Basic r-symmetric tropical polynomials

We consider tropical polynomials in nr variables, divided into n blocks of r variables, and especially r-symmetric tropical polynomials, which are invariant under the action of the symmetric group $S_n$ on the blocks. We define a set of basic r-symmetric tropical polynomials and show that the basic 2-symmetric tropical polynomials give coordinates on ${\mathbb{R}}^{2n}/S_n$ more efficiently than known polynomials. Moreover, we present special cases for $r\ge 3$ where the basic polynomials separate orbits.     

Pseudo-Gated Adsorption with Negligible Volume Change Evoked by Halogen-Bond Interaction in the Nanospace of MOFs

The enhancement of gas adsorption utilizing weak interactions in porous compounds is highly demanding for the design of energy-efficient storage materials. Here, we present a rational design for such an adsorption process by using synergistic functions between dynamic motion in a local module and weak but specific host–guest interactions, that is, halogen-bond (XB) interactions in metal–organic frameworks (MOFs). We designed a new porous coordination polymer (PCP), that is, Br-PCP, the pore surfaces of which are decorated with −CH₂Br groups and could be useful for interaction with CO₂ molecules. In accordance with our anticipation, in-situ studies suggest that the adsorption step at approximately 54 kPa during CO₂ adsorption is indeed facilitated by XB interactions with little change in the structural volume. This approach of integrating flexible XB modules in rigid PCPs is applicable for designing advanced gas storage systems.     

Efficient stereocontrol of a quaternary chiral center in the cyclohexene systems. Potential chiral synthons for vitamin D and related compounds by enzymatic approach

Cyclohexene derivatives, 8 ˜ 11, fused to γ-lactone with angular methyl are efficiently prepared in an enantio-, stereo- and regioselective manner from the chiral monoester 1.     

Diastereoselective Aldol Reaction with an Acetate Enolate: 2,6-Bis(2-isopropylphenyl)-3,5-dimethylphenol as an Extremely Effective Chiral Auxiliary

A C ₂ -symmetrical phenol was used as a chiral auxiliary in the asymmetric aldol reaction of chiral acetates with various aldehydes [Eq. (a)]. The reaction proceeds readily under mild conditions to provide aldol adducts with high enantioselectivity. LDA=lithium diisopropylamide.     

The First Enantioselective Aza-Diels–Alder Reactions of Imino Dienophiles on Use of a Chiral Zirconium Catalyst

Chiral dihydropyridone derivatives 3 are obtained in high yields and with good enantioselectivities by the title reaction of aldimines such as 1 with Danishefsky's diene 2 . 6,6′-Dibromo-1,1′-binaphthol complexes with Group 4 metals serve as catalysts; zirconium proved to be especially effective.     

Synthesis of new macro-azo-initiators having two kinds of azo linkages in repeating unit and block copolymerization by two-step radical polymerization initiated with them

Two kinds of new macro-azo-initiator (MAI) having dual decomposition temperatures were synthesized by polycondensation between 4,4′-azobis-4-cyanopentanoyl chloride (ACPC) and 2,2′-azobis-2-cyanopentanol (ACPO) (MAI [2A]), and between ACPC and 2,2′-azobis-2-methyl-N-2-hydroxyethylpropionamide (AHPA) (MAI [2B]). MAI [2A] and [2B] were compared with MAI [1] having a single decomposition temperature synthesized by polycondensation between ACPC and bisphenol-Z. Two step polymerization of styrene and methyl methacrylate initiated with MAI [1], [2A], and [2B] was carried out. It was confirmed that the new MAI [2A] and [2B] initiated effectively at each step of polymerization due to their dual decomposability, resulting in higher conversion of the comonomers to yield block copolymers than the case initiated with MAI [1]. © 1997 John Wiley & Sons, Inc.     

Density functional theory of chemical reactivity indices in some ion—molecule reaction systems

Three isoelectronic reactions, proton transfer (PT ), hydrogen abstraction (HA ), and electron transfer (ET ), of NH⁺₃ with NH,₃ H₂O, and HF have been studied using ab initio molecular orbital calculations. For the reaction of NH⁺₃ + H₂O, the energy of the transition state (TS) is higher than that of the reactants. This is consistent with the experimental observation that the rate constant is less than the average dipole orientation (ADO) rate constant. It seems reasonable that the reaction rate for the reaction NH⁺₃ + H₂O would hardly depend on the v₂ mode of NH⁺₃ at least for low-lying excited states (E_int≤ 0.714 eV) of the v₂ mode, because the v₂ mode contributes mainly to the normal mode orthogonal to the reaction coordinate at the TS . This is consistent with experimental observation. A similar prediction can be made for the NH⁺₃ + HF reaction. The electron-transfer processes for the HA reactions have been examined in terms of the intrinsic reaction coordinate (IRC ). The order of reactivity with NH⁺₃ is NH₃ > H₂O > HF. It is found that the degree of the electron transfer and the reactivity are correlated with the absolute hardness (η) of NH₃, H₂O, and HF. This is in accord with the softness as the chemical reactivity index in the density functional theory. © 1996 John Wiley & Sons, Inc.