A super Frobenius formula for the characters of Iwahori–Hecke algebras

In this article, we establish a super Frobenius formula for the characters of Iwahori–Hecke algebras. We define Hall–Littlewood supersymmetric functions in a standard manner to make supersymmetric functions from symmetric functions, and give some properties of supersymmetric functions. Based on Schur–Weyl reciprocity between Iwahori–Hecke algebras and the general quantum super algebras, which was obtained in Mitsuhashi [H. Mitsuhashi, Schur–Weyl reciprocity between the quantum superalgebra and the Iwahori–Hecke algebra, Algeb. Represent. Theor. 9 (2006), pp. 309–322.], we derive that the Hall–Littlewood supersymmetric functions, up to constant, generates the values of the irreducible characters of Iwahori–Hecke algebras at the elements corresponding to cycle permutations. Our formula in this article includes both the ordinary quantum case that was obtained in Ram [A. Ram, A Frobenius formula for the characters of the Hecke algebra, Invent. Math. 106 (1991), pp. 461–488.] and the classical super case.     

Expected Power-Utility Maximization Under Incomplete Information and with Cox-Process Observations

We consider the problem of maximization of expected terminal power utility (risk sensitive criterion). The underlying market model is a regime-switching diffusion model where the regime is determined by an unobservable factor process forming a finite state Markov process. The main novelty is due to the fact that prices are observed and the portfolio is rebalanced only at random times corresponding to a Cox process where the intensity is driven by the unobserved Markovian factor process as well. This leads to a more realistic modeling for many practical situations, like in markets with liquidity restrictions; on the other hand it considerably complicates the problem to the point that traditional methodologies cannot be directly applied. The approach presented here is specific to the power-utility. For log-utilities a different approach is presented in Fujimoto et al. (Preprint, 2012).     

Coloring-decoloring behavior of amphiphilic fluoroalkyl end-capped N-(1,1-dimethyl-3-oxobutyl)acrylamide--acryloylmorpholine cooligomer/fluorescein nanocomposites in protic and aprotic solvents

Amphiphilic fluoroalkyl end-capped N-(1,1-dimethyl-3-oxobutyl)acrylamide-acryloylmorpholine cooligomer/fluorescein nanocomposites afforded brilliant yellow-colored solutions in not only protic solvents such as methanol and ethanol but also protic-like solvents such as dichloromethane and 1,2-dichloroethane, respectively. However, the corresponding non-fluorinated cooligomer/fluorescein composites and parent fluorescein gave the colorless solutions under similar conditions. On the other hand, unexpectedly, such brilliant yellow-colored solutions provided by these fluorinated nanocomposites completely disappeared in aprotic solvents such as N,N-dimethylformamide, dimethyl sulfoxide, and tetrahydrofuran. Thus, these fluorinated fluorescein nanocomposites can exhibit a coloring-decoloring behavior through solvatochromic response.     

Practical one-pot transformation of electron-rich aromatics into aromatic nitriles with molecular iodine and aq NH3 using Vilsmeier–Haack reaction

Various electron-rich aromatics could be efficiently transformed into the corresponding aromatic nitriles in good to moderate yields by treatment with DMF and POCl₃, followed by the reaction with molecular iodine or 1,3-diiodo-5,5-dimethylhydantoin (DIH) in aq NH₃. Some of less reactive aromatics, such as anisole, 1,2-dimethoxybenzene, 1,4-dimethoxybenzene, and mesityrene, could be also transformed into the corresponding aromatic nitriles in good to moderate yields using N-methylformanilide and O(POCl₂)₂, followed by the reaction with molecular iodine in aq NH₃. Moreover, propiophenone derivatives could be successfully transformed into the corresponding β-chlorocinnamonitriles by the reaction with DMF and POCl₃, followed by the reaction with molecular iodine and aq NH₃. These reactions are novel metal-free one-pot methods for the preparation of aromatic nitriles from electron-rich aromatics and β-chlorocinnamonitriles from propiophenones.     

Efficient Swern oxidation and Corey–Kim oxidation with ion-supported methyl sulfoxides and methyl sulfides

The Swern oxidation of various benzylic and allylic alcohols, primary alcohols, and secondary alcohols with two ion-supported methyl sulfoxides A-1 (C₆) and B-1 (C₁₀), and oxalyl chloride in the presence of triethylamine in dichloromethane, followed by simple diethyl ether extraction of the reaction mixture, gave the corresponding aldehydes and ketones, respectively, in good yields with high purity. Similarly, the Corey–Kim oxidation of various benzylic and allylic alcohols, primary alcohols, and secondary alcohols with two ion-supported methyl sulfides A-2 (C₆) and B-2 (C₁₀), and N-chlorosuccinimide in the presence of triethylamine in dichloromethane, followed by simple diethyl ether extraction of the reaction mixture, furnished the corresponding aldehydes and ketones, respectively, in good yields with high purity. Both reactions did not produce any unpleasant odor at all. In the Swern oxidation, ion-supported methyl sulfides were recovered in high yields and could be re-oxidized to produce ion-supported methyl sulfoxides A-1 (C₆) and B-1 (C₁₀), for reuse in the same oxidation. In the Corey–Kim oxidation, ion-supported methyl sulfides A-2 (C₆) and B-2 (C₁₀) were recovered in high yields and could be also reused for the same oxidation.     

Novel bioactive peptides,PF1171F and PF1171G,from unidentified ascomycete OK-128

Two cyclic peptides, PF1171F (1) and PF1171G (2), were isolated from okara fermented with the unidentified ascomycete OK-128, and their structures were determined by NMR, MS, and Marfey amino acid analysis. Both peptides showed paralytic activity against silkworms.     

Synthesis of disilanyl double-pillared bisdibenzofuran with a high triplet energy

A double-pillaring strategy for the synthesis of silacyclophanes has been applied to dibenzofuran to create a new cyclophane molecule that links two dibenzofuran molecules through σ(SiSi)-π conjugation. The performance of disilanyl double-pillared dibenzofuran [(Si)DPBD(O)] in green phosphorescent organic light-emitting diode (OLED) devices was evaluated as both a carrier-transport material and a host material for an Ir-based phosphorescent emitter.     

Domain wall dynamics driven by spin transfer torque and the spin-orbit field

We have studied current-driven dynamics of domain walls when an in-plane magnetic field is present in perpendicularly magnetized nanowires using an analytical model and micromagnetic simulations. We model an experimentally studied system, ultrathin magnetic nanowires with perpendicular anisotropy, where an effective in-plane magnetic field is developed when current is passed along the nanowire due to the Rashba-like spin-orbit coupling. Using a one-dimensional model of a domain wall together with micromagnetic simulations, we show that the existence of such in-plane magnetic fields can either lower or raise the threshold current needed to cause domain wall motion. In the presence of the in-plane field, the threshold current differs for positive and negative currents for a given wall chirality, and the wall motion becomes sensitive to out-of-plane magnetic fields. We show that large non-adiabatic spin torque can counteract the effect of the in-plane field.     

Development of diversified methods for chemical modification of the 5,6-double bond of uracil derivatives depending on active methylene compounds

The reaction of 5-halogenouracil and uridine derivatives 1 and 7 with active methylene compounds under basic conditions produced diverse and selective C-C bond formation products by virtue of the nature of the carbanions. Three different types of reactions such as the regioselective C-C bond formation at the 5- and 6-positions of uracil and uridine derivatives (products 2, 5, 8, 17, 20 and 21), and the formation of fused heterocycle derivatives 2,4-diazabicyclo[4.1.0]heptane (15) and 2,4-diazabicyclo-[4.1.0]nonane (16) via dual C-C bond formations at both the 5- and 6-positions were due to the different active methylene compounds used as reagents.     

Ring-expansion reaction of oximes with aluminum reductants

The ring-expansion reactions of heterocyclic ketoximes and carbocyclic ketoximes with several reductants such as AlHCl2, AlH3 (alane), LiAlH4, LiAlH(OtBu)3, and (MeOCH2CH2O)2AlH2Na (Red-Al) were examined. Among reductants, AlHCl2 (LiAlH4:AlCl3 = 1:3) in cyclopentyl methyl ether (CPME) has been found to be a suitable reagent for the reaction, and the rearranged cyclic secondary amines were obtained in good to excellent yields.