Compact directed acyclic word graphs for a sliding window

Suffix trees are a well-known and widely-studied data structure highly useful for string matching. The suffix tree of a string w can be constructed in O(n) time and space, where n denotes the length of w. Larsson achieved an efficient algorithm to maintain suffix trees for a sliding window. It contributes to prediction by partial matching (PPM) style statistical data compression scheme. Compact directed acyclic word graphs (CDAWGs) are a more space-economical data structure for indexing strings. In this paper we propose a linear-time algorithm to maintain CDAWGs for a sliding window.     

Mixed-Valent Heptairon Complex with a Ground-State Spin Value of S=12/2 Constructed from a Triiron Cluster Ligand

The anionic triiron(III) cluster ligand [Fe(III)(3)(μ(3)-O)(bpca)(2)Cl(4)(EtO)(2)](-) (1; Hbpca=bis(2-pyridylcarbonyl)amine) was prepared as a building block for constructing larger metal assemblies. This "metal cluster complex ligand" was used in the synthesis of the mixed-valent heptairon complex [Fe(II)(1)(2)(EtOH)(2)], which has a ground-state spin value of S=12/2.     

Computer simulation for the cooligomerization system

In order to clarify the kinetic features of the styrene (A)–methyl methacrylate (B)–CCl₄(S) cooligomerization system, a computer simulation was carried out. The experimental data on the degree of polymerization and the deviation of the cooligomer composition from the statistical steady-state composition were comparatively well explained by calculations based on the kinetic equations derived from the assumed reaction scheme and the values of the velocity coefficients, although the values of the four velocity coefficients in the initiation step and the velocity coefficient of the termination by the coupling of two solvent radicals were estimated. The results of the calculation of the rate of each component reaction show that the following two reactions are the most important in the initiation and in the transfer and termination steps when the [S]/([A] + [B]) ratio is large: where, A, A*, and P are styrene, polystyryl radical, and the cooligomer, respectively. Moreover, it was concluded that the deviation of the cooligomer composition from the statistical steady-state composition was caused by these two reactions.     

A Dodecalanthanide Wheel Supported by p‐tert‐Butylsulfonylcalix[4]arene

A dodecaholmium wheel of [Ho₁₂(L)₆(mal)₄(AcO)₄(H₂O)₁₄] ( 1 ; mal=malonate) was synthesized by using p‐tert‐butylsulfonylcalix[4]arene (H₄L) as a cluster‐forming ligand. The wheel consists of three fragments of mononuclear A^3? ([Ho(L)(mal)(H₂O)]^3?), trinuclear B^3? ([Ho(H₂O)₂(mal)(Ho(L)(AcO))₂]^3?), and C³⁺ ([Ho(H₂O)₂]³⁺), and an alternate arrangement of these fragments (A^3?? C³⁺? B^3?? C³⁺? A^3?? C³⁺? B^3?? C³⁺? ) results in a wheel structure. The longest and shortest diameters of the core were estimated to be 17.7562(16) and 13.6810(13) Å, respectively, and the saddle‐shaped molecule possesses a pocketlike cavity inside.     

Low temperature synthesis and characterization of porous anatase TiO2 nanoparticles

An ethanol solution of Ti-peroxy compounds was prepared from the ethanol solution of titanium isopropoxide (Ti(O-iPr)4) and H2O2. Heating of the ethanol solution of the Ti-peroxy compounds at 348 K formed a Ti-peroxy gel, and heat treatment of the gel at 348 K for more than 6 h formed gels that consisted of anatase nanoparticles. The diameter of the anatase nanoparticles increased from 9 to 15 nm as the heating time increased from 6 to 48 h. According to the results of the N2 adsorption measurement, the anatase nanoparticles had micropores, and the specific surface area (SBET) was in the range of 254 to 438 m2/g. The particle size, lattice strain, specific surface area, and photocatalytic activity of the anatase nanoparticles can be regulated by the heating time of the Ti-peroxy gel at 348 K.     

Synthesis and properties of the first stable silylene-isocyanide complexes

The first stable silylene-isocyanide complexes, [Tbt(Mes)SiCNAr] (5 c: Ar=Tip, 5 d: Ar=Tbt, 5 e: Ar=Mes*; Tbt=2,4,6-tris[bis(trimethylsilyl)methyl]phenyl, Mes=mesityl, Tip=2,4,6-triisopropylphenyl, Mes*=2,4,6-tri-tert-butylphenyl) were successfully synthesized by the reaction of a kinetically stabilized disilene, [Tbt(Mes)Si=Si(Mes)Tbt] (1), with bulky isocyanides, ArNC (3c-e). The spectroscopic data of 5 c-e and theoretical calculations for a model molecule indicated that 5 c-e are not classical cumulative compounds but the first stable silylene-Lewis base complexes. The reactions of 5 c-e with triethylsilane and 1,3-dienes gave the corresponding silylene adducts, and they underwent isocyanide-exchange reactions in the presence of another isocyanide at room temperature. These results indicate dissociation of complexes 5 c-e to the corresponding silylene 2 and isocyanides 3 c-e under very mild conditions. The reaction of 5 c with methanol gave the MeOH adduct 16, [Tbt(Mes)SiHC(OMe)NTip], which has a hydrogen atom on the silicon atom. This regioselectivity can be explained in terms of the contribution of zwitterionic resonance structures D and E, which have an anion on the silicon atom. This result indicates that 5 c is not a classical cumulene having Si=C double bonds that should react with methanol to give adducts bearing a methoxyl group on the silicon atom. Although the reactions of 5 c-e with electrophilic reagents such as methanol, hydrogen chloride, and methyl iodide gave the formal silylene adducts, the studies on the reaction mechanism by trapping experiments and the observation of the intermediate suggested that the reaction mainly or partially proceeds by initial nucleophilic attack of the silicon atom, as is the case in the formation of 16 in the reaction of 5 c with methanol. It was revealed that 5 c-e show the nucleophilicity of the silicon atom, most likely resulting from the contribution of the zwitterionic resonance structures D and E.     

Studies on the biosynthesis of corrinoids and porphyrinoids. II. The origin of nitrogen of vitamin B12

To clarify the origin of nitrogen of vitamin B12, 15N-labeled aminolevulinic acid (ALA) was prepared and administered to Propionibacterium shermanii. Vitamin B12 thus isolated showed four signals in the nitrogen-15 nuclear magnetic resonance (15N-NMR) spectrum. The nitrogen of [5-15N]riboflavine was incorporated into the benzimidazole part of vitamin B12. Hydroxycobalamin was transformed into cyanocobalamin by treatment with [15N]potassium cyanide, and the 15N-NMR spectrum was measured. The results of these experiments revealed the origin of the nitrogen atoms of vitamin B12, and allowed the 15N-NMR signals to be assigned.     

The raised-cosine wavelets in computerized tomography

In Computerized Tomography (CT), an image must be recovered from its sampled projections in the form of values of the Radon transform. In this work a method of recovering the image is based on the properties of the raised-cosine wavelet. This wavelet has a closed form which allows for certain precomputations and avoids convolution. The rate of convergence of the resulting algorithm to the image density function is found under suitable hypotheses. This algorithm is then tested on the standard Shepp–Logan