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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

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

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

Infrared Brazing Zirconium using Two silver Based Foils

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j.urnal of Materials science & Technology 2013年第3期29卷 283-286页

作者： Cheng-Han Lee Ren-Kae shiue Department of Materials science and Engineering National Taiwan University

Ag-based brazing foils, BAg-8 （72Ag-28Cu in wt%） and Ticusil （68.8Ag-26.7Cu-4.5Ti in wt%） were selected to braze Zr. Interfacial AgCu4Zr, CuZr2 reaction layers and Ag-rich matrix dominate BAg-8 brazed j.int, and fractograph after shear test shows ductile dimple fracture with plastic sliding marks. Ticusil j.int brazed at 910℃ for 300 s is comprised of CugZr11 and AgZr intermetallics, and fractograph after shear test displays brittle cleavage fracture.

关键词： Brazing Zirconium Microstructura! evolution

The effects of gonadal hormones on learning and memory in male mammals： A review

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Current Zoology 2011年第4期57卷 543-558页

作者： stuart T. LEONARD peter j. WINsAUER Department of Pharmacology and Experimental Therapeutics Louisiana State University Health Sciences Center 1901 Perdido Street New Orleans LA 70112-1393

The primary role of the gonadal steroid hormones in mammals is to regulate reproduction and related behaviors; however, both androgens and estrogens are also integrally involved in mediating higher brain function and processes including cognition, neural development, and neural plasticity. In particular, a number of studies show that estradiol modulates dendritic spine growth and synapse density （synaptic plasticity） in the hippocampus of females, and that increased estradiol levels are generally associated with improvements on a variety of learning and memory tasks. While the maj.rity of research has focused on the beneficial effects of estradiol in females, much less attention has been given to testosterone and its effects on learning and memory in males. similar to estradiol titers in females, testosterone titers in males decline with age, albeit more gradually, and this decline has been correlated with impairment of certain cognitive tasks. Moreover, studies involving both humans and animals indicate that testosterone and its metabolites can augment responding on certain behavioral tasks, depending on the subj.ct＇s current hormonal state, the response required, and the stimuli involved （e.g., those involving spatial or nonspatial stimuli）. While the exact mechanisms by which testosterone exerts its effects on learning and memory are not fully understood, recent findings suggest that testosterone modulates learning and memory in males through an interaction with the cholinergic system. The overall obj.ctive of this review is to discuss studies investigating the role of the gonadal hormones in mediating learning and memory processes in male mammals [Current Zoology 57 （4）： 543-558, 2011].

关键词： Testosterone Learning and memory Cholinergic system Mammals Cognition Androgens

Polyelectrolyte multilayer electrostatic gating of graphene field-effect transistors

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Nano Research 2014年第11期7卷 1650-1658页

作者： Yung Yu Wang peter j. Burke Department of Chemical Engineering and Materials science University of California Irvine Irvine California 92697 USA Department of Electrical Engineering and Computer science University of California Irvine Irvine California 92697 USA

We apply polyelectrolyte multilayer films by consecutive alternate adsorption of positively charged polyallylamine hydrochloride and negatively charged sodium polystyrene sulfonate to the surface of graphene field effect transistors. Oscillations in the Dirac voltage shift with alternating positive and negative layers clearly demonstrate the electrostatic gating effect in this simple model system. A simple electrostatic model accounts well for the sign and magnitude of the Dirac voltage shift. Using this system, we are able to create p-type or n-type graphene at will. This model serves as the basis for understanding the mechanism of charged polymer sensing using graphene devices, a potentially technologically important application of graphene in areas such as DNA sequencing, biomarker assays for cancer detection, and other protein sensing applications.

关键词： dirac point graphene transistor electrostatic gating polyallylaminehydrochloride (PAH) sodium polystyrenesulfonate (Pss)

Light metal compound casting

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science China(Technological sciences) 2009年第1期52卷 46-51页

作者： Konrad j. M. PAPIs j.erg F. LOEFFLER peter j. UGGOWITZER ETH Zurich Laboratory of Metal Physics and Technology Wolfgang-Pauli-Str. 10

‘Compound casting’simplifies j.ining processes by directly casting a metallic melt onto a solid metal substrate. A continuously metallurgic transition is very important for industrial applications, such as j.int structures of spaceframe constructions in transport industry. In this proj.ct, ‘compound casting’ of light metals is investigated, aiming at weight-saving. The substrate used is a wrought aluminium alloy of type AA5xxx, containing magnesium as main alloying element. The melts are aluminium alloys, containing various alloying elements (Cu, si, Zn), and magnesium. By replacing the natural oxygen layer with a zinc layer, the inherent wetting difficulties were avoided, and compounds with flawless interfaces were successfully produced (no contraction defects, cracks or oxides). Electron microscopy and EDX investigations as well as optical micrographs of the interfacial areas revealed their continu- ously metallic constitution. Diffusion of alloying elements leads to heat-treatable microstructures in the vicinity of the j.ining interfaces in Al-Al couples. This permits significant variability of mechanical properties. Without significantly cutting down on wettability, the formation of low-melting intermetallic phases (Al3Mg2 and Al12Mg17 IMPs) at the interface of Al-Mg couples was avoided by applying a protective coating to the substrate.

关键词： compound casting aluminium alloys magnesium alloys interface structure

Making the link between ADF and 4D sTEM:Resolution,transfer and coherence

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Chinese Physics B 2024年第11期33卷 26-33页

作者： peter D.Nellist Timothy j.Pennycook Department of Materials University of OxfordOxfordUK EMAT University of AntwerpGroenenborgerlaan 1712020 AntwerpBelgium

steve Pennycook is a pioneer in the application of high-resolution scanning transmission electron microscopy(sTEM)and in particular the use of annular dark-field(ADF)*** we show how a general framework for 4D sTEM allows clear links to be made between ADF imaging and the emerging methods for reconstructing images from 4D sTEM data *** show that both ADF imaging and ptychographical reconstruction can be thought of in terms of integrating over the overlap regions of diffracted discs in the detector *** approach allows the similarities in parts of their transfer functions to be understood,though we note that the transfer functions for ptychographic imaging cannot be used as a measure of information *** also show that conditions of partial spatial and temporal coherence affect ADF imaging and ptychography similarly,showing that achromatic interference can always contribute to the image in both cases,leading to a robustness to partial temporal coherence that has enabled high-resolution imaging.

关键词： image forming and processing phase retrieval electron microscopy scanning transmission electron microscope(sTEM)