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L^p Estimates for Bi-parameter and Bilinear Fourier Integral Operators

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Acta Mathematica Sinica,English Series 2017年第2期33卷 165-186页

作者： Qing HONG Lu ZHANG school of mathematical sciences Beijing Normal University Department of mathematical sciences Binghamton University

Fourier integral operators play an important role in Fourier analysis and partial differential equations. In this paper, we deal with the boundedness of the bilinear and bi-parameter Fourier integral operators, which are motivated by the study of one-parameter FIOs and bilinear and bi-parameter Fourier multipliers and pseudo-differential operators. We consider such FIOs when they have compact support in spatial variables. If they contain a real-valued phase φ（x, ξ, η） which is jointly homogeneous in the frequency variables ξ, η, and amplitudes of order zero supported away from the axes and the anti- diagonal, we can show that the boundedness holds in the local-L2 case. Some stronger boundedness results are also obtained under more restricted conditions on the phase functions. Thus our results extend the boundedness results for bilinear and one-parameter FIOs and bilinear and bi-parameter pseudo-differential operators to the case of bilinear and bi-parameter FIOs.

关键词： Bilinear and hi-parameter FIOs Littlewood-Paley partition of unity Seeger Sogge-Stein decomposition

De novo synthesis of atropisomeric benzofurans via Cu/SPDO complex catalyzed asymmetric formal [3 + 2] annulation

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Science China Chemistry 2025年第01期 174-180页

作者： Fan-Xiao Meng Xing-Yu Wang Ka Lu Ju-Song Yang Fu-Min Zhang Ai-Jun Ma Bao Du Yong-Qiang Tu State Key Laboratory of Applied Organic Chemistry College of Chemistry and Chemical Engineering Lanzhou University school of Chemistry and Chemical Engineering Shanghai Jiao Tong University school of Biotechnology and Health sciences Wuyi University

Herein, the de novo synthesis of atropisomeric benzofurans through the Cu/spirocyclic-pyrrolidine-oxazoline(SPDO) complex catalyze asymmetric formal [3 + 2] cycloaddition between quinones and ynamides is explored, producing a range of structurally diverse axially chiral benzofurans in satisfactory yields with good to excellent enantioselectivities. Furthermore, density functional theory calculations were applied to explain the possible reaction mechanism.

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Gene therapy for spinal muscular atrophy:perspectives on the possibility of optimizing SMN1 delivery to correct all neurological and systemic perturbations

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Neural Regeneration Research 2025年第7期20卷 2011-2012页

作者： Sharon J.Brown Rafael J.Yáñez-Muñoz Heidi R.Fuller school of Pharmacy and Bioengineering Keele UniversityKeeleUK Wolfson Center for Inherited Neuromuscular Disease TORCH BuildingRJAH Orthopaedic HospitalOswestryUK *** Center of Gene and Cell TherapyDepartment of Biological SciencesSchool of Life Sciences and the EnvironmentRoyal Holloway University of LondonEghamUK

Spinal muscular atrophy(SMA)is a genetic condition that results in selective lower motor neuron loss with concomitant muscle weakness and *** genetic cause of SMA was understood in 1995 when loss or impairment of the survival motor neuron 1(SMN1)gene was identified as the main contributing factor(Lefebvre et al.,1995).This,in combination with the discovery that humans have a“back-up”gene,SMN2,which can produce low levels(approximately 10%)of the full-length functional SMN protein,has led to the generation of SMA-specific gene *** was traditionally classified according to age of symptom onset and developmental milestones achieved,with life expectancy and severity varying between ***,SMN2 copy number is used as a proxy for the prediction of disease severity,with higher SMN2 copy number typically being associated with reduced severity of SMA,although this relationship is not absolute:some individuals with low SMN2 copy number have less severe SMA phenotypes and vice ***,the etiology of SMA is further complicated by other factors,such as non-typical nucleotide variants and SMN2-independent modifiers of disease severity.

关键词： atrophy traditionally absolute

Construction of Supersaturated Design with Large Number of Factors by the Complementary Design Method

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 253-262页

作者： Yan LIU Min-Qian LIU school of mathematical sciences Tianjin Normal University Department of Statistics School of Mathematical Sciences and LPMC Nankai University

Supersaturated designs （SSDs） have been widely used in factor screening experiments. The present paper aims to prove that the maximal balanced designs are a kind of special optimal SSDs under the E（fNOD） criterion. We also propose a new method, called the complementary design method, for constructing E（fNoD） optimal SSDs. The basic principle of this method is that for any existing E（fNOD） optimal SSD whose E（fNOD） value reaches its lower bound, its complementary design in the corresponding maximal balanced design is also E（fNOD） optimal. This method applies to both symmetrical and asymmetrical （mixed-level） cases. It provides a convenient and efl：icient way to construct many new designs with relatively large numbers of factors. Some newly constructed designs are given as examples.

关键词： balanced design coincidence number complementary design equidistant design weak equidistantdesign

Liouville type theorems for Schrdinger systems

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Science China Mathematics 2015年第1期58卷 179-196页

作者： ZHUO Ran LI Feng Quan Department of mathematical sciences Yeshiva University school of mathematical sciences Dalian University of Technology

We study positive solutions to the following higher order SchrSdinger system with Dirichlet boundary conditions on a half space： where a is any even number between 0 and n. This PDE system is closely related to the integral system where G is the corresponding Green＇s function on the half space. More precisely, we show that every solution to （0.2） satisfies （0.1）, and we believe that the converse is also true. We establish a Liouville type theorem the non-existence of positive solutions to （0.2） under a very weak condition that u and v are only locally integrable. Some new ideas are involved in the proof, which can be applied to a system of more equations.

关键词： Schrodinger systems poly-harmonic operators Dirichlet boundary conditions method of movingplanes in integral forms Kelvin transforms monotonicity rotational symmetry non-existence

Cyclic Covers over Strongly Liftable Schemes

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Chinese Annals of Mathematics,Series B 2015年第6期36卷 937-946页

作者： Qihong XIE school of mathematical sciences Fudan University

A smooth scheme X over a field k of positive characteristic is said to be strongly liftable over W_2(k),if X and all prime divisors on X can be lifted simultaneously over W_2(k).In this paper,the author gives a criterion for those cyclic covers over strongly liftable schemes that are still strongly *** a corollary,cyclic covers over projective spaces of dimension at least three are strongly liftable over W_2(k).

关键词： Cyclic cover Strongly liftable scheme Positive characteristic

Inhomogeneous Quantum Codes (III):The Asymmetric Case

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Chinese Annals of Mathematics,Series B 2014年第2期35卷 271-284页

作者： Weiyang WANG Keqin FENG school of mathematical sciences Capital Normal University Department of mathematical sciences Tsinghua University

The stabilizer(additive)method and non-additive method for constructing asymmetric quantum codes have been *** this paper,these methods are generalized to inhomogeneous quantum codes.

关键词： Inhomogeneous quantum codes Mixed classical codes Asymmetricquantum codes

A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids

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Science China Mathematics 2015年第2期58卷 297-307页

作者： HU Jun ZHANG Shang You LMAM and school of mathematical sciences Peking University Department of mathematical sciences University of Delaware

A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1polynomial vectors,for all k *** main ingredients for the analysis are a new basis of the space of symmetric matrices,an intrinsic H(div)bubble function space on each element,and a new technique for establishing the discrete inf-sup *** particular,they enable us to prove that the divergence space of the H(div)bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1polynomial space on each *** optimal error estimate is proved,verified by numerical examples.

关键词： mixed finite element symmetric finite element linear elasticity conforming finite element tetrahedral grid inf-sup condition

New Construction of Complex Manifold via Conifold Transition

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Acta Mathematica Sinica,English Series 2012年第7期28卷 1347-1368页

作者： Jin Xing XU school of mathematical sciences Peking University

For a generic anti-canonical hypersurface in each smooth toric Fano 4-fold with rank 2 Picard group, we prove there exist three isolated rational curves in it. Moreover, for all these 4-folds except one, the contractions of generic anti-canonical hypersurfaces along the three rational curves can be deformed to smooth threefolds which is diffeomorphic to connected sums of S3 ~ S~. In this manner, we obtain complex structures with trivial canonical bundles on some connected sums of S^3 × S^3. This construction is an analogue of that made by Friedman [On threefolds with trivial canonical bundle. In： Complex Geometry and Lie Theory, volume 53 of Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI, 1991, 103-134], Lu and Tian [Complex structures on connected sums of S^3× S^3. In： Manifolds and Geometry, Pisa, 1993, 284 293] who used only quintics in P^4.

关键词： Calabi Yau threefolds conifold transitions complex structures on connected sums of S^3× S^3