The Enigma of Probability and Physics

Abstract

Objects 1.4. Measure of a Set of Concrete Objects 1.5. Experimental Determination of the Measures of Sets of Concrete Objects 1.6. The Statistical Method 1 .7. Pro ba bili ty. Preliminary Consideration 1.8. Mutually Adequate Sets 1.9. Probability. General Definition Problems 31 Suggested References 31 Chapter 2/ Main Theorems 2.1. Sum and Product of Events 2.2. Addition Theorem 2.3. Multiplication Theorem 2.4. Sequence of Random Tests 2.5. Law of Large Numbers 2.6. Limiting Cases of Binomial Law Problems

Quantum Measurements and Decoherence

“…7 The width of this function corresponds to the resolution of the measurement. It is a characteristic function of the measurement and may, for example, be (and typically is) a Gaussian function.…”

Introduction to Soliton Theory: Applications to Mechanics

“…p p rG HG l ) , (7.5.4) where is the blood flux entering from the i-th to j-th segment, respectively, the blood flux getting out j-th segment to k-th segment, the hydrodynamic resistance, l the blood inertia, (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,1)…”

“…If we introduce the continuous variablesˆ andˆ 1 1 n , 2 2 n , (10.6.40) for small , we have the Taylor series , 1, i i 2 In terms of the physical variables, the Bäcklund transformation yields the discrete equations Faddeev condition 5, 13 Fermi,Pasta and Ulam problem 82,107,159,173,191 Fitness function 207,208,250,266,267 Fliess expansions 34 Flow velocity 220,221,224,228,229,234,235,238,239,240 5,7,8,10,12,17,90,95,100,101,103 Gaussian curvature 41,273,291,292,294 Gauss equation 294 Gaussian function 57 Genetic algorithm 197,204,207,208,209,251,252,201 Group of symmetry 53,62,63,64,65,…”

Stochastic foundations of the universal dielectric response

“…Since the experiment probes the ensemble average in the sense that only the net effect of a large number of contributions from different relaxing entities within a sample is measured, in theoretical attempts to explain the observed relaxation laws it is unanimously assumed that they correspond to a kind of general behaviour which is independent of the details of the systems examined. The relaxation process results from an appropriate configuration of the system, imposed by nonequilibrium constraints at time t = 0, and is conditioned by specific interactions of different parts of the system [21,23,26,28]. Both the initial nonequilibrium state of a complex system and the internal interactions have, in general, random characteristics.…”