On the stability of characterizations of the exponential distribution

Summary It is shown that if the distribution of min {X ₁/a₁, X₂/a₂,…, X_N/a_N} is close to that ofX ₁, then the distribution is close to the exponential distribution. The paper was presented at the Conference on Mathematical Statistics and Probability Theory held at the New Delhi Centre of the Indian Statistical Institute, December, 1980. The Institute of Statistical Mathematics     

SCF MO calculations of heteroatomic systems with the variable Β approximation

In order to elucidate the electronic structure of protonated N-heterocycles, we have carried out SCF MO calculations, considering the -bond polarizations which are caused by the large net charge on nitrogen atom. Appropriate parametrizations of the valence state energies associated with the -bond polarization model have been proposed. Our calculations showed that a conventional covalent model for protonated N-heterocycles failed to explain the experimental electronic spectral data and an extremely polarized -core model gave quite good results in the whole. The present theory expected that the nature of electronic spectra of quinoline is considerably changed by the -bond polarization due to the protonation.

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Zusammenfassung Um die Elektronenstruktur von protonisierten N-Heterozyklen zu untersuchen, wurden SCF-MO-Rechnungen durchgeführt, bei denen die Polarisierung der -Bindung durch die Ladung am N-Atom berücksichtigt wird. Eine geeignete Parametrisierung der Valenzzustands-Energien in Verbindung mit dem Modell der Polarisierung der -Bindung wird vorgeschlagen. Die Rechnungen zeigen, da\ ein herkömmliches kovalentes Modell für die genannten Verbindungen bei der ErklÄrung des Elektronenspektrums versagt, wÄhrend ein Modell mit stark polarisierten -Bindungen befriedigende Ergebnisse liefert. Aus der vorliegenden Theorie lÄ\t sich folgern, da\ das Elektronenspektrum des Chinolins betrÄchtlich durch die Polarisierung der -Bindung infolge Protonisierung geÄndert wird.

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Résumé Afin d'éclaircir la structure électronique d'hétérocycles protonisés sur l'azote, nous avons effectué des calcules SCF MO en considérant la polarization des liaisons dûe à la forte charge nette sur l'atome d'azote. Des paramétrisations appropriées à ce modèle polarisé sont proposées pour les énergies des états de valence. Nos calculs ont montré qu'un modèle covalent conventionnel pour les N hétérocycles protonisés ne réussit pas à expliquer le spectre électronique expérimental alors qu'un modèle à forte polarisation du squelette donne des résultats dans l'ensemble satisfaisants. Cette théorie prévoit que la nature du spectre électronique de la quinoléine est considérablement modifiée par la polarisation dûe à la protonisation.

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Presented partly at the 23rd Symposium on Molecular Structure and Spectroscopy, The Ohio State University, Columbus, Ohio, U.S.A., September 1968.     

Efficient total synthesis of (+)-negamycin, a potential chemotherapeutic agent for genetic diseases

Herein, we describe an efficient strategy for the total synthesis of (+)-negamycin using commercially available achiral N-Boc-2-aminoacetaldehyde as starting material with 42% overall yield for a limited number of steps.     

Identification of estrogenic/anti-estrogenic compounds in diesel exhaust particulate extract

Diesel exhaust particulate extract (DEPE) was obtained from diesel exhaust particulates with Soxhlet extraction using dichloromethane. After separating DEPE into 11 fractions by liquid-liquid extraction, the neutral fraction (N) showed anti-estrogenic activity and the weak acid (phenol) fraction (WA(P)) showed estrogenic and anti-estrogenic activities by a yeast two-hybrid assay system expressing human estrogen receptor alpha. Both fractions were thoroughly fractionated by silica gel column chromatography and reversed-phase HPLC. In the WA(P) fraction, 3-methyl-4-nitrophenol and 2,6-dimethyl-4-nitrophenol were identified by LC-MS/MS as estrogenic compounds. This is the first study to identify 2,6-dimethyl-4-nitrophenol in DEPE and the first study to show that it is an estrogenic compound. In the N fraction, 1-hydroxypyrene was also identified by LC-MS/MS as an anti-estrogenic compound.     

Development of Proton‐Responsive Catalysts

A changeable ligand, which involves in activation of a catalyst or assists a reaction, draws an increasing attention, in contrast to a classical ligand as spectator. Proton‐responsive catalysts, which are capable of undergoing changes of properties on gaining/losing one or more protons, provides interesting features as follows: (i) catalyst activation by electronic effect, (ii) pH‐tuning of water‐solubility, and (iii) second‐coordination‐sphere interaction. On the basis of this catalyst design concept, we developed several highly efficient proton‐responsive catalysts for CO₂ hydrogenation as H₂ storage, formic acid (FA) dehydrogenation as H₂ production, and transfer hydrogenation. The transformable ligands of proton‐responsive catalysts in promoting effective catalysis have aroused our interest. In this account, we summarize our efforts for the development and application of proton‐responsive catalysts. Specifically, the important role of pH‐dependent proton‐responsive complexes will be discussed.     

Proton‐Induced Generation of Remote N‐Heterocyclic Carbene–Ru Complexes

The proton‐induced Ru?C bond variation, which was previously found to be relevant in the water oxidation, has been investigated by using cyclometalated ruthenium complexes with three phenanthroline (phen) isomers. The designed complexes, [Ru(bpy)₂(1,5‐phen)]⁺ ([ 2 ]⁺), [Ru(bpy)₂(1,6‐phen)]⁺ ([ 3 ]⁺), and [Ru(bpy)₂(1,7‐phen)]⁺ ([ 4 ]⁺) were newly synthesized and their structural and electronic properties were analyzed by various spectroscopy and theoretical protocols. Protonation of [ 4 ]⁺ triggered profound electronic structural change to form remote N‐heterocyclic carbene (rNHC), whereas protonation of [ 2 ]⁺ and [ 3 ]⁺ did not affect their structures. It was found that changes in the electronic structure of phen beyond classical resonance forms control the rNHC behavior. The present study provides new insights into the ligand design of related ruthenium catalysts.     

Linear and nonlinear inversion schemes to retrieve collision kernel values from droplet size distribution change

This study presents an attempt to retrieve collision kernel values from changes in the droplet size distribution due to collision growth. Original linear and nonlinear inversion schemes are presented, which use the simple a priori assumption that the total collision rate is given by the sum of the gravitational and turbulent contributions. Our schemes directly handle binned (discretized) size distributions and, therefore, do not require any assumptions on distribution functional forms, such as the self-similarity assumption. To validate the schemes, three-dimensional direct numerical simulation (DNS) of colliding droplets in steady isotropic turbulence is performed. In the DNS, air turbulence is calculated using a pseudo-spectral method, while droplet motions are tracked by the Lagrangian method. Comparison between the retrieved collision kernels and the collision kernels obtained directly from the DNS show that for low Reynolds number flows both the linear and nonlinear inversion schemes give good accuracy. However, for higher Reynolds number flows the linear inversion scheme gives significantly larger retrieval errors, while the errors for the nonlinear scheme remain small.     

Nonequilibrium solvation for vertical photoemission and photoabsorption processes using the symmetry-adapted cluster-configuration interaction method in the polarizable continuum model

In this paper, we present the theory and implementation of a nonequilibrium solvation model for the symmetry-adapted cluster (SAC) and symmetry-adapted cluster-configuration interaction (SAC-CI) method in the polarizable continuum model. For nonequilibrium solvation, we adopted the Pekar partition scheme in which solvent charges are divided into dynamical and inertial components. With this nonequilibrium solvation scheme, a vertical transition from an initial state to a final state may be described as follows: the initial state is described by equilibrium solvation, while in the final state, the inertial component remains in the solvation for the initial state; the dynamical component will be calculated self-consistently for the final state. The present method was applied to the vertical photoemission and absorption of s-trans acrolein and methylenecyclopropene. The effect of nonequilibrium solvation was significant for a polar solvent.