Combinatorics,graph theory,and computing

Journal of Algebraic Combinatorics -     

Star Decompositions of Cubes

 Let S _k denote the complete bipartite graph K _{1, k} and let Q _n denote the n-cube. We prove that the obvious necessary conditions for the existence of an S _k -decomposition of Q _n are sufficient. Received: July 21, 1999 Final version received: May 16, 2000     

Optimizing the monomer structure of polyhedral oligomeric silsesquioxane for ion transport in hybrid organic–inorganic block copolymers

Poly(ethylene oxide)-b-polyhedral oligomeric silsesquioxane (PEO–POSS) mixed with lithium bis(trifluoromethanesulfonyl)imide salt is a nanostructured hybrid organic–inorganic block copolymer electrolyte that may enable lithium metal batteries. The synthesis and characteristics of three PEO–POSS block copolymer electrolytes which only differ by their POSS silica cage substituents (ethyl, isobutyl, and isooctyl) is reported. Changing the POSS monomer structure results in differences in both thermodynamics and ion transport. All three neat polymers exhibit lamellar morphologies. Adding salt results in the formation of a disordered window which closes and gives way to lamellae at higher salt concentrations. The width of disordered window decreases with increasing length of the POSS alkyl chain substituent from ethyl to isobutyl and is absent in the isooctyl sample. Rheological measurements demonstrate good mechanical rigidity when compared with similar all-organic block copolymers. While salt diffusion coefficient and current ratio are unaffected by substituent length, ionic conductivity increases as the length of the alkyl chain substituent decreases: the ethyl substituent is optimal for ion transport. This is surprising because conventional wisdom suggests that ion transport occurs primarily in the PEO-rich domains, that is, ion transport should be unaffected by substituent length after accounting for the minor change in conducting phase volume fraction. © 2020 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2020 © 2020 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 363–371     

Oxoborane Formation Turns on Formazanate-Based Photoluminescence

The synthesis of compounds containing multiple bonds to boron has challenged main-group chemists for decades. Despite significant progress, the possibility that the formation of such bonds can turn on photoluminescence has received minimal attention. We report an oxoborane (B=O) complex that is electronically stabilized by a formazanate ligand in the absence of significant steric bulk and, unlike the common BX₂ (X=F, Cl) formazanate adducts, exhibits intense photoluminescence. The latter property was rationalized through density-functional calculations which indicated that the B=O bond enhances photoluminescence by drastically reducing differences between the ligand's geometries in the ground and excited states. The title oxoborane compound was synthesized from an air- and moisture-stable BCl₂ formazanate complex and subsequently converted to a redox-active boroxine. Each of these species may also serve as a precursor to functional materials.     

Magnetism and candidate muon-probe sites in RBa2Cu3O y

Key results of zero-field (ZF) and transverse-field (TF) muon-spin-relaxation (μSR) experiments on superconducting and insulating RBa₂Cu₃O _y (R123 _y , with R=Eu, Gd, Pr and Pr/Y:y=6, 7) are examined. The chemical behavior of the positive muon probe is addressed, and muon-oxygen bonding is shown to occur in all these cuprates. To explain magnetic fields at muon-probe sites in Pr _x Y_1−x Ba₂Cu₃O _y (0<=x<0.5,y=7 andx=0,y=6) samples, improvements on the reported magnetic structures from neutron diffraction are necessary. Cu magnetism in Pr123y (y=6,7) is observed belowT _N1, which is near RT. The magnetism seen belowT _N2 can be interpreted assuming an additional ordering in the Cutt-O chain layers. Alternatively, Pr ordering is also considered as the cause of the second phase transition. Considering the specific muon-probe location, a more detailed interpretation can be provided for the μSR parameters, measured in the normal and mixed states of these unconventional superconductors.     

Natural isotopes as a tool in the elucidation of elemental composition and fragmentation pathways by tandem mass spectrometry

Comparison of daughter spectra obtained by tandem quadrupole mass Spectrometry from ions selected from an isotopic cluster of the same elemental composition can be efficiently used to find out the elemental composition of a fragment. This even applies with ions of high mass and with low abundance isotopes such as ¹⁸O. By this method, loss of CO and HCO˙ from the phenol molecular ion is confirmed and the absence of CO loss from the p-tert-butyl-pbenol molecular ion is made obvious. Limitations of the method are discussed in the case of a bicyclic imidazolidinone.     

Diffraction studies of the crystalline and magnetic structures of γ-Fe2O3 iron oxide nanostructured in porous glass

The crystalline and magnetic structures of γ-Fe₂O₃ maghemite synthesized in porous glass in the form of nanoparticles with a mean diameter of 106(2) Å have been determined by the neutrons and synchrotron radiation diffraction methods. Nanostructured maghemite with the spinel structure has vacancies in the octahedral and tetrahedral positions. The magnetic structure corresponds to the usual ferrimagnetic type. The measured magnetic moments are much lower than the moments in a usual sample. Moreover, the moments are strongly different in the octahedral and tetrahedral positions; this difference is explained by the difference in the exchange interaction for moments in different positins.     

A Met-to-Val mutation in the skeletal muscle Na+ channel alpha-subunit in hyperkalaemic periodic paralysis.

HYPERKALAEMIC periodic paralysis (HYPP) is an autosomal dominant disease that results in episodic electrical inexcitability and paralysis of skeletal muscle. Electrophysiological data indicate that tetrodotoxin-sensitive sodium channels from muscle cells of HYPP-affected individuals show abnormal inactivation. Genetic analysis of nine HYPP families has shown tight linkage between the adult skeletal muscle sodium channel alpha-subunit gene on chromosome 17q and the disease (lod score, z = 24; recombination frequency 0 = 0), strongly suggesting that mutations of the alpha-subunit gene cause HYPP. We sequenced the alpha-subunit coding region isolated from muscle biopsies from affected (familial HYPP) and control individuals by cross-species polymerase chain reaction-mediated complementary DNA cloning. We have identified an A----G substitution in the patient's messenger RNA that causes a Met----Val change in a highly conserved region of the alpha-subunit, predicted to be in a transmembrane domain. This same change was found in a sporadic case of HYPP as a new mutation. We have therefore discovered a voltage-gated channel mutation responsible for a human genetic disease.     

Note on a conjecture of Kojima and Saigal

We prove there exist a finite set of (real) matrices of order n with positive determinant that, collectively, “see” all such matrices.