The Proof Complexity of Polynomial Identities
Pavel Hrubes
Iddo Tzameret
Abstract
Devising an efficient deterministicor even a non-deterministic sub-exponential time
algorithm for testing polynomial identities is a fundamental problem in algebraic complex
Joacim Rocklv
Judit Simon
Gteborgs Universitet 2005
0
Abstract.2
1.
Introduction.3
1.1
1.2
2
An introduction to Gibbs free energy.4
The balance between synthesis and hydrolysis of ATP.5
Molecular motors of ATPase.7
2.1
2.2
2.3
3
Modeling the chemical reac
Fundamentals of Thermodynamics
Chapter 14
Phase and Chemical Equilibrium
Chapter 14. Phase and Chemical Equilibrium
14.1 Requirements for equilibrium
- equilibrium quasi - equilibrium
- equilibrium : surrounding
work
- system subsystems Fig. 16.1
- 1st
Energy
Heat
Work
Heat Capacity
Enthalpy
1
Prof. Zvi C. Koren
20.07.2010
Thermodynamics vs. Kinetics
Thermo
Thermodynamics = Thermo + Dynamics
E
(Note: Absolute E can never be determined by humans!)
Can a reaction occur? (Is it spontaneous)?
Kinetics
Diam
Chemistry 202/212
Worksheet 10
Winter 2005
February 3
1. The following data are for the system:
Time (s)
PA (atm)
PB (atm
0
1.00
0.00
20
0.83
0.34
Oregon State University
A(g) 2 B(g)
40
0.72
0.56
60
0.65
0.70
80
0.62
0.76
100
0.62
0.76
(a) How long does i
Exercise 7.4A Problem 1
Correct! Argument is invalid!
Your abbreviated truth table is correct! Row 1 shows that the premises are all
true and the conclusion is false when statement letter A is assigned F, B is
assigned T, and C is assigned F, so you have
Exercise 7.3A
Argument is valid!
You are correct! The argument is valid. There is no row on which the premises
are all true and the conclusion is false.
Your truth table:
A B | A B, ~A B
-|-T T |
T
F
T
T F |
T
F
F
F T |
T
T
T
F F |
F
T
F
Argument is valid
Introduc+on to Discrete Mathema+cs
Course Outline
Prof. G. Kesidis, instructor
1
Course Outline
Introduction to logic
Introduction to methods of proof
Sequences and induction
Introduction to set theory
Counting and probability discrete random variabl
Exercise 1.3
Part A: Counterexamples
1. Lewis is a famous author only if he knows how to write. But
Lewis is not a famous author. So, Lewis does not know how to
write.
Your answer of `DA: denying the antecedent' is correct!
3. Rilke is a dreamer if he is
Exercise 6.1A
1. 1. Some works of art are books. 2. All novels are books. So, 3.
Some works of art are novels.
Your answer of `Not standard' is correct!
3. 1. All movies are films. 2. Some documentaries are not movies.
So, 3. Some documentaries are not fi
Exercise 2.1 A
1. Americans are materialistic because they are exposed to more
advertising than any other people on earth.
Your answer of `nonargument (explanation)' is correct!
3. The world fish catch dropped from its 1989 high of 100 million
tons to 97
Exercise 5.1A
1. All hungry cannibals are dangerous people
Your answer of `A' is correct!
Your answer of `Universal' is correct!
Your answer of `Affirmative' is correct!
3. Some diamonds are not valuable objects
Your answer of `O' is correct!
Your answer
Exercise 4.1A
1. To put it bluntly but fairly, anyone today who doubts that the
variety of life on this planet was produced by a process of
evolution is simply ignorant inexcusably ignorant.
Your answer of `Argument against the person' is correct!
3. As I
Exercise 7.4A Problem 1
Correct! Argument is invalid!
Your abbreviated truth table is correct! Row 1 shows that the premises are all
true and the conclusion is false when statement letter A is assigned F, B is
assigned T, and C is assigned F, so you have
Evaluation of your answers from Section 7.1A
The Logic Tutor responds:
1. (A
B C)
Your answer of `Not a WFF' is correct!
2. (~B)
Your answer of `Not a WFF' is correct!
3. (~(C)
F)
Your answer of `Not a WFF' is correct!
4. (E
(~F G)
Your answer of `Not
Exercise 7.3A Problem 1
Argument is valid!
You are correct! The argument is valid. There is no row on which the premises
are all true and the conclusion is false.
Your truth table:
A B | A B, ~A B
-|-T T |
T
F
T
T F |
T
F
F
F T |
T
T
T
F F |
F
T
F
Exercis
Exercise 1.2
Part A: True or False?
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
True
True
True
False
False
True
True
True
True
True
True
False
True
True
False
Part B: Identify the Forms
1.
A
B
If the solution turns blue litmus paper red, then t
Exercise 1.3
Part A: Counterexamples
1. Denying the antecedent
3. Unnamed invalid form
5. Denying the antecedent
7. Unnamed invalid form
9. Affirming the consequent
11. Denying the antecedent
13. Unnamed valid form
15. Unnamed valid form
17. Unnamed valid