Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.     

Counting restricted orientations of random graphs

We count orientations of avoiding certain classes of oriented graphs. In particular, we study , the number of orientations of the binomial random graph in which every copy of is transitive, and , the number of orientations of containing no strongly connected copy of . We give the correct order of growth of and up to polylogarithmic factors; for orientations with no cyclic triangle, this significantly improves a result of Allen, Kohayakawa, Mota, and Parente. We also discuss the problem for a single forbidden oriented graph, and state a number of open problems and conjectures.     

Synthesis and mechanochemical properties of biobased ABCBA-type pentablock copolymers comprising poly-d-lactide (A), poly-l-lactide (B) and poly(1,2-propylene succinate) (C)

The ABCBA pentablock copolymers (p-d -l -PPS) comprising poly(d -lactide) (PDLA: A), poly(l -lactide) (PLLA: B) and poly(propylene succinate) (PPS: C) were successfully synthesized by two-step ring-opening polymerization (ROP) of d - and l -lactide using a dihydroxy-terminated PPS as a macro-initiator. The pentablock copolymers revealed the high stereocomplex (sc) crystallinity, thermal stability and elastomeric property in their solution-cast films. It was found that the T_g was found to be proportional to the PPS content, whereas the T_m was proportional to their average block length. The thermal resistivity of the copolymer films was found to be as high as 202°C owing to their sc formation. The copolymers also showed improved stereocomplexibility compared to the enantiomeric mixtures of triblock copolymers (PLLA-PPS-PLLA and PDLA-PPS-PDLA) having similar PLLA and PDLA chain lengths. These pentablock copolymers can afford thermoplastic elastomers or flexible plastic materials having a 100% bio-based content, showing high heat-resistive property.     

The size Ramsey number of short subdivisions of bounded degree graphs

For graphs G and F, write if any coloring of the edges of G with colors yields a monochromatic copy of the graph F. Suppose is obtained from a graph S with s vertices and maximum degree d by subdividing its edges h times (that is, by replacing the edges of S by paths of length h + 1). We prove that there exists a graph G with no more than edges for which holds, provided that . We also extend this result to the case in which Q is a graph with maximum degree d on q vertices with the property that every pair of vertices of degree greater than 2 are distance at least h + 1 apart. This complements work of Pak regarding the size Ramsey number of “long subdivisions” of bounded degree graphs.     

Fast and Robust Nanocellulose Width Estimation Using Turbidimetry

The dimensions of nanocelluloses are important factors in controlling their material properties. The present study reports a fast and robust method for estimating the widths of individual nanocellulose particles based on the turbidities of their water dispersions. Seven types of nanocellulose, including short and rigid cellulose nanocrystals and long and flexible cellulose nanofibers, are prepared via different processes. Their widths are calculated from the respective turbidity plots of their water dispersions, based on the theory of light scattering by thin and long particles. The turbidity‐derived widths of the seven nanocelluloses range from 2 to 10 nm, and show good correlations with the thicknesses of nanocellulose particles spread on flat mica surfaces determined using atomic force microscopy.

     

A Normal Force on the Free Surface of a Coated Material

The three-dimensional theoretical solution of a concentrated normal force acting on the free surface of a coated material has been deduced by applying the reflection method. It is found that all stress functions defined in the local coordinate systems with their origins placed at each mirror point can be deduced from the fundamental solution of a concentrated normal force acting on the free surface of a semi-infinite homogeneous medium. The structure of the elastic solution has been illustrated by numerical analysis. It is found that only the stress functions corresponding to the first few mirror points are influential. It is also found that the effect of material combination on the stress field shall be described by three parameters, the two Dundurs' parameters and one additional parameter.     

XAFS spectra from X-ray fluorescence Kβ line using conventional energy-discriminating detector

X-ray fluorescence spectra of copper (Cu) metal, copper monoxide (CuO), and potassium chromate (K₂CrO₄) were recorded as a function of incident X-ray energy near the Cu K-edge and chromium (Cr) K-edge, respectively, using a conventional silicon drift detector. The spectra contained components due to elastic, inelastic, and multiple scattering, in addition to the Kα and Kβ lines. Cu and Cr K-edge X-ray absorption fine structure (XAFS) spectra of Cu, CuO, and K₂CrO₄ were obtained by an intensity analysis of the Kα and Kβ lines. The intensity of the Kβ line for the different incident photon energies was obtained by numerically removing the additional scattering components using the MUSCAT program. These spectra exhibited a jump near the K absorption edges, which reproduced the spectral features obtained in transmission mode for both Cu, CuO, and K₂CrO₄. A chemical shift was also clearly identified in the X-ray absorption near edges structure using the X-ray fluorescence Kβ line. In addition, the Cr K-edge extended XAFS spectrum of K₂CrO₄ was clearly observed using the Cr Kβ fluorescent line. The XAFS measurements on the Kα and Kβ lines are possible, and they carry equally valuable information.     

Side chain type ionic liquid crystalline polymers having high Preliminary communication molecular weight

Side chain type ionic liquid crystalline polymers having a 4-(1,3-dioxan-2-yl)pyridinium structure in their mesogenic side chain were synthesized. These polymers exhibited the smectic A phase. The molecular weights of these ionic liquid crystalline polymers are very high, e.g. for compound 7 - 2 M _w = 486 000.     

Neutron crystallographic and molecular dynamics studies of the structure of ammonia-cellulose I: rearrangement of hydrogen bonding during the treatment of cellulose with ammonia

The hydrogen bond arrangement in a complex of cellulose with ammonia has been studied using neutron crystallography in combination with molecular dynamics simulations. The O6 atom of the hydroxymethyl group is donor in a highly occupied hydrogen bond to an ammonia molecule. This rotating ammonia molecule is donor in partially occupied and transient hydrogen bonds to the O2, O3 and O6 atoms of the hydroxyl groups of other chains. The hydrogen atom bound to the O3 atom is disordered but it is almost always involved in some type of hydrogen bonding. It is donated in a hydrogen bond most of the time to the O5 atom on the same chain. However, it also rotates away from this O5 atom to be donated to an ammonia molecule part of the time. On the other hand the hydrogen atom bound to the O2 atom is free from hydrogen bonding most of the time. It is donated in a hydrogen bond to the O6 atom on a neighboring chain only with a relatively small probability. These results provide new insights into how hydrogen bonds are rearranged during the conversion of cellulose I to cellulose III_I by ammonia treatment.     

Highly Chemoselective Aerobic Oxidation of Amino Alcohols into Amino Carbonyl Compounds

The direct oxidation of unprotected amino alcohols to their corresponding amino carbonyl compounds has often posed serious challenges in organic synthesis and has constrained chemists to adopting an indirect route, such as a protection/deprotection strategy, to attain their goal. Described herein is a highly chemoselective aerobic oxidation of unprotected amino alcohols to their amino carbonyl compounds in which 2‐azaadamantane N‐oxyl (AZADO)/copper catalysis is used. The catalytic system developed leads to the alcohol‐selective oxidation of various unprotected amino alcohols, carrying a primary, secondary, or tertiary amino group, in good to high yield at ambient temperature with exposure to air, thus offering flexibility in the synthesis of nitrogen‐containing compounds.