CA 16-7
Dear Mr. Dolan:
I hope that the following brief explanation helps you understand why your warrants were not included in
Rhodes earnings per share calculations.
Earnings per share (EPS) provides income statement users a quick assessment of the earn
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A Treatise on Quantum Clifford Algebras
The particular functions of BIGEBRA are described below very shortly to give an overview.
For detailed help-pages and much more detailed examples use the Maple online help by typing
?Bigebra,<function>.
A.3.1
&c
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OF
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KONSTANZ
> X; # general element; dim_V = 2
X 1 Id + X 2 e1 + X 3 e2 + X 4 e1we2
27
> sol:=map(allvalues,clisolve(cmul(X,X)-X,X);
1
1
Id +
2
2
1
1
Id + X 2 e1 +
2
2
1
1
Id + X 2 e1
2
2
sol := [0, Id ,
28
29
1 + 4 X
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139
of approx. 150 help-pages, we stay with those features which were actually used in this work
and which were essential for the development and design of the BIGEBRA package. The latest
version of CLIFFORD is Cl
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holds. From 2 = 0 we nd a parabola in our diagram, which connects the Fock and dual Fock
states and shows that these states are quasi free too. Having no higher correlations means that
there is no interaction,
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A Treatise on Quantum Clifford Algebras
a single counterexample can put down the whole business immediately. This might look
distracting but saves a tremendous amount of work, since only such assertions remain for
being proved which are already tested
Appendix A
CLIFFORD and BIGEBRA packages for
Maple
A.1 Computer algebra and Mathematical physics
Computer algebra was a major tool to investigate the topics which have been presented in this
work. We had the opportunity to state even some theorems which w
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A Treatise on Quantum Clifford Algebras
We draw a diagram, see Figure 8.1, where every point in the afne Euclidean plane corresponds
to a state w . The positive states form a triangle. We want to discuss the states in and on the
borders of the triangl
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A Treatise on Quantum Clifford Algebras
values
w (Id) = 1
w (a1 a ) =
1
w (a2 a ) =
2
w (a1 a2 a a ) = w.
2 1
(8-62)
This is the result of Kerschner [79], which he obtained by C -algebraic considerations. However,
note that the above basis is not an
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A Treatise on Quantum Clifford Algebras
which is two dimensional, and in fact a spinor representation. However, our treatment is totally
arbitrary w.r.t. the name of the operators, and we could have introduced a dual Fock space
demanding that
a |0
F
=
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KONSTANZ
If we are interested in the normal-ordered energy equation, where only the fermions are normalordered, we have to add the propagator term in the Clifford map for the fermionic eld operators
and get as result
E
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KONSTANZ
therefore a parameter , which represents the antisymmetric part, in the following way
0
0 1
= 1 2 +
0
1 0
2
[B ] =
1
2
= [g] + [F ].
0
1 +
2
0
(8-50)
This form is chosen for convenience to be able to make con
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A Treatise on Quantum Clifford Algebras
The crucial point is to investigate what kind of physical reason is behind this additional
reordering. There are two possibilities:
(i) Since usually one reorders by the free propagator and not w.r.t. the exact
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A Treatise on Quantum Clifford Algebras
for bosons and fermions
cfw_I1 , I2 t := AI1 I2 = C0 1(r1 r2)
+
i)
[BK , I ]t := 0
ii)
[BK1 , BK2 ]t =: CK1 K2 .
iii)
(8-41)
The second equation states that the bosons are considered to be elementary and are not
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A Treatise on Quantum Clifford Algebras
the algebra morphism which transformes from time- to normal-ordering by changing the basis
from the wedge to the dotted wedge basis
N (u v) = N (u) N (v).
(8-33)
Applying this operation to a time ordered functio
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KONSTANZ
A.3.15 gswitch graded (i.e. Gramann) switch
The graded switch is the natural switch of the Gramann Hopf gebra. It is not the generic switch
of a Clifford algebra if the bilinear form is not identical zero. The
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A Treatise on Quantum Clifford Algebras
A.3.19 make BI Id cup tangle need for &cco
This function computes the cap tangle for a certain co-scalar product either unassigned or dened
as a matrix named BI. See either &cco above or the online help-page of
FINANCIAL REPORTING PROBLEM
(a) 1.
Under M&Ss share-based compensation plan 7,716,437 options were
granted during 2008.
2.
At March 29, 2008, 948,372 options were exercisable by eligible
managers.
3.
In 2008, 10,212,015 options were exercised at an averag
CA 16-4
(a)
Generally, the requirements indicate that employee share options be treated like all other types of
compensation and that their value be included in financial statements as part of the costs of employee
services. This requires that all types o
CA 16-4 (Continued)
Neutrality does not mean that accounting should not influence human behavior. We expect that
changes in financial reporting will have economic consequences, just as economic consequences
are inherent in existing financial reporting pra
CA 16-3 (Continued)
(b)
Because the purpose of issuing warrants to existing shareholders is to raise new equity capital,
the price specified in the warrants must be sufficiently below the current market price to
reasonably assure that they will be exercis
SOLUTIONS TO CONCEPTS FOR ANALYSIS
CA 16-1
(1)
Both convertible debt and debt issued with share warrants are accounted for as compound
instruments. IFRS requires that compound instruments be separated into their liability and equity
components.
Debt issue
TIME AND PURPOSE OF CONCEPTS FOR ANALYSIS
CA 16-1 (Time 1520 minutes)
Purposeto provide the student with an opportunity to answer a variety of questions related to convertible
debt versus debt with share warrants, adjusting compensation expense for share
CA 16-6
(a)
Earnings per share, as it applies to a corporation with a capitalization structure composed of only one
class of ordinary shares is the amount of earnings applicable to each ordinary share outstanding
during the period for which the earnings a
PROBLEM 16-8 (Continued)
EPS calculations =
Net income Preference dividends
Weighted-average ordinary shares
Preference dividends = 40,000 X $100 X .06 = $240,000
Extraordinary loss
per share calcuation
=
Loss
Weighted-average ordinary shares
1
($840,000
PROBLEM 16-8
(a)
Total as of June 1, 2009
Issue of September 1, 2009
Total as of May 31, 2011
Weighted-Average Shares
Before Share
After Share
Dividend
Dividend
1,000,000
1,200,000
400,000
480,000
1,400,000
1,680,000
1. 1,200,000 X 3/12 =
1,680,000 X 9/12
PROBLEM 16-6
(a) The number of shares used to compute basic earnings per share is
4,951,000, as calculated below.
Dates
Shares
Fraction
Event
Outstanding
Outstanding Restatement
of Year
Beginning Balance,
including 5% share
dividend
Jan. 1Apr. 1
2,100,000