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Let n and k be positive integers with $n\ge k+1$ and let $\{a_i\}_{i=1}^n$ be a strictly increasing sequence of positive integers. Let $S_{n, k}:=\sum _{i=1}^{n-k} {1}/{\mathrm {lcm}(a_{i},a_{i+k})}$ . In 1978, Borwein [‘A sum of reciprocals of least common multiples’, Canad. Math. Bull.20 (1978), 117–118] confirmed a conjecture of Erdős by showing that $S_{n,1}\le 1-{1}/{2^{n-1}}$ . Hong [‘A sharp upper bound for the sum of reciprocals of least common multiples’, Acta Math. Hungar.160 (2020), 360–375] improved Borwein’s upper bound to $S_{n,1}\le {a_{1}}^{-1}(1-{1}/{2^{n-1}})$ and derived optimal upper bounds for $S_{n,2}$ and $S_{n,3}$ . In this paper, we present a sharp upper bound for $S_{n,4}$ and characterise the sequences $\{a_i\}_{i=1}^n$ for which the upper bound is attained.

Background Asthma and psychological-behavioral problems co-occur more frequently than would be expected based on chance. Several previous studies have shown that the association between childhood asthma and behavioral problems was unclear. Methods Three hundred and thirty seven 6-to-14-year children with asthma in a case group and 674 children without asthma in a control group, matched with age and sex in 1:2, was investigated from Gansu Provincial Maternal and Child Health Hospital. We obtained socio-demographic data on children and health-seeking caregivers. The Rutter’s Behaviour Scale for Children (Parents’ Scale) (RBSC-PS) was used to assess children’ behavioral problems. The quantitative relationship between childhood asthma and behavioral problems was evaluated with a conditional logistic regression. Results The overall prevalence of behavioral problems in the case group and the control group were 37.39% and 18.69% respectively, and the prevalence of type A, M, and N behavioral problems in the case group were all higher than those in the control group respectively (A:14.54% vs 10.68%; M: 6.53% vs 4.15%; N: 16.32% vs 3.86%). The results of multiple conditional logistic regression analysis showed that a statistically significant association was found between childhood asthma and behavior problems (adjusted odds ratio (aOR) = 1.46; 95% confidence interval (95%CI):1.16 ~ 1.83); The regression analysis for different types of behavioral problems showed that type A behavioral problem (aOR = 1.25;95%CI:0.91 ~ 1.71) or type M (aOR = 1.20; 95%CI:0.77, 1.88) were not associated with childhood asthma but type N behavioral problem had a statistically significant association with childhood asthma(aOR = 1.90;95%CI:1.40 ~ 2.57). Conclusion The type N behavioral problem was associated with childhood asthma, highlighting the importance of behavioral problem prevention for children with asthma in pediatric asthma clinics.

We have successfully prepared a bio-photodetector based on chlorophyll derivatives as all photosensitive materials. We used zinc methyl 3-devinyl-3-hydroxymethyl-pyropheophorbide-a (Chl-A) and methyl 131-deoxo-131-dicyanomethylene-pyropheophorbide-a (Chl-D) to function as an electron acceptor...

Development of efficient photocatalysts with a wide spectral range for the photocatalytic hydrogen evolution reaction (HER) is a promising way to address the current energy and environmental crises.

Development of efficient photocatalytic hydrogen evolution reaction (HER) with illumination of visible light is challenging. In this work, five chlorophyll derivatives (M-Chls; M = H2/Cu/Ni/Co/Zn) with different central ions in its cyclic tetrapyrrole ring including free base, copper, nickel, cobalt, and zinc were synthesized and employed as the effective visible-light harvester for efficient HER. In addition, two-dimensional (2D) noble metal-free co-catalyst Ti3C2Tx MXene was used as an excellent electron capturer due to its outstanding conductivity property. These M-Chls are modified on the surface of Ti3C2Tx MXene with 2D accordion-like morphology by means of a simple deposition process to form noble metal-free Chl/Ti3C2Tx-based photocatalysts for HER. It is found that the best HER performance as high as 49 μmol/h/gcat was achieved with the Co-Chl@Ti3C2Tx hybrid, which was much higher than those of other M-Chl@Ti3C2Tx composites. This research provides a specific way to synthesize low-cost and environmentally friendly natural Chls for developing highly efficient photocatalytic HER through molecular engineering.

MXenes, a new family of 2D nanostructured materials, have been widely studied in the field of artificial photosynthesis due to their outstanding physicochemical properties. In this work, a series of 2,4-bis[4-(N,N-dibutylamino)phenyl] squaraine (SQ) derivatives with different number of hydroxyl groups were hybridized with Ti

In order to solve the problem of inapplicability of NIR quantitative models due to the large difference between the modeling samples and the samples to be tested, Directed DOSC-SBC（DDOSC-SBC）algorithm is proposed in this paper based on Direct Orthogonal Signal Correction combined with Slope/Bias Correction (DOSC-SBC) algorithm. To obtain the suitable spectral matrix transfer parameters for the test set during DDOSC spectral preprocessing, several representative test samples in the test set were selected, then the spectral systematic errors between the modeling set and the test set were corrected with the SBC method in order to realize the trans-scale prediction of the NIR quantitative model. NIR data and the critical quality attributes（CQAs）were detected in the small scale and pilot scale pharmaceutical process of the fluidized bed granulation of dextrin and water extraction of honeysuckle. After the small scale model was calibrated via the directed DOSC-SBC algorithm which was guided by representative pilot scale samples, the small scale model was able to predict the pilot scale test samples more accurately. The NIR quantitative model trans-scale calibration from small scale to pilot scale was also successfully realized with a RPD value higher than 3.5 and RSEP value lower than 10%. DDOSC-SBC algorithm is a successful model trans-scale calibrated method that can be applied to NIR real-time monitoring of CQAs in the preparation process of Chinese herbal medicine.

Hydrogen energy is an abundant, clean, sustainable and environmentally friendly renewable energy source. Therefore, the production of hydrogen by photocatalytically splitting water on semiconductors has been considered in recent years as a promising and sustainable strategy for converting solar energy into chemical energy to replace conventional energy sources and to solve the growing problem of environmental pollution and the global energy crisis. However, highly efficient solar-driven photocatalytic hydrogen production remains a huge challenge due to the poor visible light response of available photocatalytic materials and the low efficiency of separation and transfer of photogenerated electron-hole pairs. In the present work, organic heterojunction structures based on bacteriochlorophyll (BChl) and chlorophyll (Chl) molecules were introduced and used for solar-driven photocatalytic hydrogen production from water under visible light. Also, noble metal-free photocatalyst was successfully constructed on Ti

The Z-scheme process is a photoinduced electron-transfer pathway in natural oxygenic photosynthesis involving electron transport from photosystem II (PSII) to photosystem I (PSI). Inspired by the interesting Z-scheme process, herein a photocatalytic hydrogen evolution reaction (HER) employing chlorophyll (Chl) derivatives, Chl-1 and Chl-2, on the surface of Ti3 C2 Tx MXene with two-dimensional accordion-like morphology, forming Chl-1@Chl-2@Ti3 C2 Tx composite, is demonstrated. Due to the frontier molecular orbital energy alignments of Chl-1 and Chl-2, sublayer Chl-1 is a simulation of PSI, whereas upper layer Chl-2 is equivalent to PSII, and the resultant electron transport can take place from Chl-2 to Chl-1. Under the illumination of visible light (>420 nm), the HER performance of Chl-1@Chl-2@Ti3 C2 Tx photocatalyst was found to be as high as 143 μmol h-1 gcat-1 , which was substantially higher than that of photocatalysts of either Chl-1@Ti3 C2 Tx (20 μmol h-1 g-1 ) or Chl-2@Ti3 C2 Tx (15 μmol h-1 g-1 ).

Background: Digital twins are gaining ever-increasing attention from academies and industries to standardization bodies worldwide owing to their great capabilities and fundamental values in the coming fourth industrial revolution. However, there is no consistent set of definitions or concept system of the digital twin domain yet. Especially, the polysemy problem of the term “digital twin” is leading to ambiguities and an obstacle to standardization. Methods: This paper summarizes the principles and guidelines of developing a concept system mentioned in two international standards, enriches them to a methodology of developing a concept system with (1) system thinking viewpoints and systems engineering methods, (2) procedures for analyzing the semantic relationships among candidate superordinate concepts, and (3) a three-dimensional taxonomy framework with procedures of developing a taxonomy, and proposed a maturity level model for terminology work which offers a high-level vision of digital twin terminology work. Results: This paper analyzes the polysemy phenomenon of the term "digital twin” and identifies the necessity to differentiate digital twin entity and digital twin system from the general term “digital twin”. After analyzing twenty-one definitions of digital twin and summarizing ten superordinate concepts from them, this paper proposes that a digital twin entity is a kind of digital asset rather than digital representation. Based on the new superordinate concept and definition of digital twin entity, a systematic digital twin concept system is developed with one hundred concepts and fifty definitions. Conclusions: This work resolves the polysemy problem of the term “digital twin” and demonstrates the effectiveness of the enhanced methodology of developing a concept system. The proposed digital twin concept system could be a benchmark for future digital twin terminology work and useful input to the development of digital twin system reference architecture standard and lays a solid foundation for future concept systems development of other domains.

Text Let G be a finite abelian group and S be a sequence with elements of G. Let Σ ( S ) ⊂ G denote the set of group elements which can be expressed as a sum of a nonempty subsequence of S. We call S zero-sum free if 0 ∉ Σ ( S ) . In this paper, we study | Σ ( S ) | when S is a zero-sum free sequence of elements from G and 〈 S 〉 is not cyclic. We improve the results of A. Pixton and P. Yuan on this topic. In particular, we show that if S is a zero-sum free sequence with elements of G of length | S | = exp ⁡ ( G ) + 3 , then | Σ ( S ) | ≥ 5 exp ⁡ ( G ) − 1 , where exp ⁡ ( G ) denotes the exponent of G. This gives a positive answer to a case of a conjecture of B. Bollobas and I. Leader as well as to a case of a conjecture of W. Gao et al. Video For a video summary of this paper, please visit https://youtu.be/cvK4nZkY4lo .

Let G be a finite abelian group and S be a sequence with elements of G. We say that S is a regular sequence over G if ∣SH∣ ⩽ ∣H∣ − 1 holds for every proper subgroup H of G, where SH denotes the subsequence of S consisting of all terms of S contained in H. We say that S is a zero-sum free sequence over G if 0 ∉ Ω(S), where Ω(S) ⊂ G denotes the set of group elements which can be expressed as a sum of a nonempty subsequence of S. In this paper, we study the inverse problems associated with Ω(S) when S is a regular sequence or a zero-sum free sequence over G = Cp ⊕ Cp, where p is a prime.

A ring is nil clean if each of its elements is the sum of an idempotent and a nilpotent. In Sahinkaya et al. [13], it was shown that, for a ring R and a symmetric group S 3, the group ring RS 3 is ...

Text For a positive integer k, let f ( k ) denote the largest integer t such that for every finite abelian group G and every zero-sum free subset S of G, if | S | = k then | Σ ( S ) | ≥ t . In this paper, we prove that f ( k ) ≥ 1 6 k 2 , which significantly improves a result of J.E. Olson. We also supply some interesting results on f ( k ) . Video For a video summary of this paper, please visit https://youtu.be/ZEHZFRUVJKY .

A self-designed mini gas–solid reaction device was applied as promising equipment to investigate the oxidation characteristics and kinetics of the glycerol ester of rosin (GER) under 254 nm UV irradiation in air. Peroxide formation during the photo-oxidation process was analyzed by iodimetry. The peroxide concentration is related to the light intensity (I) and the temperature (T), and increasing I and T would destabilize the GER by accelerating peroxide generation. The photo-oxidation of GER followed pseudo-first-order reaction kinetics under a given hypothesis. A linear relationship was observed between activation energy and the logarithm of light intensity (ln I), which can be expressed as Ea = −3.575 ln I + 34.943 under the experimental conditions. This research indicated that under 254 nm UV irradiation GER could be easily oxidized even at room temperature.

The thermal oxidation characteristics of abietic acid were investigated through tracing the oxidation process in custom-designed mini closed pressure vessel test under isothermal and step temperatu...

Let [Formula: see text] be a finite abelian group and [Formula: see text] be a subset of [Formula: see text]. Let [Formula: see text] denote the set of group elements which can be expressed as a sum of a nonempty subset of [Formula: see text]. We say that [Formula: see text] is zero-sum free if [Formula: see text]. In this paper, we show that if [Formula: see text] is zero-sum free with [Formula: see text], then [Formula: see text]. Furthermore, if [Formula: see text] is zero-sum free and [Formula: see text], with the assumption that the subgroup generated by [Formula: see text] is noncyclic and the order [Formula: see text], we are able to show that [Formula: see text].

In this work, thermal oxidation reaction of dimethoxymethane (DMM) at low temperature was investigated with a custom-designed mini closed pressure vessel test (MCPVT) employed. The initial auto-oxidation, thermal decomposition and deep radical oxidation processes were revealed by analyzing the behavior of oxidation temperature (T) and pressure (P) in the process of MCPVT monitoring. Peroxides generated from DMM auto-oxidation were measured by iodimetry and thin-layer chromatography (TLC). The dominant peroxide was separated from oxidation products via column chromatography, with structure characterized by mass spectrometry (MS), 1H and 13C nuclear magnetic resonance (NMR). The thermal decomposition characteristics were determined by differential scanning calorimeter (DSC). Results show that the oxidation was mainly initiated by hydrogen abstraction on the methylenedioxy (O-CH2-O) of DMM when temperature was above about 310 K. The primary product of hydroperoxide, hydroperoxy(methoxymethoxy)methane was found in DMM oxidation for the first time, with a high level. Its exothermic onset temperature (T0) and decomposition heat (QDSC) are 372.87 K and 2431.37 J·g−1, respectively. The thermal decomposition could lead to thermal runaway of oxidation, and further transform into an explosion. In most cases, the release of radical pool after peroxides decomposition would induce a rapidly radical oxidation of DMM through an endothermic reaction at about 410 K.

The Z-scheme process is a photoinduced electron-transfer pathway in natural oxygenic photosynthesis involving electron transport from photosystem II (PSII) to photosystem I (PSI). Inspired by the interesting Z-scheme process, herein a photocatalytic hydrogen evolution reaction (HER) employing chlorophyll (Chl) derivatives, Chl-1 and Chl-2, on the surface of Ti

Let $G$ be a multiplicatively written finite group. We denote by $\mathsf E(G)$ the smallest integer $t$ such that every sequence of $t$ elements in $G$ contains a product-one subsequence of length $|G|$. In 1961, Erd\H{o}s, Ginzburg and Ziv proved that $\mathsf E(G)\leq 2|G|-1$ for every finite abelian group $G$ and this result is known as the Erd\H{o}s-Ginzburg-Ziv Theorem. In 2005, Zhuang and Gao conjectured that $\mathsf E(G)=\mathsf d(G)+|G|$ for every finite group, where $\mathsf d(G)$ is the small Davenport constant. Very recently, we confirmed this conjecture for the case when $G=\langle x, y| x^p=y^m=1, x^{-1}yx=y^r\rangle$ where $p$ is the smallest prime divisor of $|G|$ and $\mbox{gcd}(p(r-1), m)=1$. In this paper, we study the associated inverse problems on $\mathsf d(G)$ and $\mathsf E(G)$. Our main results characterize the structure of any product-one free sequence with extremal length $\mathsf d(G)$, and that of any $|G|$-product-one free sequence with extremal length $\mathsf E(G)-1$., Comment: 25 pages. This paper deals with the inverse problem related to arXiv:2107.06969

Background: Asthma can increase the risk of anxiety and abnormal behavior among children but the correlation between anxiety and behavioral abnormalities in children with asthma was unclear. Methods: The Self-Rating Anxiety Scale and the Rutter Children’s Behavior Questionnaire were used to conduct surveys with 337 children aged 6 to 14 years who were diagnosed in the asthma clinic of Gansu Provincial Maternity and Child Care Hospital in Lanzhou, China from January to December 2019. SPSS 22.0 software was used to perform multivariate logistic regression and factor analysis on the items of the anxiety scale to extract different anxiety manifestations. Results: The abnormal behavior rate was 37.1% among the 337 investigated children with asthma. A total of 3 factors were extracted by factor analysis on the 20 items of the anxiety scale, namely mental, sensory, and hand-and-foot manifestations. The 3 factors were divided into 3 groups using tertiles (Q1~Q3). After controlling for sex, age, wheezing history, marital status of parents, caregiver awareness, and caregiver’s home care situation, compared with Q1, the multivariate logistic regression model showed that Q3 had a statistically significant relationship with abnormal behavior, regardless of mental or hand-and-foot manifestation. No connection between Q2 and behavior abnormalities was found. For sensory manifestations, neither Q3 nor Q2 was significantly related to abnormal behavior. Conclusions: Abnormal behavior was related to only severe anxiety among children with asthma. Therefore, psychological intervention should be carried out as early as possible in the treatment of children with asthma to prevent and correct abnormal behavior.

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Pressure and temperature behavior of the cinnamaldehyde oxidation process was determined using a custom-designed mini closed pressure vessel test (MCPVT), which is a new method to investigate the stability and hazard assesment of the cinnamaldehyde oxidation reaction. The oxidation products were analyzed by gas chromatography-mass spectrometry (GC-MS). The results showed that cinnamaldehyde was stable under nitrogen atmosphere but very unstable under oxygen atmosphere. The initial oxidation products were analyzed by iodimetry and the cinnamaldehyde peroxide value could reach 139.44 mmol kg−1 when the oxidation temperature was 308 K. The oxidation kinetics of cinnamaldehyde were studied by using the pressure versus time (P–t) curves obtained from the MCPVT process. The reaction is a second-order reaction, the kinetic equation is ln k = −2233.66 × (1/T) + 11.19, and the activation energy Ea is 18.57 kJ mol−1 at 308–338 K. The explosion of the cinnamaldehyde oxidation reaction was observed by MCPVT, in which the onset temperature was 373 K. The main products of cinnamaldehyde oxidation are acetaldehyde, benzaldehyde, phenylacetaldehyde, acetophenone, 2-hydroxyphenyl acetone, cinnamaldehyde epoxide, benzoic acid, and cinnamic acid. Oxidation is a three-step process: (1) cinnamaldehyde reacts with oxygen to form peroxides; (2) complex oxidation reactions are caused by the thermal decomposition of peroxides; (3) rapid oxidation and thermal decomposition lead to explosion hazard.

The purpose of the paper is to provide a unified way to formulate zero-sum invariants. Let [Formula: see text] be a finite additive abelian group. Let [Formula: see text] denote the monoid of all zero-sum sequences over [Formula: see text]. For [Formula: see text], let [Formula: see text] be the smallest integer [Formula: see text] such that every sequence [Formula: see text] over [Formula: see text] of length [Formula: see text] has a subsequence in [Formula: see text]. We provide some first results and open problems on [Formula: see text].

Chlorophylls (Chls) are the most abundant natural pigments having excellent opt-electrical and semi-conductive properties. Ti3C2Tx MXene, one of the most extensively studied 2D noble metal-free co-catalyst, features outstanding electrochemical properties. This work compares three aggregate-forming chlorophyll derivatives (Chl-n; n = 1–3), namely, zinc methyl 3-devinyl-3-hydroxymethyl-pyropheophorbide-a (Chl-1), zinc dodecyl 3-devinyl-3-hydroxymethyl-pyropheophorbide-a (Chl-2) and zinc dodecyl 131-deoxo-3-devinyl-131-dicyanomethylene-3-hydroxymethyl-pyropheophorbide-a (Chl-3), as light-harvesting antenna pigments in the MXene-based photocatalytic system for hydrogen evolution under the white light illumination (λ > 420 nm). The hydrogen evolution reaction (HER) of these Chls depends on the peripheral substituent groups at the C13- and/or C17-positions of the chlorin macrocyclic π-system. Differences among these Chl-n sensitized Ti3C2Tx MXene (Chl-n@Ti3C2Tx) are compared in terms of their light-harvesting ability, morphology, charge transfer efficiency and photocatalytic performance. The best HER performance is found to be as high as 122 μmol/h/gcat with the Chl-3@Ti3C2Tx composite. This work leads the direction in synthesizing Chls in Chl/MXene hybrid structure suitable for highly efficient photocatalytic HER.

Multilevel switching (MS) behaviors in Ta 2 O 5 -based resistive random-access-memory (ReRAM) have been drawing attentions as hardware artificial synapse. However, operating resistances, which decide the power consumption of whole system, are relatively low for future integration. In this work, we investigated the characteristics of two kinds of ReRAMs operating with different mechanisms; Cu-top-electrode and Ta-top-electrode Ta 2 O 5 -based ReRAMs. By taking account of resistance of high resistive state (HRS), we clarify the difference of MS characteristics between the two kinds of ReRAM devices.

The initial electrical properties of tantalum oxide resistive memory were investigated using four metal electrodes (TiN, Ti, Ta, and Al) and two kinds of tantalum oxide with different amounts of intrinsic oxygen vacancies. The initial resistance depended on the electrode material. This indicated that oxygen scavenging by the electrodes contributed to a reduction in the resistance. However, the resistance change depended on the intrinsic oxygen vacancy concentration introduced during the tantalum oxide deposition. The forming voltage also depended on the electrode metal. For the device with an Al electrode, a clear aluminum oxide layer was identified at the electrode–insulator interface, which was hypothesized to be the origin of the high forming voltage. All factors concerning the oxygen vacancies, i.e. intrinsic vacancies introduced via film deposition and extrinsic vacancies caused by the electrode scavenging effect, influenced the initial state of tantalum oxide, and thus, its switching performance as a resistive memory.

Let [Formula: see text] be an additively written finite cyclic group of order [Formula: see text] and let [Formula: see text] be a minimal zero-sum sequence with elements of [Formula: see text], i.e. the sum of elements of [Formula: see text] is zero, but no proper nontrivial subsequence of [Formula: see text] has sum zero. [Formula: see text] is called unsplittable if there do not exist an element [Formula: see text] in [Formula: see text] and two elements [Formula: see text] in [Formula: see text] such that [Formula: see text] and the new sequence [Formula: see text] is still a minimal zero-sum sequence. In this paper, we investigate long unsplittable minimal zero-sum sequences over [Formula: see text]. Our main result characterizes the structures of all such sequences [Formula: see text] and shows that the index of [Formula: see text] is at most 2, provided that the length of [Formula: see text] is greater than or equal to [Formula: see text] where [Formula: see text] is a positive integer with least prime divisor greater than [Formula: see text].

Let D be a generalized dihedral group and AutCol(D) its Coleman automorphism group. Denote by OutCol(D) the quotient group of AutCol(D) by Inn(D), where Inn(D) is the inner automorphism group of D. It is proved that either OutCol(D) = 1 or OutCol(D) is an elementary abelian 2-group whose order is completely determined by the cardinality of π(D). Furthermore, a necessary and sufficient condition for OutCol(D) = 1 is obtained. In addition, whenever OutCol(D) ≠ 1, it is proved that AutCol(D) is a split extension of Inn(D) by an elementary abelian 2-group for which an explicit description is given.

A group G is said to be a B(n, k) group if for any n-element subset A of G, |A2| ≤k. In this paper, a characterization of B(5, 18) groups is given. It is shown that G is a B(5, 18) group if and only if one of the following statements holds: (1) G is abelian; (2) |G| ≤18; (3) G ≅ ⟨ a, b | a5 = b4 = 1, ab = a−1 ⟩.

In this study, silicoaluminophosphate (SAPO)-34 and Me (Me = Cr, Co)-modified SAPO-34 were synthesized and used as catalysts to investigate the catalytic performance by means of a probe reaction from ethanol to ethylene. The metal oxides were loaded on the SAPO-34 support via an impregnation method. The synthesized catalysts were characterized using XRD, SEM, EDX, FT-IR, NH3-TPD, BET, and TGA techniques. Compared to SAPO-34, SAPO-34 doped with metal oxides showed the same chabazite (CHA) topology. The structure and properties of the catalyst were further optimized by varying the amount of Me. The experimental results showed that Co-Cr/SAPO-34 exhibited the best catalytic performance when the reaction temperature reached 400 &deg, C at a weight hourly space velocity (WHSV) of 3.5 h&minus, 1, for which the single-pass conversion of ethanol was determined as 99.15%, and the selectivity of ethylene was 99.4% at an optimum catalytic performance in the reaction of up to 600 min. In addition, Co-Cr/SAPO-34 exhibited better catalytic activity and anti-coking ability than pure SAPO-34, which was attributed to its enhanced pore structure and moderate acidity. It can also be concluded from the results of this experiment that the performance of the Co-Cr bimetal-supported catalyst is better than that of the Cr mono-metal catalyst.

A ring R is said to be clean if each element of R can be written as the sum of a unit and an idempotent. In a recent article (J. Algebra, 405 (2014), 168-178), Immormino and McGoven characterized when the group ring Z ( p ) [ C n ] is clean, where Z ( p ) is the localization of the integers at the prime p. In this paper, we consider a more general setting. Let K be an algebraic number field, O K be its ring of integers, and R be a localization of O K at some prime ideal. We investigate when R [ G ] is clean, where G is a finite abelian group, and obtain a complete characterization for such a group ring to be clean for the case when K = Q ( ζ n ) is a cyclotomic field or K = Q ( d ) is a quadratic field.

Because the hazard of flood disaster is mainly related to the natural attribute of flood disaster, this paper makes full use of multi-source remote sensing information to reflect the meteorological and underlying surface conditions in Ya’an City, constitutes an evaluation index system according to selecting the rainfall, runoff depth, the basin storage capacity, elevation, slope and water system, from the two aspects of disaster-inducing factors and disaster-pregnant environment; trains historical flood occurrence sites by using BP neural network, obtains the weights of each research index; overlays analysis each index according to the index model, based on the GIS technology; and obtains the torrential flood hazard distribution map of Ya’an City as well as comparing it with the occurrence sites of historical flood disasters. The results show that the flood hazard level is the highest in the eastern part of Ya’an, the lowest level area of the flood hazard is the southern part. The evaluation results well reflect the actual situation of regional flood spatial distribution, which can provide a scientific basis for the development of reasonable flood control and disaster mitigation planning in Ya’an City.

Efficient photocatalytic hydrogen evolution reaction (HER) in the visible‐to‐near infrared region at a low cost remains a challenging issue. This work demonstrates the fabrication of organic‐inorganic composites by deposition of supramolecular aggregates of a chlorophyll derivative, namely, zinc methyl 3‐devinyl‐3‐hydroxymethyl‐pyropheophorbide a (Chl) on the surface of Ti3C2Tx MXene with 2D accordion‐like morphology. This composite material is employed as noble metal‐free catalyst in photocatalytic HER under the white light illumination, where Chl serves as a small molecule organic semiconductor component instead of ordinary inorganic and polymer organic semiconductors such as TiO2 and g‐C3N4, and Ti3C2Tx serves as a co‐catalyst. Different composition ratios of Chl/Ti3C2Tx are compared for their light‐harvesting ability, morphology, charge transfer efficiency, and photocatalytic performance. The best HER performance is found to be as high as 52 ± 5 µmol h−1 gcat−1 after optimization. Such a large HER activity is attributed to the efficient light harvesting followed by exciton transfer in Chl aggregates and the resultant charge separation at the interface of Chl/Ti3C2Tx.

In an additively written abelian group, a sequence is called zero-sum free if each of its nonempty subsequences has sum different from the zero element of the group. In this paper, we consider the structure of long zero-sum free sequences and n-zero-sum free sequences over finite cyclic groups $${\mathbb{Z}_n}$$ . Among which, we determine the structure of the long zero-sum free sequences of length between $${n/3+1 }$$ and $${n/2}$$ , where $${n\ge 50}$$ is an odd integer, and we provide a general description on the structure of n-zero-sum free sequences of length n + l, where $${\ell\geq n/p+p-2}$$ and p is the smallest prime dividing n.

A ring with involution * is called *-clean if each of its elements is the sum of a unit and a projection (*-invariant idempotent). Recently, Gao, Chen, and Li obtained necessary and sufficient conditions for RG to be *-clean, where R is a commutative local ring and G is one of C3, C4, S3, and Q8. Most recently, Li, Yuan, and Parmenter gave a complete characterization of when the group algebra FCp is *-clean, where F is a field and Cp is a cyclic group of prime order p. In this article, we extend the above mentioned result from FCp to FqCpk, where Fq is a finite field and Cpk is a cyclic group of an odd prime power order pk. For the general case when G = Cn is cyclic group of order n, we also provide a necessary condition and a few sufficient conditions for FqCn to be *-clean.