Buchsbaum homogeneous algebras with minimal multiplicity

In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous k-algebras A in terms of the dimension d, the codimension c, the initial degree q, and the length of the local cohomology modules of A. Next, we introduce the notion of Buchsbaum k-algebras with minimal multiplicity of degree q, and give several characterizations for those rings. In particular, we will show that those algebras have linear free resolutions. Further, we will give many examples of those algebras.     

Fuzzy logic in measurements

Our main interest in this paper is to translate from “natural language” into “system theoretical language”. This is of course important since a statement in system theory can be analyzed mathematically or computationally. We assume that, in order to obtain a good translation, “system theoretical language” should have great power of expression. Thus we first propose a new frame of system theory, which includes the concepts of “measurement” as well as “state equation”. And we show that a certain statement in usual conversation, i.e., fuzzy modus ponens with the word “very”, can be translated into a statement in the new frame of system theory. Though our result is merely one example of the translation from “natural language” into “system theoretical language”, we believe that our method is fairly general.     

Decision making under uncertainty with fuzzy targets

This paper discusses the issue of how to use fuzzy targets in the target-based model for decision making under uncertainty. After introducing a target-based interpretation of the expected value on which it is shown that this model implicitly assumes a neutral behavior on attitude about the target, we examine the issue of using fuzzy targets considering different attitudes about the target selection of the decision maker. We also discuss the problem for situations on which the decision maker’s attitude about target may change according to different states of nature. Especially, it is shown that the target-based approach can provide an unified way for solving the problem of fuzzy decision making with uncertainty about the state of nature and imprecision about payoffs. Several numerical examples are given for illustration of the discussed issues.     

Effect of particle size and shape on nonresonant random laser action of dye-doped polymer random media

We present an experimental study of the light emission from dye-doped polymer random media dispersed with TiO₂ particles of various sizes, shapes, and structures. Random lasing with nonresonant feedback, similar to that for spherically shaped particles that are used for conventional random lasers, is observed for almost all types of particles and aggregates. The efficiency of random lasing for each medium is analyzed using the relationship between the emission spectrum and the transport mean free path (TMFP), which is measured by enhanced backscattering experiments. Results show that the peak emission intensity depends strongly on the particle shape and structure, whereas the spectral linewidth is governed by the TMFP.     

Pulse laser ablation at water–air interface

We studied a new pulse laser ablation phenomenon on a liquid surface layer, which is caused by the difference between the refractive indices of the two materials involved. The present study was motivated by our previous study, which showed that laser ablation can occur at the interface between a transparent material and a gas or liquid medium when the laser pulse is focused through the transparent material. In this case, the ablation threshold fluence is reduced remarkably. In the present study, experiments were conducted in water and air in order to confirm this phenomenon for a combination of two fluid media with different refractive indices. This phenomenon was observed in detail by pulse laser shadowgraphy. A high-resolution film was used to record the phenomenon with a Nd:YAG pulse laser with 10-ns duration as a light source. The laser ablation phenomenon on the liquid surface layer caused by a focused Nd:YAG laser pulse with 1064-nm wavelength was found to be followed by the splashing of the liquid surface, inducing a liquid jet with many ligaments. The liquid jet extension velocity was around 1000 m/s in a typical case. The liquid jet decelerated drastically due to rapid atomization at the tips of the ligaments. The liquid jet phenomenon was found to depend on the pulse laser parameters such as the laser fluence on the liquid surface, laser energy, and laser beam pattern. The threshold laser fluence for the generation of a liquid jet was 20 J/cm². By increasing the incident laser energy with a fixed laser fluence, the laser focused area increased, which eventually led to an increase in the size of the plasma column. The larger the laser energy, the larger the jet size and the longer the temporal behavior. The laser beam pattern was found to have significant effects on the liquid jet’s velocity, shape, and history.     

Two-step preparation for catalyst-free biodiesel fuel production

Biodiesel fuel was prepared by a two-step reaction: hydrolysis and methyl esterification. Hydrolysis was carried out at a subcritical state of water to obtain fatty acids from triglycerides of rapeseed oil, while the methyl esterification of the hydrolyzed products of triglycerides was treated near the supercritical methanol condition to achieve fatty acid methyl esters. Consequently, the two-step preparation was found to convert rapessed oil to fatty acid methyl esters in considerably shorter reaction time and milder reaction condition than the direct supercritical methanol treatment. The optimum reaction condition in this two-step preparation was 270°C and 20 min for hydrolysis and methyl esterification, respectively. Variables affecting the yields in hydrolysis and methyl esterification are discussed.     

On-line liquid chromatography and circular dichroism detection of stereo-isomers of alpha-tocopherol derivatives generated by an electrochemical reaction

The electrochemical oxidation of (+/-)-alpha-tocopherol on a porous graphite electrode was performed in the presence of methanol, and successive separation and detection of the products were performed by an on-line liquid chromatography/mass spectrometry system. Three products were identified, one of which was determined to be alpha-tocopheryl quinone, because its m/z was 469 [M+Na](+). The other two products showed identical mass and UV spectra, and were suspected to be diastereomers of 9-methoxy-alpha-tocopheron, because their molecular weights were m/z 483 [M+Na](+), and also because it is known that the chemical oxidation of alpha-tocopherol by benzoyl peroxide or N-bromosuccinimide in the presence of methanol should provide 9-methoxy-alpha-tocopheron. To confirm that these two compounds were diastereomers, a circular dichroism detector was used. The signs of both peaks detected by the circular dichroism detector at 230 nm were opposite. In addition to observations of identical mass and ultraviolet spectra, these results indicated that the two products were diastereomers of 9-methoxy-alpha-tocopheron, whose stereochemistry is different at the newly generated chiral center of the 9-position. The on-line use of a circular dichroism detector with an electrochemical cell/liquid chromatography system may expand the utility of the system to study the metabolism of a chiral drug.     

Decomposition behaviors of various crystalline celluloses as treated by semi-flow hot-compressed water

Various types of crystalline cellulose consisting of group I (cell I, III_I, IV_I) and group II (cell II, III_II, IV_II) prepared from cotton linter were adjusted for their degree of polymerization (DP) as starting materials. These celluloses were then treated by semi-flow hot-compressed water (HCW) at 230–270 °C/10 MPa/2–15 min to study their decomposition behaviors. The treatments performed resulted in residues of celluloses and water-soluble (WS) portions. Consequently, the crystallinity of the residues was found to remain the same, but the DP was reduced as the temperature increased. Additionally, X-ray diffractometry and Fourier transform-infrared analyses demonstrated that crystallographic changes occurred for residues of cell III_I, IV_I and III_II. Despite these changes, the overall results of the residues showed that group I has higher resistance to decomposing than group II. As for the WS portions, the yields of the hydrolyzed and degraded products were higher in group II than group I, indicating that group II is less resistant to decomposition by HCW treatment. Results for both the residues and WS portions are in agreement with each other, showing that the degree of difficulty of decomposition was higher in group I than group II. Therefore, the decomposition behaviors of the celluloses are due to differences in the crystalline forms.     

A double-functionalized cyclen with carbamoyl and dansyl groups (cyclen = 1,4,7,10-tetraazacyclododecane): a selective fluorescent probe for Y(3+) and La(3+).

A cyclen (=1,4,7,10-tetraazacyclododecane) doubly functionalized with three carbamoylmethyl groups and one dansylaminoethyl (dansyl = 2-(5-(dimethylamino)-1-naphthalenesulfonyl) group (L(2) = 1-(2-(5-(dimethylamino)-1-naphthalenesulfonylamido)ethyl)-4,7,10-tris(carbamoylmethyl)-cyclen) was synthesized and characterized. Potentiometrtic pH titration and UV spectrophotometric titration of L(2) served to determine deprotonation of the pendant dansylamide (L(2) --> H(-1)L(2)) with a pK(a) value of 10.6, while the fluorometric titration disclosed a pK(a) value of 8.8 +/- 0.2, which was assigned to the dansyl deprotonation in the excited state. The 1:1 M(3+)-H(-1)L(2) complexation constants (log K(app) = 6.0 for Y(3+) and 5.2 for La(3+), where K(app)(M-H(-1)L(2)) = [M(3+)-H(-1)L(2)]/[M(3+)](free)[L(2)](free) (M(-1)) at pH 7.4) were determined by potentiometric pH titration and UV and fluorescence spectrophotometric titrations (excitation at 335 nm and emission at 520 nm) in aqueous solution (with I = 0.1 (NaNO(3))) and 25 degrees C. The X-ray structure analysis of the Y(3+)-H(-1)L complex showed nine-coordinated Y(3+) with four nitrogens of cyclen, three carbamoyl oxygens, and the deprotonated nitrogen and a sulfonyl oxygen of the dansylamide. The crystal data are as follow: formula C(28)H(49)N(11)O(13.5)SY (Y(3+)-H(-1)L(2) x 2(NO(3)(-)) x 2.5H(2)O), M(r) = 876.73, monoclinic, space group P2(1)/n (No. 14), a = 18.912(3) A, b = 17.042(3) A, c = 24.318(4) A, beta = 95.99(1) degrees, V = 7794(2) A(3), Z = 8, R1 = 0.099. Upon M(3+)-H(-1)L(2) complexation, the dansyl fluorescence greatly increased (8.6 and 3.8 times for Y(3+) and La(3+), respectively) in aqueous solution at pH 7.4. Other lanthanide ions also yielded Ln(3+)-H(-1)L(2) complexes with similar K(app) values, although all the dansyl fluorescences were weakly quenched. On the other hand, zinc(II) formed only a 1:1 Zn(2+)-L(2) complex at neutral pH with negligible fluorescence change. The X-ray crystal structure of the Zn(2+)-L(2) complex confirmed the pendant dansylamide being noncoordinating. The crystal data are as follow: formula C(28)H(51)N(11)O(14)SZn (Zn(2+)-L(2) x 2(NO(3)(-)) x 3H(2)O), M(r) = 863.22, monoclinic, space group C2/n (No. 15), a = 35.361(1) A, b = 13.7298(5) A, c = 18.5998(6) A, beta = 119.073(2) degrees, V = 7892.3(5) A(3), Z = 8, R1 = 0.084. Other divalent metal ions did not interact with L(2) at all (e.g., Mg(2+) and Ca(2+)) or interacted with L(2) with the dansyl fluorescence quenched (e.g., Cu(2+)).