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Reciprocal sums of a class of additive functions in short intervals

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Chinese Science Bulletin 1997年第2期42卷 102-105页

作者： zhai wenguangdepartment of mathematics, shandong normal university, jinan 250014, china Department of mathematics Shandong Normal University Jinan China

USING the method of probabilistic number-theory, De Koninck, and De Koninck and Galambos studied the reciprocal sum of the additive function f（n） satisfying f（n）≥t0>0 （n≥2） and f（p）≡1 and obtained an asymptotic formula, where t0 is an absolute positive constant. Let B（x） denote the number of n≤x not satisfying the inequality loglogn-R（x）≤f（n）≤loglogn+R（x）, （1） where R（x） is a function tending to infinity. Then in refs. [1, 2], it is proved that if R（x）=o（loglogx） and B（x）=o（x/loglogx）,

关键词： additive functions Riemann zeta-function asymptotic formula.

Number of β-free numbers in short intervals

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Chinese Science Bulletin 2000年第3期45卷 208-212页

作者： zhai wenguangdepartment of mathematics, shandong normal university, jinan 250014, china

The -B -free number is a generalization of the well-known squarefree numbers. The result that if θ>33/80, then the interval [x-xθ,x] must contain a B-free number for large x has been proved.

关键词： β-free number squarefree number exponential sum.

On the Average Number of Unitary Factors of Finite Abelian Groups (Ⅱ)

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Acta Mathematica Sinica,English Series 2000年第4期16卷 549-554页

作者： Wenguang zhai Department of mathematics, shandong normal university. jinan 250014. P. B. china Department of mathematics Shandong Normal University Jinan 250014 P. R. China

Let t（G） be the number of unitary factors of finite abelian group G. In this paper we prove T（x）=∑(G≤（）t（G） =main terms+O(x(（1+2k）/（3+4k）for any exponent pair （k, 1/2+2K）. which improves on the exponen... 详细信息

关键词： Unitary factor Finite Abelian group Exponential sum Divisor problem

On the error term in Weyl’s law for the Heisenberg manifolds (Ⅱ)

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Science china mathematics 2009年第5期52卷 857-874页

作者： zhai WenGuang School of Mathematical Sciences, shandong normal university, jinan 250014, china 1. School of Mathematical Sciences Shandong Normal University Jinan 250014 China

In this paper we study the mean square of the error term in the Weyl's law of an irrational (2l + 1)-dimensional Heisenberg manifold. An asymptotic formula is established.

关键词： Heisenberg manifold Weyl’s law error term mean square

Enhanced nitrite electroreduction to ammonia via interfacial dual-site adsorption

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Journal of Energy Chemistry 2024年第9期96卷 328-335页

作者： Xiaokang Chen Shengliang zhai Yi Tan Le Su Dong zhai Wei-Qiao Deng Hao Wu Institute of Frontier Chemistry School of Chemistry and Chemical EngineeringShandong UniversityQingdao 266071ShandongChina College of Physics and Information Engineering Shanxi Normal UniversityTaiyuan 030031ShanxiChina Suzhou Research Institute of shandong university Suzhou 215123JiangsuChina

The nitrite(NO_(2)^(−))to ammonia(NH3)electroreduction reaction(NO_(2)^(−)RR)would be impeded by sluggish proton-coupled electron transfer kinetics and competitive hydrogen evolution reaction(HER).A key to improving the NH_(3) selectivity is to facilitate adsorption and activation of NO_(2)^(−),which is generally undesirable in unitary *** this work,an efficient NO_(2)^(−)RR catalyst is constructed by cooperating Pd with In2O3,in which NO_(2)^(−)could adsorb on interfacial dual-site through“Pd–N–O–In”linkage,leading to strengthened NO_(2)^(−)adsorption and easier N=O bond cleavage than that on unitary Pd or ***,the Pd/In_(2)O_(3)composite exhibits moderate H^(*)adsorption,which may facilitate protonation kinetics while inhibiting competitive *** a result,it exhibits a fairly high NH_(3)yield rate of 622.76 mmol h^(−1)g^(−1)cat with a Faradaic efficiency(FE)of 95.72%,good selectivity of 91.96%,and cycling stability towards the NO_(2)^(−)RR,surpassing unitary In_(2)O_(3)and Pd/C ***,computed results indicate that NH_(3)production on Pd/In_(2)O_(3)follows the deoxidation to hydrogenation *** work highlights the significance of H^(*)and NO_(2)^(−)adsorption modulation and N=O activation in NO_(2)^(−)RR electrochemistry by creating synergy between a mediocre catalyst with an appropriate cooperator.

关键词： Dual-site adsorption Nitrite electroreduction Ammonia Pd Hydrogenation

Taxonomy and phylogeny of the section Chaetoceros(Chaetocerotaceae,Bacillariophyta),with description of two new species

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Journal of Oceanology and Limnology 2024年第4期42卷 1286-1311页

作者： Xudan LU Mengyi zhai Nina LUNDHOLM Yang LI Guangdong Provincial Key Laboratory of Biotechnology for Plant Development Guangzhou Key Laboratory of Subtropical Biodiversity and BiomonitoringCollege of Life ScienceSouth China Normal UniversityGuangzhou 510631China Natural History Museum of Denmark University of CopenhagenCopenhagen K 1353Denmark

Chaetoceros Ehrenberg is one of the most diverse genera of planktonic *** species in section Chaetoceros are characterized by cells and setae having numerous chloroplasts and being widely ***,the delimitations of some species are problematic because of limited morphological information in the classical *** strains of the section Chaetoceros were established,morphological features were studied using light and electron microscopy,and the hypervariable D 1-D 3 region of the nuclear ribosomal large subunit gene was sequenced to address phylogenetic *** species belonging to the section Chaetoceros were recorded,including two new species,*** *** *** *** hainanensis was characterized by straight chains,narrowly lanceolate to hexagonal apertures,sibling setae diverging in nearly right angles,stipule-shaped spines on terminal setae and arrowhead-shaped spines on intercalary *** had short straight chains,narrowly lanceolate apertures,arrowhead-shaped spines and circular poroids arranged in a grid pattern on terminal and intercalary *** phylogenetic analyses revealed six groups formed by 19 species within the section Chaetoceros,which was found to be *** subdivision of the section is still not well *** morphological characters within each group varied considerably and molecular information on more species are needed to enrich the phylogenetic profiling.

关键词： morphology large subunit ribosomal RNA encoding gene(LSU) section Chaetoceros Chaetoceros hainanensis Chaetoceros tridiscus

Electronic structure and geometric construction modulation of carbon-based single/dual atom catalysts for electrocatalysis

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Energy Reviews 2024年第3期3卷 76-91页

作者： Shaolong Zhang Jing Huang Li Ma Dong zhai Bin Wei Hengpan Yang Chuanxin He College of Chemistry and Environmental Engineering Shenzhen UniversityShenzhen518060PR China Pharmaceutical College Guangxi Medical UniversityNanning530021PR China Key Laboratory of New Electric Functional Materials of Guangxi Colleges and Universities Nanning Normal UniversityNanning530023PR China Institute of Molecular Sciences and Engineering Institute of Frontier and Interdisciplinary ScienceShandong UniversityQingdao266237PR China School of Materials Sun Yat-sen UniversityShenzhen518107PR China

Both carbon-based single atom catalysts(SACs)and dual atom catalysts(DACs)have garnered significant attention in the field of electrochemical reactions because of the impressive attributes,including exceptional catalytic activity,selectivity,and *** ability to modulate the electronic structure and geometric construction of active sites within SACs/DACs is paramount for unleashing their complete potential,which in turn can ultimately dictate catalytic behavior with unprecedented *** this review,the recent major developments of the regulation strategies for modulating electronic structure and geometric construction of carbon-based SACs/DACs are *** the SACs,the recently reported modulation methods are categorized into four strategies,including adjusting the density of single atoms,defect engineering,confinement effect and strain *** for the DACs,the five methods contain bonded dual-atom adjustment,non-bonded and bridged dual-atom adjustment,metal and nonmetal dual-atom adjustment,bilayer dual-atom adjustment and homogeneous dual-atom *** recently developed synthetic strategies are comprehensively summarized,especially their electronic structure and geometric configuration are discussed in detail,the different catalytic applications of electrochemical reactions,and their unique catalytic mechanism are ***,the challenges and prospects of SACs/DACs for tailoring their electronic structures and geometric arrangements are further discussed.

关键词： Electronic structure Geometric construction Single atom catalysts Dual atom catalysts Modulation