On Hadamard Product of Hypercomplex Numbers

Certain product rules take various forms in the set of hypercomplex numbers. In this paper, we introduce a new multiplication form of the hypercomplex numbers that will be called «the Hadamard product», inspired by the analogous product in the real matrix space, and investigate some algebraic properties of that, including the norm of inequality. In particular, we extend our new definition and its applications to the complex matrix theory.

Cyclobutyl methyl ketone as a model compound for pinonic acid to elucidate oxidation mechanisms

3-Methyl-1,2,3-tricarboxylic acid (MBTCA), terpenylic acid and diaterpenylic acid acetate were identified in secondary organic aerosol (SOA) from α-pinene photooxidation or ozonolysis. These compounds display interesting structural features: MBTCA has a high oxygen to carbon ratio, terpenylic acid contains a lactone ring in its structure and diaterpenylic acid acetate possesses an ester functional group. The reaction mechanisms leading to these products are still unknown, but it was demonstrated experimentally in earlier studies that MBTCA is formed from pinonic acid, a primary ozonolysis product of α-pinene. Because the direct observation of pinonic acid oxidation in a smog chamber would be difficult due to its relatively low volatility, a model compound possessing the substructure of interest was used instead: cyclobutyl methyl ketone (CMK). From its oxidation, several organic acids could be measured with ion chromatography (IC) coupled to a mass spectrometer (MS). Succinic acid, the analogous product of MBTCA is formed at molar yields of 2 to 5%. Butyrolactone is detected as butanoic acid, due to hydrolysis in the sampling device. A monocarboxylic acid with nominal mass 146 was detected in the absence of nitrogen oxides (NOx) and could be the analogous product of diaterpenylic acid acetate. However, due to a lack of available standards, the exact structure of this compound remains unelucidated. Finally, 4-oxobutanoic acid could also be measured and two structures of its expected analogous compound from pinonic acid oxidation are proposed. Because these compounds are primary products of the CMK oxidation, reaction mechanisms capable of adding one or two carboxylic functional groups without formation of stable intermediate products needs to be formulated. Such a formation mechanism of MBTCA from pinonic acid was found in the literature; however, it includes a hydrogen atom migration to an acyloxy radical, which is expected to loose carbon dioxide (CO2) very rapidly. A competitive reaction pathway is expected to lead to the formation of a monocarboxylic acid with nominal mass 144, instead of this acyloxy radical; however, no such monocarboxylic acid was measured and other reaction pathways still need to be explored.

Increasing Innovation: A Trilogy of Experiments Towards a Design-by-Analogy Method

Design by analogy is a noted approach for conceptual design. This paper seeks to develop a robust design-by-analogy method. This endeavor is sought through a series of three experiments focusing on understanding the influence of representation on the design-by-analogy process. The first two experiments evaluate the effects of analogous product description—presented in either domain-general or domain-specific language—on a designer’s ability to later use the product to solve a novel design problem. Six different design problems with corresponding analogous products are evaluated. The third experiment in the series uses a factorial design to explore the effects of the representation (domain specific or general sentinel descriptions) for both the design problem and the analogous product on the designer’s ability to develop solutions to novel design problems. Results show that a more general representation of the analogous products facilitates later use for a novel design problem. The highest rates of success occur when design problems are presented in domain specific representations and the analogous product is in a domain general representation. Other insights for the development of design by analogy methods and tools are also discussed.

A Simple High-Yield Synthesis of Gallium(I) Tetrachlorogallate(III) and the Reaction of Digallium Tetrachloride Tetrahydrofuran Solvate with 1,2-Diols

Gallium(I) tetrachlorogallate(III) Ga[GaCU] was prepared in quantitative yield by thermal de­composition of dichlorogallane [HGaCl2]2, which is readily available from Et3SiH and [GaCl3]2. The reaction of catechol with solutions of this gallium(I) tetrachlorogallate(III) in tetrahydrofuran leads to the evolution of hydrogen gas and affords a dinuclear gallium(III) complex with penta-coordinate metal atoms chelated and bridged by mono-deprotonated catechol ligands. In the crystalline phase tetrahydrofuran molecules are hydrogen-bonded to the hydroxy groups: [Ga(1,2 -OC6H4OH)Cl2(C4H8O)]2. The reaction with pinacol also gives hydrogen and the analogous product [Ga(OCMe2CMe2OH)Cl2(C4H8O)]2. The structures of the two compounds have been determined by X-ray diffraction. A mechanism of the new reaction has been proposed which involves oxidative addition of the diol to the solvate (THF)Cl2Ga-GaCl2(THF) present in the tetrahydrofuran solution to give a gallium hydride intermediate.

A reaction for the simple sensitive fluorimetric assay of heparin and 2-amino sugars

1. 3,5-Diaminobenzoic acid reacted rapidly with the product from HNO2 deamination of heparin, heparan sulphate and 2-amino-2-deoxyhexoses under very mild conditions (pH3.0 and 37°C) to give stable fluorescent derivatives. 2. The fluorescence yield was rectilinearly related to the concentration of heparin etc. Less than 0.1μg of 2-amino-2-deoxyhexose was easily measurable in standard cuvettes. 3. The deamination products of glucosamine and (particularly) galactosamine were labile in the HNO2 reagent, with half-lives of 20–40min at room temperature. At 0°C they were much more stable. The analogous product from heparin was not so labile. 4. Under the standard conditions, and at room temperature, relative fluorescence yields (d-glucosamine=1.0) were: d-galactosamine, 0.75; d-gulosamine, 0.38; d-mannosamine, approx. 0.20. 5. Neutral sugars, chondroitin sulphates, DNA and N-acetylneuraminic acids did not react, nor did N-acetylamino sugars or non-deaminated hexosamines. 6. It is suggested that the Dische–Borenfreund [Dische & Borenfreund (1950) J. Biol. Chem.184, 517–522] indole method, the Kissane–Robins [Kissane & Robins (1962) J. Biol. Chem.233, 184–188] DNA assay and the proposed amino sugar method are all examples of simple aldehyde reactions. The specificity of the proposed method is considerably greater than that of the Dische–Borenfreund procedure, partly because of the much milder reaction conditions. 7. The proposed method is very reproducible, about 50–100 times as sensitive as the Elson–Morgan reaction, and 10–50 times as sensitive as the Dische–Borenfreund procedures. It is also convenient; acid hydrolysates of amino sugar-containing compounds can be directly neutralized with sodium acetate solution.

Photochemical and thermal rearrangements of some 3H-pyrazoles

Low temperature (−70 °C) irradiation of 3,3,4,5-tetramethyl-3H-pyrazole (2a) leads to the formation of the 1,2-diazabicyclo[2.1.0]pent-2-ene (3a), as has been reported previously. Irradiation of 3,3-dimethyl-4,5-diphenyl-3H-pyrazole (2b) under identical conditions did not result in formation of the analogous product but lead instead to formation of the cyclopropene via decomposition of the vinyl diazo compound. The thermal rearrangements of 2a and a series of 5-aryl-3,3-dimethyl-4-phenyl-3H-pyrazoles (2b–d) lead to formation of the 4H-pyrazoles 6a–d and the N-methylpyrazoles 5a–d, resulting from competitive methyl migrations to carbon and nitrogen. The Arrhenius parameters for the rearrangement of 2b were determined. Decomposition of the methiodides derived from the 4H-pyrazoles 6a–d leads to formation of the N-methylpyrazoJes 5a–d; the mechanism of this decomposition was examined by high temperature 1Hmr spectroscopy. The N-methylpyrazoles were synthesized by independent routes and the structures were assigned with the aid of lanthanide shift reagents, 1Hmr solvent shift studies, and 13Cmr spectroscopy. The thermodynamic equilibria of the isomeric N-methylpyrazoles were determined and found to be influenced by a small substituent effect. The photochemical and thermal behaviour of 3H-pyrazoles is discussed and compared to that of 1-pyrazolines.

Quinoxaline derivatives. VIII. Betaine structures of dihydroquinoxalinium and benzimidazolium barbiturates formed from o-dialkylaminoanilines and alloxan

Condensation of alloxan and o-dimethylaminoaniline gives 1,2,3,4.tetrahydro-4-methylquinoxaline-2-spiro-5-(hexahydro-2,4,6-trioxopyrimidine) (I) formed as a result of a unique ring-closure involving a methyl group of the o-dimethylamino substituent. The structure of the closely related compound previously formulated as its 3-hydroxy derivative (a carbinolamine) (II) is now revised to the corresponding betaine, a dihydroquinoxalinium barbiturate (III; R = H). The 6-methyl, 7-methyl, and 6,7-dimethyl analogues of the spiran (I), like the parent compound, were regarded as anils by Rudy and Cramer. Betaine structures (cf. III) may be assigned to the 6,7-dimethyl and 6,7-dichloro analogue of the barbiturate (III; R = H). o-Diethylaminoaniline reacts differently from o-dimethylaminoaniline with alloxan in giving a benzimidazolium barbiturate (VIII; R = H). We propose a similar benzimidazolium barbiturate structure for the analogous product from 4,5-dimethyl-2-dipropylaminoaniline. Mass spectra of the lowly volatile betaines and some of their deuterated derivatives were obtained and rationalized in terms of the assigned structures. Several dihydrobenzimidazoles have been prepared, and their N.M.R. and light absorption spectra recorded.