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FINITE ELEMENT AND DISCONTINUOUS GALERKIN METHOD FOR STOCHASTIC HELMHOLTZ EQUATION IN TWO-AND THREE-DIMENSIONS

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Journal of Computational Mathematics 2008年第5期26卷 702-715页

作者： Yanzhao Cao ran zhang Kai zhang Department of Mathematics Florida A&M University TaUahassee FL32307 USA Department of Mathematics Jilin University Changchun 130023 China

In this paper, we consider the finite element method and discontinuous Galerkin method for the stochastic Helmholtz equation in R^d （d = 2, 3）. Convergence analysis and error estimates are presented for the numerical solutions. The effects of the noises on the accuracy of the approximations are illustrated. Numerical experiments are carried out to verify our theoretical results.

关键词： Stochastic partial differential equation Finite element method Discontinuous Galerkin method Stochastic Helmholtz equation.

Characteristics of combustion zone and evolution of mineral phases along bed height in ore sintering

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International Journal of Minerals,Metallurgy and Materials 2017年第10期24卷 1087-1095页

作者： Yao-zu Wang Jian-liang zhang Zheng-jian Liu Ya-peng zhang Dong-hui Liu Yi-ran Liu School of Metallurgical and Ecological Engineering University of Science and Technology Beijing Beijing 100083 China

Quantitative parameters of bed combustion, including the thickness of the combustion zone(TCZ), the maximum temperature of the combustion zone(MTCZ), and the bed shrinkage, were characterized through a series of sinter pot tests in transparent quartz pots. The results showed that TCZ first ascended and then descended as the sintering process proceeded. The sintering process was divided into four stages according to the variation rate of the TCZ. A "relative-coordinate" method was developed to obtain the actual reaction temperature of sinter along the height direction. With increasing the sintering temperature, the reactants transformed and entered into liquid phases. The mineral composition and microstructure of the sinter were characterized through X-ray diffraction and scanning electron microscopy–energy-dispersive X-ray spectroscopy. Liquid phases with greater Fe and Al contents were more likely to form acicular-like silico-ferrite of calcium and aluminum after crystallization because of the outward spread of Al, which led to a better fluidity of the liquid. An evolution mechanism of "solid-state reaction—liquid phases formation—crystallization" of the mineral phases is proposed.

关键词： flame front mineral phases sintering evolution mechanism transparent quartz pots

Temperature-dependent Raman spectroscopic study of ferroelastic K_2Sr(MoO_4)

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Chinese Physics B 2018年第11期27卷 591-595页

作者： Ji zhang De-Ming zhang ran-ran zhang An hui Xin Hua University Hefei 230088 China Anhui Institute of Optics and Fine Mechanics Chinese Academy of Sciences Hefei 230031 China High Magnetic Field Laboratory of the Chinese Academy of Sciences Hefei 230031 China

Raman scattering measurements of K_2 Sr（MoO_4）2 were performed in the temperature range of 25–750？C. The Raman spectrum of the low-temperature phase α-K_2 Sr（MoO_4）2 that was obtained by first-principle calculations indicated that the Raman bands in the wavenumber region of 250–500 cm-1 are related to Mo–O bending vibrations in MoO4 tetrahedra,while the Raman bands in the wavenumber region of 650–950 cm-1 are attributed to stretching vibrations of Mo–O *** temperature-dependent Raman spectra reveal that K_2 Sr（MoO_4）2 exhibits two sets of modifications in the Raman spectra at ～ 150？C and ～ 475？C, attributed to structural phase transitions. The large change of the Raman spectra in the temperature range of 150？C to 475？C suggests structural instability of the medium-temperature phase β-K_2 Sr（MoO_4）2.

关键词： ferroelastics K2Sr(MoO4)2 crystal Raman spectroscopy phase transition

Primary hyperparathyroidism in a woman with multiple tumors: A case report

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World Journal of Clinical Cases 2019年第19期7卷 3132-3137页

作者： Can-Can hui Xue zhang Jian-ran Sun Da-Tong Deng Department of Endocrinology The First Affiliated Hospital of Anhui Medical UniversityHefei 230022Anhui ProvinceChina Department of Endocrinology The First Affiliated Hospital of USTC Anhui Provincial HospitalHefei 230001Anhui ProvinceChina

BACKGROUND Parathyroid adenoma(PTA)is known as an adenomatous hyperparathyroidism *** earlier times,the major symptoms of this disease included high blood calcium and low *** is a benign neuroendocrine *** have reviewed the literature and found that it is rare for patients with hyperparathyroidism to have benign tumors with multiple organs at the same *** report describes a patient with a PTA and four nonfunctional *** SUMMARY We report a case of primary hyperparathyroidism in a 39-year-old woman with multiple organ *** patient was admitted to hospital because of ***,imaging,and histological examinations confirmed a left parathyroid *** thyroid adenoma was discovered during *** had a medical history of uterine fibroids,right benign mammary gland tumor,and *** patient recovered after surgical and conservative *** Primary hyperparathyroidism with multiple organ tumors is uncommon,and further studies should be conducted to determine if there is genetic heterogeneity.

关键词： Primary hyperparathyroidism Parathyroid neoplasm Thyroid adenoma Meningioma Breast neoplasm Case report

Fixed Points of Meromorphic Functions and of Their Differences,Divided Differences and Shifts

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Acta Mathematica Sinica,English Series 2016年第10期32卷 1189-1202页

作者： ran ran zhang Zong Xuan CHEN Department of Mathematics Guangdong University of Education School of Mathematical Sciences South China Normal University

Let f（z） be a finite order meromorphic function and let c ∈ C ／ {0} be a constant. If f（z） has a Borel exceptional value α∈ C, it is proved that max{τ（f（z））, τ（ △cf（z）） } = max{τ（f（z））, τ（f（z ＋ c））} = max{T（ τ（△cf（z））, τ（f（z ＋ c））} = σ（f（z））. If f（z） has a Borel exceptional value b ∈ （C ／ {0}） ∪ {∞}, it is proved that max{τ（f（z））,τ（△cf（z）/f（z）}=max（τ（△cf（z）/f（z））,τ（f（z＋c））}=σ（f（z））unless f（z） takes a special form. Here T（g（z）） denotes the exponent of convergence of fixed points of the meromorphic function g（z）, and a（g（z）） denotes the order of growth of g（z）.

关键词： Fixed point meromorphic function complex difference shift

Effect of TiO_(2) addition on microstructures and properties of Mgo-Cao refractory aggregates

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Journal of Iron and Steel Research International 2024年第6期31卷 1547-1554页

作者： Shuai zhang Jing-ran Wang Yuan-gao Li Feng-you Li Wen Yan hui-ying Shi The State Key Laboratory of Refractories and Metallurgy Wuhan University of Science and TechnologyWuhan 430081HubeiChina Joint International Research Laboratory of Refractories and Metallurgy Wuhan 430081HubeiChina Shanxi Luweibao Taigang Refractory Co. Ltd.Taiyuan 030003ShanxiChina

MgO-CaO(40 wt.%CaO)refractory aggregates were prepared using the calcined dolomite and light-burned magnesia fine powder as raw materials and TiO_(2) as *** effect of TiO_(2) on their phase composition,microstructures and properties was investigated by X-ray diffraction and scanning electron *** properties such as bulk density,apparent porosity,relative aggregate tube strength and hydration resistance were also *** results showed that the CaTiO_(3) generated by the reaction between CaO and TiO_(2) was distributed around the CaO grain boundaries and intermittently distributed with MgO,which formed an isolation layer around CaO and greatly improved the hydration ***,the introduction of TiO_(2) promoted sintering and increased the grain size,further improving the strengths and hydration resistance of the *** addition,the most significant enhancement in the hydration resistance and strengths of the samples was achieved when 1.0-2.0 wt.%TiO_(2) was *** this case,the relative strength of aggregate increased from 33.3% to 37.3%-43.1%,and the mass gain after the hydration test decreased from 3.13% to 1.26%-1.45%.

关键词： MgO-CaO refractory aggregate TiO_(2)addition Phase composition Microstructure Hydration resistance

Convenient Synthesis of 1-Thiohydroxypyrene by Newman-Kwart Rearrangement

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Chemical Research in Chinese Universities 2015年第2期31卷 224-227页

作者： zhang ran XU Lihua CHEN hui QIN Zhihong ZHAO Yu Ni Zhonghai School of Chemical Engineering and Technology China University of Mining and Technology Xuzhou 221116 P. R. China

l-Thiohydroxypyrene（l） and its two intermediates, l-pyrenyl-O-thiocarbamate（2） and l-pyrenyl-S-thiocarbamate（3）, were synthesized using l-hydroxypyrene as the starting material. The key synthetic step is New- manoKwart rearrangement. The results indicate that the Newman-Kwart rearrangement is more effective in suitable solvent than conventional method based on pure organic compound. The structures of compounds 1-3 were characterized by FTIR, NMR, CJC-MS and elementary analysis. The crystal structures of two new compounds（2 and 3） were determined by single crystal X-ray diffraction analysis. The whole synthetic process is simple, mild and with high yield.

关键词： Newman-Kwart rearrangement l-Thiohydroxypyrene Crystal structure

Cutting performance of saw blades with microtextured rougher and finisher sawteeth

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Advances in Manufacturing 2024年第2期12卷 317-334页

作者： Yang Lu Jian-Xin Deng Zhi-hui zhang Jia-Xing Wu ran Wang Yi-Chen Bao Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MOE School of Mechanical EngineeringShandong UniversityJinan250061People’s Republic of China

The problems of severe sawtooth wear,harsh sawing noise,and low surface quality during the processing of circular saw blades need to be *** improve the cutting performance of TiC-based cermet saw blades,microtextures parallel to the cutting edge were fabricated on rough and fine sawteeth by laser *** cutting tests were performed on a sawing platform under lubricated *** of the sawing arc length and working sawtooth cutting force variations were developed for sawing steel pipes,and the accuracy of the sawing force model was verified *** results indicate that the variations in the sawing force are proportional to the sawing arc *** circular saw blades with microtextures that did not penetrate the sawtooth rake face exhibited the lowest cutting force,sawing noise,and highest machined surface ***,the worn-out distance of the rougher and finisher sawteeth was reduced by approximately 7.4%and 44.1%,respectively,compared with conventional circular saw *** main failure modes of sawteeth were tip wear,rake face adhesion,and oxidative *** addition,the mechanism by which the textures improve the cutting and wear properties of TiC-based circular saw blades was *** study provided a significant concept for enhancing the cutting performance of circular saw blades and improving the machined surface quality.

关键词： Circular saw blades Micro textures Cutting performance Wear performance

A HIGH-ORDER ACCURACY METHOD FOR SOLVING THE FRACTIONAL DIFFUSION EQUATIONS

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Journal of Computational Mathematics 2020年第2期38卷 239-253页

作者： Maohua ran Chengjian zhang School of Mathematics and Software Science Sichuan Normal UniversityChengdu 610066China School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China

In this paper,an efficient numerical method for solving the general fractional diffusion equations with Riesz fractional derivative is proposed by combining the fractional compact difference operator and the boundary value *** order to efficiently solve the generated linear large-scale system,the generalized minimal residual(GMRES)algorithm is *** accelerating the convergence rate of the it erative,the St rang-type,Chantype and P-type preconditioners are *** suggested met hod can reach higher order accuracy both in space and in time than the existing met *** the used boundary value method is Ak1,K2-stable,it is proven that Strang-type preconditioner is invertible and the spectra of preconditioned matrix is clustered around *** implies that the iterative solution is convergent *** experiments with the absorbing boundary condition and the generalized Dirichlet type further verify the efficiency.

关键词： Boundary value method Circulant preconditioner High accuracy Generalized Dirichlet type boundary condition