Ampliation

Definitions

  • Webster's Revised Unabridged Dictionary
    • Ampliation (Civil Law) A postponement of the decision of a cause, for further consideration or re-argument.
    • Ampliation Enlargement; amplification.
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Century Dictionary and Cyclopedia
    • n ampliation Enlargement; amplification.
    • n ampliation In Roman law, a delaying to pass sentence; a postponement of a decision in order to obtain further evidence.
    • n ampliation In logic, such a modification of the verb of a proposition as makes the subject denote objects which without such modification it would not denote, especially things existing in the past and future. Thus, in the proposition, “Some man may be Antichrist,” the modal auxiliary may enlarges the breadth of man, and makes it apply to future men as well as to those who now exist.
    • n ampliation In French law: A duplicate of an acquittance or other instrument.
    • n ampliation A notary's copy of acts passed before him, delivered to the parties.
    • n ampliation In medicine, dilatation or distention of a canal or cavity.
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Chambers's Twentieth Century Dictionary
    • Ampliation enlarging, an enlargement
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Etymology

Webster's Revised Unabridged Dictionary
L. ampliatio,: cf. F. ampliation,
Chambers's Twentieth Century Dictionary
Fr.—L. amplus, large.

Usage

In literature:

Hence such a proposition has been called ampliative.
"Logic" by Carveth Read
Ampliate -us: moderately dilated.
"Explanation of Terms Used in Entomology" by John. B. Smith
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In science:

We denote all scalar products by h., .i and identify operators and their ampliations if no confusion arises.
Filtered random variables, bialgebras and convolutions
Xk (σ) ⊗ 1⊗∞)(P (σ)⊗(l−1) ⊗ 1 ⊗ P (σ)⊗∞) of an ampliation of Xk (σ) into bB⊗∞ and a pro jection indexed by σ .
Filtered random variables, bialgebras and convolutions
X = X(l, k) is the (l, k)-th ampliation of x ∈ Al into bA1 and P = P(l, σ), where l ∈ L, k ∈ N, σ ∈ P (N).
Filtered random variables, bialgebras and convolutions
This is exactly what is not true of ampliative inference, and it is what has led some writers (e.g., [Morgan, 1998]) to deny that there is any such thing as a nonmonotonic logic.
Evaluating Defaults
For m ≥ 0, let us consider the ampliation of the maps Θ, b and β as maps from A N B(Γfr( ˆk0 )) into itself.
Quantum random walks and their convergence
B ) given by the generators of the ν : B 7→ B δµ quantum Itˆo equation (3.2) and ıµ ν is the ampliation of B .
Quantum Stochastic Positive Evolutions: Characterization, Construction, Dilation
The w*-representation  : B → L (G ) of B = L (H) is always an ampliation  (B ) = B ⊗ J , where J is an orthopro jector onto a subspace K1 ⊆ K, corresponding to the minimal dilation in G1 = H ⊗ K1 .
Quantum Stochastic Positive Evolutions: Characterization, Construction, Dilation
The algebra B = L (H) is represented on G by the ampliation (B ) = B ⊗ J, where J = 1 ⊕ J ⊕ 1, and (B ) Lgη ∈ G ◦ , where the pre-Hilbert space D ⊕ D• is isometrically embedded into D ⊕ D• ⊕ D as g (η ⊕ η• ) = 0 ⊕ η• ⊕ η .
Quantum Stochastic Positive Evolutions: Characterization, Construction, Dilation
It is shown that although the spectrum of the analytic generator of a one– parameter group of isometries of a Banach space may be equal to C (cf [VD] and [ElZs]), a simple operation of ampliating the analytic generator onto its graph locates its spectrum in IR+ .
A remark on the spectrum of the analytic generator
We denote by Un the natural ampliation of U to H0 ⊗ T Φ where Un acts as U on the tensor product of H0 and the n-th copy of H and U acts as the identity of the other copies of H.
Repeated Quantum Interactions and Unitary Random Walks
We denote by ai j (n) their natural ampliation to T Φ acting on the n-th copy of H only.
Repeated Quantum Interactions and Unitary Random Walks
Let H(∞) = H ⊗ ℓ2 be the infinite ampliation of H.
Conjugate Dynamical Systems on C*-algebras
When the random-walk generator acts by ampliation and multiplication or conjugation by a unitary operator, necessary and sufficient conditions are given for the quantum stochastic cocycle which arises in the limit to be driven by an isometric, co-isometric or unitary process.
Quantum random walks and thermalisation II
It suffices to show that PxLGPx is unitarily equivalent to an ampliation of Ln , such that generators are mapped to generators.
Isomorphisms of algebras associated with directed graphs
If α is a cardinal number, we let H α denote the direct sum of α copies of H , and for x ∈ B(H ), we let x ⊗ 1α be the ampliation of x acting on H α .
Local Operator Multipliers and Positivity
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