Anionic Sublattices in Halide Solid Electrolytes: A Case Study with the High-Pressure Phase of Li3ScCl6

The Li₃MX₆ compounds (M=Sc, Y, In; X=Cl, Br) are known as promising ionic conductors due to their compatibility with typical metal oxide cathode materials. In this study, we have successfully synthesized γ-Li₃ScCl₆ using high pressure for the first time in this family. Structural analysis revealed that the high-pressure polymorph crystallizes in the polar and chiral space group P6₃mc with hexagonal close-packing (hcp) of anions, unlike the ambient-pressure α-Li₃ScCl₆ and its spinel analog with cubic closed packing (ccp) of anions. Investigation of the known Li₃MX₆ family further revealed that the cation/anion radius ratio, r_M/r_X, is the factor that determines which anion sublattice is formed and that in γ-Li₃ScCl₆, the difference in compressibility between Sc and Cl exceeds the ccp r_M/r_X threshold under pressure, enabling the ccp-to-hcp conversion. Electrochemical tests of γ-Li₃ScCl₆ demonstrate improved electrochemical reduction stability. These findings open up new avenues and design principles for lithium solid electrolytes, enabling routes for materials exploration and tuning electrochemical stability without compositional changes or the use of coatings.     

Highly selective photoinduced perfluoroalkylation of vinylsilanes and its application to synthesis of water-shedding polysilanes

The functionalization of polysilanes is an important subject in materials science because functionalized polysilanes are expected to exhibit potentially innovative properties. This research aims at the addition of a water-shedding property to polysilanes by introducing perfluoroalkyl groups into their skeleton. The photoinduced iodoperfluoroalkylation of various vinylsilanes takes place successfully upon irradiation with a xenon lamp: vinylmonosilanes undergo iodoperfluoroalkylation with perfluoroalkyl iodides (R_fI) regioselectively, and the corresponding perfluoroalkylated silanes are obtained in moderate to high yields. Detailed optimization of the photoinduced iodoperfluoroalkylation has been investigated to apply this method to the functionalization of polysilanes. Polysilanes having vinyl groups can be synthesized by the reductive coupling of dichlorovinylsilanes with samarium diiodide (SmI₂) and samarium metal (Sm) upon irradiation with visible light. The synthesized vinylpolysilanes and R_fI (about 1.0 mM CHCl₃ solution) are coated on a glass plate sequentially, and then the following photoirradiation with light of a wavelength over 300 nm successfully adds an excellent water-shedding property to the glass plate.     

Organoaluminium reagents induced isomerization of 5-hydroxy-3,3,6-trimethyl-5-heptenoic acid δ-lactone to 2,2,5,5-tetramethyl-1,3-cyclohexanedione

Treatment of the title lactone and the related δ or ε-lactones with Et₂AlSR (R = Et or Ph) gave 1,3-cyclohexanediones or 1,3-cycloheptanediones in excellent yields.     

Basic Properties of the (t, n)-Threshold Visual Secret Sharing Scheme with Perfect Reconstruction of Black Pixels

In this paper we consider the (t, n)-threshold visual secret sharing scheme (VSSS) in which black pixels in a secret black-white images is reproduced perfectly as black pixels when we stack arbitrary t shares. This paper provides a new characterization of the (t, n)-threshold visual secret sharing scheme with such a property (hereafter, we call such a VSSS the (t, n)-PBVSSS for short). We use an algebraic method to characterize basis matrices of the (t, n)-PBVSSS in a certain class of matrices. We show that the set of all homogeneous polynomials each element of which yields basis matrices of the (t, n)-PBVSSS becomes a set of lattice points in an (n−t+1)-dimensional linear space. In addition, we prove that the optimal basis matrices in the sense of maximizing the relative difference among all the basis matrices in the class coincides with the basis matrices given by Blundo, Bonis and De Santis [3] for all n≥ t ≥ 2.     

Edge proximity and matching extension in projective planar graphs

A graph $G$ with at least $2m+2$ vertices is said to be distance $d$ $m$-extendable if, for any matching $M$ of $G$ with $m$ edges in which the edges lie at distance at least $d$ pairwise, there exists a perfect matching of $G$ containing $M$. In this paper we prove that every 5-connected triangulation on the projective plane of even order is distance 3 7-extendable and distance 4 $m$-extendable for any $m$.     

Hausdorff measures and packing measures of limit sets of CIFSs of generalized complex continued fractions

ABSTRACT

We consider a certain family of CIFSs of the generalized complex continued fractions with a complex parameter space. We show that for each CIFS of the family, the Hausdorff measure of the limit set of the CIFS with respect to the Hausdorff dimension is zero and the packing measure of the limit set of the CIFS with respect to the Hausdorff dimension is positive (main result). This is a new phenomenon of infinite CIFSs which cannot hold in finite CIFSs. We prove the main result by showing some estimates for the unique conformal measure of each CIFS of the family and by using some geometric observations.     

Oxidation of alcohols with oxoperoxobis(N-phenylbenzohydroxamato)molybdenum(VI)

The title complex oxidizes primary and secondary alcohols to the corresponding carbonyl compounds. Stereoselective epoxidation of allylic alcohols is also described.     

Interaction cohomology of forward or backward self-similar systems

We investigate the dynamics of forward or backward self-similar systems (iterated function systems) and the topological structure of their invariant sets. We define a new cohomology theory (interaction cohomology) for forward or backward self-similar systems. We show that under certain conditions, the space of connected components of the invariant set is isomorphic to the inverse limit of the spaces of connected components of the realizations of the nerves of finite coverings U of the invariant set, where each U consists of (backward) images of the invariant set under elements of finite word length. We give a criterion for the invariant set to be connected. Moreover, we give a sufficient condition for the first cohomology group to have infinite rank. As an application, we obtain many results on the dynamics of semigroups of polynomials. Moreover, we define postunbranched systems and we investigate the interaction cohomology groups of such systems. Many examples are given.     

Transversality family of expanding rational semigroups

We study finitely generated expanding semigroups of rational maps with overlaps on the Riemann sphere. We show that if a d$d$-parameter family of such semigroups satisfies the transversality condition, then for almost every parameter value the Hausdorff dimension of the Julia set is the minimum of 2 and the zero of the pressure function. Moreover, the Hausdorff dimension of the exceptional set of parameters is estimated. We also show that if the zero of the pressure function is greater than 2$2$, then typically the 2-dimensional Lebesgue measure of the Julia set is positive. Some sufficient conditions for a family to satisfy the transversality conditions are given. We give non-trivial examples of families of semigroups of non-linear polynomials with the transversality condition for which the Hausdorff dimension of the Julia set is typically equal to the zero of the pressure function and is less than 2$2$. We also show that a family of small perturbations of the Sierpinski gasket system satisfies that for a typical parameter value, the Hausdorff dimension of the Julia set (limit set) is equal to the zero of the pressure function, which is equal to the similarity dimension. Combining the arguments on the transversality condition, thermodynamical formalisms and potential theory, we show that for each a∈C$a\in \mathbb{C}$ with |a|≠0,1$\left|a\right|\ne 0,1$, the family of small perturbations of the semigroup generated by {z²,az²}$\{z^2,a{z}^2\}$ satisfies that for a typical parameter value, the 2-dimensional Lebesgue measure of the Julia set is positive.     

Topological spectrum of locally compact Cantor minimal systems

We show that there exists a locally compact Cantor minimal system whose topological spectrum has a given Hausdorff dimension.