Congruences modulo $$10^3$$ for Euler numbers

For a non-negative integer \(n\), let \(E_n\) be the \(n\) th Euler number. In this note, for any positive integer \(n\), we prove the following congruences:

$$\begin{aligned} {\left\{ \begin{array}{ll} E_{4n} \equiv 380n-375 \pmod {10^3}, \\ E_{4n+2} \equiv -460n+399 \pmod {10^3}. \end{array}\right. } \end{aligned}$$

Our proof is based on induction on \(n\) and elementary direct calculations.

     

Synthesis and electronic, photophysical, and electrochemical properties of a series of thienylcarbazoles

A series of thienylcarbazoles were synthesized by Suzuki-Miyaura and Ullmann coupling reactions. In these compounds, the 2-thienyl or 2,2'-bithiophen-5-yl group is connected at the N-, 1,8-, 3,6-, 2,7-, 2,7,N-, or 1,8,N-positions of the carbazole ring. The effects of structural variations on their electronic, photophysical, and electrochemical properties were explored by UV-vis and fluorescence spectroscopies, cyclic voltammetry (CV), and DFT calculations in evaluation of their potential as material components. The thienyl substituents at the 2,7-positions in 4, 5, and 10 are responsible for a high degree of π-conjugation and strong emission with fluorescence quantum yields up to 0.61. The CV on a series of thienylcarbazoles revealed a good electron-donating ability of 3,6-substituted carbazoles 3 and 9. The number of thiophene units was found to affect the extent of π-conjugation, the resulting HOMO-LUMO gaps, and fluorescence efficiency. The crystal structures of 5 and 9 were also disclosed.     

Effect of inorganic salt on the dose sensitivity of polymer gel dosimeter

The effect of inorganic salts, non-transition metal chlorides, on the dose sensitivity of methacrylic-acid-based polymer gel dosimeter is investigated. Dose-R₂ responses are obtained from magnetic resonance imaging data. Temperature increase due to exothermic polymerization reaction in the gel is also measured directly during irradiation. As a result, substantial increases in R₂ response are observed in the polymer gel dosimeter containing inorganic salt, especially with MgCl₂. The sensitivity of the gel with 1.0 M MgCl₂ is approximately 2.8 times higher than that of without MgCl₂. As the salt concentration increases, an increase of polymerization rate is also observed via the temperature measurements. These results indicate that inorganic salt acts as an accelerator for radiation-induced free-radical polymerization in methacrylic-acid-based gel.     

Synthesis of metal-hydrazone complexes and vapochromic behavior of their hydrogen-bonded proton-transfer assemblies

We synthesized and investigated a new series of metal-hydrazone complexes, including deprotonated [MX(mtbhp)] and protonated forms [MX(Hmtbhp)](ClO(4)) (M = Pd(2+), Pt(2+); X = Cl(-), Br(-); Hmtbhp = 2-(2-(2-(methylthio)benzylidene)hydrazinyl)pyridine) and hydrogen-bonded proton-transfer (HBPT) assemblies containing [PdBr(mtbhp)] and bromanilic acid (H(2)BA). The mtbhp hydrazone ligand acts as a tridentate SNN ligand and provides a high proton affinity. UV-vis spectroscopy revealed that these metal-hydrazone complexes follow a reversible protonation-deprotonation reaction ([MX(mtbhp)] + H(+) ? [MX(Hmtbhp)](+)), resulting in a remarkable color change from red to yellow. Reactions between proton acceptor [PdBr(mtbhp)] (A) and proton donor H(2)BA (D) afforded four types of HBPT assemblies with different D/A ratios: for D/A = 1:1, {[PdBr(Hmtbhp)](HBA)·Acetone} and {[PdBr(Hmtbhp)](HBA)·2(1,4-dioxane)}; for D/A = 1:2, [PdBr(Hmtbhp)](2)(BA); and for D/A = 3:2, {[PdBr(Hmtbhp)](2)(HBA)(2)(H(2)BA)·2Acetonitrile}. The proton donor gave at least one proton to the acceptor to form the hydrogen bonded A···D pair of [PdBr(Hmtbhp)](+)···HBA(-). The strength of the hydrogen bond in the pair depends on the kind of molecule bound to the free monoanionic bromanilate OH group. Low-temperature IR spectra (T < 150 K) showed that the hydrogen bond distance between [PdBr(Hmtbhp)](+) and bromanilate was short enough (ca. 2.58 ?) to induce proton migration in the [PdBr(Hmtbhp)](2)(BA) assembly in the solid state. The hydrogen bonds formed not only between [PdBr(Hmtbhp)](+) and HBA(-) but also between HBA(-) and neutral H(2)BA molecules in the {[PdBr(Hmtbhp)](2)(HBA)(2)(H(2)BA)·2Acetonitrile} assembly. The H(2)BA-based flexible hydrogen bond network and strong acidic host structure result in an interesting vapor adsorption ability and vapochromic behavior in this assembly because the vapor-induced rearrangement of the hydrogen bond network, accompanied by changes in π-π stacking interactions, provides a recognition ability of proton donating and accepting properties of the vapor molecule.     

Hybrid observation of crystal growth using laser confocal microscope with atomic force microscope

We built up a hybrid microscope system that consists of an atomic force microscope (AFM) and a laser confocal microscope with differential interference contrast microscope (LCM-DIM) and investigated the combined imaging of a potassium dihydrogen phosphate (KDP) crystal surface and its growth. Using this integrated setup, we were able to approach a AFM cantilever tip to several-ten μm$\mathrm{\mu }\mathrm{m}$ crystals using an optical microscope with AFM and to observe steps with measuring the height using LCM-DIM/AFM. Evaluation of the accuracy of the setup was studied and resulted in less than 100 nm of the AFM tip accuracy using LCM-DIM/AFM. We also demonstrated an in-situ observation of a KDP crystal growth using LCM-DIM/AFM. The interference fringes at the cantilever and the movements of steps were simultaneously observed.     

Ultrafast capture of the hot electron by the surface defects on the Si(001) surface

This paper investigates the process of the capture by the surface defects of the photoexcited electron on Si(001) at 100 K by means of the time-resolved two-photon photoelectron spectroscopy. A rapid decrease in sub-ps of the electron population at the conduction band and the simultaneous increase and subsequent decrease of the electron population at the defect states are observed. They are interpreted as the capture of the hot electrons in the conduction band by the surface defect states. The electron–temperature-dependence of the surface recombination velocity, which determines the capture rate of the bulk electron by the surface defects, is estimated assuming the multiphonon emission capture mechanism.     

Pore surface engineering of microporous coordination polymers

Pore surface control of microporous coordination polymers is of great interest due to the potentially exciting functionalities it presents, such as highly selective separation, chemisorption, and novel catalysts and sensors. A discussion of our unique strategy aimed at surface engineering using metalloligands, i.e., introduction of coordinatively unsaturated metal centers, is presented.     

Construction of highly glycosylated mucin-type glycopeptides based on microwave-assisted solid-phase syntheses and enzymatic modifications

A MUC1-related glycopeptide having five core-2 hexasaccharide branches (C330H527N46O207, MW = 8450.9) was synthesized by a new strategy using a combination of microwave-assisted solid-phase synthesis (MA-SPGS) and enzymatic sugar elongation. Synthesis of a key glycopeptide intermediate was best achieved in a combination of PEGA [poly(ethylene glycol)-poly-(N,N-dimethylacrylamide) copolymer] resin and MA-SPGS using glycosylated amino acid building blocks with high speed and high purity. Deprotection of the glycopeptide intermediate and subsequent glycosyltransferase-catalyzed sugar elongations were performed for generation of the additional diversities with the sugar moieties of glycopeptides using beta1,4-galactosyltransferase (beta1,4-GalT) and two kinds of alpha2,3-sialyltransferases [ST3Gal III; alpha2,3-(N)-SiaT and ST3Gal II; alpha2,3-(O)-SiaT]. These reactions proceeded successfully in the presence of 0.2% Triton X-100 to convert the chemically synthesized trisaccharide glycans to disialylated hexasaccharide.