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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

Enantiomeric hybrid high-temperature multiaxial ferroelectrics with a narrow bandgap and high piezoelectricity

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Chinese Chemical Letters 2023年第8期34卷 462-466页

作者： chang-feng Wang Na Wang Lang Liu Le-ping Miao Heng-Yun Ye Yi Zhang Chao Shi Chaotic Matter Science Research Center Department of MaterialsMetallurgy and ChemistryJiangxi University of Science and TechnologyGanzhou 341000China

Ferroelectric semiconductors have sparked growing attention in the field of optoelectronics,due to their unique ferroelectric photovoltaic ***,substantial efforts have been devoted to the development of ferroelectric semiconductors,including inorganic oxides,organic-inorganic hybrids,and metal-free ***,reports of ferroelectric semiconductors with a bandgap of less than 2 eV have been ***,in combination with the incorporation of triiodide(I_(3)−)and the introduction of chiral cations,we successfully constructed a pair of enantiomeric organic-inorganic hybrid ferroelectric semiconductors,(S-1,2-DAP·I)_(4)·I_(3)·BiI_(6)and(R-1,2-DAP·I)_(4)·I_(3)·BiI_(6)(R/S-1,2-DAP=(R/S)-(–)-1,2-diaminopropane),which possess high-temperature multiaxial ferroelectric phase transition with an Aizu notation of 422F2(s)at 405 K,a narrow bandgap of 1.56 eV comparable to that of CH3NH3PbI_(3)(∼1.5 eV),and an impressive piezoelectric response(piezoelectric coefficient,d22 of 35 pC/N)on par with PVDF(polyvinylidene fluoride,30 pC/N).With intriguing attributes,(S-1,2-DAP·I)_(4)·I_(3)·BiI_(6)and(R-1,2-DAP·I)_(4)·I_(3)·BiI_(6)exhibit great potential for application of self-power polarized-light detection and piezoelectric sensors.

关键词： Chirality Hybrid materials Multiaxial ferroelectrics Semiconductors Piezoelectricity

Interest rate swap pricing with default risk under variance gamma process

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Applied Mathematics(A Journal of Chinese Universities) 2017年第1期32卷 93-107页

作者： YANG Xiao-feng YU Jin-ping College of Economics and Management Hangzhou Normal University Hangzhou 311121 China. Zhejiang Yongan Technology Limited Corporation Hangzhou 310014 China.

Under the assumption that the dynamic assets price follows the variance gamma process, we establish a new bilateral pricing model of interest rate swap by integrating the reduced form model for swap pricing and the structural model for default risk *** pricing model preserves the simplicity of the reduced form model and also considers the dynamic evolution of the counterparty assets price by incorporating with the structural model for default risk measurement. We divide the swap pricing framework into two parts, simplifying the pricing model relatively. Simulation results show that, for a one year interest rate swap, a bond spread of one hundred basis points implies a swap credit spread about 0.1054 basis point.

关键词： swap pricing default gamma variance bilateral Brownian assets assumption implies

Borel Subalgebras of the Witt Algebra

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Acta Mathematica Sinica,English Series 2015年第8期31卷 1348-1358页

作者： Yu feng YAO Hao chang Department of Mathematics Shanghai Maritime University Department of Mathematics East China Normal University

Let F be an algebraically closed field of characteristic p 〉 3, and g be the Witt algebra over F. Let N be the nilpotent cone of g. An explicit description of N is given, so that the conjugacy classes of Borel subalgebras of g under the automorphism group of g are determined. In contrast with only one conjugacy class of Borel subalgebras in a classical simple Lie algebra, there are two conjugacy classes of Borel subalgebras in g. The representatives of conjugacy classes of Borel subalgebras, i.e.,the so-called standard Borel subalgebras, are precisely given.

关键词： Witt algebra Borel subalgebra nilpotent element nilpotent cone automorphism group

Role of sea level pressure in variations of the Canadian Arctic Archipelago throughflow

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Advances in Climate change Research 2021年第4期12卷 539-552页

作者： ZHANG Yu CHEN chang-Sheng SHEN Xin-Yi XU Dan-Ya SHAO Wei-Zeng Robert C.BEARDSLEY chang Liang feng Gui-ping College of Marine Sciences Shanghai Ocean UniversityShanghai201306China Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai) Zhuhai519082China International Center for Marine Studies Shanghai Ocean UniversityShanghai201306China School for Marine Science and Technology University of Massachusetts-DartmouthNew Bedford02744USA Department of Physical Oceanography Woods Hole Oceanographic InstitutionWoods Hole02543USA

The throughflow in the Canadian Arctic Archipelago(CAA)had a significant impact on the North Atlantic Ocean with the Arctic climate *** findings of physical mechanisms driving the throughflow in the CAA differed and few studies about the impact of sea level pressure(SLP)on the CAA throughflow were made.A high-resolution ice-ocean coupled Arctic Ocean Finite-Volume Community Ocean Model(AO-FVCOM)was used over the period 1978-2016 to examine the interannual and seasonal variability of the outflows in the CAA and the mechanism of SLP in driving the variation of the CAA throughflow *** simulated volume transport through Davis Strait,Nares Strait,Lancaster Sound and Jones Sound showed consistent increasing trends over 1978-2016 and the larger flux in winter and spring than in summer and *** variation of volume transport through Nares Strait contributed more than Lancaster and Jones Sound to the variation through Davis *** process-oriented experiments were made to further explore the role of SLP in setting up and controlling the sea surface height(SSH)difference and thus the throughflow transport in the *** SLP was a primary forcing to control the SSH difference and the outflow transport compared with the wind *** memory of the SSH to the SLP was short and an equilibrium state could be reached if the SLP varied with *** upstream and downstream SLP difference,however,made a slight direct contribution to driving the volume transport of the CAA *** addition to the external forcing of SLP and wind,the variability of the CAA outflow was also influenced by the variability of the inflow/outflow and SSH on boundaries connected to the Pacific and Atlantic *** choice of SLP datasets from CORE-v2,ECMWF and NCEP was sensitive to the simulated uncertainty of volume transport.

关键词： Sea level pressure Volume transport Canadian Arctic Archipelago FVCOM Sea surface height

The Global Existence of Solutions for Two Classes of Chemotaxis Models

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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 555-570页

作者： feng-long QU Ya-ping WU School of Mathematics and Informational Science Yantai University Department of Mathematics Capital Normal University

This paper is concerned with the global existence and uniform boundedness of solutions for two classes of chemotaxis models in two or three dimensional spaces. Firstly, by using detailed energy estimates, special interpolation relation and uniform Gronwall inequality, we prove the global existence of uniformly bounded solutions for a class of chemotaztic systems with linear chemotactic-sensitivity terms and logistic reaction terms. Secondly, by applying detailed analytic semigroup estimates and special iteration techniques, we obtain the global existence of uniformly bounded solutions for a class of chemotactic systems with nonlinear chemotacticsensitivity terms, which extends the global existence results of [6] to other general cases.

关键词： chemotactic systems global existence uniformly boundedness energy estimates.

Regularity Criteria of Axisymmetric Weak Solutions to the 3D Magnetohydrodynamic Equations

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 289-302页

作者： Bao-quan YUAN feng-ping LI School of Mathematics and Information Science Henan Polytechnic University

In this paper, we study the regularity criteria for axisymmetric weak solutions to the MHD equa- tions in R3. Let we, Jo and ue be the azimuthal component of w, J and u in the cylindrical coordinates, respectively. Then the axisymmetric weak solution （u,b） is regular on （0, T） if （wo,Jo） E Lq（O,T;Lp） or （oae,V（uoeo）） e Lq（0,T;Lp） with 3 ＋ 2 〈 2, 3 〈 p 〈 oo. In the endpoint case, one needs conditions （we, Jo） C LI（0, T;B∞∞） or （wo, V（uoeo）） C LI（0, T;B ∞∞）.

关键词： regularity criteria axisymmetric solutions Besov space

Effective capacity of delay quality-of-service constrained spectrum sharing cognitive radio with outdated channel feedback

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Science China(Information Sciences) 2013年第6期56卷 115-127页

作者： XU Ding feng ZhiYong ZHANG ping Key Laboratory of Universal Wireless Communications Ministry of EducationBeijing University of Posts and Telecommunications

In this paper,we consider a spectrum sharing cognitive radio network coexisting with a primary ***,the channel state information(CSI) between the secondary transmitter and the primary receiver is assumed to be outdated due to channel feedback *** secondary user(SU) is assumed to satisfy a given delay quality-of-service(QoS) constraint as well as the average interference power *** aim to derive the maximum arrival rate of the SU under aforementioned constraints with the outdated *** this respect,we derive the optimal power allocation to achieve the maximum effective capacity,and further derive the effective *** closed-form expressions for the lower and upper bounds on the effective capacity are also *** addition,we obtain the effective capacities under two widely adopted adaptive transmission schemes,i.e.,optimal power and rate allocation(OPRA) and truncated channel inversion with fixed rate(TIFR).Numerical results are conducted to corroborate our *** is shown that the effective capacities of the SU under various transmission schemes are insensitive to the channel correlation coefficient especially under low channel correlation *** is also shown that the lower and upper bounds on the effective capacity are significantly tight under stringent delay QoS constraint.

关键词： cognitive radio effective capacity outdated channel feedback delay QoS constraint interferencepower constraint

Synthesis of binaphthyl bridged chiral bis-corrole

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Chinese Chemical Letters 2009年第1期20卷 21-24页

作者： ping Lian Hai Yang Liu Lan Ying Liu Lei Shi Huan feng Jiang Chi Kwong chang Department of Chemistry and Life Sicence Gannan Normal University Ganzhou 341000 China Department of Chemistry South China University of Technology Guangzhou 510641 China Department of Chemistry The Hong Kong University of Science and Technology Hong Kong China

Chiral bis-corrole 1 and 2 were prepared by reaction of （s）-2,2′-bis（bromomethyl）-1, 1′-binaphthyl and 10-（4-hydroxylphenyl）- 5,15-bis（pentafluorophenyl）corrole or 10-（3-hydroxylphenyl）-5,15-bis（pentafluorophenyl）corrole in DMF at 60 ℃ in the presence of anhydrous K2CO3 with an isolated yield -8%. Both 1 and 2 exhibit unsymmetrical induced circular dichroism （ICD） in the soret band with positive exciton chirality.

关键词： Chiral bis-corrole Synthesis ICD