Participation of Non-Conjugated Double Bonds in Diels-Alder Reactions. A kinetic study of the addition of tropone to norbornens

A kinetic study of Diels-Alder additions between norbornene derivatives acting as dienophiles and the dienes tropone, perchlorocyclopentadiene and 9,10-dimethylanthracene is presented. The results suggest that tropone thereby acts as an electron acceptor, classifying these reactions then as Diels-Alder additions with ‘inverse electron demand’. The role of non-reacting double bonds was investigated using 7-alkylidenorbornene derivatives as dienophiles. These show comparable reactivity in ‘normal’ but enhanced reactivity in ‘inverse electron demand’ Diels-Alder additions. This outcome is interpreted in terms of frontier orbital interactions between the reactants using photoelectron spectroscopical results as a basis for the qualitative perturbation treatment. It is suggested that the enhanced reactivity in the case of the 7-alkylidene derivatives does not necessitate the consideration of a direct (‘through-space’) participation of the non-reacting double bond.     

Calorimetric study of the glassy state XII. Plural glass-transition phenomena of ethanol

Ethanol was found to give a metastable crystalline phase (crystal-II) when the liquid was cooled at a moderate rate. Glassy states of liquid and of newly found crystal-II were obtained in the calorimeter cell by controlling the cooling rate of the liquid. The heat capacities of these phases as well as that of the stable crystal-I were measured by an adiabatic calorimeter in the temperature range between 14 and 300 K. The glass transition temperature T_g, the heat-capacity jump at T_g, and the residual entropy were found to be 97 K, 35.3 J K^?1 mol^?1, and 8.93 J K^?1 mol^?1 for the glassy liquid, and 97 K, 22.8 J K^?1 mol^?1, and 4.24 J K^?1 mol^?1 for the glassy crystal-II, respectively. The values for the residual entropy are referred to the third-law entropy for crystal-I.The heat capacities reported previously for the supercooled liquid by Gibson et al. and by Parks and Kelley agree well with those for the metastable crystal-II. Those of the supercooled liquid connect smoothly with those obtained for the liquid above the melting temperature. Thus, ethanol is found to be another example of a low-molecular-weight compound which shows multiple glass-transition phenomena.     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

The temperature dependence of the zero-field splitting of trimethylenemethane

Trimethylenemethane was generated by γ-irradiating polycrystalline methylenecyclopropane, and studied by EPR at various temperatures. The zero-field splitting constant, D, was observed to change from 0.0260 cm^?1 at 4 K to 0.0212 cm^?1 at 126 K, though the hyperfine coupling showed little temperature dependence.     

Thermodynamic studies of clathrate hydrates

Thermodynamic studies of clathrate hydrates, mainly of structures I and II, are considered in this review which is based on 147 references. There are two main subjects. The first is the host lattice energy and the guest-host interaction energy, both of these quantities being related to the enthalpy of dissociation and composition of the hydrates. The second subject concerns orientational ordering phenomena occurring in both host and guest, as reflected in the low temperature heat capacity. The classical theoretical treatment of clathrate formation has been reconsidered on the basis of recent experimental results. Particular emphasis has been given to orientational ordering since this topic is undoubtedly central to clarifying the nature of clathrate hydrates.Ausgehend von 147 Literaturangaben wurden in diesem Review thermodynamische Untersuchungen von Klathrathydraten hauptsächlich der Struktur I und II betrachtet. Es gibt zwei Hauptaugenmerke. Als erstes die Wirtsgitterenergie und die Gast-Wirt-Wechselwirkungsenergie, beide bezogen auf die Dissoziationsenthalpie und die Bildungsenthalpie der Hydrate. Das zweite Hauptaugenmerk betrifft Orientierungs-Konditionierungserscheinungen sowohl in Wirt als auch Gast, wie in den Wärmekapazitäten bei niedrigen Temperaturen widergespiegelt wird. Auf der Basis jüngster experimenteller Ergebnisse wurde die klassische theoretische Betrachtung über die Bildung von Klathraten überprüft. Der Orientierung-Konditionierung wurde besonderer Nachdruck verliehen, da dies zweifellos eine entscheidende Rolle bei der Klärung der Natur der Klathrathydrate spielt. 147 I II. . «» « — », . «» « », . . , .

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Contribution No. 155 from the Chemical Thermodynamics Laboratory.     

Preliminary calculations on excited states of the oxygen molecule

It is well known that the energy interval separating ³ _u ^– and ³ _u ⁺ states of O₂, as given by the conventional ASMO method, is too large. In order to resolve this difficulty, removal of the equivalence restrictions usually employed in the orbital theory is proposed. Thus the orbital exponent of one antibonding _g MO is allowed to take a different value from the other _g's. Variational calculations show that the resulting outermost orbital is much more diffuse than the others. This model of a single diffuse orbital brings about a considerable energy lowering for the ³ _u ^– state and thus the agreement of the ³ _u ^– - ³ _u ⁺ interval with experiment is improved.

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Zusammenfassung Die konventionelle ASMO-Theorie liefert bekanntlich eine viel zu große Differenz der Terme ³ _u ^– und ³ _u ⁺ von O₂, weswegen der Vorschlag gemacht wird, die üblicherweise vorgenommene Äquivalenz-Einschränkung fallen zu lassen. Der Orbital-Exponent eines lockernden MO's kann von dem der übrigen _g's abweichen. Rechnungen zeigen, daß das äußerste MO viel diffuser als die anderen ist und daß die Energie des ³ _u ^– -Zustandes beträchtlich erniedrigt wird.

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Résumé La séparation entre les états ³ _u ^{– 3} _u ⁺ de O₂ donnée par la méthode ASMO conventionnelle est connue pour être trop grande. Afin de résoudre cette difficulté la levée des restrictions d'équivalence ordinairement utilisées est proposée. Ainsi l'exposant orbital d'une des orbitales moléculaires antiliantes _g peut prendre une valeur différente de celui de l'autre orbitale antiliante _g. Des calculs variationnels montrent que l'orbitale la plus haute ainsi obtenue est beaucoup plus diffuse que les autres. Ceci a pour effet de diminuer considérablement l'énergie de l'état ³ _u ^– , améliorant la séparation entre les états ³ _u ^– et ³ _u ⁺ .

     

Formulation study for lansoprazole fast-disintegrating tablet. II. Effect of triethyl citrate on the quality of the products

The purpose of this study was to develop enteric-coated microgranules for the lansoprazole fast-disintegrating tablet (LFDT), which is a rapidly disintegrating tablet containing enteric-coated microgranules. In our previous study, it was clarified that sufficient flexibility of the enteric layer was achieved by the optimized combined ratio of methacrylic acid copolymer dispersion to ethyl acrylate-methyl methacrylate copolymer dispersion and adding the optimized concentration of triethyl citrate to reduce the damage during the compression process. However, since triethyl citrate has an unpleasant bitter taste and is especially incompatible with lansoprazole, it adversely affects the taste and stability of lansoprazole in the enteric-coated microgranules. The enteric layer containing macrogol 6000 was proven useful to improve the unpleasant bitter taste and stability of lansoprazole, because macrogol 6000 does not have an unpleasant bitter taste and is more compatible than triethyl citerate. By covering the inner (first enteric layer) and outer side (third enteric layer) of the enteric layer containing triethyl citrate (second enteric layer) with the enteric layer containing macrogol 6000, we resolved the stability problem of lansoprazole and the unpleasant bitter taste. Finally, we developed enteric-coated microgranules comprising seven layers: 1) core, 2) active compound layer, 3) intermediate layer, 4) first enteric layer, 5) second enteric layer, 6) third enteric layer, and 7) over coating layer. The enteric-coated microgranules have the multiple functions of reducing the damage to the enteric layer during the compression process, improving the stability of lansoprazole, and masking the unpleasant bitter taste.     

Bounding the diameter of a distance regular graph by a function ofk d

Let be a distance regular graph with diameterd, and _d () the set of vertices at distanced from. is said to be thin if the induced subgraph on _d () is a union of cliques for every vertex. We show that the diameterd is bounded above by a function depending only onk _d, which is the cardinality of _d (), if is not thin. We also investigate thin distance regular graphs witha _d 0.     

Efficient algorithms for solving rank two and rank three bilinear programming problems

Finitely convergent algorithms for solving rank two and three bilinear programming problems are proposed. A rank k bilinear programming problem is a nonconvex quadratic programming problem with the following structure: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaacaWFTbGaa8% xAaiaa-5gacaWFPbGaa8xBaiaa-LgacaWF6bGaa8xzaiaa-bcacaWF% 7bacbiGaa43yamaaDaaaleaacaGFWaaabaGaa4hDaaaakiaa+Hhaca% GFRaGaa4hzamaaDaaaleaacaGFWaaabaGaa4hDaaaakiaa+LhacaGF% RaWaaabuaeaacaGFJbWaa0baaSqaaiaa+PgaaeaacaGF0baaaOGaam% iEaiabl+y6NjaadsgadaqhaaWcbaGaamOAaaqaaiaadshaaaGccaWG% 5bGaaiiFaaWcbaGaa8NAaiaa-1dacaWFXaaabeqdcqGHris5aOGaa4% hEaiabgIGiolaa+HfacaGFSaGaa4xEaiabgIGiolaa+LfacaWF9bGa% a8hlaaaa!5D2E!\[minimize \{ c_0^t x + d_0^t y + \sum\limits_{j = 1} {c_j^t xd_j^t y|} x \in X,y \in Y\} ,\]where X Rⁿ¹ and Y R ⁿ² are non-empty and bounded polytopes. We show that a variant of parametric simplex algorithm can solve large scale rank two bilinear programming problems efficiently. Also, we show that a cutting-cake algorithm, a more elaborate variant of parametric simplex algorithm can solve medium scale rank three problems.This research was supported in part by Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture, Grant No. 63490010.