Molecular dynamics refers to the computer simulation of a material at the atomic level. An open problem in numerical analysis is to explain the apparent reliability of molecular dynamics simulations. The difficulty is that individual trajectories computed in molecular dynamics are accurate for only short time intervals, whereas apparently reliable information can be extracted from very long-tim...

A raster-based computer graphics method of imaging volumetric data (data sampled on a three-dimensional grid) has been added to an existing molecular rendering program. Any molecular property expressed as a 30 grid of scalar data values can be displayed around and inside of the molecular van der Waals surface as a collection of colored clouds and transparent surfaces. Different antical properti...

In this paper, we introduce two new types of enriched contractions, viz., A-contraction and A-contraction. Then obtain fixed points mappings satisfying such contractions using the point property average operator mappings. Further, study well-posedness limit shadowing problem involving give some examples to validate results proved. Our work improves Berinde P?curar?s recent on different kinds we...

This paper presents acoustic analysis for the purpose of automatic evaluation of shadowing speech. We use selfchecked scores of understanding, manual prosodic scores, and TOEIC scores as reference scores of learners’ shadowing speech, and compare these scores with automatic scores based on acoustic features that can reflect phoneme intelligibility and prosodic fluency in terms of intonation, an...

Nuclear shadowing in the structure function F 3 is investigated as a possible test of shadowing models. The F 3 shadowing is studied in two different theoretical models: a parton-recombination model with Q 2 rescaling and an aligned-jet model. We find that predictions in these models differ completely in the small x region. It suggests that the F 3 shadowing could be used for discriminating amo...