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On the construction of irreducible characters in p-blocks with normal metacyclic defect groups

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Science China Mathematics 2012年第6期55卷 1179-1188页

作者： gao sheng Department of Mathematics University of Science and Technology of ChinaHefei 230026China

The author carries out a detailed study of p-blocks with normal metacyclic defect groups provided that p is odd and the defect groups are splitting and *** particular,the author constructs all the irreducible ordinary... 详细信息

关键词： characters blocks metacyclic groups defect groups

On the control of fusion in the local category for the p-block with a minimal nonabelian defect group

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Science China Mathematics 2011年第2期54卷 325-340页

作者： YANG sheng gao sheng School of Mathematical Sciences Peking University Beijing 100871 China

If B is a p-block of a finite group G with a minimal nonabelian defect group D (p is an odd prime number) and (D, b D ) is a Sylow B-subpair of G, then N G (D, b D ) controls B-fusion of G in most cases. This result is of great importance, because we can use it to obtain a complete set of representatives of G-conjugate classes of B-subsections and to calculate the number of ordinary irreducible characters in B. This result is key to the calculation of the structure invariants of the block with a minimal nonablian defect group. On the other hand, we improve Brauer's famous formula k(B) =Σ (ω,b ω ) l(b ω ),where (ω, b ω ) ∈ [(G : sp(B))]. Let p be any prime number, B be a p-block of a finite group G and (D, b D ) be a Sylow B-subpair of G. H is a subgroup of N G (D, b D ) satisfying N G (R, b R ) = N H (R, b R )C G (R), (R, b R ) ∈ A 0 (D, b D ), N G ( w , b w' ) = N H ( w , b w' )C G (w' ), (w' , b w' ) ∈ (D, b D ). If w 1 , . . . , w l is a complete set of representatives of H-conjugate classes of D, then (w 1 , b w 1 ), . . . , (w l , b w l ) is a complete set of representatives of G-conjugate classes of B-subsections in G. In particular, we have k(B) =Σ l j=1 l(b w j ).

关键词： defect group subpair control of fusion Brauer's net

On the Number of Irreducible Characters in a 3-block with a Minimal Nonabelian Defect Group

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Acta Mathematica Sinica,English Series 2017年第9期33卷 1267-1274页

作者： sheng YANG sheng gao Chong Bin XU Department of Mathematics Wenzhou University Department of Mathematics Hefei University of Technology

Let B be a 3-block of a finite group G with a defect group D. In this paper, we are mainly concerned with the number of characters in a particular block, so we shall use Isaacs＇ approach to block structure. We consider the block B of a group G as a union of two sets, namely a set of irreducible ordinary characters of G having cardinality k（B） and a set of irreducible Brauer characters of G having cardinality l（B）. We calculate k（B） and l（B） provided that D is normal in G and D = （x, y, z｜x3n=y3m = z3 = [x, z] = [y, z] = 1, [x, y] = z）（n 〉 m 〉 2）.

关键词： Characters blocks defect groups inertial groups

Microstructure of ferrospheres in fly ashes: SEM, EDX and ESEM analysis

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2008年第11期9卷 1595-1600页

作者： Qing-feng XUE sheng-gao LU Zhejiang Provincial Key Laboratory of Subtropical Soil and Plant Nutrition College of Environmental and Resource Sciences Zhejiang University Hangzhou 310027 China

Ferrospheres in fly ashes from a coal-fired power plant were extracted by a magnetic separation technique and their microstructure was studied by scanning electron microscopy (SEM), energy dispersive X-ray analysis (EDX) and environmental scanning electron microscopy (ESEM). Ferrospheres in fly ashes show significant iron enrichment compared to their respective fly ashes. Iron oxides in ferrospheres mainly occur as minerals magnetite (Fe3O4) and hematite (α-Fe2O3), which are derived mainly from the decomposition and oxidation of iron-bearing minerals in coal during combustion. EDX data indicate that ferrospheres also contain Si, S, Al and Ca resulting from quartz, mullite, anhydrite and amorphous materials. A large percentage of ferrospheres are commonly 5～50 μm in size. The microstructure of ferrospheres includes smooth, polygonal, dendritic, granular and molten drop characteristics. SEM coupled with EDX provided fast and accurate results of the microstructure and chemical composition of ferrospheres, and helped us to assess environmental issues related to the disposal and utilization of fly ashes.

关键词： Fly ash Ferrosphere Microstructure Scanning electron microscopy (SEM)

Liutex based new fluid kinematics

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Journal of Hydrodynamics 2022年第3期34卷 355-371页

作者： Chaoqun Liu Yifei Yu Yi-sheng gao Department of Mathematics University of Texas at ArlingtonArlingtonTexas76019USA College of Aerospace Engineering Nanjing University of Aeronautics and AstronauticsNanjing210016China

The traditional Cauchy-Stokes(C-S)decomposition states that the velocity gradient tensor can be decomposed into a symmetric tensor and an anti-symmetric tensor,namely the strain-rate tensor and the vorticity ***,there are two problems with the C-S *** is that the anti-symmetric(vorticity)tensor cannot represent the fluid rotation or *** is that the symmetric(strain-rate)tensor cannot distinguish the stretching/compression and *** vorticity cannot distinguish between the non-rotational shear and the rigid rotation,vorticity has been decomposed into a rigid rotation part called“Liutex”and an anti-symmetric shear in our previous work.A Liutex-based principal coordinate system has been proposed,and the corresponding velocity gradient tensor decomposition,called the principal decomposition,is presented in this principal coordinate system,which results in:(1)a Liutex tensor that represents rigid rotation,(2)a tensor that represents pure shear and(3)a tensor that represents stretching/***,each point has its own principal coordinate system,which implies that the principal decomposition is performed in different principal coordinate systems,not the original(global)coordinate *** address this issue,the principal decomposition in the original coordinate system is derived in this paper,and,therefore,provides a new kinematic approach to study the local rigid rotation,pure shear,and stretching/*** principal decomposition is unique,Galilean invariant and has clear physical *** new velocity gradient tensor decomposition could become a foundation for new fluid kinematics.

关键词： Liutex principal coordinates principal decomposition Helmholtz Cauchy-Stokes(C-S)

Pore Size Distribution of Clayey Soils and Its Correlation with Soil Organic Matter

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Pedosphere 2015年第2期25卷 240-249页

作者： Malik ZAFFAR LU sheng-gao Zhejiang Provincial Key Laboratory of Subtropical Soil and Plant Nutrition College of Environmental and Resource SciencesZhejiang University Ministry of Education Key Laboratory of Environmental Remediation and Ecosystem Health College of Environmental and Resource SciencesZhejiang University

Soil pore size distribution(PSD) directly influences soil physical,chemical,and biological properties,and further knowledge of soil PSD is very helpful for understanding soil functions and *** this study,PSD of three clayey soils collected from the topsoil(0-20 cm) of Vertisols in Northern China was analyzed using the N_2 adsorption(NA) and mercury intrusion porosimetry(MIP) *** effect of soil organic matter(SOM) on the PSD of clayey soils was also *** differential curves of pore volume of clayey soils by the NA method exhibited that the pores with diameter 75 μm,31.4%),cryptopores(0.1-0.007μm,16.0%),micropores(30-5 μm,9.7%) and mesopores(75-30 μm,7.3%).The SOM greatly affected the pore structure and PSD of aggregates in clayey *** particular,SOM removal reduced the volume and porosity of 5-100 μm pores while increased those of <5 μm pores in the 5-2 and 2-0.25 mm aggregates of clayey *** increase in the volume and porosity of < 5 μm pores may be attributed to the disaggregation and partial emptying of small pores caused by the destruction of SOM.

关键词： mercury intrusion porosimetry N2 adsorption pore volume porosity soil aggregate Vertisol

Demixing microwave signals using system-on-chip photonic processor

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Light(Science & Applications) 2024年第3期13卷 399-401页

作者： sheng gao Chu Wu Xing Lin Department of Electronic Engineering Tsinghua University100084 BeijingChina Beijing National Research Center for Information Science and Technology Tsinghua University100084 BeijingChina

The integrated photonic processor,co-packaged with electronic peripherals,is proposed for blind source separation of microwave signals,which separates signal-of-interest from dynamic interference with real-time adapta... 详细信息

关键词： processor microwave mixing

On cross-correlation indicators of an S-box

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Frontiers of Computer Science 2011年第4期5卷 448-453页

作者： sheng gao Wenping MA Zepeng ZHUO Fenghe WANG Key Laboratory of Computer Network and Information Security Ministry of Education Xidian University Xi＇an 710071 China State Key Laboratory of Integrated Service Networks Xidian University Xi＇an 710071 China

Substitution boxes （S-boxes） are often used as the most important nonlinear components in many symmetric encryption algorithms. The cryptographic properties of an S-box directly affect the security of the whole cipher system. Recently, generalized global avalanche characteristics （GGAC） were introduced to measure the correlation between two arbitrary Boolean functions. In this paper, to better evaluate the security of an S-box, we present two cross-correlation indicators for it. In addition, by studying the related properties of the cross-correlation between two balanced Boolean func- tions, we propose the lower bounds on the sum-of-squares indicator related to GGAC for two balanced functions and also for an S-box.

关键词： cryptography Boolean functions substitu-tion boxes balancedness generalized global avalanchecharacteristics cross-correlation

On the Phase Transitions of (k,q)-SAT

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Acta Mathematicae Applicatae Sinica 2016年第3期32卷 605-610页

作者： Jun LIU Zong-sheng gao Ke XU State Key Laboratory of Software Development Environment Beihang University LMIB and School of Mathematics and Systems Science Beihang University

Call a sequence of k Boolean variables or their negations a k-tuple. For a set V of n Boolean variables, let Tk（V） denote the set of all 2^kn^k possible k-tuples on V. Randomly generate a set C of k-tuples by including every k-tuple in Tk（V） independently with probability p, and let Q be a given set of q ＂bad＂ tuple assignments. An instance I = （C, Q） is called satisfiable if there exists an assignment that does not set any of the k-tuples in C to a bad tupie assignment in Q. Suppose that θ, q 〉 0 are fixed and ε=ε（n）〉 0 be such in 2 that ε Inn/ In Inn → ∞. Let k ≥ （1 ＋ θ） log2 n and let p0 = ln2/qn^k-1. We prove thatlim∞ P[I issatisfiable] ={1,p≤（1-ε）p0, 0,p≥（1＋ε）p0.

关键词： constraint satisfaction phase transition the second moment method