Four thousand ships passed through the lock: Object-induced measure functions on events

1990 ◽  
Vol 13 (5) ◽  
pp. 487-520 ◽  
Author(s):  
Manfred K
Keyword(s):  
Induced Measure

scholarly journals Effective Action and Measure in Matrix Model of IIB Superstrings

1997 ◽  
Vol 12 (31) ◽  
pp. 2331-2340 ◽  
Author(s):  
L. Chekhov ◽  
K. Zarembo
Keyword(s):  
Matrix Model ◽  
Effective Action ◽  
Continuum Limit ◽  
Auxiliary Field ◽  
Large N ◽  
The Matrix ◽  
Reparametrization Invariance ◽  
The Continuum ◽  
Induced Measure

We calculate an effective action and measure induced by the integration over the auxiliary field in the matrix model recently proposed to describe IIB superstrings. It is shown that the measure of integration over the auxiliary matrix is uniquely determined by locality and reparametrization invariance of the resulting effective action. The large-N limit of the induced measure for string coordinates is discussed in detail. It is found to be ultralocal and, thus, is possibly irrelevant in the continuum limit. The model of the GKM type is considered in relation to the effective action problem.

scholarly journals A NOTE ON SIMULTANEOUS AND MULTIPLICATIVE DIOPHANTINE APPROXIMATION ON PLANAR CURVES

2007 ◽  
Vol 49 (2) ◽  
pp. 367-375 ◽  
Author(s):  
DZMITRY BADZIAHIN ◽  
JASON LEVESLEY
Keyword(s):  
Diophantine Approximation ◽  
Hausdorff Measure ◽  
General Class ◽  
Simultaneous Approximation ◽  
Convergence Result ◽  
Planar Curves ◽  
Planar Curve ◽  
Induced Measure

AbstractLet $\mathbb C$ be a non-degenerate planar curve. We show that the curve is of Khintchine-type for convergence in the case of simultaneous approximation in $\mathbb R^2$ with two independent approximation functions; that is if a certain sum converges then the set of all points (x,y) on the curve which satisfy simultaneously the inequalities ||qx|| < ψ1(q) and ||qy|| < ψ2(q) infinitely often has induced measure 0. This completes the metric theory for the Lebesgue case. Further, for multiplicative approximation ||qx|| ||qy|| < ψ(q) we establish a Hausdorff measure convergence result for the same class of curves, the first such result for a general class of manifolds in this particular setup.

scholarly journals Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Paul B. Slater ◽  
Charles F. Dunkl
Keyword(s):  
Hypergeometric Function ◽  
High Precision ◽  
Quantum States ◽  
Approximation Procedure ◽  
Density Approximation ◽  
Density Matrices ◽  
Qubit States ◽  
Induced Measure

Previously, a formula, incorporating a5F4hypergeometric function, for the Hilbert-Schmidt-averaged determinantal momentsρPTnρk/ρkof4×4density-matrices (ρ) and their partial transposes (|ρPT|), was applied withk=0to the generalized two-qubit separability probability question. The formula can, furthermore, be viewed, as we note here, as an averaging over “induced measures in the space of mixed quantum states.” The associated induced-measure separability probabilities (k=1,2,…) are found—viaa high-precision density approximation procedure—to assume interesting, relatively simple rational values in the two-re[al]bit (α=1/2), (standard) two-qubit (α=1), and two-quater[nionic]bit (α=2) cases. We deduce rather simple companion (rebit, qubit, quaterbit, …) formulas that successfully reproduce the rational values assumed forgeneral  k. These formulas are observed to share certain features, possibly allowing them to be incorporated into a single master formula.

Basins of measures on inverse limit spaces for the induced homeomorphism

2009 ◽  
Vol 30 (4) ◽  
pp. 1119-1130 ◽  
Author(s):  
JUDY KENNEDY ◽  
BRIAN E. RAINES ◽  
DAVID R. STOCKMAN
Keyword(s):  
Invariant Measure ◽  
Metric Space ◽  
Inverse Limit ◽  
Compact Metric Space ◽  
Srb Measure ◽  
Inverse Limit Spaces ◽  
Induced Measure

AbstractLet f:X→X be continuous and onto, where X is a compact metric space. Let $Y:=\invlim {X,f}$ be the inverse limit and F:Y →Y the induced homeomorphism. Suppose that μ is an f-invariant measure, and let m be the measure induced on Y by (μ,μ,…). We show that B is a basin of μ if and only if π−11(B) is a basin of m. From this it follows that if μ is an SRB measure for f on X, then the induced measure m on Y is an inverse-limit SRB measure for F. Conversely, if m is an inverse-limit SRB measure for F on Y, then the induced measure μ on X is an SRB measure for f.

Katok formula for the induced measure-theoretic entropy

2017 ◽  
Vol 33 (2) ◽  
pp. 195-206
Author(s):  
Zhitao Xing ◽  
Ercai Chen ◽  
Zheng Yin
Keyword(s):  
Induced Measure
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