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Let [Formula: see text] be a domain. In this paper, we show that if [Formula: see text] is one-dimensional, then [Formula: see text] is a Noetherian Warfield domain if and only if every maximal ideal of [Formula: see text] is 2-generated and for every maximal ideal[Formula: see text] of [Formula: see text], [Formula: see text] is divisorial in the ring [Formula: see text]. We also prove that a Noetherian domain [Formula: see text] is a Noetherian Warfield domain if and only if for every maximal ideal [Formula: see text] of [Formula: see text], [Formula: see text] can be generated by two elements. Finally, we give a sufficient condition under which all ideals of [Formula: see text] are strongly Gorenstein projective.

Two-dimensional (2D) transition metal dichalcogenides (TMDs) have attracted significant attention for their outstanding optoelectrical properties. Unlike most TMDs with layer-dependent photoresponsivity, rhenium disulfide (ReS2) shows excellent thickness-independent photoresponsivity. Herein, we show a surfactant-free polyvinyl alcohol (PVA)-assisted exfoliation method for 2D-TMDs in aqueous solution and a transparent photosensitive memristor synapse device based on ReS2 nanosheets composited with PVA. ReS2 nanosheets are obtained via PVA-assisted exfoliation. After exfoliation, the ReS2-PVA dispersion solution is spin-coated on a substrate and dried to form a nanocomposite film without additional processing. Transparent memristors are then fabricated on plastic or glass substrates to demonstrate the applicability of the ReS2-PVA film. The devices show "write once, read many" memory behavior with a high ON/OFF current ratio (1.0 × 104 at 0.5 V) during electrical operation. In the high resistive state, synaptic functions with long-term memory behavior are successfully mimicked by applying photonic stimuli to the transparent ReS2-PVA memristors. The excitatory postsynaptic current stimulated by the photosignal is gradually reduced by electric stimuli. The proposed PVA-assisted exfoliation method is cost-effective, environmentally friendly, and applicable to various TMD nanomaterials. Furthermore, the ReS2-PVA nanocomposite film obtained via a simple solution-based process demonstrates excellent photosynaptic behavior.

In this study, the back passivation layers (BPLs) were developed to protect hydrogenated amorphous silicon (a-Si:H) thin films of transparent solar cells from humidity and contaminants. Metal oxide compound films with Al (Al2O3) and Ti (AlxTiyOz (ATO)) were fabricated by plasma-enhanced atomic layer deposition for the BPLs on transparent solar cells. The BPLs of Al2O3 films applied to the transparent solar cells were deposited in different thicknesses to evaluate the performance, and the ATO film thickness was fixed at 30 nm. Even at the thinnest thickness of 30 nm, the water vapor transmission rates of BPLs were very low at 1.96 × 10-3 (Al2O3) and 1.23 × 10-2 g/m2·day (ATO). In addition to moisture protection, measures of cell performance, including open-circuit voltage and short-circuit current density, were improved by blocking the leakage current and through the optical interference effects of the BPLs. The solar cell with ATO BPLs exhibited an increase in efficiency of more than 12% compared with those of conventional reference cells. Furthermore, by varying the refractive index and thickness of the BPLs, the reflection and transmission spectra were modulated to implement various cell colors without serious loss in cell efficiency.

Let [Formula: see text] be a one-dimensional Noetherian domain and [Formula: see text] be a two-generated fractional ideal of [Formula: see text]. In this paper, we prove that [Formula: see text] is [Formula: see text]-projective if and only if [Formula: see text] and [Formula: see text] are equivalent, i.e. there exists a projective fractional ideal [Formula: see text] of [Formula: see text] such that [Formula: see text]. We also give an example to show that [Formula: see text] being [Formula: see text]-projective does not necessarily imply that [Formula: see text] and [Formula: see text] are isomorphic.

Let(Γ,≤)({\mathrm{\Gamma}},\le )be a strictly ordered monoid, and letΓ⁎=Γ\{0}{{\mathrm{\Gamma}}}^{\ast }\left={\mathrm{\Gamma}}\backslash \{0\}. LetD⊆ED\subseteq Ebe an extension of commutative rings with identity, and letIbe a nonzero proper ideal ofD. SetD+〚EΓ⁎,≤〛≔f∈〚EΓ,≤〛|f(0)∈DandD+〚IΓ⁎,≤〛≔f∈〚DΓ,≤〛|f(α)∈I,forallα∈Γ⁎.\begin{array}{l}D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt] := \left\{f\in [\kern-2pt[ {E}^{{\mathrm{\Gamma}},\le }]\kern-2pt] \hspace{0.15em}|\hspace{0.2em}f(0)\in D\right\}\hspace{.5em}\text{and}\\ \hspace{0.2em}D+[\kern-2pt[ {I}^{{\Gamma }^{\ast },\le }]\kern-2pt] := \left\{f\in [\kern-2pt[ {D}^{{\mathrm{\Gamma}},\le }]\kern-2pt] \hspace{0.15em}|\hspace{0.2em}f(\alpha )\in I,\hspace{.5em}\text{for}\hspace{.25em}\text{all}\hspace{.5em}\alpha \in {{\mathrm{\Gamma}}}^{\ast }\right\}.\end{array}In this paper, we give necessary conditions for the ringsD+〚EΓ⁎,≤〛D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt]to be Noetherian when(Γ,≤)({\mathrm{\Gamma}},\le )is positively ordered, and sufficient conditions for the ringsD+〚EΓ⁎,≤〛D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt]to be Noetherian when(Γ,≤)({\mathrm{\Gamma}},\le )is positively totally ordered. Moreover, we give a necessary and sufficient condition for the ringD+〚IΓ⁎,≤〛D+[\kern-2pt[ {I}^{{\Gamma }^{\ast },\le }]\kern-2pt]to be Noetherian when(Γ,≤)({\mathrm{\Gamma}},\le )is positively totally ordered. As corollaries, we give equivalent conditions for the ringsD+(X1,…,Xn)E[X1,…,Xn]D+({X}_{1},\ldots ,{X}_{n})E{[}{X}_{1},\ldots ,{X}_{n}]andD+(X1,…,Xn)I[X1,…,Xn]D+({X}_{1},\ldots ,{X}_{n})I{[}{X}_{1},\ldots ,{X}_{n}]to be Noetherian.

Let n⩾1 and k⩾0 be fixed integers and R be a ring. We show that R is (n, k)-SG with G‐gldim(R)=k if and only if R[x1,x2,…,xm] is (n,k+m)-SG with G‐gldim(R[x1,x2,…,xm])=k+m. We also give an example ...

Let R = (Rn)n≥0 be an ascending chain of commutative rings with identity and H(R) (resp., h(R)) the generalized composite Hurwitz series ring (resp., generalized composite Hurwitz polynomial ring)....

Let [Formula: see text] be a domain. It is proved that if [Formula: see text], then the class of finitely generated [Formula: see text]-flat modules and the class of finitely generated [Formula: see text]-projective modules coincide. It is also proved that an integrally closed domain [Formula: see text] is a Prüfer domain if and only if [Formula: see text], if and only if [Formula: see text].

Neuromorphic devices have been investigated extensively for technological breakthroughs that could eventually replace conventional semiconductor devices. In contrast to other neuromorphic devices, the device proposed in this paper utilizes deep trap interfaces between the channel layer and the charge-inducing dielectrics (CID). The device was fabricated using in-situ atomic layer deposition (ALD) for the sequential deposition of the CID and oxide semiconductors. Upon the application of a gate bias pulse, an abrupt change in conducting states was observed in the device from the semiconductor to the metal. Additionally, numerous intermediate states could be implemented based on the number of cycles. Furthermore, each state persisted for 10,000 s after the gate pulses were removed, demonstrating excellent synaptic properties of the long-term memory. Moreover, the variation of drain current with cycle number demonstrates the device’s excellent linearity and symmetry for excitatory and inhibitory behaviors when prepared on a glass substrate intended for transparent devices. The results, therefore, suggest that such unique synaptic devices with extremely stable and superior properties could replace conventional semiconducting devices in the future.

A ring R is called weakly SG-hereditary if every ideal of R is SG-projective. In this note, we prove that a local domain R is a Noetherian Warfield domain if and only if it is weakly SG-hereditary. Furthermore, we prove that any countably generated submodule of any free module over a Noetherian local Warfield domain is SG-projective.

Background: Previous studies have not quantitatively analyzed the site of acute Achilles tendon rupture. Purpose: To investigate the site of acute Achilles tendon rupture via magnetic resonance imaging (MRI). Study Design: Cross-sectional study; Level of evidence, 4. Methods: The medical records and MRIs of 195 patients with acute Achilles tendon rupture were retrospectively reviewed. The rupture site was measured as the distance from the most distal fibers of the Achilles tendon at the calcaneal insertion to the proximal end of the distal stump. The relationship between the site of rupture and patient characteristics was analyzed, and the intra- and interobserver reliability of the measurements was assessed using intraclass correlation coefficients. Results: The rupture site had a mean distance of 6.4 cm (SD, 1.5) and the 10th to 90th percentile range was 5.0 to 8.4 cm. There was no significant difference in location of the rupture according to patient characteristics and the time of imaging. The intra- and interobserver reliability of measurements was excellent. Conclusion: Most acute Achilles tendon ruptures visible on MRI occurred 5 to 8 cm above the distal end of the calcaneal insertion, which is more proximal than the previously reported 2 to 6 cm location.

For the effective deicing of the windows of electric vehicles, we fabricated asymmetric multilayered transparent (AMT) film heaters exhibiting a low resistance (5.4 Ω/sq.) and high visible transmittance (88%), resulting in the highest figure of merit (759) reported to date. Also, the simulated transmittance of the AMT films better matched the experimental results when considering the microstructure of the reaction layer between the Ga-doped ZnO and Ag layers. Herein, an unconventional approach considering heat transfer by conduction is described because heat loss from the thick glass (>3 mm) inevitably occurs in the real-world application of vehicle windows. We formulated and simultaneously solved two derivative heat transfer equations considering the thermal loss in the thick glass and heat transfer in the heating films to accurately predict the temperature of the outside glass. To verify our model, we performed a heating test by inserting heated windows in a small-scale automobile model and were able to accurately predict deicing time and heating rates.

In this study, the back passivation layers (BPLs) were developed to protect hydrogenated amorphous silicon (a-Si:H) thin films of transparent solar cells from humidity and contaminants. Metal oxide compound films with Al (Al

Let R be a commutative ring with identity, and let S be a (not necessarily saturated) multiplicative subset of R. We define R to be a nonnil-S-Noetherian ring if each nonnil ideal of R is S-finite. In this paper, we study some properties of nonnil-S-Noetherian rings. More precisely, we investigate nonnil-S-Noetherian rings via the Cohen-type theorem, the flat extension, the faithfully flat extension, the polynomial ring extension, and the power series ring extension.

With the development of the Internet of Things (IoT), indoor photovoltaics are attracting considerable interest owing to their potential to benefit various IoT-related fields. Therefore, this study investigates the use of transparent hydrogenated amorphous silicon (a-Si:H) solar cells for a broad range of applications, including indoor light harvesting. High-gap triple layers were employed in the a-Si:H solar cells to obtain a high shunt resistance and high short-circuit current

We give a new proof of the Cohen type theorem for [math] -Noetherian rings and a slight generalization of the Eakin–Nagata type theorem for [math] -Noetherian rings.

Let D be an integral domain and w be the so-called w-operation on D. We define D to be a w-FF domain if every w-flat w-ideal of D is of w-finite type. This paper presents some properties of w-FF domains and related domains. Among other things, we study the w-FF property in the polynomial extension, the t-Nagata ring and the pullback construction.

Let R &sube, T be an extension of commutative rings with identity and H ( R , T ) (respectively, h ( R , T )) the composite Hurwitz series ring (respectively, composite Hurwitz polynomial ring). In this article, we study equivalent conditions for the rings H ( R , T ) and h ( R , T ) to be PF-rings and PP-rings. We also give some examples of PP-rings and PF-rings via the rings H ( R , T ) and h ( R , T ) .

We investigated the thermal stability of multilayered transparent electrodes composed of ZnO:Ga (GZO)/Ag/GZO layers for the application of large-scale perovskite solar cell (PSC) modules, which require a post-annealing temperature of 450 °C. The sheet resistance and transmittance of the GZO/Ag/GZO (50 nm/12 nm/50 nm) electrodes were encouragingly improved by an annealing test with a temperature variation from 25° to 450°C. The optimum value of the sheet resistance was 4.48 Ω/square at an annealing temperature of 450 °C. By a simulation of PSC module performance, we confirmed that PSC modules with our GZO/Ag/GZO multilayered transparent electrodes (4–5 Ω/square) suffer less performance degradation compared to those with conventional FTO transparent electrodes (8–15 Ω/square).

Let D be an integral domain, ∗ a star-operation on D, and S a multiplicative subset of D. We define D to be an S-∗w-principal ideal domain if for each nonzero ideal I of D, there exist an element s ∈ S and a principal ideal (c) of D such that [Formula: see text]. In this paper, we study some properties of S-∗w-principal ideal domains. Among other things, we study the local property, the Nagata type theorem, and the Cohen type theorem for S-∗w-principal ideal domains.

We reported highly flexible a-Si:H thin film solar cells with p-type poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) window. We firstly adopted the substrate-type cell structure on 75 μm-thick polyimide (PI) film unlike earlier studies in which the superstrate-type cell structures were utilized and the deformation of PEDOT:PSS was inevitably caused by subsequent deposition processes. We clearly demonstrated that the performance of the hybrid a-Si:H thin film solar cells with the substrate-type structure was superior to that of the superstrate-type cells. A highly boron-doped interlayer (IL) of 5 nm thickness was introduced at the hetero-interface between the p-type PEDOT:PSS and intrinsic a-Si:H to enhance built-in potential and form a homogeneous p/i-junction in the cell, which led to further improvement in the cell performance. The efficiencies of the cells with the PEDOT:PSS/IL window on glass and PI substrates were 7.40% and 6.52%, respectively, which were considerably higher than that of the cell with a conventional p-type microcrystalline (μc-) Si:H window. Also, the degradation of the cell with PEDOT:PSS window by bending was much smaller than the cell with p-type μc-Si:H window, particularly at bending radius

This work reports a breakthrough technique for achieving high quality and uniform molybdenum dichalcogenide (MoX2 where X = S, Se) films on large-area wafers via metal-agglomeration-suppressed growth (MASG) with small chalcogen (X-) molecules at growth temperatures (TG) of 600 °C or lower. In order to grow MoS2 films suitable for field effect transistors (FETs), S-molecules should be pre-deposited on Mo films at 60 °C prior to heating the substrate up to TG. The pre-deposited S-molecules successfully suppressed the agglomeration of Mo during sulfurization and prevented the formation of protruding islands in the resultant sulfide films. The small X-molecules supplied from a thermal cracker reacted with Mo-precursor film to form MoX2. The film quality strongly depends on the temperatures of cracking and reservoir zones, as well as TG. The MoS2 film grown at 570 °C showed a thickness variation of less than 3.3% on a 6 inch-wafer. The mobility and on/off current ratio of 6.1 nm-MoS2 FET at TG = 570 °C were 59.8 cm2 V−1 s−1 and 105, respectively. The most significant advantages of the MASG method proposed in this work are its expandability to various metal dichalcogenides on larger substrates as well as a lower TG enabled by using reactive small molecules supplied from a cracker, for which temperature is independently controlled.

Transparent hydrogenated amorphous silicon (a-Si:H) thin-film solar cells, in which the colors of the front and rear faces can be adjusted individually, were developed for implementation in building-integrated photovoltaic (BIPV) windows. The proposed ultrathin transparent multilayered electrodes (TMEs) are highly conductive and transparent, consisting of a bottom layer of gallium-doped zinc oxide (GZO), a thin metal layer of Ag, and an optoelectronic controlling layer (OCL) of GZO. They can be used for both the front and rear electrodes of transparent a-Si:H solar cells, and the resulting solar cells show a 5.0% average power conversion efficiency and 18.3% average transmittance. The various dual colors on the front and rear of the cell can be individually adjusted by changing the thickness of the OCL on each face of the TME, without significantly changing the efficiency. The cell colors were quantitatively investigated using the color coordinates in a chromaticity diagram based on the International Commission on Illumination (CIE; 1931) standard to show that the simulated and observed colors match well under both LED and fluorescent light sources. We also show that the observable color of the BIPV windows is determined by indoor and outdoor light sources, and dynamically varies as a function of illuminance of the light source as the day gradually progresses into night. This study helps to elucidate the color behavior of the BIPV windows and to develop a-Si:H BIPV windows that show various colors with stable electrical power generation.

Let D be an integral domain with quotient field K, $$\Gamma $$ a nonzero torsion-free grading monoid and $$\Gamma ^*=\Gamma {\setminus } \{0\}$$ . In this paper, we characterize when the semigroup ring $$D[\Gamma ]$$ is an almost Prufer v-multiplication domain or an almost Prufer domain. We also give an equivalent condition for the composite semigroup ring $$D+K[\Gamma ^*]$$ to be an almost Prufer v-multiplication domain or an almost Prufer domain when $$\Gamma \cap -\Gamma =\{0\}$$ .

In this paper, we study chain conditions on composite Hurwitz series rings and composite Hurwitz polynomial rings. More precisely, we characterize when composite Hurwitz series rings and composite Hurwitz polynomial rings are Noetherian, S-Noetherian or satisfy the ascending chain condition on principal ideals.

We fabricated hydrogenated amorphous silicon (a-Si: H) transparent solar cells using ultrathin transparent multi-layered electrodes (TMEs) as rear-side transparent electrodes for building-integrated photovoltaic (BIPV) windows. Each TME included a bottom layer, thin Ag layer, and optoelectronic controlling layer (OCL). The TMEs were experimentally designed to have high transparency and conductance. The fabricated a-Si:H transparent solar cells showed optimal performance with a 6.36% power-conversion efficiency and 23.5% average transmittance (500–800 nm) when TMEs with a thickness less than 160 nm were incorporated. We demonstrated that the reflection color of the cell could be tuned without serious loss of cell efficiency by varying the thickness of the OCL. The backside colors were predicted to be the coordinates on a CIE 1931 chromaticity diagram using the reflection spectrum from the cell and emission spectrum of a 50 W LED light source. The developed a-Si:H transparent solar cells exhibited high efficiency and show feasibility for incorporating various colors in the photovoltaic and aesthetic functionalities of BIPV windows.

Two-dimensional MoX

Let $D \subseteq E$ be an extension of commutative rings with identity, $I$ a nonzero proper ideal of $D$, $(\Gamma , \leq )$ a strictly totally ordered monoid such that $0 \leq \alpha $ for all $\alpha \in \Gamma $, and $\Gamma ^*=\Gamma \setminus \{0\}$. Let $D+[\![E^{\Gamma ^*, \leq }]\!]=\{f \in [\![E^{\Gamma , \leq }]\!] \mid f(0) \in D\}$ and $D+[\![I^{\Gamma ^*, \leq }]\!] =\{f \in [\![D^{\Gamma , \leq }]\!] \mid f(\alpha ) \in I$ for all $\alpha \in \Gamma ^*\}$. In this paper, we give some conditions for the rings $D+[\![E^{\Gamma ^*, \leq }]\!]$ and $D+[\![I^{\Gamma ^*, \leq }]\!]$ to satisfy the ascending chain condition on principal ideals.

The electrical properties of Al 2 O 3 films have been studied as the dielectric materials for electronic devices which require a low leakage current and high breakdown field. In this work, Al 2 O 3 films with various thicknesses (as low as 10⿿30 nm) were deposited onto Si substrates by plasma-enhanced atomic layer deposition (PEALD), and current density⿿ field curves were measured after post-annealing to verify their electrical properties. One thing to note is that, during PEALD, nitrogen gas was introduced to improve the thermal stability of the Al 2 O 3 films. Breakdown field for add-nitrogen Al 2 O 3 of 30 nm-thick film was enhanced from 6 MV/cm to 10 MV/cm as incorporating nitrogen.