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A Mean Value of Cochrane Sum

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Acta Mathematica Sinica,English Series 2009年第2期25卷 223-234页

作者： zhe feng XU College of Science Xi'an Jiaotong University Xi'an 710049 P. R. China Department of Mathematics Northwest University Xi'an 710069 P. R. China

Let q 〉 4 be an integer. The main purpose of this paper is to study the mean value of Cochrane sum C（a, q） in quarter intervals, and obtain a sharp asymptotic formula for it.

关键词： Dedekind sum Cochrane sums mean value asymptotic formula

On the Mean Value of the Complete Trigonometric Sums with Dirichlet Characters

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Acta Mathematica Sinica,English Series 2007年第7期23卷 1341-1344页

作者： zhe feng XU Department of Mathematics Northwest University

The main purpose of this paper is, using the analytic method, to study the mean value properties of the complete trigonometric sums with Dirichlet characters, and give an exact calculating formula for its fourth power... 详细信息

关键词： complete trigonometric sums Dirichlet character mean value

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Twin cogenesis

Communications in Theoretical Physics 2023年第4期75卷 34-49页

作者： Wan-zhe feng Jiang-Hao Yu Center for Joint Quantum Studies and Department of Physics School of ScienceTianjin UniversityTianjin 300350China Institute of Theoretical Physics Chinese Academy of SciencesBeijing 100190China School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China

We investigate a cogenesis mechanism within the twin Higgs setup that can naturally explain the nature of dark matter,the cosmic coincidence puzzle,little hierarchy problem,leptogenesis,and the tiny neutrino *** heavy Majorana neutrinos are introduced to the standard model sector and the twin sector respectively,which explain the tiny neutrino masses and generate the lepton asymmetry and the twin lepton asymmetry at the same *** twin cogenesis mechanism applies to any viable twin Higgs model without an explicit Z_(2)breaking in the leptonic sector and evading theΔN_(eff) *** illustrate the twin cogenesis mechanism using the neutrino-philic twin two Higgs doublet model,a newly proposed model to lift the twin neutrino masses with spontaneous Z_(2)*** dark photon with a Stueckelberg mass O(10)MeV ensures the energy in the twin sector as well as the symmetric component of twin sector particles can be *** lightest twin baryons are the dark matter candidates with masses of approximately 5.5 GeV,which explains naturally the amount of dark matter and visible matter in the Universe are of the same *** also demonstrate twin cogenesis in the fraternal twin Higgs setup,in which the dark matter candidate is the twin bottom bound stateΩ’_(b’b’b’).

关键词： cogenesis cosmic coincidence asymmetric dark matter leptogenesis neutrino mass

High-dimensional *** Problem over Short Intervals

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Acta Mathematica Sinica,English Series 2014年第2期30卷 213-228页

作者： zhe feng XU Tian Ping ZHANG Department of Mathematics Northwest University College of Mathematics and Information Science Shaanxi Normal University

Letk be a positive integer and n a nonnegative integer,0 〈 λ1,...,λk＋1 ≤ 1 be real numbers and w =（λ1,λ2,...,λk＋1）.Let q ≥ max{[1/λi ]：1 ≤ i ≤ k ＋ 1} be a positive integer,and a an integer coprime to *** by N（a,k,w,q,n） the 2n-th moment of（b1··· bk c） with b1··· bk c ≡ a（mod q）,1 ≤ bi≤λiq（i = 1,...,k）,1 ≤ c ≤λk＋1 q and 2（b1＋ ··· ＋ bk ＋ c）.We first use the properties of trigonometric sum and the estimates of n-dimensional Kloosterman sum to give an interesting asymptotic formula for N（a,k,w,q,n）,which generalized the result of *** we use the properties of character sum and the estimates of Dirichlet L-function to sharpen the result of N（a,k,w,q,n） in the case ofw =（1/2,1/2,...,1/2） and n = *** order to show our result is close to the best possible,the mean-square value of N（a,k,q） φk（q）/2k＋2and the mean value weighted by the high-dimensional Cochrane sum are studied too.

关键词： D. H. Lehmer problem short intervals trigonometric sum character sum Cochrane sum

Torsional Fatigue Cracking and Fracture Behaviors of Cold-Drawn Copper:Effects of Microstructure and Axial Stress

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Acta Metallurgica Sinica(English Letters) 2019年第12期32卷 1521-1529页

作者： Rong-Hua Li Peng Zhang zhe-feng Zhang School of Mechanical Engineering Liaoning Shihua UniversityFushun 113001China Laboratory of Fatigue and Fracture for Materials Institute of Metal ResearchChinese Academy of SciencesShenyang 110016China

The fatigue cracking and fracture behavior of cold-drawn copper subjected to cyclic torsional loading were investigated in this *** was found that with increasing stress amplitude,the fracture mode of cold-drawn copper gradually changes from a shear fracture on transverse maximum shear stress plane to a mixed shear mode on both transverse and longitudinal shear planes and finally turns to the shear fracture on multiple longitudinal shear *** the cracking morphology and the relationship between torsional fatigue cracking and the grain boundaries,the fracture mechanism of cold-drawn copper under cyclic torsional loading was analyzed and proposed by considering the effects of the microstructure and axial stress caused by *** of the promotion of the grain boundary distribution on longitudinal crack propagation and the inhibition of axial stress on transverse crack grown,the tendency of crack propagation along the longitudinal direction increases with increasing stress levels.

关键词： Torsion Fatigue behavior Crack propagation Fracture mechanisms Axial stress Copper

Tearing Toughness of Ductile Metals

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Acta Metallurgica Sinica(English Letters) 2016年第2期29卷 150-155页

作者： Cui-Hong Li Qi-Qiang Duan zhe-feng Zhang Shenyang National Laboratory for Materials Science Institute of Metal Research Chinese Academy of Sciences

A new parameter, i.e., tearing toughness, was employed to characterize the mechanical properties of some ductile metals （Cu, Cu-2 wt% Be, Cu-Al alloys, and some steels） by using three-leg trousers tearing tests. The experi- mental results demonstrate that their tearing toughness is not a physical constant and shows a close relationship with the materials＇ types and microstructures. It can be inferred that the tearing toughness of different ductile metals has their respective variation range, expectantly, and may be represented by the comprehensive mechanical properties of strength and ductility for various ductile materials.

关键词： Ductile metals Strength Ductility Tearing toughness

Failure analysis of crevice corrosion on 304 stainless steel tube heat exchanger

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Journal of Iron and Steel Research International 2023年第8期30卷 1490-1498页

作者： Chen Dong Shen Qu Chang-ming Fu zhe-feng Zhang Failure Analysis Center for Materials Institute of Metal ResearchChinese Academy of SciencesShenyang 110016LiaoningChina

The cause of the premature failure of 304 stainless steel tube heat exchanger was *** unique skeleton structure inside the leakage point reveals that this is a new damage mechanism caused by a δ+γ two-phase structure and crevice *** three-dimensional structure of the leakage point was demonstrated using X-ray diffraction *** results of scanning electron microscope examination show the microstructure of the weld to be columnar and *** is found by electron probe microscope analysis and transmission electron microscopy that columnar dendrites consisted of γ-dendrite and an amount of δ-ferrite phases at the dendrite *** corrosion test results confirmed that the corrosion medium was the chloride *** corrosion of chloride ions occurred at weld defects on the inner wall thus forming a concentration *** of columnar dendrites were then corroded by chloride ions and δ-ferrite phases on the grain boundaries were retained,which formed the particular skeleton corrosion *** a result,it led to leakage when the corrosion of weld occurred from the inner wall to the outer wall.

关键词： Crevice corrosion Weld defect Chloride ions δ-ferrite Skeleton structure 304 stainless steel

Detection of endogenous foreign bodies in Chinese hickory nuts by hyperspectral spectral imaging at the pixel level

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International Journal of Agricultural and Biological Engineering 2022年第2期15卷 204-210页

作者： zhe feng Weihao Li Di Cui College of Biosystems Engineering and Food Science Zhejiang UniversityHangzhou 310058China Key Laboratory of On Site Processing Equipment for Agricultural Products Ministry of Agriculture and Rural AffairsHangzhou 310058China

It is difficult to differentiate small,but harmful,shell fragments of Chinese hickory nuts from their kernels since they are very similar in *** shell fragments of Chinese hickory nuts by mistake may create safety hazards for ***,there is a need to develop an effective method to differentiate the shells from the kernels of Chinese hickory *** this study,a deep learning approach based on a two-dimensional convolutional neural network(2D CNN)and long short-term memory(LSTM)integrated with hyperspectral imaging for distinguishing the shells and kernels of Chinese hickory nuts at the pixel level was *** classical classification methods,principal component analysis-K-nearest neighbors(PCA-KNN)and the support vector machine(SVM),were employed to establish identification models for *** results showed that the 2D CNN-LSTM model achieved the best performance with an overall classification accuracy of 99.0%.Moreover,the shells in mixtures of shells and kernels were detected based on the proposed deep learning method and visualized for subsequent operations for the removal of foreign bodies.

关键词： Chinese hickory nut endogenous foreign body hyperspectral spectral imaging pixel level detection

High-Temperature Oxidation Behavior and Related Mechanism of RuT400 Vermicular Graphite Iron

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Acta Metallurgica Sinica(English Letters) 2022年第7期35卷 1117-1130页

作者： Yu Chen Jian-chao Pang Shou-xin Li zhe-feng Zhang Henan Institute of Advanced Technology Zhengzhou UniversityZhengzhou 450001China Shi-Changxu Innovation Center for Advanced Materials Institute of Metal ResearchChinese Academy of SciencesShenyang 110016China

The vermicular graphite iron is an important material with excellent combination properties for cylinder heads of diesel engines,and the high-temperature oxidation is a crucial problem during service of the *** this study,the oxidation experiment of RuT400 vermicular graphite iron was performed at 500 ℃,and the oxidation time was chosen as 100 h,200 h,300 h,400 h,and 500 h,***,the corresponding microstructure evolution,oxidation kinetics,and oxidation mechanism were *** is found that oxidation pores and oxide layer often appear at the vermicular graphite on the specimen surface;the vermicular graphite plays the role of oxidation channel,and it tends to diff use along the adjacent pearlite and then connect with each other to form oxidation bridges as the oxidation time prolongs.A linear relationship between oxidation weight gain and the thickness of the oxide layer was established and verifi ed *** results will give a more comprehensive understanding on the oxidation mechanism of vermicular graphite iron and provide certain guidance for design and preparation of anti-oxidation cast irons.

关键词： Vermicular graphite iron High-temperature oxidation Microstructure evolution Oxidation mechanism