Special simplices and Gorenstein toric rings

Athanasiadis [Ehrhart polynomials, simplicial polytopes, magic squares and a conjecture of Stanley, J. Reine Angew. Math., to appear.] studies an effective technique to show that Gorenstein sequences coming from compressed polytopes are unimodal. In the present paper we will use such the technique to find a rich class of Gorenstein toric rings with unimodal h-vectors arising from finite graphs.     

The upper and lower second order directional derivatives of a sup-type function

The purpose of this paper is to give a formula for expressing the second order directional derivatives of the sup-type functionS(x) = sup{f(x, t); t T} in terms of the first and second derivatives off(x, t), whereT is a compact set in a metric space and we assume thatf, f/x and ² f/x ² are continuous on ⁿ × T. We will give a geometrical meaning of the formula. We will moreover give a sufficient condition forS(x) to be directionally twice differentiable.     

Electron spin resonance study of polymerization of butadiene with tris(acetylacetonato)titanium and triethylaluminum

ESR spectra of homogeneous catalyst derived from tris(acetylacetonato)titanium(III) and triethylaluminum were observed at several temperatures from ?78°C, to +25°C, at molar ratios of aluminum to titanium of 1–108. At ?78°C, this catalyst yields a violet complex which shows an ESR signal with a g value of 1.959 and is associated with the first intermediate. At ?40°C to ?30°C, this signal decreases, and two signals with g values of 1.947 and 1.960 are observed. The latter two signals diminish at ?5°C to +10°C, while two kinds of new signals with g values of 1.965 and 1.969 appear overlapping each other. The structures of the species corresponding to these five signals are discussed on the basis of the ESR spectra, the intensity change, and the unpaired spin distribution. A new signal with a g value of 1.978 is found in the presence of butadiene at 25°C at Al/Ti > 8 and is assigned to a growing end of polybutadiene with this catalyst. The polymer yield increases remarkedly at Al/Ti molar ratios greater than 10. The microstructure of the resulting polymer consists almost completely of 1,2 units. The structure of the growing end is proposed to be a titanium (III) species containing two 1-substituted allyl groups, by comparison with the structure ascribed to the growing end of polybutadiene with n-butyl titanate-triethylaluminum catalyst.     

Electron spin resonance study on polymerization of alkyl acrylates with n-butyl titanate(IV)–triethylaluminum catalyst

n-Butyl titanate(IV)–triethylaluminum catalyst at Al/Ti molar ratios greater than 6 polymerizes methyl and n-butyl acrylates at ?78°C. The polymerization system which includes methyl acrylate at ?78°C, gives two ESR signals with g factors of 1.958 and 1.961 that overlap each other. The absorption intensity of the latter signal is approximately proportional to the polymer chain concentration calculated from polymer yield and the molecular weight. The polymerization system at Al/Ti ratios smaller than 3 has no catalytic activity on the polymerization and shows only the ESR signal with the g factor of 1.958. On the basis of these facts the ESR signal with the g factor of 1.961 is attributed to the active growing end of poly(methyl acrylate) with this catalyst. The character of this active growing end is discussed.     

Trifluoromethyl‐Radical‐Mediated Carbonylation of Alkanes Leading to Ethynyl Ketones

The carbonylation of alkanes 1 under radical‐reaction conditions was examined by using ethynyl triflone A as the unimolecular chain‐transfer (UMCT) reagent. Good to moderate yields of ethynyl ketones 2 were prepared by means of this three‐component coupling reaction. Higher CO pressures as well as lower concentrations of triflone A improved the efficiency of the reaction over the direct addition, the latter leading to alkylated ethynes 3 . In contrast to the reaction with A , the reaction of cyclohexane ( 1a ) with allyl triflone B (= ethyl 2‐methylene‐3‐[(trifluoromethyl)sulfonyl]propanoate) in the presence of CO gave a mixture of carbonylation products, including 8a formed from two molecules each of cyclohexane, CO, and allyl triflone B .     

Total synthesis of cis-solamin

[structure: see text] A convergent total synthesis of cis-solamin and its diastereomer was accomplished using VO(acac)2-catalyzed diastereoselective epoxidation followed by cyclization of bis-homoallylic alcohol as the key step. By comparison of the optical rotation of two possible diastereomers, it is suggested that the absolute configuration of natural cis-solamin is 1a.     

Novel rearrangement of twisted 2,4-di-alkyl 2-trans-4-trans pentadienals: An approach to cyclopentenones based on molecular mechanical consideration

Rearrangement of 2,4-di-$\text{trans}$-pentadienals $\text{IVa-d}$ was described as a consequence of the successive alkyl substitutions on the C-2 and C-4 positions. ¹H-FT nmr spectroscopy suggested that the reaction involves ketene $\text{VIII}$ as an intermediate.     

Polymerization of coordinated monomers. XVI. Stereoregulation in the alternating copolymerization of methyl methacrylate with styrene in the presence of metal halides

Triad cotacticities of alternating copolymers of methyl methacrylate with styrene prepared in the presence of zinc chloride, ethylaluminium sesquichloride, and ethylboron dichloride are investigated from the mechanistic point of view by means of ¹H- and ¹³C-NMR. The cotacticities from ¹H-NMR spectra are obtained accurately by using α-d-styrene in the place of styrene and by measuring the spectra on the copolymer in o-dichlorobenzene at 170°C. The relative intensities of three peaks of the splitting signal for the methoxy protons in the nonalternating copolymers obtained by the use of benzoyl peroxide in the absence of metal halides agree well with the cotacticity distribution calculated theoretically by the Lewis-Mayo mechanism with the stereoregulation following Bernoullian statistics. The splitting signals in the ¹H- and ¹³C-NMR spectra of the alternating copolymers prepared in the presence of metal halides cannot be explained by the same mechanism. The relative intensities of three peaks of the splitting signals for the methoxy protons and for the carbonyl carbon in the methyl methacrylate unit (the contents of cotactic triads centered by the methyl methacrylate unit) are not equal to those for the aromatic C₁ carbon in the styrene unit (the contents of cotactic triads centered by styrene unit). The value of f²Y - 4fxfz is not equal to zero, where fx, fy, and fz are the cosyndiotactic, coheterotactic, and coisotactic triad contents, respectively, in the alternating copolymer. Copolymers obtained in the presence of zinc chloride are not exactly equimolar alternating but always contain a methyl methacrylate unit in excess, and the relative intensities of the three peaks for the aromatic C₁ carbon change with the copolymer composition. These results are explained by a proposed mechanism: the alternating copolymerization proceeds through the homopolymerization of a ternary molecular complex composed of a metal halide, methyl methacrylate, and styrene, accompanied with the stereoregulation following first-order Markovian statistics; the increase of methyl methacrylate content in the copolymer prepared in the presence of zinc chloride is caused by the participation of the binary molecular complex composed of a metal halide and methyl methacrylate in addition to the ternary molecular complex.     

Study of Interactions Between Sugammadex and Penicillins Using Affinity Capillary Electrophoresis

Sugammadex, a new modified gamma cyclodextrin, reverses the neuromuscular blockage induced by rocuronium by forming a strong complex with this muscle relaxant. To evaluate possible interactions with potentially co-administered drugs, interactions between sugammadex and penicillins were investigated using the affinity capillary electrophoresis method for the first time. Capillary electrophoresis coupled to an ultra violet detector was used as an analytical device for the analysis and detection of cyclodextrin inclusion complexes. Changes in the effective mobility of guest drugs (amoxicillin, ampicillin, oxacillin, dicloxacillin and azlocillin) were correlated with the increasing concentration of host molecules in background electrolyte, and successfully fitted into a non-linear curve equation; assuming 1:1 stoichiometric interaction. The calculated association constants (K _a) were: 383.44, 184.54, 265.34 and 95.06 M⁻¹ for amoxicillin, ampicillin, oxacillin and dicloxacillin, respectively. No complex formation with sugammadex could be detected for both penicillin G and piperacillin. The difference in the chemical structure of the penicillins, especially in the (R) side chains, is suggested to be responsible for the variety of binding strength between penicillins and sugammadex. The displacement study demonstrated that interactions between sugammadex and co-administered penicillins could reduce the pharmacological effects of both.