CHAPTER 20- The Cardiovascular System: The Heart
Choose the single best answer to each of the following questions.
1) The heart
A) lies just inferior to the diaphragm.
B) lies lateral to the lungs.
C) lies within the mediastinum
D) lies anterior to the st
Chapter 24: Digestive System
Multiple Choice
1.
Which of the following is a function performed by the digestive system?
A)
cellular respiration
B)
food selection
C)
elimination of undigested food
D)
regulation of blood pH
E)
integration and coordination o
Chapter 21: Cardiovascular System: Peripheral Circulation
and Regulation
Multiple Choice
1.
Systemic blood vessels transport blood
A)
from the left ventricle through the body to the left atrium.
B)
from the left ventricle through the body to the right atr
Chapter 17: Functional Organization of the Endocrine System
Multiple Choice
1.
The endocrine system
A)
releases neurotransmitters into ducts.
B)
secretes chemicals that reach their targets through the bloodstream.
C)
communicates via frequency-modulated s
232
SOLUTIONS TO EXERCISES
null hypothesis of equality of the proportions, the estimate of the common proportion
becomes p = 104 + 226 443 = 0 745. The estimate of V p1 p2 is pq
1 n1 + 1 n2 = 0 0019. Now, S E p1 p2 = 0 0436 and z = 0 085 0 0436 =
1 95. Th
1.2 Examples and exercises
7
of x such that sx T plus one (to cater for the edge back towards the root), or
just the number of such x if s is the root node.
Exercise 1.12 Prove the following generalisation of Konigs Lemma: an infinite tree in which every
Contents
Preface
How to read this book
page vii
xii
1
Konigs Lemma
1.1
Two ways of looking at mathematics
1.2
Examples and exercises
1.3
Konigs Lemma and reverse mathematics*
1
1
6
9
2
Posets and maximal elements
2.1
Introduction to order
2.2
Examples and
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The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
ww
6
Konigs Lemma
Proof Suppose T is an infinite binary tree. For a sequence s of length n let
Ts be cfw_r T : r ! n = s cfw_s ! k : k < n, which we will call the subtree of T
below s. You will be able to check easily that Ts is a tree. In general it may or
12
Posets and maximal elements
There is another kind of partial order relation corresponding to ! instead of
<. Here, the order relation is allowed to relate equal elements. In other words,
we will allow (x, x) R to be true. (This was explicitly disallowe
The Mathematics of Logic
A guide to completeness theorems and their applications
This textbook covers the key material for a typical first course in logic for
undergraduates or first year graduate students, in particular, presenting a
full mathematical ac
x
Preface
b < c then a < c. The system also has a way of expressing statements of the
form a is not less than b, and this is handled using a Reductio Ad Absurdum
Rule, a rule that is used throughout the rest of the book. By this stage, it
should be clear
266
INDEX
left-sided alternative hypotheses tests
and estimated variance, 7172
and means
null hypothesis, 69
power of the test, 7071
p-value, 70
sample size, 71
proportions and percentages
critical region, 8586
power of the test, 86
p-value, 86
sample siz
Preface
xi
The method of proof of the Completeness Theorem is by Henkinising the
language and then using Zorns Lemma to find a maximal consistent set of
sentences. This is easier to describe to first-timers than tree-constructions of
sets of consistent se
Preface
ix
Thus logic is not only about such connectives as and and or, though the
main systems, including propositional and first-order logic, do have symbols
for these connectives. The power of the logical technique for the mathematician arises from the
1.1 Two ways of looking at mathematics
5
Definition 1.5 A tree is a set of sequences T such that for any s T of length
n and for any l < n then s ! l T .
Think of a sequence s T as a finite path starting from the root and arriving
at some node. The indivi
256
APPENDIX TABLES
Table T10.1 (b)
Age
Weight
Fit
LDL
HDL
Table T10.1 (c)
Age
Weight
Fit
LDL
HDL
Variances and Covariances of the measurements.
Age
Weight
Fit
LDL
HDL
126.20
124.36
250.66
328.82
42.16
224.35
171.71
501.11
69.48
746.05
534.47
83.68
1566.0
4
Konigs Lemma
information, and one working from the point of view of much more limited information, and shows that they actually say the same thing.
As with all if and only if theorems, there are two directions that must be
proved. The first, that if the
8
Konigs Lemma
Now consider infinite sequences u0 u1 u2 . . . of the digits 0, 1, 2, . . ., k 1. We
will call such sequences k-sequences. Say a k-sequence s is xn -free if there is
no finite sequence, x, of digits 0, 1, 2, . . ., k 1, such that the finite
10
Konigs Lemma
and in any case there are likely to be choices involved. In our proof of Konigs
Lemma, to keep track of all these individual choices, we used the concept of a
certain subtree Ts being infinite. Being infinite is of course a powerful mathem
III. 1. PARAMETERS, GENERATING FUNCTIONS, AND DISTRIBUTIONS
117
0.3
0.25
0.2
0.15
0.1
0.05
0
0.2
0.4
0.6
0.8
1
F IGURE 3. Plots of the binomial distributions for
. The
horizontal axis is normalized and rescaled to , so that the curves display
, for
.
It e
III. 4. RECURSIVE PARAMETERS
135
there immediately results that
(31)
(Distribute nodes in their corresponding subtrees: distances to the subtree roots must be
corrected by 1; regroup terms.)
From this point on, we specialize the discussion to general plan
Bibliography
1. Alfred V. Aho and Margaret J. Corasick, Efficient string matching: an aid to bibliographic search, Communications of the ACM 18 (1975), 333340.
2. David Aldous and Persi Diaconis, Longest increasing subsequences: from patience sorting to t
INDEX
nonplane tree, 4647, 89
(asymptotic notation), 166
(asymptotic notation), 166
OGF, see ordinary generating function
order constraints (in constructions), 98105, 149
151
ordinary generating function (OGF), 4
outdegree, see degree (of tree node)
pairi
III. 3. INHERITED PARAMETERS AND EXPONENTIAL MGFS
127
constructions stated in Theorem II.1 apply provided the multi-index convention (22) is
used. The associated operators on exponential MGFs are then:
Union:
Product:
Sequence:
Cycle:
.
Set:
P ROOF. Disjo
A. AUXILIARY RESULTS & NOTIONS
173
7. Stirling numbers. These numbers count amongst the most famous ones of combinatorial analysis. They appear in two kinds:
the Stirling cycle number (also called of the first kind)
enumerates permutations of size having
III. 2. INHERITED PARAMETERS AND ORDINARY MGFS
119
With a natural extension of the notation used for constructions, one shall write
For instance, the class of natural numbers,
has OGF
.
Let be the parameter that takes the constant value 1 on all elements