Physics 8805: Nuclear Few- and Many-Body Physics
... with the numerical calculations!] (g) Extract the scattering lengths (and effective ranges, if possible) from the phase shift data for np scattering and compare to quoted answers. (h) Neutrons form Cooper pairs in neutron stars. At low densities/momenta, neutrons pair in the 1 S0 channel where the N ...
... with the numerical calculations!] (g) Extract the scattering lengths (and effective ranges, if possible) from the phase shift data for np scattering and compare to quoted answers. (h) Neutrons form Cooper pairs in neutron stars. At low densities/momenta, neutrons pair in the 1 S0 channel where the N ...
Logic in Proofs (Valid arguments) A theorem is a hypothetical
... A theorem is a hypothetical statement of the form H 6 C, where H is a (compound) statement which is taken as being true, and C is a statement which follows from H by logical reasoning. Example: [(p 6 q) v (q 6 r) v (¬ r)] 6 (¬ p) An argument in logic is a way to reach a conclusion based on prior sta ...
... A theorem is a hypothetical statement of the form H 6 C, where H is a (compound) statement which is taken as being true, and C is a statement which follows from H by logical reasoning. Example: [(p 6 q) v (q 6 r) v (¬ r)] 6 (¬ p) An argument in logic is a way to reach a conclusion based on prior sta ...
Computing Default Extensions by Reductions on OR
... the authors state a modal reduction theorem to the effect that a formula O Rϕ is logically equivalent to a disjunction Oϕ1 ∨ · · · ∨ Oϕn , where each ϕk is a propositional formula. Because each such disjunct Oϕ k has a unique model, it is possible, within the logic itself, to break down a formula O ...
... the authors state a modal reduction theorem to the effect that a formula O Rϕ is logically equivalent to a disjunction Oϕ1 ∨ · · · ∨ Oϕn , where each ϕk is a propositional formula. Because each such disjunct Oϕ k has a unique model, it is possible, within the logic itself, to break down a formula O ...
Binary Decision Diagrams for First Order Predicate Logic
... Proof: The transformation operators can be formulated as rewrite rules.l1 and l2 are ...
... Proof: The transformation operators can be formulated as rewrite rules.l1 and l2 are ...
full text (.pdf)
... Stockmeyer (1981) that PSPACE is equivalent to APTIME, so it suffices to give an alternating PTIME Turing machine to decide membership of sentences in R A N D O M (a). It is convenient to describe first an alternating PTIME algorithm which decides, for any g, any 0-description D(~), and any formula ...
... Stockmeyer (1981) that PSPACE is equivalent to APTIME, so it suffices to give an alternating PTIME Turing machine to decide membership of sentences in R A N D O M (a). It is convenient to describe first an alternating PTIME algorithm which decides, for any g, any 0-description D(~), and any formula ...
Chapter 3
... operations by obtaining a → b as the polynomial ab + a + 1 (where ab abbreviates a · b as usual). This equivalence can be seen either by exhaustively considering all four values for a and b, or by the reduction ab + a + 1 = a(b + 1) + 1 = ¬(a ∧ ¬b) = a→b. Zhegalkin polynomials. Unlike other moduli, ...
... operations by obtaining a → b as the polynomial ab + a + 1 (where ab abbreviates a · b as usual). This equivalence can be seen either by exhaustively considering all four values for a and b, or by the reduction ab + a + 1 = a(b + 1) + 1 = ¬(a ∧ ¬b) = a→b. Zhegalkin polynomials. Unlike other moduli, ...
In order to integrate general relativity with quantum theory, we
... used to index creation and annihilation operators representing particles (fields) with the quantum numbers described. The fundamental entities must be in the representation space of these operators and their Lie algebra. But while the known elementary particle states can easily be fit into this infi ...
... used to index creation and annihilation operators representing particles (fields) with the quantum numbers described. The fundamental entities must be in the representation space of these operators and their Lie algebra. But while the known elementary particle states can easily be fit into this infi ...
What is Reality? New Scientist
... countless possibilities where the particle could be at any moment, one is chosen, while all the others are rejected? First of all, we have to ask ourselves when this choice is made. In the example described above, it seems to happen just before the flash on the phosphor screen. At this moment, a mea ...
... countless possibilities where the particle could be at any moment, one is chosen, while all the others are rejected? First of all, we have to ask ourselves when this choice is made. In the example described above, it seems to happen just before the flash on the phosphor screen. At this moment, a mea ...
Scoring Rubric for Assignment 1
... Research selected is not relevant to the argument or is vague and incomplete – components are missing or inaccurate or unclear. Theory is not relevant or only relevant for some aspects; theory is not clearly articulated and/or has incorrect or incomplete components. Relationship between theory and r ...
... Research selected is not relevant to the argument or is vague and incomplete – components are missing or inaccurate or unclear. Theory is not relevant or only relevant for some aspects; theory is not clearly articulated and/or has incorrect or incomplete components. Relationship between theory and r ...
Answer Sets for Propositional Theories
... equivalent: (i) Γ1 is strongly equivalent to Γ2 , (ii) Γ1 is equivalent to Γ2 in the logic of here-and-there, and (iii) for each set X of atoms, Γ1X is equivalent to Γ2X in classical logic. The equivalence between (i) and (ii) is a generalization of the main result of [Lifschitz et al., 2001], and i ...
... equivalent: (i) Γ1 is strongly equivalent to Γ2 , (ii) Γ1 is equivalent to Γ2 in the logic of here-and-there, and (iii) for each set X of atoms, Γ1X is equivalent to Γ2X in classical logic. The equivalence between (i) and (ii) is a generalization of the main result of [Lifschitz et al., 2001], and i ...
PPT
... variables (letters upper/lower X, Y, Z, … A, B, C ) symbols , , ~, and parentheses ( , ) also we add two more , , • Propositional expressions (propositional forms) are formed using these elements of alphabet as follows: 1. Each variable is propositional expression 2. IF p and q are propositinal ...
... variables (letters upper/lower X, Y, Z, … A, B, C ) symbols , , ~, and parentheses ( , ) also we add two more , , • Propositional expressions (propositional forms) are formed using these elements of alphabet as follows: 1. Each variable is propositional expression 2. IF p and q are propositinal ...
Propositional/First
... • The 3rd sentence is entailed by the first two, but we need an explicit symbol, R, to represent an individual, Confucius, who is a member of the classes person and mortal ...
... • The 3rd sentence is entailed by the first two, but we need an explicit symbol, R, to represent an individual, Confucius, who is a member of the classes person and mortal ...
mathematical logic: constructive and non
... Applications of Gödel's completeness theorem to algebra were noted about 1946-7 by Tarski, Henkin and A. Robinson, and have been cultivated since. We have been supposing the number of symbols at most countably infinite, as must be the case of any language in actual use. However, Malcev (1936) extend ...
... Applications of Gödel's completeness theorem to algebra were noted about 1946-7 by Tarski, Henkin and A. Robinson, and have been cultivated since. We have been supposing the number of symbols at most countably infinite, as must be the case of any language in actual use. However, Malcev (1936) extend ...
notes
... Let P be a propositions containing the (distinct) atomic formulas A 1 , . . . , An and v1 , . . . v2n its interpretations. We denote with v P the boolean function associated with P , i.e. vP : {0, 1}n → {0, 1} is defined as follows: for each (a 1 , . . . , an ), ai ∈ {0, 1}, there exists i ∈ {1, . ...
... Let P be a propositions containing the (distinct) atomic formulas A 1 , . . . , An and v1 , . . . v2n its interpretations. We denote with v P the boolean function associated with P , i.e. vP : {0, 1}n → {0, 1} is defined as follows: for each (a 1 , . . . , an ), ai ∈ {0, 1}, there exists i ∈ {1, . ...
universality
... effective theories : where observations are made effective theory may involve different degrees of freedom as compared to microscopic theory example: microscopic theory only for fermionic atoms , macroscopic theory involves bosonic collective degrees of freedom ( φ ) ...
... effective theories : where observations are made effective theory may involve different degrees of freedom as compared to microscopic theory example: microscopic theory only for fermionic atoms , macroscopic theory involves bosonic collective degrees of freedom ( φ ) ...
Entanglement of Identical Particles
... particles is generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise. Because of the nature of quantum measurement, howe ...
... particles is generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise. Because of the nature of quantum measurement, howe ...
Mathematical Logic
... • Definition: Methods of reasoning, provides rules and techniques to determine whether an argument is valid • Theorem: a statement that can be shown to be true (under certain conditions) – Example: If x is an even integer, then x + 1 is an odd integer • This statement is true under the condition tha ...
... • Definition: Methods of reasoning, provides rules and techniques to determine whether an argument is valid • Theorem: a statement that can be shown to be true (under certain conditions) – Example: If x is an even integer, then x + 1 is an odd integer • This statement is true under the condition tha ...
Quantum Field Theory
... and make it “relativistic”. One obvious step is to replace non-relativistic kinematics by relativistic kinematics, but that is not enough. The famous relation E = mc2 allows mass to be converted to energy, which in its turn can be converted to masses of other particles. This allows the creation of p ...
... and make it “relativistic”. One obvious step is to replace non-relativistic kinematics by relativistic kinematics, but that is not enough. The famous relation E = mc2 allows mass to be converted to energy, which in its turn can be converted to masses of other particles. This allows the creation of p ...
Normal modal logics (Syntactic characterisations)
... a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ simply when A ∈ Σ. Which closure conditions? See below. Systems of modal logic can also be defined (syntactically) in other ways, usually by reference to some kind of proof system. For example: • Hilber ...
... a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ simply when A ∈ Σ. Which closure conditions? See below. Systems of modal logic can also be defined (syntactically) in other ways, usually by reference to some kind of proof system. For example: • Hilber ...