FIGURE P7.26 THE CH07_SALECO DATABASE
26. Write a query to count the number of invoices.
27. Write a query to count the number of customers with a customer balance over $500.
28. Generate a listing of all purchases made by the customers, using the output
FIGURE P7.26 THE CH07_SALECO DATABASE
26. Write a query to count the number of invoices.
SELECT COUNT(*) FROM INVOICE;
27. Write a query to count the number of customers with a customer balance over $500.
SELECT COUNT(*)
FROM
CUSTOMER
WHERE CUS_BALANCE >5
Discrete Mathematics I
MATH/CSCI 2112 Assignment 3
Due: 12 Oct 2016/Start of Class
#(1), #(2), #(3) Problems 7, 8 & 9 from A2.
#(1) A chess club has 2n members. They need to pair up the members for chess matches.(i)
In how many ways can they pair up all t
Exercise questions for Lab 5
Use the schema given below as a basis for Questions 1 to 5
CREATE SCHEMA SALECO;
CREATE TABLE CUSTOMER (
CUST_NUM
INT PRIMARY KEY,
CUST_LNAME VARCHAR(20),
CUST_FNAME VARCHAR(20),
CUST_BALANCE
NUMERIC(8,2);
CREATE TABLE CUSTOME
Dalhousie University Faculty of Computer Science
Introduction to Computer Organisation with Assembly
Assignment 3 Solution
Due: 20 Oct 2016
(1) Use an appropriately sized decoder and OR gates, to implement a full adder.
Soln: First, you need to consider t
Dalhousie University Faculty of Computer Science
Introduction to Computer Organization with Assembly
Assignment 1 Solutions
Due: 29 Sept 2016
(1) Suppose the LMC had been implemented as a 16-bit binary machine. Assume that
this binary machine provides the
Discrete Mathematics I MATH/CSCI 2112
Lec 24/10 and 26/10 Number Theory 2/gcd
To work out an algorithm to compute the gcd(m, n), we need two lemmae:
lemma (Latin for something one assumes).
Lemma 1 If r > 0; gcd(r, 0) = r
Lemma 2 For a, b Z+ , let a = bq
Dalhousie University Faculty of Computer Science
Introduction to Computer Organization with Assembly
Assignment 2 Solutions Due: Thursday 13 Oct 2016
(1) The imprecision of floating-point arithmetic can have disastrous consequences if not
understood. On F
Discrete Mathematics I MATH/CSCI 2112 Lec. 10 21 Oct Proofs 2
Intro. to Number Theory
Defn: Q indicates the set of all Rational numbers.
Defn: x Q p, q Z, (q 6= 0) 3 x = p/q
Defn: A ratio p/q is in its lowest form iff there is NO integer d such that xd/yd
Discrete Mathematics I MATH/CSCI 2112
Assignment 3 Due Fri 23 Oct 2016
(1) (a) Let n N. Which is larger:
n
X
2n + 1
r=0
answer.
r
or
2n+1
X
j=n+1
Fall 2016
2n + 1
? Prove your
j
ANSWER:
We expand the terms of each summation, except that we (i.e. me and m
Note that the angle is a complex
number. Note importantly that the
diffractive effects of dichroism enter solely
via the complexification i, and
therefore vanish in the focal image plane
= 0. 4.3.1 Conical refraction complexified
The optical path length
theory, but at the end of this section we
will briefly consider the extreme case, in
which dichroic anisotropy dominates over
birefringent anisotropy and Hamiltons
cone becomes imaginary. Combined with
biaxiality the paraxial effect of the crystal is
ther
(dashed curves), for the 0 values
indicated. 4.5.5 Torque on the crystal The
change in angular momentum associated
with conical diffraction must be
accompanied by a torque on the crystal
that conserves momentum. This tends to
rotate the crystal about the
yielding the optic axis formulae (4.2.51)
without any complexification. As in the
nonchiral case, the axial intensity is
preserved when the optic axis bifurcates
into branch axes. 124 The Phenomena of
So-Called Conical Diffraction 4.5 Angular
Momentum in
consider only a gaussian incident beam, for
which P = 1 2 and we can write Jorb = 1 2
Jinc 1 e 2 2E1 2 + F (0, ) Jsp =
Jince 2 2E1 2 + F (0, ) , (4.5.7) in
terms of the exponential integral E1 (x)
Z x dss1 e s , (4.5.8) and an integral F
(0, ) 2 Z ds s 2
ring is not perfectly circular and a simple
analytic expression is lacking. 30/2 (a) (b)
(c) u (d) Figure 4.38: Chiral transition:
logarithmic density plot of wave intensity
in the = 0/3 plane with 0 = 50, = 1,
and values: (a) 0, (b) 1, (c) 2, (d) 5. The
the two dimensional integrals (4.1.4)
prevents any exact simulations for a
pinhole beam being presented here, and
our investigation will have to rely on
asymptotic techniques. This will be
remedied in section 4.3.3 for a gaussian
beam, where the complex r
the caustic surface and the cusp under
dichroism, features that must be
understood in terms of Stokes sets. In
particular the anti-Stokes sets have already
been seen to dominate over focal features
when absorption is present. The most
striking feature of
adsorption ring, where higher order
endpoint interference is visible. The dark
anti-Stokes ring crosses the axis at r .
The most severe divergence of the
asymptotic expansion with endpoint
contributions is on the complexified
Hamilton dark ring (the lines
sec2 1 2 tan 1 2 . (4.3.26) The
polarisation differs from the transparent
pattern most greatly near the anti-Stokes
surface (4.3.17), becoming quite intricate,
and we will not study it further here. 4.3.3
Gaussian beams and the transition to
double refrac
figure 4.44 shows how, at a typical value of
, the transparent features of the bright
Airy rings associated with the caustic, and
the axial focal spike, are swamped by
exponential damping as dichroism
increases. Finally, figure 4.45 shows the
geometric in
focusing now occurs along the branch
points of the complex transverse position
vector, which we call the branch axes, =
0 = b e3 . (4.3.14) Thus the
familiar bright axial spike is spread out
along a branch cut of . Antifocusing will
occur where | 0|, or e
company Vision Crystal Technology AG
(Goexe, Germany), to experimentally test
the theory in section 4.1 and demonstrate
the ease with which the asymptotic
phenomena can be observed. The crystal is
of good optical quality, cut to a thickness
of 25mm along
4.49. This compares well to the theoretical
transition in 130 The Phenomena of SoCalled Conical Diffraction laser beam
biaxial crystal z image lens object lens
polariser Figure 4.48: Observing conical
diffraction: a collimated circularly polarised
laser b
Somewhat surprisingly, this accuracy of the
geometric approximation in the presence
of dichroism allows it to describe the axial
shoulders faint interference rings
decorating the axial spike given in a
transparent medium by (4.1.42), and here
manifesting
images calculated from the exact integrals,
showing that the branch axis divergence is
smoothed away by diffraction. In a
constant plane, such as an image screen,
these appear as darker spots decorating
the already dark ring, shown in figure
4.31(b). The
constituting the intersection of the
unresolved conical diffraction cylinders
with the eye, appearing in the focal image
plane approximately halfway through the
crystal. The phenomenon viewed in this
manner must be reminiscent of that seen
by Lloyd during
singularities, and this is the effect of wave
interference. Figure 4.33(d) shows this
more clearly: the remnants of the
secondary inner rings are visible out- 108
The Phenomena of So-Called Conical
Diffraction side the anti-Stokes ring. This
occurs in the
polarisations degenerate, remaining linear
but ultimately exhibiting the same
polarisation as each other, which rotates a
half-turn in a circuit of the optic axis. This
is observed by passing the exit 4.6
Observations of Biaxial Conical Diffraction
131 be
0 2 e 2p 2 0 2 a ip0 2
cosh 2p0 . (4.3.37) In contrast with the
bright and dark cylinders that characterise
transparent conical diffraction, this
predicts one expanding bright cone of light
beyond the crystal, due to a sort of antifocusing of absorbative