Computing an Integer Point of a Class of Convex Sets

A simplicial algorithm is proposed for computing an integer point of a convex set ^CRn satisfying

Development of highly potent chiral discrimination methods that solve the problems of the diastereomer method

The development of highly potent chiral discrimination methods that solve the problems of the diastereomer method, in which it is impossible to discriminate the diastereomers having chiral centers separated by more than four bonds, is described. On the basis of the results obtained, a new hypothesis, Induced Chiral Fields that the achiral reversed phase can provide chiral fields depending on the structures of the eluents, is proposed to explain the significant results of separation of the diastereomers derived from newly developed chiral and fluorescent labeling reagents and optical isomers by reversed-phase HPLC, which was hitherto impossible.     

Quantification of ATRP initiator density on polymer latex particles by fluorescence labeling technique using copper‐catalyzed azide‐alkyne cycloaddition

We developed a novel fluorescence labeling technique for quantification of surface densities of atom transfer radical polymerization (ATRP) initiators on polymer particles. The cationic P(St‐CPEM‐C₄DMAEMA) and anionic P(St‐CPEM) polymer latex particles carrying ATRP‐initiating chlorine groups were prepared by emulsifier‐free emulsion polymerization of styrene (St), 2‐(2‐chloropropionyloxy)ethyl methacrylate (CPEM), and N‐n‐butyl‐N,N‐dimethyl‐N‐(2‐methacryloyloxy)ethylammonium bromide (C₄DMAEMA). ATRP initiators on the surface of polymer particles were converted into azide groups by sodium azide, followed by fluorescent labeling with 5‐(N,N‐dimethylamino)‐N′‐(prop‐2‐yn‐1‐yl)naphthalene‐1‐sulfonamide (Dansyl‐alkyne) by copper‐catalyzed azide‐alkyne cycloaddition (CuAAC). The reaction time required for both azidation of ATRP‐initiating groups and successive fluorescence labeling of azide groups with Dansyl‐alkyne by CuAAC were investigated in detail by FTIR and fluorescence spectral measurement, respectively. The ATRP initiator densities on the cationic P(St‐CPEM‐C₄DMAEMA) and anionic P(St‐CPEM) particle surfaces were estimated to be 0.21 and 0.15 molecules nm^?2, respectively, which gave close agreement with values previously determined by a conductometric titration method. The fluorescence labeling through click chemistry proposed herein is a versatile technique to quantify the surface ATRP initiator density both on anionic and cationic polymer particles. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4042–4051     

Development of a high-sensitivity chromatographic separation system for pyridylaminated aldopentoses and aldohexoses

A rare sugar is considered to be a monosaccharide rarely found in nature. To investigate their natural distribution and biological roles, a robust analytical system must be used to isolate, identify, and quantify them. Herein, we report the development of such a system that can specifically quantify and chromatographically separate four aldopentoses and eight aldohexoses tagged with 2-aminopyridine. Purified monosaccharides derivatized with a pyridylamino moiety (PA–monosaccharides) are first chromatographed over a high-performance anion-exchange resin. But, because two of the PA–aldohexoses used in this study, PA–talose and PA–idose, co-elute with the common saccharides, PA–glucose and PA–mannose, respectively, a second chromatographic step, reversed-phase high-performance liquid chromatography, is used to completely separate them. Thus, as shown by the results of this study, chromatographic separation of PA–monosaccharides is achievable and provides a quantitative measurement of common and rare isomeric aldopentoses and aldohexoses.     

Constructing all magic squares of order three

We find by applying MacMahon's partition analysis that all magic squares of order three, up to rotations and reflections, are of two types, each generated by three basis elements. A combinatorial proof of this fact is given.     

On friendly index sets of 2-regular graphs

Let G be a graph with vertex set V and edge set E, and let A be an abelian group. A labeling f:V→A induces an edge labeling f^∗:E→A defined by f^∗(xy)=f(x)+f(y). For i∈A, let v_f(i)=card{v∈V:f(v)=i} and e_f(i)=card{e∈E:f^∗(e)=i}. A labeling f is said to be A-friendly if |v_f(i)−v_f(j)|≤1 for all (i,j)∈A×A, and A-cordial if we also have |e_f(i)−e_f(j)|≤1 for all (i,j)∈A×A. When A=Z₂, the friendly index set of the graph G is defined as {|e_f(1)−e_f(0)|:the vertex labelingf is Z₂-friendly}. In this paper we completely determine the friendly index sets of 2-regular graphs. In particular, we show that a 2-regular graph of order n is cordial if and only if n?2 (mod 4).     

Strong edge-magic graphs of maximum size

An edge-magic total labeling on G is a one-to-one map λ from V(G)∪E(G) onto the integers 1,2,…,|V(G)∪E(G)| with the property that, given any edge (x,y), λ(x)+λ(x,y)+λ(y)=k for some constant k. The labeling is strong if all the smallest labels are assigned to the vertices. Enomoto et al. proved that a graph admitting a strong labeling can have at most 2|V(G)|-3 edges. In this paper we study graphs of this maximum size.     

Superstochastic matrices and magic Markov chains

A brief account of the conceptual formulation of the two entities in this paper’s title, plus an initial preliminary investigation of some of their mathematical properties, is given.     

Selective lighting up of segments around Gly,Ala and Ser/Thr in proteins

Direct detection of ¹³C nucleus can be used as a valuable alternative where ¹H detection poses a challenge due to relaxation effects, chemical exchange and poor chemical shift dispersion. In this context, we have designed a suite of 2D ¹³C^α‐detected hNCA experiments that provide sequential correlations of ¹³C^α with ¹⁵N on one hand and efficient spectroscopic labeling of certain groups of residues, namely, Gly, Ala, Ser and Thr, on the other. These residues act as checkpoints in the sequential walk, which in turn offer new possibilities of backbone assignment of small proteins from a set of 2D experiments, thereby providing great economy in terms of spectrometer time. The direct identification of peptide segments around Gly, Ala, Ser and Thr residues along a protein chain will be highly valuable for deriving important information on sites of ligand binding, phosphorylation, inhibitor/substrate binding, understanding protein folding pathways, comprehending local conformational dynamics etc. without having to obtain complete sequence‐specific assignments, which can be time consuming and at times formidable, especially in large proteins. We have illustratively demonstrated the multifaceted applications of these variants of 2D experiments on ubiquitin and M‐crystallin. We foresee that these 2D hNCA experiments will provide economic and efficient strategies for studying the structure and function of proteins. Copyright © 2012 John Wiley & Sons, Ltd.