In the 1920s, Ackermann and von Neumann, in pursuit of Hilbert’s Programme, were working on consistency proofs for arithmetical systems. One proposed method of giving such proofs is Hilbert’s epsilon-substitution method. There was, however, a second approach which was not reflected in the publications of the Hilbert school in the 1920s, and which is a direct precursor of Hilbert’s first epsilon...

We examine energy spectra, fluxes, and transfers of two-dimensional forced incompressible turbulence with linear drag in the energy range, and find marked departures from 5/3 law and the idea of locality. Any attempt to bring the system into the "ideal cascade state" would result either in spectral (bulge) or flux distortion. We corroborate this observation by DNS (spectral code) and eddy-dampe...

Deliberate control of thermal emission properties using nanophotonics has improved a number of applications including thermophotovoltaics (TPV), radiative cooling and infrared spectroscopy. In this work, we study the effect of simultaneous control of angular and spectral properties of thermal emitters on the efficiencies of TPV systems. While spectral selectivity reduces sub-bandgap losses, ang...

Investment managers are multi-objective decision-makers (DMs) who make portfolio decisions by maximizing profits and minimizing risks over a multi-period planning horizon. Portfolio decisions are complex multi-objective problems which include both tangible and intangible factors. We propose an integrated multi-objective framework for project portfolio selection with respect to both the profits ...

A simple procedure for phenotyping apolipoprotein (apo) E directly from plasma has been developed for use in the lipid clinic laboratory. In this new method, 10 microL of serum or plasma is pretreated with neuraminidase (EC 3.2.1.18), which removes the sialic acid residues from apo E and eliminates additional bands, thereby ensuring correct phenotype assignment. After a rapid delipidation step,...

In this paper, the wear resistance and antifriction of epsilon phase layer and diffusion layer of gas nitrided D2 steel and M2 steel have been studied. The changes m wear mechanism of epsilon phase under the load from 20N to 200N are analysed. When the load is lighter than 100N, it is mainly oxidizing wear on friction surface. The adhesion, peeling off and abrasive wear appear on friction surfa...

In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible ...

This paper studies some existence results for generalized epsilon-vector equilibrium problems and generalized epsilon-vector variational inequalities. The existence results for solutions are derived by using the celebrated KKM theorem. The results achieved in this paper generalize and improve the works of many authors in references.

In this study, a series of interaction coefficients of the Brønsted-Guggenheim-Scatchard specific interaction theory (SIT) have been estimated up to 200 degrees C and 400 bars. The interaction coefficients involving Cl- estimated include epsilon(H+, Cl-), epsilon(Na+, Cl-), epsilon(Ag+, Cl-), epsilon(Na+, AgCl2 -), epsilon(Mg2+, Cl-), epsilon(Ca2+, Cl-), epsilon(Sr2+, Cl-), epsilon(Ba2+, Cl-), ...