In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the wellknown deformation theory of algebras developed by Gerstenhaber. As part of our deformation theory we define a notion of flatness for abelian categories. We show that various basic properties are preserved under flat deformations and we construct sever...

lapping is one of the most important polishing processes which can be used to fabricate flat and smooth surfaces. in this paper, the effect of lapping characteristics and mesh number of abrasive particles are studied on the surface roughness and flatness for the machining of hardened aisi 52100 rings. the most significant lapping characteristics are pressure, lap plate speed and time. scanning ...

Flatness -- the absence of spacetime curvature is a well-understood property macroscopic, classical spacetimes in general relativity. The same cannot be said about concepts and flatness nonperturbative quantum gravity, where microscopic structure not describable terms small fluctuations around fixed background geometry. An interesting case are two-dimensional models which lack limit therefore m...

Despite their overwhelming capacity to overfit, deep learning architectures tend to generalize relatively well to unseen data, allowing them to be deployed in practice. However, explaining why this is the case is still an open area of research. One standing hypothesis that is gaining popularity, e.g. Hochreiter & Schmidhuber (1997); Keskar et al. (2017), is that the flatness of minima of the lo...

We describe a novel method for measuring the unconstrained flatness error of thin, plane-parallel precision optics. Test parts are floated on high-density aqueous metatungstate solutions while measuring the flatness error with an interferometer. The support of the flat optics by the uniform hydrostatic pressure at the submerged face of the flat optic eliminates flatness errors caused by mountin...

In angle calibrations the uncertainty contributions of the autocollimator and index table are easily estimated as these uncertainties are well documented, but it is more difficult to determine the uncertainties associated with flatness deviations, eccentricity and pyramidal errors of the measuring faces. Deviations in the flatness of angle surfaces have been held responsible for the lack of agr...

Background: During intensity modulated radiation therapy (IMRT) technique, theoretically, presence of flattening filter (FF) across the beamline of clinical linear accelerator (linac) is not essential to obtain uniform lateral profiles due to intensity modulation of photon beams by multileaf collimators (MLCs). The aim of this study was to investigate the dosimetrical properties of 18 MV photon...

Abstract Evidence for almost spatial flatness of the Universe has been provided from several observational probes, including Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations (BAO) galaxy clustering data. However, other than inflation, in this case only limit infinite time, there is no strong a priori motivation spatially flat Universe. Using renormalization group (RG) techniqu...

in this paper, an intelligent control strategy based on combination of the “flatness based control technique” and the “perturbation and observation (p&o;) mppt algorithm” is developed and investigated to control a hybrid electric energy source (heps). this ehps is composed of a fuel cell system (fc) and a solar panel (sp), as the main source and a supercapacitor bank (sc), as the auxiliary sour...

In this article we study the metric property and the function theory of asymptotically locally Euclidean (ALE) Kähler manifolds. In particular, we prove the Ricci flatness under the assumption that the Ricci curvature of such manifolds is either nonnegative or nonpositive. The result provides a generalization of previous gap type theorems established by Greene and Wu, Mok, Siu and Yau, etc. It ...