Distinguishing non-standard natural numbers in a set theory within Łukasiewicz logic

In , a set theory with the comprehension principle within Łukasiewicz infinite-valued predicate logic, we prove that a statement which can be interpreted as “there is an infinite descending sequence of initial segments of ω” is truth value 1 in any model of , and we prove an analogy of Hájek’s theorem with a very simple procedure.      

Optodynamers: expression of color and fluorescence at the interface between two films of different dynamic polymers

Color and fluorescence changes were expressed at the interface between two different polyhydrazone polymer films, induced by hydrazone bond exchange and component recombination through the interface, resulting in an extension of conjugation.     

Mn(III)-mediated formal [3+3]-annulation of vinyl azides and cyclopropanols: a divergent synthesis of azaheterocycles

Mn(III)-mediated formal [3+3]-annulation has been developed using readily available vinyl azides and cyclopropanols with a wide range of substituents. Vinyl azides were successfully applied as a three-atom unit including one nitrogen to prepare pyridines and δ-lactams by the reactions with monocyclic cyclopropanols as well as to construct 2-azabicyclo[3.3.1] and 2-azabicyclo[4.3.1] frameworks with bicyclic cyclopropanols, bicyclo[3.1.0]hexan-1-ols, and bicyclo[4.1.0]heptan-1-ols. These reactions were initiated by a radical addition of β-carbonyl radicals, generated by the one-electron oxidation of cyclopropanols with Mn(III), to vinyl azides to give iminyl radicals, which cyclized with the intramolecular carbonyl groups. In addition, application of the present methodology to a synthesis of the quaternary indole alkaloid, melinonine-E, was accomplished.     

Diamine-catalyzed conjugate addition to acrylate derivatives

Diamines were found to promote catalytic conjugate addition of α-cyano active methine nucleophiles to various acrylate derivatives.     

Ferromagnetic exchange couplings showing a chemical trend in Cu-Ln-Cu complexes (Ln = Gd, Tb, Dy, Ho, Er)

Exchange couplings in isomorphous [LnCu(2)] were evaluated by high-frequency electron paramagnetic resonance and magnetization studies. The exchange parameter J(Ln-Cu) was decreased with an increase in the atomic number; J(Ln-Cu)/k(B) = 4.45(11), 2.27(6), 0.902(10), 0.334(3), and 0.136(8) K for Ln = Gd, Tb, Dy, Ho, and Er, respectively.     

Screening of cosmological constant in non-local gravity

We discuss a possible mechanism to screen a cosmological constant in non-local gravity. We find that in a simple model of non-local gravity with the Lagrangian of the form, R+f(^□−1R)−2Λ$R+f({\square }^{-1}R)-2\Lambda$ where f(X)$f(X)$ is a quadratic function of X, there is a flat spacetime solution despite the presence of the cosmological constant Λ. Unfortunately, however, we also find that this solution contains a ghost in general. Then we discuss the condition to avoid a ghost and find that one can avoid it only for a finite range of ‘time’. Nevertheless our result suggests the possibility of solving the cosmological constant problem in the context of non-local gravity.     

Concise Synthesis of Well‐Defined Linear and Branched Oligothiophenes with Nickel‐Catalyzed Regiocontrolled Cross‐Coupling of 3‐Substituted Thiophenes by Catalytically Generated Magnesium Amide

The synthesis of linear and branched oligothiophenes of well‐defined structures is performed with regioselective deprotonation of 3‐substituted thiophenes and nickel‐catalyzed cross‐coupling of the thus formed metalated species with a bromothiophene. The reaction of 3‐hexylthiophene with EtMgCl and 2,2,6,6‐tetramethylpiperidine (TMP‐H, 10 mol %) induces the metalation selectively at the 5‐position by use of the catalytically generated hindered magnesium amide (TMPMgCl) and the subsequent reaction of a 2‐halo‐3‐hexylthiophene (bromide or chloride) in the presence of a nickel catalyst affords a head‐to‐tail (HT)‐type dimer. By repeating the same sequence, the linear oligothiophene up to a 4‐mer is synthesized in good yield. The reaction of 3‐hexylthiophene with 2,3‐dibromothiophene also takes place to afford a branched oligothiophene 3‐mer in quantitative yield. The obtained 3‐mer is also metalated at the sterically less‐hindered position in a regioselective manner furnishing a 7‐mer in >99 % yield after a further coupling reaction with 2,3‐dibromothiophene. These dendrimers react with several multifunctionalized organic electrophiles, leading to a variety of branched oligothiophenes.     

Power spectrum and blood flow velocity images obtained by dual-beam backscatter laser Doppler velocimetry

We developed a micro multipoint laser Doppler velocimeter (μ-MLDV) for noninvasive in-vivo measurements of blood flow and we presented the results of demonstrations performed on experimental animals. In this paper, we investigate the validity of power spectrum analysis for determining the flow velocity and the minimum power of the semiconductor laser in the μ-MLDV. Although average velocity is generally estimated from a peak position (f _peak) in the power spectrum, the power spectrum of blood flow included an additional component in the high-frequency region. The conventional method for determining the average velocity of flows of transparent artificial fluids, which involves determining the average velocity from f _peak, is unsuitable for in-vivo measurements of blood flow. The laser power was reduced from 140 to 30mW since 30mW was the minimum power at which images of blood flow velocity in microvessels could be obtained. About 30mW (power density of 15mW/mm²) is the maximum power which can be irradiated to humans. Further reduction in the laser power is necessary before this technique can be applied to humans.