Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.

We present here a combinatorial method for computing cup-i products and Steenrod squares of a simplicial set X. This method is essentially based on the determination of explicit formulae for the component morphisms of a higher diagonal approximation (i.e., a family of morphisms measuring the lack of commutativity of the cup product on the cochain level) in terms of face operators of X. A genera...

We study the semiclassical limit of the Sp(N) generalization of the pyrochlore lattice Heisenberg antiferromagnet by expanding about the N --> infinity saddlepoint in powers of a generalized inverse spin. To leading order, we write down an effective Hamiltonian as a series in loops on the lattice. Using this as a formula for calculating the energy of any classical ground state, we perform Monte...

Evaluative conditioning (EC) is a change in the valence of a stimulus that results from pairing the stimulus with an affective stimulus. Two high-powered studies (total N = 1,161) investigated the nature of the relationship between EC and contingency awareness measured as contingency memory. Stronger EC occurred among people with more accurate and more confident memory of the pairings. Awarenes...

We show that models of generalized modified gravity, with inverse powers of the curvature, can explain the current accelerated expansion of the Universe without resorting to dark energy and without conflicting with solar system experiments. We have solved the Friedmann equations for the full dynamical range of the evolution of the Universe and performed a detailed analysis of supernovae data in...

In a noncontextual hidden variable model of quantum theory, hidden variables determine the outcomes of every measurement in a manner that is independent of how the measurement is implemented. Using a generalization of this notion to arbitrary operational theories and to preparation procedures, we demonstrate that a particular two-party information-processing task, "parity-oblivious multiplexing...

We present here a combinatorial method for computing cup-i products and Steenrod squares of a simplicial set X. This method is essentially based on the determination of explicit formulae for the component morphisms of a higher diagonal approximation (i.e., a family of morphisms measuring the lack of commutativity of the cup product on the cochain level) in terms of face operators of X. A genera...

Explanation is a central concept in human psychology. Drawing upon philosophical theories of explanation, psychologists have recently begun to examine the relationship between explanation, probability and causality. Our study advances this growing literature at the intersection of psychology and philosophy of science by systematically investigating how judgments of explanatory power are affecte...

This paper brings together results from the philosophy and the psychology of explanation to argue that there are multiple concepts of explanation in human psychology. Specifically, it is shown that pluralism about explanation coheres with the multiplicity of models of explanation available in the philosophy of science, and it is supported by evidence from the psychology of explanatory judgment....