We study a representation for the inverse transform of the generalised Fourier–Feynman transform on the function space $C_{a,b}[0,T]$ which is induced by a generalised Brownian motion process. To do this, we define a transform via the concept of the convolution product of functionals on $C_{a,b}[0,T]$. We establish that the composition of these transforms acts like an inverse generalised Fourier–Feynman transform and that the transforms are vector space automorphisms of a vector space ${\mathcal{E}}(C_{a,b}[0,T])$. The vector space ${\mathcal{E}}(C_{a,b}[0,T])$ consists of exponential-type functionals on $C_{a,b}[0,T]$.

In this paper, we establish a translation theorem for the generalised analytic Feynman integral of functionals that belong to the Banach algebra ${\mathcal{F}}(C_{a,b}[0,T])$.

Background: The influences of demographics, culture, language, and environmental changes on Mini-Mental State Examination (MMSE) scores are considerable.

Methods: Using a sample of 7452 healthy, community-dwelling elderly Koreans, aged 55 to 94 years, who participated in the four ongoing geriatric cohorts in Korea, we investigated demographic influences on MMSE scores and derived normative data for this population. Geropsychiatrists strictly excluded subjects with cognitive disorders according to the protocol of the Korean version of the Consortium to Establish a Registry for Alzheimer's Disease Assessment Packet (CERAD-K) Clinical Assessment Battery (CERAD-K-C).

Results: Education (standardized β = 0.463), age (standardized β = −0.303), and gender (standardized β = −0.057) had significant effects on MMSE scores (p < 0.001). The score of MMSE increase 0.379 point per 1-year education, decrease 0.188 per 1-year older, and decrease 0.491 in women compared to men. Education explained 30.4% of the scores’ total variance, which was much larger than the variances explained by age (8.4%) or gender (0.3%). Accordingly, we present normative data for the MMSE stratified by education (0, 1–3, 4–6, 7–9, 10–12, and ≥ 13 years), age (60–69, 70–79, and 80–89 years), and gender.

Conclusions: We provide contemporary education-, age-, and gender-stratified norms for the MMSE, derived from a large, community-dwelling elderly Korean population sample, which could be useful in evaluating individual MMSE scores.

Background: This study aims to establish the incidence rates of Alzheimer's disease (AD) and to understand the relations between illiteracy and AD in the Korean Yonchon survey cohort.

Methods: A community-based, dementia-free cohort of 966 people aged 65 years and older was followed up for an average of 5.4 ± 1.60 years to detect incident AD cases using a two-phase procedure. Age-specific incidence rates were calculated using a person-years approach with Poisson distribution confidence intervals. Data were analyzed using the Cox proportional hazards model to find the hazard ratio of illiteracy.

Results: The participating percentage of the survivors was 86.4% and 74 subjects were diagnosed with AD. Incidence rates per 1000 person-years were 20.99 (95% CI 16.48 to 26.35) for AD. The hazard ratio of illiteracy was 1.78 (95% CI 1.08 to 2.93) adjusted for age, sex, educational level. AD developed more rapidly with aging in the illiterate group than in the literate group.

Conclusions: Illiteracy is associated with a higher risk of AD and the risk increases with age.

Electron tomography and high-resolution transmission electron microscopy were used to characterize the unique three-dimensional structures of helical or zigzagged GaN, ZnGa2O4 and Zn2SnO4 nanowires. The helical GaN nanowires adopt a helical structure that consists of six equivalent <0-111> growth directions with the axial [0001] direction. The ZnGa2O4 nanosprings have four equivalent <011> growth directions with the [001] axial direction. The zigzagged Zn2SnO4 nanowires consisted of linked rhombohedrons structure having the side edges matched to the <011> direction, and the [111] axial direction.

We investigated the photoluminescence as well as the crystal structure and optical energy gaps of the Zn1-xCdxAl2Se4-4xS4x solid solution system based on the Al-related compounds of ZnAl2Se4, ZnAl2S4, CdAl2Se4, and CdAl2S4. The single crystals of the system with 0.0 ≤ x ≤ 1.0 were grown by the chemical transport reaction technique. The Zn1-xCdxAl2Se4-4xS4x crystallizes in a defect chalcopyrite structure for a whole composition and has an optical energy gap ranging from 3.525 to 3.577 eV at 13 K. The photoluminescence spectra at 13 K showed a strong emission band in the blue spectral region and a weak broad emission band in the visible region due to donor–acceptor pair recombination. The composition and temperature dependence of these bands were examined in the investigated regions. The simple energy band scheme for the radiative mechanisms of the Zn1-xCdxAl2Se4-4xS4x is proposed on the basis of our experimental results along with photo-induced current transient spectroscopy measurements.

We investigated the photoluminescence spectra as well as the crystal structure and optical energy gaps of the Zn1-xCdxAl2Se4 single crystals grown by the chemical transport reaction method. It was shown from the analysis of the observed x-ray diffraction patterns that these crystals have a defect chalcopyrite structure for a whole composition. The lattice constant a increases from 5.5561 A for x = 0.0 (ZnAl2Se4) to 5.6361 A for x = 1.0 (CdAl2Se4) with increasing x, whereas the lattice constant c decreases from 10.8890 A for x = 0.0 to 10.7194 A for x = 1.0. The optical energy gaps at 13 K were found to range from 3.082 eV (x = 1.0) to 3.525 eV (x = 0.0). The temperature dependence of the optical energy gaps was well fitted with the Varshni equation. We observed two emission bands consisting of a strong blue emission band and a weak broad emission band due to donor–acceptor pair recombination in the Zn1-xCdxAl2Se4 for 0.0 ⩽ x ⩽ 1.0. These emission bands showed a red shift with increasing x. The energy band scheme for the radiative mechanism of the Zn1-xCdxAl2Se4 was proposed on the basis of the photoluminescence thermal quenching analysis along with the measurements of photo-induced current transient spectroscopy. The proposed energy band model permits us to assign the observed emission bands.