Mathematical Approaches to the NMR Peak-Picking Problem

Nuclear magnetic resonance (NMR) spectroscopy and X-ray crystallography are two experimental techniques used to determine the three-dimensional structures of proteins. 

NMR spectroscopy has the unique ability to capture proteins in vivo. Currently, protein structure determination by NMR follows the procedure proposed by Kurt Wüth rich in 1986. This procedure consists of peak picking, resonance assignment, nuclear overhauser effect (NOE) assignment and structure calculation steps. Among the four steps, peak picking is time consuming and requires extensive expert knowledge. Computational methods designed to automate and improve this step are still needed. The inputs to the peak picking problem are an NMR spectrum or a set of spectra, whereas the outputs are the lists of peaks (signals) identified from these spectra.

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More Comprehensive Computational Number Theory

Computational number theory, also known as algorithmic number theory, is the study of algorithms for performing number theoretic computations. The best known problem in the field is the integer factorization, the great common divisor or the least common multiple.The largest known primes, which are usually Mersenne primes, and they were usually found by GIMPS, the Great Internet Mersenne Prime Search.

But in my opinion, the concepts of computational number theory could be more comprehensive, covering a wide range,including all the study of number theory by computers. For me, computers are so important for number theorists, just like telescopes for astronomers.

Non-metallic Particles Manipulation in Liquid Metals During Electromagnetic Processing

Research in manipulation of non-metallic particles in a liquid metal by using an electromagnetic (EM) field is promoted by both the requirement of more efficient materials design and the development of cost-effective electromagnetic apparatus. The particles of sub/micrometer size scan be agglomerated, segregated, aligned and/ or removed by applying a suitable EM field during liquid metal processing. The efficiency and applicability depends highly on the nature of the particles and the difference from the liquid metal matrix. In the present paper, the fundaments/physics of non-metallic particles manipulation by EM processing are discussed and some potential application possibilities in industry are proposed.

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Fixed Point Theory for Three φ–Weak Contraction Functions

Alber and Guerre-Delabriere demonstrated the “concept of weak contraction” in 1997. Actually in concept of weak contraction, the authors defined such mappings for single-valued maps on Hilbert spaces and proved the existence of fixed points. Rhoades showed that most results of concept of weak contraction are still true for any Banach space along with that he has proved the following very interesting fixed point theorem which is one of generalizations of the Banach contraction principle because it contains contractions as special cases (φ(t)=(1–k)t).

Advances in Logic, Operations and Computational Mathematics

Journal of Applied & Computational Mathematics Volume 5, Issue 2 comprised of 7 research articles and 4 opinion articles and are focused on the innovation of polygon, Euler, linear and non-linear equations.

EL-Kholy et al., in their research article discussed about balanced folding over a polygon and Euler numbers. The study proved that for a balanced folding of a simply connected surface M, there is a subgroup of the group which is called all homeomorphisms of M that will acts 1- transitively on the 2-cells of M.

Gil et al., in their research have reported about the exponentially stabile non-linear, non-autonomous multi variable discrete systems. Based on the recent estimates on matrix equations, the findings suggest that a class of non-autonomous discrete-time systems is governed by semi-linear vector difference equations along with slowly varying linear parts.