Characterization of $$H^1$$ H 1 Sobolev Spaces by Square Functions of Marcinkiewicz Type

We establish characterization of \(H^1\) Sobolev spaces by certain square functions of Marcinkiewicz type. The square functions are related to the Lusin area integrals. Also, in the one dimensional case, the non-periodic version of the function of Marcinkiewicz is applied to characterize weighted \(H^1\) Sobolev spaces.

     

Redox-Induced Modulation of Exchange Interaction in a High-Spin Ground-State Diradical/Triradical System

A triplet ground-state diradical molecule, bis(nitronyl nitroxide)-substituted diphenyldihydrophenazine ( 1 ^..), that can be converted into a one-electron oxidized species, 1 ^{… +} , in the quartet ground state has been developed. Surprisingly, these species, 1 ^.. and 1 ^{… +} , can be used under ambient conditions because they are reasonably stable under aerobic conditions, even in solution. The temperature-dependent magnetic susceptibilities reveal that 1 ^.. and 1 ^{… +} are in the triplet state, with a weak exchange interaction (J₁/k_B = +3.1 K) and quartet ground state with a strong exchange interaction (J₂/k_B = +160 K), respectively. The interconversion between the neutral and one-electron oxidized species can be realized through electrochemical reactions. Significantly different absorption bands in the near-IR region newly appeared in the electronic spectra acquired during electrochemical oxidation/reduction.     

Synthesis of Selectively gem-Difluorinated Molecules; Chiral gem-Difluorocyclopropanes via Chemo-Enzymatic Reaction and gem-Difluorinated Compounds via Radical Reaction

The incorporation of fluorine atoms into an organic compound can alter the chemical reactivity or biological activity of the resulting compound due to the strong electron withdrawing nature of the fluorine atom. We have synthesized many original gem-difluorinated compounds and described the results in four sections. The first section describes the synthesis of optically active-gem-difluorocyclopropanes via the chemo-enzymatic reaction; we applied these compounds to liquid crystalline molecules, then further discovered a potent DNA cleavage activity for the gem-difluorocyclopropane derivatives. The second section describes the synthesis of selectively gem-difluorinated compounds via a radical reaction; we synthesized fluorinated analogues of a sex pheromone of the male African sugarcane borer, Eldana saccharina, and used the compounds as proof for investigating the origin of pheromone molecule recognition on the receptor protein. The third involves the synthesis of 2,2-difluorinated-esters by visible light-driven radical addition of 2,2-difluoroacetate with alkenes or alkynes in the presence of an organic pigment. The last section describes the synthesis of gem-difluorinated compounds via the ring-opening of gem-difluorocyclopropanes. We further developed a novel method of synthesizing gem-difluorohomoallylic alcohols via the ring-opening of gem-difluorocyclopropane and aerobic oxidation by photo-irradiation in the presence of an organic pigment. Since gem-difluorinated compounds that were prepared by the present method have two olefinic moieties with a different reactivity at the terminal position, we accomplished the synthesis of four types of gem-difluorinated cyclic alkenols via the ring-closing-metathesis (RCM) reaction.     

Catalytic Enantioselective Reaction of α‐Phenylthioacetonitriles with Imines Using Chiral Bis(imidazoline)–Palladium Catalysts

The catalytic enantioselective reaction of α‐phenylthioacetonitriles with imines has been developed. The reaction of various imines proceeds in good yields and diastereo‐ and enantioselectivities in the presence of chiral bis(imidazoline)–palladium catalysts. The obtained products can be converted into β‐aminonitrile or β‐aminoamide compounds without loss of enantiopurity.     

Geometric analysis of anharmonic downward distortion following paths

A mathematical aspect of the anharmonic downward distortion following (ADDF) path is discussed. The ADDF method is utilized as an automated reaction path search method, which can explore transition state geometries on a potential energy surface from a potential minimum. We show that the maximum number of the ADD stationary paths intersecting the potential minimum is 2^{f + 1} ? 2 , where f denotes the degree of freedom of the system. We also show that the bifurcation of the ADD stationary path is essential to detect all the transition states connected from a given minimum. The ADDF computation is demonstrated for a H₂O molecule in which pitchfork bifurcation is observed.     

Identification of novel EED-EZH2 PPI inhibitors using an in silico fragment mapping method

Journal of Computer-Aided Molecular Design - Enhancer of zeste homolog 2 (EZH2) is a histone lysine methyltransferase that is overexpressed in many cancers. Numerous EZH2 inhibitors have been...     

Cubic phases of binary systems of 4′-n-tetradecyloxy-3′-nitrobiphenyl-4-carboxylic acid (ANBC-14)-n-alkane

The phase behaviour of the binary systems 4′- ⁿ -tetradecyloxy-3′-nitrobiphenyl-4-carboxylic acid (ANBC-14)- ⁿ -alkane ( ⁿ -tetradecane or ⁿ -hexadecane) was investigated by differential scanning calorimetry, polarizing optical microscopy, and X-ray diffraction. The phase behaviour was a function of temperature ( ^T ) and the effective carbon number of the system ( ^n*), where ^n* involves carbon atoms both from the alkoxy group of ANBC-14 and from the ⁿ -alkane added. ANBC-14 shows no cubic phase, but the addition of ⁿ -alkane induced cubic phases when ^n*≧c. 15. An interesting point is that the type of cubic phase is ^Ia 3 ^d for 15^≦n*≦17, while an ^Im 3 ^m type is formed for 18^≦n*≦20. Furthermore, for ^n* = 22, two types of cubic phase, one with ^Im 3 ^m symmetry in the low temperature region and the other with ^Ia 3 ^d in the high temperature region, were observed both on heating and cooling. The phase diagram with respect to ^T and ^n* is very similar to that of pure one-component ANBC- ⁿ , which is a function of ^T and the number of carbon atoms in the alkoxy group ⁿ .     

Cubic phases of 4′-n-alkoxy-3′-nitrobiphenyl-4-carboxylic acids (ANBC-n)

The structure of the thermotropic cubic phases of 4′- ⁿ -alkoxy-3′-nitrobiphenyl-4-carboxylic acids (ANBC- ⁿ , where ⁿ indicates the number of carbon atoms in the alkoxy group) was studied by X-ray diffraction. For the homologues with ⁿ = 15, 16, 17, and 18, the cubic phase was of an ^Ia 3 ^d type, whereas the homologues with ⁿ = 19, 20, and 21 exhibited an ^Im 3 ^m cubic structure; for these seven homologues the same type of cubic structure was observed both on heating and cooling. Further lengthening of the alkoxy chain to ⁿ = 22 and 26, however, gave two types of cubic structure in the cubic phase region on heating, one with ^Im 3 ^m symmetry in the low temperature region and the other with ^Ia 3 ^d symmetry in the high temperature region. On cooling, the two homologues exhibited the ^Ia 3 ^d cubic structure only. This is the first example in the cubic phase region of a series of homologues containing two types of structure, dependent on temperature and ⁿ . Such a complicated phase diagram in the cubic region is clearly understood qualitatively in terms of Gibbs free energy-temperature diagrams. The dependence of structural parameters such as the cubic lattice constant on the alkoxy chain length ⁿ are also presented and discussed.     

Dissipative structure for symmetric hyperbolic systems with memory

We study symmetric hyperbolic systems with memory-type dissipation and investigate their dissipative structures. We treat two cases: memory-type diffusion and memory-type relaxation, and observe that the dissipative structures of these two cases are essentially different. Namely, we show that the dissipative structure of the system with memory-type diffusion is of the standard type, while that of the system with memory-type relaxation is of the regularity-loss type.