Synthesis and absolute configuration of +-lineatin,the pheromone of trypodendronlineatum

A new synthesis of (±), (+)- and (-)-lineatin (3,3,7-trimethyl-2, 9-dioxatricyclo [3.3.1.0^4,7] nonane, $\text{1}$) was achieved. The stereochemistry of (+)-lineatin was established as 1$\text{R}$, 4$\text{S}$, 5$\text{R}$, 7$\text{R}$ by an X-ray crystallographic analysis of an intermediate $\text{1}$$\text{5}$.     

Perfect state transfer in Laplacian quantum walk

For a graph G and a related symmetric matrix M, the continuous-time quantum walk on G relative to M is defined as the unitary matrix \(U(t) = \exp (-itM)\), where t varies over the reals. Perfect state transfer occurs between vertices u and v at time \(\tau \) if the (u, v)-entry of \(U(\tau )\) has unit magnitude. This paper studies quantum walks relative to graph Laplacians. Some main observations include the following closure properties for perfect state transfer. If an n-vertex graph has perfect state transfer at time \(\tau \) relative to the Laplacian, then so does its complement if \(n\tau \in 2\pi {\mathbb {Z}}\). As a corollary, the join of \(\overline{K}_{2}\) with any m-vertex graph has perfect state transfer relative to the Laplacian if and only if \(m \equiv 2\pmod {4}\). This was previously known for the join of \(\overline{K}_{2}\) with a clique (Bose et al. in Int J Quant Inf 7:713–723, 2009). If a graph G has perfect state transfer at time \(\tau \) relative to the normalized Laplacian, then so does the weak product \(G \times H\) if for any normalized Laplacian eigenvalues \(\lambda \) of G and \(\mu \) of H, we have \(\mu (\lambda -1)\tau \in 2\pi {\mathbb {Z}}\). As a corollary, a weak product of \(P_{3}\) with an even clique or an odd cube has perfect state transfer relative to the normalized Laplacian. It was known earlier that a weak product of a circulant with odd integer eigenvalues and an even cube or a Cartesian power of \(P_{3}\) has perfect state transfer relative to the adjacency matrix. As for negative results, no path with four vertices or more has antipodal perfect state transfer relative to the normalized Laplacian. This almost matches the state of affairs under the adjacency matrix (Godsil in Discret Math 312(1):129–147, 2011).     

Interpretation of structure formation during the sol-gel transition of a resorcinol-formaldehyde solution by population balance

Growth of colloidal particles formed during the sol-gel transition of a resorcinol-formaldehyde (RF) solution was simulated based on the population balance equation by using the discrete-sectional model (DSM). During the early stage of the sol-gel transition, the transient change of sizes of colloidal particles estimated by this method agreed well with the previous experimental observation by dynamic light scattering (DLS), which confirmed the influence of the catalyst concentration of a starting RF solution on the growth rate of the particles. From the size distribution of colloidal particles predicted at the gelation time, the surface area of a RF hydrogel after the completion of the sol-gel transition was estimated, which coincided with the BET surface area of a RF aerogel because the porous structure of a hydrogel was maintained and few micropores were formed during supercritical drying.     

Porous microfibers and microhoneycombs synthesized by ice templating

Recently we introduced the “ice templating” method, a new method which allows the synthesis of nanoporous materials with unique morphology, such as microfibers and microhoneycombs. In this method, materials are synthesized by freezing their parent hydrosols or hydrogels unidirectionally. Ice crystals which grow within the precursor during freezing act as the template. Therefore, the template can be easily removed through simple thawing and drying, which is a unique and beneficial feature of this method. This paper will first describe the outline of this new method and next, the details about methods to control the dimensions of the materials obtained through it. Comments about the range of applicability of this method will also be provided.     

Catalyzed intramolecular olefin insertion into a carbon-carbon single bond

Intramolecular insertion of a C-C double bond into a C-C single bond was achieved by treatment of cyclobutanone bearing an o-styryl group at the 3-position with a catalytic amount of a cationic rhodium(I)-dppp complex. Initially, rhodium is inserted between the carbonyl carbon and the alpha-carbon of the cyclobutanone. Intramolecular coordination of the vinyl group results in its migratory insertion into the C-Rh linkage. Reductive elimination affords benzobicyclo[3.2.1]octan-3-one. Notably, a ring-opened alpha,beta-unsaturated ketone was obtained when dppe was used instead of dppp. In this reaction, rhodium cleaved the bond between the alpha sp3 carbon and the beta sp3 carbon of the cyclobutanone. The coordinating vinyl group directs this new regioselectivity of cleavage observed with the dppe ligand.     

Dynamic and static light scattering study on the sol-gel transition of resorcinol-formaldehyde aqueous solution

Structure formation during the sol-gel transition of resorcinol-formaldehyde (RF) solutions was traced by dynamic light scattering (DLS) and static light scattering (SLS) techniques. The decay time spectra obtained by DLS revealed that both the growth rates of colloidal particles formed during the early stage of the sol-gel transition and the time required for the colloidal particles to form a firm network structure could be related to the ratio of catalyst to water (C/W) of the starting RF solution. SLS results indicated that the molecular weight of colloidal particles increased with the progress of the sol-gel transition, the rate of which was also affected by the value of C/W. The mesoporosity of RF aerogels, which were prepared by drying RF hydrogels with supercritical carbon dioxide, was confirmed to depend on the size of colloidal particles estimated from the decay time spectrum collected at the last stage of the sol-gel transition.     

Embedding a Pair of Graphs in a Surface, and the Width of 4-dimensional Prismatoids

A prismatoid is a polytope with all its vertices contained in two parallel facets, called its bases. Its width is the number of steps needed to go from one base to the other in the dual graph. The first author recently showed that the existence of counter-examples to the Hirsch conjecture is equivalent to that of d-prismatoids of width larger than d, and constructed such prismatoids in dimension five. Here we show that the same is impossible in dimension four. This is proved by looking at the pair of graph embeddings on a 2-sphere that arise from the normal fans of the two bases of Q.     

Formation of monolithic silica gel microhoneycombs (SMHs) using pseudosteady state growth of microstructural ice crystals

Monolithic silica gel microhoneycombs, which have an array of straight macropores within their structure and developed micro/mesopores inside their walls, were prepared using pseudosteady state growth of ice crystals which occurs during the unidirectional freeze-gelation of freshly gelled aqueous silica hydrogels, followed by a pore-protecting drying method, freeze drying.     

Synthesis of the optically active forms of 4,10-dihydroxy-1,7-dioxaspiro[5.5]undecane and their conversion to the enantiomers of 1,7-dioxaspiro[5.5]undecane,the olive fly pheromone

Both the enantiomers of l,7-dioxaspiro[5.5]undecane, the major component of the pheromone of the olive fly (Dacus oleae), were synthesized from (S)-malic acid.