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Application of Polynomial Interpolation in the Chinese Remainder Problem

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j.urnal of Mathematical Research with Applications 2017年第1期37卷 90-96页

作者： Tianxiao HE scott MACDONALD peter j.-s.shiue Department of Mathematics Illinois Wesleyan University Math Learning Center University of Nevada Las Vegas Department of Mathematical sciences University of Nevada

This paper presents an application of polynomial interpolation in the solution of the Chinese Remainder Problem for bother integers and polynomials.

关键词： Chinese Remainder problem Chinese Remainder theorem Lagrange interpolation Newton interpolation

Matrix Representation of Recursive sequences of Order 3 and Its Applications

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j.urnal of Mathematical Research with Applications 2018年第3期38卷 221-235页

作者： Tianxiao HE j.ff H.-C.LIAO peter j.-s.shiue Department of Mathematics Illinois Wesleyan University Department of Mathematics Taiwan Normal University Department of Mathematical sciences University of Nevada

Here presented is a matrix representation of recursive number sequences of order 3 defined by a;= pa;+ qa;+ ra;with arbitrary initial conditions a;, a;= 0, and a;and their special cases of Padovan number sequence and Perrin number sequence with initial conditions a;= a;= 0 and a;= 1 and a;= 3, a;= 0, and a;= 2, respectively. The matrix representation is used to construct many well known and new identities of recursive number sequences as well as Pavodan and Perrin sequences.

关键词： recursive number sequence of order 3 matrix representation of recursive number sequences Padovan number sequence Perrin number sequence Tribonacci polynomial sequence

The Global Energy and Water Exchanges(GEWEX)Proj.ct in Central Asia:The Case for a Regional Hydroclimate Proj.ct

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Advances in Atmospheric sciences 2024年第5期41卷 777-783页

作者： Michael BRODY Maksim KULIKOV sagynbek ORUNBAEV peter j.VAN OEVELEN International Agricultural University Tashkent 111200Uzbekistan George Mason University FairfaxVirginia 22030USA University of Central Asia Bishkek 720001Kyrgyz Republic American University of Central Asia Bishkek 720060Kyrgyz Republic International GEWEX proj.ct George Mason UniversityFairfaxVirginia 22030USA

Central Asia consists of the former soviet Republics,Kazakhstan,Kyrgyz Republic,Taj.kistan,Turkmenistan,and *** region’s climate is continental,mostly semi-arid to *** is a significant part of the region’s *** its nature of intensive water use,agriculture is extremely vulnerable to climate *** growth and irrigation development have significantly increased the demand for water in the *** climate change issues include melting glaciers and a shrinking snowpack,which are the foundation of the region’s water resources,and a changing precipitation *** glaciers are located in Kyrgyzstan and Taj.kistan,leading to transboundary water resource *** already has extremely high *** indicate that Central Asia has been warming and precipitation might be *** warming is expected to increase,but its spatial and temporal distribution depends upon specific global *** of future precipitation show significant uncertainties in type,amount,and *** Hydroclimate Proj.cts(RHPs)are an approach to studying these *** steps to develop an RHP began in 2021 with a widely distributed online survey about these climate *** was followed up with an online workshop and then,in 2023,an in-person workshop,held in Tashkent,*** for the Global Energy and Water Exchanges(GEWEX)proj.ct for the region include both observations and modeling,as well as development of better and additional precipitation observations,all of which are topics for the next workshop.A well-designed RHP should lead to reductions in critical climate uncertainties in policy-relevant timeframes that can influence decisions on necessary investments in climate adaptation.

关键词： GEWEX Central Asia climate change agriculture

Algorithms for enumeration problem of linear congruence modulo m as sum of restricted partition numbers

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Frontiers of Mathematics in China 2015年第1期10卷 69-89页

作者： Tian-Xiao HE peter j. -s. shiue Department of Mathematics Illinois Wesleyan University Bloomington IL 61702 USA Department of Mathematical sciences University of Nevada Las Vegas Las Vegas NV 89154-4020 USA

We consider the congruence x1＋ x2 ＋… ＋ xr - c （mod m）, wherem and r are positive integers and c ∈Zm ：= {0, 1, ..., m- 1} （m ≥ 2）. Recently,W.-s. thou, T. X. He,and peter j.-s. shiue considered the enumerationproblems of this congruence, namely, the number of solutions with the restriction x1≤~ x2≤ ... ≤ xr, and got some properties and a neat formula ofthe solutions. Due to the lack of a simple computational method for calculating the number of the solution of the congruence, we provide an algebraic and a recursive algorithms for those numbers. The former one can also give a new and simple approach to derive some properties of solution numbers.

关键词： Congruence multiset congruence solution restricted integerpartition

Full-spectrum Bi@srTiO_(3) for bi-directional promotion effects on photocatalytic redox reaction:Insight into intermediates and mechanism

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j.urnal of Rare Earths 2024年第5期42卷 917-929,I0004页

作者： Bin Liu Nanhao Zhou j.n Liu Xinglei Wang peter K.j.Robertson Xiaoyuan Chen Chao Chen j.anmin Luo Chuanyi Wang school of Chemistry and Civil Engineering Shaoguan UniversityShaoguan512005China Chengdu Customs Technology Center Chengdu610041China Key Laboratory of Pollutant Chemistry and Environmental Treatment College of Chemistry and Environmental ScienceYili Normal UniversityYining835000China school of Chemistry and Chemical Engineering Queen's University BelfastStranmillis RoadBelfastBT95AGUnited Kingdom Guangzhou Institute of Industrial Intelligence(GIII) Guangzhou511400China

The development of full-spectrum photocatalysts active in the near-infrared(NIR)region has gained increasing attention for deleterious pollutant *** integration of plasmonic metals with semico nductors is an effective way to widen the light re sponse range of photocatalysts due to the strong light absorption and fast plasmonic energy transfer of the localized surface plasmon resonance(LsPR).In this work,the full-spectrum responsive Bi@srTiO_(3) was prepared via facile solvothermal chemical *** optimal Bi@srTiO_(3) achieves exceptional photocatalytic Cr(VI)reduction efficiency and tetracycline degradation,realizing bi-directional promotion effects on redox *** to density functional theory(DFT)simulations,the extraordinary photocatalytic performance is attributed to the tunable builtin electric field(IEF)of the Ohmic *** favorable adaptability in real water and high stability of BsTO-25 were proved by experime ntal *** the po ssible photocatalytic mechanism was proposed based on theoretical calculation and experimental ***,the non-toxicity of the BsTO-25 was evaluated by *** cultivation,which further proves the feasibility of treating wastewater with *** work provides a new perspective on constructing full-spectrum-driven photocatalysts for applications dealing with environmental remediation.

关键词： Full-spectrum photocatalysts Localized surface plasmon resonance Ohmic contact Cr(Ⅵ)reduction Antibiotic degradation Rare earths

Identific tion of quantitative trait loci and associated candidate genes for pregnancy success in Angus–Brahman crossbred heifers

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j.urnal of Animal science and Biotechnology 2024年第1期15卷 162-170页

作者： Quinn A.Hoorn Gabriel A.Zayas Eduardo E.Rodriguez Laura M.j.nsen Raluca G.Mateescu peter j.Hansen Department of Animal sciences Donald Henry Barron Reproductive and Perinatal Biology Research Programand the Genetics InstituteUniversity of FloridaGainesvilleFLUSA school of Applied systems Biology La Trobe UniversityBundooraVIC 3083Australia

Background In beef cattle, more than 50% of the energy input to produce a unit of beef is consumed by the female that produced the calf. Development of genomic tools to identify females with high genetic merit for reproductive function could increase the profitability and sustainability of beef *** Genome-wide association studies(GWAs) were performed using a single-step genomic best linear unbiased prediction approach on pregnancy outcome traits from a population of Angus–Brahman crossbred heifers. Furthermore, a validation GWAs was performed using data from another farm. Heifers were genotyped with the Bovine GGP F250 array that contains 221,077 sNPs. In the discovery population, heifers were bred in winter breeding seasons involving a single round of timed artificial insemination(AI) followed by natural mating for 3 months. Two phenotypes were analyzed: pregnancy outcome to first-service AI(PAI;n = 1,481) and pregnancy status at the end of the breeding season(PEBs;n = 1,725). The heritability was estimated as 0.149 and 0.122 for PAI and PEBs, respectively. In the PAI model, one quantitative trait locus(QTL), located between 52.3 and 52.5 Mb on BTA7, explained about 3% of the genetic variation, in a region containing a cluster of γ-protocadherin genes and sLC25A2. Other QTLs explaining between 0.5% and 1% of the genetic variation were found on BTA12 and 25. In the PEBs model, a large QTL on BTA7 was synonymous with the QTL for PAI, with minor QTLs located on BTA5, 9, 10, 11, 19, and 20. The validation population for pregnancy status at the end of the breeding season were Angus–Brahman crossbred heifers bred by natural mating. In concordance with the discovery population, the large QTL on BTA7 and QTLs on BTA10 and 12 were *** In summary, QTLs and candidate sNPs identified were associated with pregnancy outcomes in beef heifers, including a large QTL associated with a group of protocadherin genes. Confirmation of these associations

关键词： Beef cattle Fertility GWAs QTL

ON AN EXTENsION OF ABEL-GONTsCHAROFF's EXPANsION FORMULA

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Analysis in Theory and Applications 2005年第4期21卷 359-369页

作者： Tianxiao He Leetsch C. Hsu peter j. s. shiue Illinois Wesleyan University USA Dalian University of Technology China University of Nevada Las Vegas USA

We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algo... 详细信息

关键词： Abel-Gontscharoff's Expansion Formula Abel-Gontscharoff-Gould polynomial multivariate Abel-Gontscharoff interpolation higher dimensional dot product annihilation coefficients

Management of distal cholangiocarcinoma with arterial involvement: systematic review and case series on the role of neoadj.vant therapy

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World j.urnal of Gastrointestinal surgery 2024年第8期16卷 2689-2701页

作者： Lewis A Hall Duncan Loader santiago Gouveia Marta Burak j.mes Halle-smith peter Labib Moath Alarabiyat Ravi Marudanayagam Bobby V Dasari Keith j.Roberts syed s Raza Michail Papamichail David C Bartlett Robert P sutcliffe Nikolaos A Chatzizacharias Department of Hepatopancreatobiliary surgery and Liver Transplantation University Hospitals Birmingham NHS Foundation TrustBirmingham B152GWUnited Kingdom Institute of Immunology and Immunotherapy University of BirminghamBirmingham B152TTUnited Kingdom College of Medical and Dental sciences University of BirminghamBirmingham B152TTUnited Kingdom Institute of Clinical sciences University of BirminghamBirmingham B152TTUnited Kingdom

BACKGROUND The use of neoadj.vant therapy(NAT)in distal cholangiocarcinoma(dCCA)with regional arterial or extensive venous involvement,is not widely accepted and evidence is *** To synthesise evidence on NAT for dCCA and present the experience of a highvolume tertiary-centre managing dCCA with arterial *** A systematic review was performed according to PRIsMA guidance to identify all studies reporting outcomes of patients with dCCA who received *** patients from 2017 to 2022 who were referred for NAT for dCCA at our centre were retrospectively collected from a prospectively maintained *** characteristics,NAT type,progression to surgery and oncological outcomes were *** Twelve studies were *** definition of“unresectable”locally advanced dCCA was *** studies reported outcomes for 9 patients who received NAT for dCCA with extensive vascular involvement.R0 resection rate ranged between 0 and 100%but without survival benefit in most *** studies considered either NAT in resectable dCCA or inclusive with extrahepatic *** presented case series includes 9 patients(median age 67,IQR 56-74 years,male:female 5:4)referred for NAT for borderline resectable or locally advanced *** patients progressed to surgery and 2 were *** patient died at 14 months with evidence of recurrence at 6 months and the other died at 51 months following recurrence 6 months *** Evidence for benefit of NAT is *** on criteria for uniform definition of resectability for dCCA is *** propose using the established National-Comprehensive-Cancer-Network®criteria for pancreatic ductal adenocarcinoma.

关键词： Cholangiocarcinoma Neoadj.vant therapy Arterial involvement Locally advanced systematic review

地球演化历史中氧逸度变化对壳幔循环启动、风化和超大陆循环的指示

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science Bulletin 2024年第1期69卷 97-102页

作者：王瑞邬绍宸 Roberto F.Weinberg William j.Collins peter A.Cawood state Key Laboratory of Geological Processes and Mineral Resources Institute of Earth SciencesChina University of GeosciencesBeijing 100083China Frontiers science Center for Deep-time Digital Earth China University of Geosciences(Beijing)Beijing 100083China school of Earth Atmosphere and EnvironmentMonash UniversityClayton VIC 3800Australia The Institute for Geoscience Research Curtin UniversityPerth WA 6102Australia

We apply a zircon redox index to a global compilation of detrital zircons to track the variation of oxidation state,expressed asΔFMQ,through Earth's *** from I-type rocks,which comprise mantle and crustal igneous protoliths,including tonalite–trondhj.mite–granodiorites(TTGs),generally have a high oxidation state(ΔFMQ>0).In contrast,zircons from igneous rocks derived from supracrustal source rocks(s-type)are commonly reduced(ΔFMQsity function derived from the Gaussian-Kernel-Density-Estimation,we use the maximum likelihood estimation(MLE)to distinguish stype from I-type zircons through Earth's history using zircon *** s-type magma production shows a ca.600 Ma cyclicity that is closely related to the supercontinent *** link a cyclic drop in redox values after 2.6 Ga to periodic s-type magma generation associated with burial and melting of metasedimentary rocks during supercontinent assembly and ***ΔFMQ of the detrital zircons rise at~3.5 Ga followed by a consistent averageΔFMQ>0 over the last 3 *** that the redox state of magmas is independent of crustal thickness and silica variation,and elevated values are likely more closely related to tectonic setting,we suggest that the consistent averageΔFMQ>0 from ca.3.5 Ga onwards relates to recycling of oceanic lithosphere back into the mantle in what eventually became established as subduction *** more reduced magmas associated with sedimentary sources,became established at 2.6 Ga,presumably in response to continental rocks rising above sealevel,and follow peaks of productivity associated with the supercontinent cycle.

关键词： Oxidation state supercontinent Weathering subduction Zircon Granite