A Linear Time Algorithm for Finding ak-Tree Core

Given a tree containingnvertices, consider the sum of the distance between all vertices and ak-leaf subtree (subtree which contains exactlykleaves). Ak-tree core is ak-leaf subtree which minimizes the sum of the distances. In this paper, we propose a linear time algorithm for finding ak-tree core for a givenk.     

Prospective study to assess the clinical efficacy of bone scintigraphy--comparative study of the efficacy in breast carcinoma and prostate carcinoma

Prospective study of bone scintigraphy was performed on 414 patients with breast carcinoma and 88 patients with prostate carcinoma. In 468 of them, confirmative diagnoses of bone, whether metastasis was existent or not, were made after the observations over a year. Finally, the incidences of bone metastasis were 11 percent for breast carcinoma and 54 percent for prostate carcinoma respectively. The efficacy of preoperative bone scintigraphy in breast carcinoma was comparable to that in prostate carcinoma with regard to improvement of predictive probability of bone metastasis: raising up the probability in the positive cases and bringing down in the negative cases.     

Structural studies of polyhydroxybis(tetrahydrofuran)acetogenins from Annona squamosa using the combination of chemical derivatization and precursor-ion scanning mass spectrometry

The structure of squamocin polyhydroxybis(tetrahydrofuran)acetogenin from Annona squamosa L., was characterized by a combination of the chemical derivatization and precursor-ion scanning mass spectrometry. The lactone part of squamocin was modified with N,N-dimethylethylenediamine in the vapour phase to afford a strong positive charge at one end of the skeleton. The derivative was ionized by fast atom bombardment (FAB), and the product ion spectrum from [M + H]⁺ and the precursor ion spectrum from the m/z 72 ion [CH₂?CHN⁺H(CH₃)₂] generated by low-energy collision were acquired. The structure of the derivative could be characterized by the precursor-ion spetrum from the m/z 72 ion, but little structural information could be obtained from the production spectrum from [M + H]⁺ of the derivative. By the attachment of a tertiary amino group to one end of the skeleton, charge-remote fragmentation was facilitated and abundant and unique fragment ions were observed in the precursor-ion spectrum. Structural characterization of six other isolated compounds was also carried out, and two novel compounds were found by this technique. A similar derivatization was applied in the peptide leu-enkephalin, and full sequencing from the C-terminus using precursor-ion scanning from m/z 72 could be achieved.     

Texture analysis of speckles due to random Koch fractals by lacunarity

We analysed the textures of speckles produced from random Koch fractals to quantitatively confirm the existence of speckle clustering which we investigated in a previous paper. The texture analysis involved using the lacunarity of these speckles, which is defined as fluctuations of the intensity integrated within a box, and comparing this quantity with that for ordinary fully-developed speckles. The lacunarity of clustered speckles was found to be greater than that of ordinary speckles throughout the whole range of the size of the box under examination, indicating the existence of long correlation tails in speckles. We also discuss the physical origin of these long correlation tails.     

Reactive polypeptides. II. Photochemistry of poly(γ-cinnamyl L-glutamate)

Poly(γ-cinnamyl L -glutamate) was irradiated in the presence and absence of benzophenone in dichloroethane. The irradiated polymers were analyzed by gas chromatography after hydrolysis. It was possible to assign the transformation in the presence of benzophenone to trans-cis photoisomerization by comparing the effects with those observed for a model compound cinnamyl acetate. The equilibrium composition of cis and trans isomers in the photostationary state was similar for the model compound and the polypeptide. Photoisomerization was found to be accompanied by marked side reactions for the direct irradiation. Circular dichroism spectra were empolyed to study the structure, and no changes in the structure were found for the irradiated polymers.     

Ruthenium-catalysed linear-selective allylic alkylation of allyl acetates

The regioselectivity in the ruthenium-catalysed allylic alkylation of mono substituted allyl acetates with the malonate anion was highly controlled by Ru3(CO)12 with 2-(diphenylphosphino)benzoic acid, and the linear-type alkylated product was obtained.