Given a sequence of sets An ⊆ {0, . . . , n − 1}, the Furstenberg correspondence principle provides a shift-invariant measure on 2 that encodes combinatorial information about infinitely many of the An’s. Here it is shown that this process can be inverted, so that for any such measure, ergodic or not, there are finite sets whose combinatorial properties approximate it arbitarily well. The finit...

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck used Bohr’s correspondence principle and Einstein’s quantum theory of radiation to find quantum formulae for the emission, absorption, and dispersion of radiation. The paper is similar but...

Previous research on the redundancy principle in multimedia learning has shown that although exact correspondence between on-screen text and narration generally impairs learning, brief labels within an animation can improve learning. To clarify and extend the theoretical and practical implications of these results, the authors of the present research examined the extent to which varying degrees...

The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz variation principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn variation principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Hav...

1. Introduction. Idempotent Mathematics is based on replacing the usual arithmetic operations by a new set of basic operations (e.g., such as maximum or minimum), that is on replacing numerical fields by idempotent semirings and semifields. Typical (and the most common) examples are given by the so-called (max, +) algebra R max and (min, +) algebra R min. Let R be the field of real numbers. The...

An orthodox formulation of quantum mechanics relies on a set postulates in Hilbert space supplemented with rules to connect it classical such as quantisation techniques, correspondence principle, etc. Here we deduce qubit and its dynamics straightforwardly from discrete deterministic conservation the collision entropy. No is required although can be inferred this approach if necessary.

We study principles of the form: if a name σ is forced to have certain property φ, then there ground model filter g such that σg satisfies φ. prove general correspondence connecting these forcing axioms. Special cases main theorem are: Any axiom can be expressed as principle. For instance, PFA equivalent to: A principle for rank 1 names (equivalently, nice names) subsets ω1. 2 sets reals. λ-bou...

A fast multipole formulation for 2D linear viscoelastic problems is presented in this paper by incorporating the elastic–viscoelastic correspondence principle. Systems of multipole expansion equations are formed and solved analytically in Laplace transform domain. Three commonly used viscoelastic models are introduced to characterize the time-dependent behavior of the materials. Since the trans...

During the last twenty-five years evidence has been mounting that a blackhole surface area has a discrete spectrum. Moreover, it is widely believed that area eigenvalues are uniformally spaced. There is, however, no general agreement on the spacing of the levels. In this letter we use Bohr’s correspondence principle to provide this missing link. We conclude that the area spacing of a black-hole...

A review is made of recent efforts to find relations between the commutation relations which define a noncommutative geometry and the gravitational field which remains as a shadow in the commutative limit. The position x and the momentum p of a classical particle can be simultaneously measured and (x, p) defines a point in classical phase-space. The set of polynomials in the variables (x, p) ca...