Asymptotic analysis for linear difference equations

We are concerned with asymptotic analysis for linear difference equations in a locally convex space. First we introduce the profile operator, which plays a central role in analyzing the asymptotic behaviors of the solutions. Then factorial asymptotic expansions for the solutions are given quite explicitly. Finally we obtain Gevrey estimates for the solutions. In a forthcoming paper we will develop the theory of cohomology groups for recurrence relations. The main results in this paper lay analytic foundations of such an algebraic theory, while they are of intrinsic interest in the theory of finite differences.

     

Proton and Li-7 NMR study on the effect of the OH− anion upon the Li+-ion conduction in the solid solution Li5NI2LiOH

From ¹H and ⁷LiNMR relaxation times T₁, T₂ and T_1ρ in Li₅NI₂ and the solid solution Li₅NI₂?0.77LiOH, the diffusive motion of the Li⁺ ion was studied to make clear the role of the OH^? ion in improving the Li⁺ ionic conduction. At temperatures as low as 140 K, each Li⁺ ion jumps among four available positions. Its activation energies are 9.26 and 11.8 kJ mol^?1 for Li₅NI₂ and Li₅NI₂?0.77LiOH, respectively. Diffusive motion was observed in T₂ and T_1ρ above 240 K. The mode of the cation distribution and the diffusion mechanism are not affected by the presence of the OH^? anion. The most noticeable fact is that the OH^? ion is substituted selectively for the N^3? ion that is the nearest neighbour of the Li⁺ ion. This selective substitution increases the concentration of the Li⁺ vacancy most effectively up to 4.2% of the total Li positions. At the same time it diminishes the strong attractive force of the N^3? anion binding the Li⁺ ion to the position, and thus the activation energy. For the diffusion, an anomalously low attempt frequency of 3̃ × 10⁹Hz was obtained from T_1ρ, while the normal value of 4.8 × 10¹²Hz was obtained from the ionic conductivity. The large discrepancy was attributed to the collective nature of the Li⁺ diffusive motion.     

A graphical symmetric group approach for a spin adapted full configuration interaction: partitioning of a configuration graph into sets of closed-shell and open-shell graphs

We developed a spin adapted full configuration interaction (FCI) method which was expected to be effective for parallel processing. The graphical symmetric group approach (GSGA) was employed, where a configuration graph was partitioned into several sets of closed-shell and open-shell graphs. The configuration state functions (CSFs) bearing the same number of closed-shells and open-shells were assembled in a configuration group. The graphical approach provided a number to identify each CSF in a sequential order within the group. Combination of this partitioning and an intermediate configuration-driven algorithm in calculating the so-called σ vectors allowed us to use symbolic coupling constants. Furthermore, this combination made it easy to implement an efficient algorithm suitable to task-distributed parallel procedure for evaluating σ vectors. A program was written and some test calculations were carried out with high parallel efficiency. The largest size of FCI used 10 million CSFs (20 million determinants).     

Reaction of electron deficient NN bonds with acyloxyketenes and mesoionic 1,3-dioxolium-4-olates: fast equilibrium between acyloxyketenes and mesoionic 1,3-dioxolium-4-olates

Reaction of azodicarboxylates with acyloxyketenes arising from dehydrochlorination of acyloxyphenylacetyl chlorides was carried out to give triacylamidine derivatives in good yields. The same triacylamidine derivatives were also obtained in good yields from the reaction with mesoionic 1,3-dioxolium-4-olates generated by Rh₂(OAc)₄-catalyzed decomposition of phenyldiazoacetic anhydride derivatives. Formation of the same compounds from different starting materials is explained by 1,3-dipolar addition between electron deficient NN bonds and mesoionic 1,3-dioxolium-4-olates, indicating fast equilibrium between acyloxyketenes and mesoionic 1,3-dioxolium-4-olates.     

Microscopic environment of metal ion controlled by the balance between preferential solvation and coordination

The preferential solvation and the coordination characterizing metal ions (Mg2+ and Zn2+) in solution, which control the microscopic environments around the metal ions, were directly observed through the mass spectrometric analysis of clusters isolated from liquid droplets.     

Electron-transfer mechanism in radical-scavenging reactions by a vitamin E model in a protic medium

The scavenging reaction of 2,2-diphenyl-1-picrylhydrazyl radical (DPPH.) or galvinoxyl radical (GO.) by a vitamin E model, 2,2,5,7,8-pentamethylchroman-6-ol (1H), was significantly accelerated by the presence of Mg(ClO4)2 in de-aerated methanol (MeOH). Such an acceleration indicates that the radical-scavenging reaction of 1H in MeOH proceeds via an electron transfer from 1H to the radical, followed by a proton transfer, rather than the one-step hydrogen atom transfer which has been observed in acetonitrile (MeCN). A significant negative shift of the one-electron oxidation potential of 1H in MeOH (0.63 V vs. SCE), due to strong solvation as compared to that in MeCN (0.97 V vs. SCE), may result in change of the radical-scavenging mechanisms between protic and aprotic media.     

Generalized doubly symbolic formulation for integral-driven direct configuration interaction method

Summary A direct configuration interaction (CI) scheme using the generalized double symbolism both for the external space and for the internal space is proposed in an integral-driven context. The reason why the double symbolism is used in the present formulation is that the main target is in investigating large molecular systems. The integrals, configuration state functions, and energy expressions are systematically classified in terms of the orbital labels and their mutual relations. Various types of CI wavefunctions can be set up flexibly. The resulting structure of integral processings in the sigma vector construction is complicated. The number of unique loop types for two-electron integrals is 1325. Because the parallel architecture is gaining importance in the recent computational platforms, the parallelism is also addressed.     

A practical approach for the chemical synthesis of 2′-deoxyguanosine-C8 adducts with mutagenic/carcinogenic amino- or nitro-arenes

Synthetic methods for the preparation of 2′-deoxyguanosine-C8 (dG-C8) adducts with several mutagenic and carcinogenic amino- or nitro-arenes were developed using the palladium-mediated cross-coupling reaction of protected 8-amino-dG with bromoarenes in around 80% yields, followed by conventional deprotection procedures. This approach can be applied to preparation of a variety of authentic dG-C8 adducts with amino or nitro-arenes.