Theta Subgroups and the Solvability of FiniteGroups

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＤｅｆｉｎｉｔｉｏｎＡｌｌｇｒｏｕｐｓｔｒｅａｔｅｄａｒｅｆｉｎｉｔｅ．Ｉｎ［１］，Ｎ．Ｐ．ＭｕｋｈｅｒｊｅｅａｎｄＰ．Ｂｈａｔｔａｃｈａｒｙａｄｅｆｉｎｅｄｔｈｅｃｏｎｃｅｐｔｏｆθ－ｐａｉｒｓａｓｓｏｃｉａｔｅｄｔｏａｍａｘｉｍａｌｓｕｂｇｒｏｕｐＭｏｆａｇｒｏｕｐＧａｓｆｏｌｌｏｗｓ：ａθ－ｐａｉｒｆｏｒＭｉｓａｎｙｐａｉｒｏｆｓｕｂｇｒｏｕｐｓ（Ｃ，Ｄ）ｏｆＧｓｕｃｈｔｈａｔ（１）ＤＧ，Ｄ＜Ｃ，（２）〈Ｍ，Ｃ〉＝Ｇ，〈Ｍ，Ｄ〉＝Ｍａｎｄ（３）Ｃ／Ｄ…     

On the Supersolvability of QCLT-Groups

ＯｎｔｈｅＳｕｐｅｒｓｏｌｖａｂｉｌｉｔｙｏｆＱＣＬＴ－ＧｒｏｕｐｓＷａｎｇＰｉｎｃｈａｏ（王品超）；ＬｕＺａｉｐｉｎｇ（路在平）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｑｕｆｕ，Ｓｈａｎｄｏｎｇ，...     

A Note on the Non—existence of Negatively Weighted Derivations

ＡＮｏｔｅｏｎｔｈｅＮｏｎ－ｅｘｉｓｔｅｎｃｅｏｆＮｅｇａｔｉｖｅｌｙＷｅｉｇｈｔｅｄ　ＤｅｒｉｖａｔｉｏｎｓＪｉａｎｇＧｕａｎｇｆｅｎｇ（姜广峰）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＪｉｎｚｈｏｕＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ，Ｊｉｎｚｈｏｕ，Ｌｉａｏｎ...     

On Theorem of the “Mountain Impasse” Type

ＬｅｔＦ（ｕ），Ｇ（ｕ）ｂｅＣ１－ｆｕｎｃｔｉｏｎａｌｓｏｎａＨｉｌｂｅｒｔｓｐａｃｅＨａｎｄｓｕｐｕ∈ＨＦ（ｕ）＝∞．ＬｅｔＫｂｅａｃｏｍｐａｃｔｍｅｔｒｉｃｓｐａｃｅａｎｄｌｅｔＫｂｅａｎｏｎ－ｅｍｐｔｙｃｌｏｓｅｄｓｕｂｓｅｔ≠Ｋ，ｐ∈Ｃ（Ｋ；Ｈ）．ＤｅｎｏｔｅＦＲ＝｛ｕ∈Ｈ｜Ｆ（ｕ）Ｒ｝；　　　　　　ΦＲ＝｛ｐ∈Ｃ（Ｋ；ＦＲ）｜ｐ＝ｐｏｎＫ｝；ｃ（Ｒ）＝ｉｎｆｐ∈ΦＲｍａｘξ∈ＫＧ（ｐ（ξ））；ｃ０＝ｍａｘξ∈ＫＧ（ｐ（ξ））；Φ∞＝｛ｐ∈Ｃ（Ｋ；Ｈ）｜ｐ＝ｐｏｎＫ｝；…     

On the Structure of the B—cocleft Module Coalgebra

§１．　ＴｈｅＥｑｕｉｖａｌｅｎｔＴｈｅｏｒｅｍｏｆｔｈｅＣｒｏｓｓｅｄＣｏｐｒｏｄｕｃｔＬｅｔＣｂｅａｌｅｆｔＨ－ｗｅａｋｌｙｃｏｍｏｄｕｌｅｃｏａｌｇｅｂｒａ［４］ｗｉｔｈｔｈｅｓｔｒｕｃｔｕｒｅρ－Ｃ（ｃ）＝∑ｃ（１）ｃ（２）．ＤｂｅｌｅｆｔＨ－ｍｏｄｕｌｅｃｏａｌｇｅｂｒａ［２］ｗｉｔｈｔｈｅｓｔｒｕｃｔｕｒｅ“”．Ｆｏｒα∈Ｈｏｍκ（Ｃ，ＨＨ）ｄｅｎｏｔｅα（ｃ）＝∑α１（ｃ）α２（ｃ）．Ｄｅｆｉｎｅ△－：ＣＤ→（ＣＤ）（ＣＤ）ａｎｄε－：ＣＤ→κａｓｆｏｌｌｏｗ－ｉ…     

Remarks on the Global Attractor of the Weakly Dissipative Benjamin－Ono Equation

ＲｅｍａｒｋｓｏｎｔｈｅＧｌｏｂａｌＡｔｔｒａｃｔｏｒｏｆｔｈｅＷｅａｋｌｙＤｉｓｓｉｐａｔｉｖｅＢｅｎｊａｍｉｎ－ＯｎｏＥｑｕａｔｉｏｎＧｕｏＢｏｌｉｎｇ（郭柏灵）ａｎｄＷｕＹｏｎｇｈｕｉ（吴永辉）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃ...     

Approximation of Generalized Szasz—Mirakjan Operator

Ａｐｐｒｏｘｉｍａｔｉｏｎ　ｏｆ　Ｇｅｎｅｒａｌｉｚｅｄ　Ｓｚáｓｚ－Ｍｉｒａｋｊａｎ　ＯｐｅｒａｔｏｒＣｈｅｎｇＨａｉｌａｌ（程海来）（ＡｎｈｕｉＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｔｈｅａｕｔｈｏ...     

Zero-free Regions for Dirichlet L-functions and the Exceptional Set of Goldbach Numbers

Ｚｅｒｏ－ｆｒｅｅＲｅｇｉｏｎｓｆｏｒＤｉｒｉｃｈｌｅｔＬ－ｆｕｎｃｔｉｏｎｓａｎｄｔｈｅＥｘｃｅｐｔｉｏｎａｌＳｅｔｏｆＧｏｌｄｂａｃｈＮｕｍｂｅｒｓＬｉＨｏｎｇｚｅ（李红泽）ＭＲ（１９９１）ＳｕｂｊｅｃｔＣｌａｓｉｆｉｃａｔｉｏｎ：１１Ｎ１３，１...     

A Duality Theorem Associated with the Smash Product of Graded Ring and G-set

ＬｅｔＲｂｅａＧ－ｇｒａｄｅｄｒｉｎｇｗｉｔｈｉｄｅｎｔｉｔｙ１；ｔｈａｔｉｓＲｇ∈ＧＲｇａｎｄＲｇＲｈＲｇｈｆｏｒａｌｌｇ，ｈ∈Ｇ．ＴｈｅａｓｓｏｃｉａｔｉｖｅｒｉｎｇＲ＃ＧｄｅｎｏｔｅｓｔｈｅｓｍａｓｈｐｒｏｄｕｃｔｆｏｒｔｈｅｇｒｏｕｐＧａｎｄｔｈｅｇｒａｄｅｄｒｉｎｇＲ（ｓｅｅ［３］ｏｒ［４］）．Ｉｎ［１］，ＣｏｈｅｎａｎｄＭｏｎｔｇｏｍｅｒｙｐｒｏｖｅｄｔｈｅｄｕａｌｉｔｙＴｈｅｏｒｅｍｓｆｏｒａｃｔｉｏｎｓａｎｄｃｏａｃｔｉｏｎｓｆｏｒｆｉｎｉｔｅｇｒｏｕｐＧ．Ｉｎ［２］，ａｆ…     

Asymptotic Behavionr of solutions for the CoupledKlein－Gordon－Schrodinger Eqnations

ＡｓｙｍｐｔｏｔｉｃＢｅｈａｖｉｏｎｒｏｆｓｏｌｕｔｉｏｎｓｆｏｒｔｈｅＣｏｕｐｌｅｄＫｌｅｉｎ－Ｇｏｒｄｏｎ－ＳｃｈｒｏｄｉｎｇｅｒＥｑｎａｔｉｏｎｓＧｕｏＢｏｌｉｎｇ（郭柏灵）＊；ＭｉａｏＣｈａｎｇｘｉｎｇ（苗长兴）（ＢｅｉｊｉｎｇＩｎｓｔｉｔｕ...     

Relaxation Phenomenon of the P—systems

ＲｅｌａｘａｔｉｏｎＰｈｅｎｏｍｅｎｏｎｏｆｔｈｅＰ－ｓｙｓｔｅｍｓＬｉＹｉｆａｎｇ（ＮｏｒｔｈＣｈｉｎａＩｎｓｔｉｔｕｔｅｏｆＷａｔｅｒＣｏｎｓｅｒｖａｎｃｙａｎｄＨｙｄｒｏｅｌｅｃｔｒｉｃＰｏｗｅｒ，Ｚｈｅｎｇｚｈｏｕ，４５００４５）ＬｉｕＦａｇ...     

On the P-Torsion Subgrup of Homotopy Group

ＯｎｔｈｅＰ－ＴｏｒｓｉｏｎＳｕｂｇｒｏｕｐｏｆＨｏｍｏｔｏｐｙＧｒｏｕｐＳｈｅｎＸｉｎｙａｏ（沈信耀）（Ｉｎｓｔ．ｏｆＭａｔｈ．ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ，１０００８０，Ｃｈｉｎａ）ＲｅｃｅｉｖｅｄＮｏｖｅｍｂｅｒ２６．１９９３Ｏ...     

On the Set of Element Orders of a Finite Group

ＦｏｒａｎｙｇｒｏｕｐＧ，ｄｅｎｏｔｅｂｙπｅ（Ｇ）ｔｈｅｓｅｔｏｆａｌｅｌｅｍｅｎｔｏｒｄｅｒｓｏｆＧ．Ｇｉｖｅｎａｆｉｎｉｔｅ（ｒｅｓｐ．ｉｎｆｉｎｉｔｅ）ｇｒｏｕｐＧ，ｌｅｔｈ（πｅ（Ｇ））ｂｅｔｈｅｎｕｍｂｅｒｏｆｉｓｏｍｏｒｐｈｉｓｍｃｌａ...     

The Jacobson and Brown—McCoy Radicals of Certain Group Rings

ＴｈｅＪａｃｏｂｓｏｎａｎｄＢｒｏｗｎ－ＭｃＣｏｙＲａｄｉｃａｌｓｏｆＣｅｒｔａｉｎ　Ｇｒｏｕｐ　ＲｉｎｇｓＺｈｏｕＹｏｎｇｘｉｎ（周永新）（Ｍａｔｈ．Ｄｅｐｔ．，ＨｅｂｅｉＴｅａｃｈｅｒｓ＇Ｕｎｉｖｅｒｓｉｔｙ，Ｓｈｉｊｉａｚｈｕａｎｇ，０５００１...     

Closed Geodesics and Non一Differentiability of the Metric in Infinite－Dimensional Teichmuller Spaces

ＣｌｏｓｅｄＧｅｏｄｅｓｉｃｓａｎｄＮｏｎ一ＤｉｆｆｅｒｅｎｔｉａｂｉｌｉｔｙｏｆｔｈｅＭｅｔｒｉｃｉｎＩｎｆｉｎｉｔｅ－ＤｉｍｅｎｓｉｏｎａｌＴｅｉｃｈｍｕｌｌｅｒＳｐａｃｅｓＬｉｚｈｏｎｇ（李忠）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，...     

The Meta-Grothendieck Group of a Ring

ＴｈｅＭｅｔａ┐ＧｒｏｔｈｅｎｄｉｅｃｋＧｒｏｕｐｏｆａＲｉｎｇ＊）ＦｅｎｇＬｉａｎｇｇｕｉ（冯良贵）（ＤｅｐａｒｔｍｅｎｔｏｆＭｅｔｈｅｍａｔｉｃｓ，ＮＵＤＴ，Ｃｈａｎｇｓｈａ，４１００７３）ＡｂｓｔｒａｃｔＷｅｉｎｔｒｏｄｕｃｅｔｈｅｍｅｔａ－Ｇ...     

On the Construction of d-Continuous Modules over Some Special Rings

ＯｎｔｈｅＣｏｎｓｔｒｕｃｔｉｏｎｏｆｄ－ＣｏｎｔｉｎｕｏｕｓＭｏｄｕｌｅｓｏｖｅｒＳｏｍｅＳｐｅｃｉａｌＲｉｎｇｓ￥ＣｈｅｎＪｉｎｊｉａｎ（ＧｕａｎｇｄｏｎｇＮａｔｉｏｎａｌＩｎｓｔｉｔｕｔｅ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｅｐｅｐｅｒ，ｗｅｕｓｉｎｇ...     

On the Prime Solutions of the Diophantine Equation (X~m-1)/(X-1)=Y~n

ＯｎｔｈｅＰｒｉｍｅＳｏｌｕｔｉｏｎｓｏｆｔｈｅＤｉｏｐｈａｎｔｉｎｅＥｑｕａｔｉｏｎ（Ｘ~ｍ－1）/（Ｘ－１）＝Ｙ~ｎＬｅＭａｏｈｕａ（乐茂华）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＺｈａｎｊｉａｎｇＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，Ｚｈａｎｊｉａｎ，Ｇｕａｎｇｄ...     

Graded Singular Properties of Graded Quotient Rings

ＧｒａｄｅｄＳｉｎｇｕｌａｒＰｒｏｐｅｒｔｉｅｓｏｆＧｒａｄｅｄＱｕｏｔｉｅｎｔＲｉｎｇｓ＊）ＷｅｉＪｕｎｃｈａｏ（魏俊潮）ａｎｄＢｅｉＳｈｕｋｕｎ（贝淑坤）（ＹａｎｇｚｈｏｕＵｎｉｖｅｒｓｉｔｙ－ＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ，Ｙａｎｇ...     

Global Attractors for the Initial Value Problems of Cahn－Hilliard Equations on Compact Manifolds

ＧｌｏｂａｌＡｔｔｒａｃｔｏｒｓｆｏｒｔｈｅＩｎｉｔｉａｌＶａｌｕｅＰｒｏｂｌｅｍｓｏｆＣａｈｎ－ＨｉｌｌｉａｒｄＥｑｕａｔｉｏｎｓｏｎＣｏｍｐａｃｔＭａｎｉｆｏｌｄｓＧｕｏＢｏｌｉｎｇ（郭柏灵）ＷａｎｇＹｏｕｄｅ（王友德）（ＩｎｓｔｉｔｕｔｅｏｆＡ...