2)e−i k
z (xx ′+y y′)d x′d y′
(Fresnel approximation) (10.13)
This approximation may look a bit messier than before, but in terms of being able
to make progress on integration our chances are somewhat improved.
Figure 10.8 Field amplitude fol-
lowing a rectangular aperture com-
puted in the Fresnel approxima-
tion.
Example 10.3
Compute the Fresnel diffraction field following a rectangular aperture (dimensions
∆x by ∆y) illuminated by a uniform plane wave.
Solution: According to (10.13), the field downstream is
E
¡
x, y, z
¢
= −i E0
ei kz
λz ei k
2z (x2+y2)
∆x/2Z
−∆x/2
d x′ei k
2z x′2
e−i kx
z x′
∆y/2Z
−∆y/2
d y′ei k
2z y′2
e−i k y
z y′
Unfortunately, the integration in the preceding example must be performed
numerically. This is often the case for diffraction integrals in the Fresnel approx-
imation, but at least numerical fast Fourier transforms can aid in the process.
Figure 10.8 shows the result of integration for a rectangular aperture with a height
twice its width.
Paraxial Wave Equation
If we assume that the light coming through the aperture is highly directional, such
that it propagates mainly in the z-direction, we are motivated to write the field
as E(x, y, z) = ˜E(x, y, z)ei kz . Upon substitution of this into the scalar Helmholtz
equation (10.5), we arrive at
∂2 ˜E
∂x2 + ∂2 ˜E
∂y2 +2i k∂ ˜E
∂z + ∂2 ˜E
∂z2 = 0 (10.14)
At this point we make the paraxial wave approximation,5 which is |2k ∂ ˜E
∂z | ≫ |∂2 ˜E
∂z2 |.
That is, we assume that the amplitude of the field varies slowly in the z-direction
5P . W . Milonni and J. H. Eberly,Laser, Sect. 14.4 (New York: Wiley, 1988)., source_sentence: with	the	origin	of	the	coal	formed	during	the	carboniferous	epoch,	two	or	three
considerations	suggest	themselves.
In	the	first	place,	the	great	phantom	of	geological	time	rises	before	the	student	of
this,	as	of	all	other,	fragments	of	the	history	of	our	earth—	springing
irrepressibly	out	of	the	facts,	like	the	Djin	from	the	jar	which	the	fishermen	so
incautiously	opened;	and	like	the	Djin	again,	being	vaporous,	shifting,	and
indefinable,	but	unmistakably	gigantic.	However	modest	the	bases	of	one's
calculation	may	be,	the	minimum	of	time	assignable	to	the	coal	period	remains
something	stupendous.
Principal	Dawson	is	the	last	person	likely	to	be	guilty	of	exaggeration	in	this
matter,	and	it	will	be	well	to	consider	what	he	has	to	say	about	it:—
"The	rate	of	accumulation	of	coal	was	very	slow.	The	climate	of	the	period,	in
the	northern	temperate	zone,	was	of	such	a	character	that	the	true	conifers	show
rings	of	growth,	not	larger,	nor	much	less	distinct,	than	those	of	many	of	their
modern	congeners.	The	
Sigillarioe
	and	
Calamites
	were	not,	as	often	supposed,
composed	wholly,	or	even	principally,	of	lax	and	soft	tissues,	or	necessarily
short-lived.	The	former	had,	it	is	true,	a	very	thick	inner	bark;	but	their	dense
woody	axis,	their	thick	and	nearly	imperishable	outer	bark,	and	their	scanty	and
rigid	foliage,	would	indicate	no	very	rapid	growth	or	decay.	In	the	case	of	the
Sigillarioe
,	the	variations	in	the	leaf-scars	in	different	parts	of	the	trunk,	the
intercalation	of	new	ridges	at	the	surface	representing	that	of	new	woody	wedges
in	the	axis,	the	transverse	marks	left	by	the	stages	of	upward	growth,	all	indicate
that	several	years	must	have	been	required	for	the	growth	of	stems	of	moderate
size.	The	enormous	roots	of	these	trees,	and	the	condition	of	the	coal-swamps,
must	have	exempted	them	from	the	danger	of	being	overthrown	by	violence.
They	probably	fell	in	successive	generations	from	natural	decay;	and	making
every	allowance	for	other	materials,	we	may	safely	assert	that	every	foot	of
thickness	of	pure	bituminous	coal	implies	the	quiet	growth	and	fall	of	at	least
fifty	generations	of	
Sigillarioe
,	and	therefore	an	undisturbed	condition	of	forest
growth	enduring	through	many	centuries.	Further,	there	is	evidence	that	an
immense	amount	of	loose	parenchymatous	tissue,	and	even	of	wood,	perished	by
decay,	and	we	do	not	know	to	what	extent	even	the	most	durable	tissues	may
have	disappeared	in	this	way;	so	that,	in	many	coal-seams,	we	may	have	only	a
very	small	part	of	the	vegetable	matter	produced."
Undoubtedly	the	force	of	these	reflections	is	not	diminished	when	the
sentences: 81
13.13 RODLESS CYLINDERS
The rodless cylinder is a device that requires particular attention whenever used, 
because in contrast to the traditional cylinders, where the load is placed in line with 
the rod, in the rodless cylinder the weight is anchored on a carriage that runs on the 
top part of the cylinder, and between the cylinder axis and the load’s barycentre there 
is always a more or less accentuated arm according to the shape of the object to be 
moved.    
The piston’s force is transmitted to an external carriage by a mechanic arm that comes 
out from an opening located in the barrel along the entire stroke and is connected to 
the piston solidly. Sealing is guaranteed by an internal metallic strap fixed at the ends 
of the body that completely covers the opening. The piston’s gaskets, their internal 
pressure and a magnetic band properly positioned make the metallic plate adhere to 
the internal surface of the tube, ensuring sufficient outward sealing and also between 
the two cylinder chambers.
A further metallic strap placed outside, in correspondence with the opening, prevents 
dust collection in the sliding areas. Sealing in this type of cylinder is never perfect. Par-
ticular guide systems obtained on the carriage and on the piston, open the two plates 
in order to allow mechanic connection between piston and slider/cursor. In opposition 
to rod cylinders, the forces expressed by the cylinder in the two directions are identi-
cal. In fact, there is no difference in sections on the two sides of the piston since the 
rod does not exist. The regulating air-cushion absorption function is exactly identical 
to the one performed in the rod cylinders.
 96 
 
 
In realtà gli in gombri totali del cilindro compatto sono superioni rispetto al cilindro a 
corsa breve, per questo motivo  le due versioni sono tuttora presenti sul mercato  e l’uno 
non sostituisce l’altro. 
Il cilindro compatto, al contrario del corsa breve, viene sviluppato  sin dall’inizio 
seguendo, per scelta del primo produttore che lo realizzò, gli ingombri imposti dall’ente 
nazionale di unificazione francese (UNITOP) e quindi esiste intercambia bilità tra 
differenti produttori. 
Alcuni di questi produttori hanno inserito anche una versione ISO che unifica di fatto le 
quote di fissaggio degli accessori utilizzabili quindi in differenti serie di cilindri. 
Tutto ciò consente all’utilizzatore finale di razionalizzare il proprio magazzino. 
 
13.13  Cilindri senza stelo 
 
Il cilind ro senza stelo è un apparecchio che merita particolare attenzione quando 
applicato, perché al contrario dei cilindri tradizionali in cui il carico è posi zionato in 
asse con lo stelo, nel cilindro senza stelo il peso viene ancorato su di un carrello che 
scorre sulla parte superiore dello stesso e, tra asse del cilindro e baricentro del carico, vi 
è sempre un braccio più o meno accentuato a seconda della forma dell’oggetto da  
movimentare.      
 
  
                                                                                                      
 
 
 
 
 
                                                                                           
 
 
 
  
 
 
 
 
Chapter 13
Pneumatic devices 
Pneumatic Guide_GB.indd   81 15/04/2015   08:46:21, 4.2 Density operators and normal states 109
4.2 Density operators and normal states
Deﬁnition 2.4 of a state still makes good sense in the inﬁnite-dimensional case, as
it simply specializes the general deﬁnition of a state on a C*-algebra A to the case
A = B(H). Thus we continue to say that a state on B(H) is a complex-linear map
ω : B(H) →C satisfying ω(b∗b) ≥0 for each b ∈B(H) and ω(1H )= 1. Despite
this lack of novelty in the deﬁnition of a state (i.e., compared to ﬁnite-dimensional
Hilbert spaces), Theorem 2.7 no longer holds if H is inﬁnite-dimensional: although
it (almost trivially) remains true that density operatorsρ on H deﬁne states on B(H)
through the fundamental correspondenceω(a)= Tr(ρa), a ∈B(H), cf. (2.33), there
are (many) states that are not given in that way (see below). Fortunately, states that
do arise through (2.33) can be characterized in a simple way.
Deﬁnition 4.11. A state ω : B(H) →C is called normal if for each orthogonal
family (ei) of projections (i.e., e∗
i = ei and eiej = δij ei) one has
ω
(
∑
i
ei
)
= ∑
i
ω(ei). (4.28)
Here ∑i ei is deﬁned as the projection on the smallest closed subspace K of H that
contains each eiH (that is, ∑i ei = ∨iei, i.e., the supremum in the poset P(H) of all
projections on H with respect to the partial order e≤fi f f e H⊆f H). Furthermore,
the sum over i on the right-hand side is deﬁned by (B.11), i.e., as the supremum (in
R) of the set of all sums ∑i∈F ω(ei) over ﬁnite subsets F ⊂I of the index set I in
which i takes values. It is ﬁnite because∑i∈F ei ≤1H and hence, since ω is positive,
∑
i∈F
ω(ei) ≤ω(1H )= 1.
For example, let(υi) be a basis ofH with associated one-dimensional projections
ei = |υi⟩⟨υi|. (4.29)
If ω is assumed to be a state, then the additivity condition (4.28) implies
∑
i
ω(ei)= 1, (4.30)
or, equivalently, using Deﬁnition B.6 etc. as well as the notationeF ≡∑i∈F ei,
lim
F
ω(eF )= 1. (4.31)
If H is separable, any orthogonal family (ei) of projections is necessarily countable,
and (4.28) is analogous to the countable additivity condition deﬁning a measure.
Theorem 4.12. A state ω on B(H) takes the form ω(a)= Tr(ρa) for some (unique)
density operator ρ ∈D(H) iff it is normal., C.9 Ideals in C*-algebras 675
by Deﬁnition C.35 and the proof of Proposition C.51. The second term on the right-
hand side goes to zero for λ →∞, since j ∈J. Hence
lim
λ→∞
∥a −a1λ∥≤∥ a + j∥. (C.115)
For each ε > 0 we can choose j ∈J so that (C.102) holds. For this speciﬁc j,w e
combine (C.112), (C.115), and (C.102) to ﬁnd
lim
λ→∞
∥a −a1λ∥−ε ≤∥τ(a)∥≤∥ a −a1λ∥. (C.116)
Letting ε →0 proves (C.111). □
We now prove (C.2) in A/J. Successively using (C.111), (C.2) in ˙A, (C.114),
(C.111), (C.99), and (C.110), we ﬁnd
∥τ(a)∥2 = lim
λ→∞
∥a −a1λ∥2 = lim
λ→∞
∥(a −a1λ)∗(a −a1λ)∥
= lim
λ→∞
∥(1A −1λ)a∗a(1A −1λ)∥≤ lim
λ→∞
∥1 −1λ∥∥a∗a(1A −1λ)∥
≤ lim
λ→∞
∥a∗a(1A −1λ)∥= ∥τ(a∗a)∥= ∥τ(a)τ(a∗)∥
= ∥τ(a)τ(a)∗∥. (C.117)
As in the proof of Proposition C.30, this implies (C.2), and hence Theorem C.60.□
We now state and prove the key result about morphisms.
Theorem C.62. Let α : A →B be a nonzero homomorphism between C*-algebras.
1. The homomorphism α is continuous, with norm ∥α∥= 1.
2. Its kernel ker(α) is an ideal in A.
3. If α is injective, then it is isometric.
4. An isomorphism of C*-algebras is automatically isometric.
5. The rangeα(A) is a C*-subalgebra of B; in particular,α(A) is closed in B.
Proof. If necessary, we ﬁrst reduce the proof of the ﬁrst claim to the case where
A and B have units and α is unital: we do so by replacing A and B by ˙A and ˙B,
respectively (even if A and/or B was already unital in the ﬁrst place, but α was not),
and replacing α by the homomorphism ˙α : ˙A → ˙B deﬁned in (C.66). If we do so,
it follows from Lemma C.34 that in the worst case the spectrum of a or α(a) is
modiﬁed by adding 0, which does not change the spectral radius. Therefore, the
move fromα to ˙α makes no difference to the argument to follow, so we assume
that 1A ∈A and 1B ∈B, and α(1A)= 1B.I f z ∈ρ(a), so that (a −z)−1 exists in
A, then α(a −z) is certainly invertible in B, for (C.4) implies that (α(a −z))−1 =
α((a −z)−1). Hence ρ(a) ⊆ρ(α(a)), so that
σ(α(a)) ⊆σ(a). (C.118)
Replacing a by a∗a this gives r(α(a∗a)) ≤r(a∗a), and since α(a∗a)= α(a)∗α(a),
eq. (C.55) yields ∥α(a)∥≤∥a∥, and hence ∥α∥≤ 1. This proves continuity of α., source_sentence: with	the	origin	of	the	coal	formed	during	the	carboniferous	epoch,	two	or	three
considerations	suggest	themselves.
In	the	first	place,	the	great	phantom	of	geological	time	rises	before	the	student	of
this,	as	of	all	other,	fragments	of	the	history	of	our	earth—	springing
irrepressibly	out	of	the	facts,	like	the	Djin	from	the	jar	which	the	fishermen	so
incautiously	opened;	and	like	the	Djin	again,	being	vaporous,	shifting,	and
indefinable,	but	unmistakably	gigantic.	However	modest	the	bases	of	one's
calculation	may	be,	the	minimum	of	time	assignable	to	the	coal	period	remains
something	stupendous.
Principal	Dawson	is	the	last	person	likely	to	be	guilty	of	exaggeration	in	this
matter,	and	it	will	be	well	to	consider	what	he	has	to	say	about	it:—
"The	rate	of	accumulation	of	coal	was	very	slow.	The	climate	of	the	period,	in
the	northern	temperate	zone,	was	of	such	a	character	that	the	true	conifers	show
rings	of	growth,	not	larger,	nor	much	less	distinct,	than	those	of	many	of	their
modern	congeners.	The	
Sigillarioe
	and	
Calamites
	were	not,	as	often	supposed,
composed	wholly,	or	even	principally,	of	lax	and	soft	tissues,	or	necessarily
short-lived.	The	former	had,	it	is	true,	a	very	thick	inner	bark;	but	their	dense
woody	axis,	their	thick	and	nearly	imperishable	outer	bark,	and	their	scanty	and
rigid	foliage,	would	indicate	no	very	rapid	growth	or	decay.	In	the	case	of	the
Sigillarioe
,	the	variations	in	the	leaf-scars	in	different	parts	of	the	trunk,	the
intercalation	of	new	ridges	at	the	surface	representing	that	of	new	woody	wedges
in	the	axis,	the	transverse	marks	left	by	the	stages	of	upward	growth,	all	indicate
that	several	years	must	have	been	required	for	the	growth	of	stems	of	moderate
size.	The	enormous	roots	of	these	trees,	and	the	condition	of	the	coal-swamps,
must	have	exempted	them	from	the	danger	of	being	overthrown	by	violence.
They	probably	fell	in	successive	generations	from	natural	decay;	and	making
every	allowance	for	other	materials,	we	may	safely	assert	that	every	foot	of
thickness	of	pure	bituminous	coal	implies	the	quiet	growth	and	fall	of	at	least
fifty	generations	of	
Sigillarioe
,	and	therefore	an	undisturbed	condition	of	forest
growth	enduring	through	many	centuries.	Further,	there	is	evidence	that	an
immense	amount	of	loose	parenchymatous	tissue,	and	even	of	wood,	perished	by
decay,	and	we	do	not	know	to	what	extent	even	the	most	durable	tissues	may
have	disappeared	in	this	way;	so	that,	in	many	coal-seams,	we	may	have	only	a
very	small	part	of	the	vegetable	matter	produced."
Undoubtedly	the	force	of	these	reflections	is	not	diminished	when	the
sentences: 31 
 
 
2.Chapter Two:………………………………………………………….. Causes of Aging 
 
 
 There are many types of free radicals and the most related to the 
biological process are those which derived from oxygen: the  Reactive 
Oxygen Species ( ROS ). These ROS include superoxide anion , peroxide 
and hydro radicals . ROS are produced in vivo within the mitochondria 
during electron tra nsport chain. They are also produced as intermediate 
products in different enzymatic reactions and by different physiological 
processes such as: 
 Phagocytic activity of white blood cells, specifically neu trophils. 
Neutrophils generate ROS during phagocytic activity in order to kill the 
invading pathogens as a host defense mechanism. 
 
 When the cells are exposed to abnormal conditions -such as hypoxia 
or hperoxia -produce ROS. Some drugs have the ability to induce the 
cells to produce ROS due to their oxidizing effect. 
 
 An exposure to radiation may induce the biological systems to 
produce ROS., Figure 4.2: Particle plots of the dark matter density in cold dark matter
dominated models. The simulation box is 240Mpc/h on a side, the thickness
of the shown slices is around 8Mpc/h. The particle distribution is very
lamentary, a consequence of the large amount of large scale power in this
model. The higher density laments delineate nearly spherical under dense
voids. Very high density haloes occur on the intersection between laments.
Dierent redshifts (z = 3, 1, 0) are shown from left to right. Plots from top to
bottom are (1) a Universe with cosmological constant (
 m = 0:3;
 = 0:3),
(2) Einstein-de Sitter Universe (
 m = 1:0;
 = 0:0), (3) a cosmology with
a tilted power-spectrum (
 m = 1:0;
 = 0:0), (4) an 
 m = 0:3 Open model
(
m = 0:3;
 = 0:0). (Jenkins et al, 1998 Astrophysical Journal,499,20-40)
79, THEINHERITANCEOFDURATION177
preferredtostatetheconclusionintermsofdeath,rates,
asitwasoriginallystatedbyPearson,becauseofthe
bearingithasuponagreatdealofthepublichealth
propagandasolooselyflungabout.Itneedonlybere-
memberedthatthereisaperfectlydefinitefunctional
relationbetweendeathrateandaveragedurationoflife
inanapproximatelystablepopulationgroup,expres-
siblebyanequation,inordertoseethatanyconclusion
astotherelativeinfluenceofheredityandenvironment
uponthegeneraldeathratemustapplywithequalforce
tothedurationoflife.
THESELECTIVEDEATHBATEINMAN
Ifthedurationo; lifewereinheriteditwouldlogical-
lybeexpectedthatsomeportionofthedeathratemust
beselectiveincharacter.Forinheritanceofduration
oflifecanonlymeanthatwhenapersondiesisinpart
determinedbythatindividual'sbiologicalconstitutionor
makeup.Andequallyitisobviousthatindividualsof
weakandunsoundconstitutionmust,ontheaverage,
dieearlierthanthoseofstrong,sound,andvigorouscon-
stitution."Whenceitfollowsthatthechancesofleaving
offspringwillbegreaterforthoseofsoundconstitution
thanfortheweaklings.Themathematicaldiscussion
whichhasjustbeengivenindicatesthatfromone-half
tothree-fourthsofthedeathrateisselectiveinchar-
acter,becausethatproportionisdeterminedbyhereditary
factors.Justinproportionashereditydetermines
thedeathrate,soisthemortalityselective.Therealityof
thefactofaselectivedeathrateinmancanbeeasily
showngraphically.
InFigure44areseenthegraphsofsomedatafrom
Europeanroyalfamilies,wherenoneglectofchildren,
12
pipeline_tag: sentence-similarity
library_name: sentence-transformers
metrics: cosine_accuracy, cosine_accuracy_threshold, cosine_f1, cosine_f1_threshold, cosine_precision, cosine_recall, cosine_ap, cosine_mcc
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name: Binary Classification
dataset: name: Unknown
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metrics: type: cosine_accuracy
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name: Cosine Ap
verified: no, type: cosine_mcc
value: 0.4793492257096312
name: Cosine Mcc
verified: no
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