构造法简证一类三角不等式

１９９６年,周永良先生在全国第三届初等数学研究学术交流会论文集中提出如下三角不等式在锐角三角形ＡＢＣ中,有ｃｏｓ（Ｂ－Ｃ）ｃｏｓＡ＋ｃｏｓ（Ｃ－Ａ）ｃｏｓＢ＋ｃｏｓ（Ａ－Ｂ）ｃｏｓＣ≥６（１）ｃｏｓＡｃｏｓ（Ｂ－Ｃ）＋ｃｏｓＢｃｏｓ（Ｃ－Ａ）＋ｃｏｓ...     

Bordism Classes of Involutions on RP（2n）、CP（2n） and HP（2n）

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ,ＲＰ（ｎ）,ＣＰ（ｎ）,ＨＰ（ｎ）ｒｅｐｒｅｓｅｎｔｓｎ－ｄｉｍｅｎｓｉｏｎａｌｒｅａｌｐｒｏｊｅｃｔｉｖｅｓｐａｃｅ,ｃｏｍｐｌｅｘｐｒｏｊｅｃｔｉｖｅｓｐａｃｅ,ｑｕａｔｅｒｎｉｏｎｉｓｐｒｏｊｅｃｔｉｖｅｓｐａｃｅｒｅｓｐｅｃｔｉｖｅｌｙ．Ｍ～２ＲＰ（ｎ）ｍｅａｎｓｔｈｅｍｏｄ２ｃｏｈｏｍｏｌｏｇｙｒｉｎｇｏｆＭｉｓｉｓｏｍｏｒｐｈｉｃｔｏｔｈａｔｏｆＲＰ（ｎ）：Ｈ（Ｍ;Ｚ２）≈Ｈ（ＲＰ（ｎ）;Ｚ２）．Ｗｅｉｎｔｒｏｄｕｃｅｔｈｅ…     

Remark on Some Classes of P—valent Functions

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＡ（ｎ,ｐ）ｂｅｔｈｅｃｌａｓｓｏｆｐ－ｖａｌｅｎｔｆｕｎｃｔｉｏｎｓｏｆｔｈｅｆｏｒｍｆ（ｚ）＝ｚｐ＋∑∞ｊ＝ｐ＋ｎａｊｚｊ,　　（ｎ,ｐ∈Ｎ）ｗｈｉｃｈａｒｅａｎａｌｙｔｉｃｉｎｔｈｅｕｎｉｔｄｉｓｃＵ＝｛ｚ;｜ｚ｜＜１｝．Ｓｕｐｐｏｓｅｆ（ｚ）ａｎｄｇ（ｚ）ａｒｅａｎａｌｙｔｉｃｉｎＵ．Ｉｆｔｈｅｒｅｅｘｉｓｔｓａｆｕｎｃｔｉｏｎｗ（ｚ）,ｗｈｉｃｈｉｓａｎａｌｙｔ－ｉｃｉｎＵａｎｄｓａｔｉｓｆｉｅｓｔｈｅｃｏｎｄｉｔｉｏｎ｜ｗ（ｚ）｜｜ｚ｜,ｓｕｃ…     

Equicontinuous Seton Locally Convex Spaces

Ｌｅｔ（Ｅ，γ）ｂｅａｌｏｃａｌｌｙｃｏｎｖｅｘｓｐａｃｅａｎｄＥ′ｉｔｓｃｏｎｊｕｇａｔｅｓｐａｃｅ．ＡＥ′ｂｅａｎｅｑｕｉｃｏｎｔｉｎｕ－ｏｕｓｓｅｔｏｎ（Ｅ，γ）．ＴｈｅｗｅｌｌｋｎｏｗｎＡｌａｏｇｌｕ－ＢｏｕｒｂａｋｉＴｈｅｏｒｅｍ（［１］Ｐ２４８）ｓｔａｔｅｓｔｈａｔｅａｃｈｅ－ｑｕｉｃｏｎｔｉｎｕｏｕｓｓｅｔｏｎ（Ｅ，γ）ｉｓσ（Ｅ′，Ｅ）ｒｅｌａｔｉｖｅｌｙｃｏｍｐａｃｔｓｕｂｓｅｔ．Ｎｅｖｅｒｔｈｅｌｅｓｓ，ｅｑｕｉｃｏｎｔｉｎｕｏｕｓｓｅｔｉｓσ（Ｅ′，Ｅ）ｒｅｌａｔｉｖｅｌ…     

Boundary Extension of μ（z）—homeomorphism

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔｔｈｅＢｅｌｔｒａｍｉｅｑｕａｔｉｏｎｆｚ＝μ（ｚ）ｆｚ（１．１）ｈａｓａｕｎｉｑｕｅｈｏｍｅｏｍｏｒｐｈｉｃｓｏｌｕｔｉｏｎｕｎｄｅｒｎｏｒｍａｌｉｚａｔｉｏｎｃｏｎｄｉｔｉｏｎｗｈｅｎｙμ（ｚ）ｙ∞＜１．Ｔｈｉｓｓｏｌｕｔｉｏｎｉｓｈａｂｉｔｕａｌｌｙｃａｌｌｅｄａｑｕａｓｉｃｏｎｆｏｒｍａｌｍａｐｐｉｎｇｗｉｔｈｃｏｍｐｌｅｘｄｉｌａｔａｔｉｏｎμ（ｚ）［１］．Ｗｉｔｈｏｕｔｔｈｉｓｅｓｓｅｎｔｉａｌｒｅｓｔｒｉｃｔｉｏｎ…     

The H-stability of the Solution for Infinite Delay Functional Differential Equation

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＮｏｗａｄａｙｓ，ｔｈｅｒｅｓｅａｒｃｈｏｆｔｈｅｉｎｆｉｎｔｅｄｅｌａｙｆｕｎｃｔｉｏｎａｌｄｉｆｆｅｒｅｎｔｉａｌｑｕａｔｉｏｎｈａｓｄｅｖｅｌｏｐｅｄｄｅｅｐｌｙ．Ｍａｎｙｌｉｔｅｒａｔｕｒｅｓｈａｖｅｂｅｅｎｃｏｎｃｅｒｎｅｄｆｏｒｒｅｓｅａｒｃｈｔｈｅｉｎｔｅｇｒａｌｄｉｆｆｅｒｅｎｔｉａｌｑｕａｔｉｏｎａｓｆｏｌｌｏｗｓｘ（ｔ）＝－ａ（ｔ）ｘ（ｔ）＋∫ｔ－∞ｋ（ｔ，ｓ－ｔ，ｘ（ｓ））ｄｓ．（１）　　Ｉｎｏｒｄｅｒｔｏｓｔｕｄｙｔｈｅｉｎｆｉｎｉｔｅｄ…     

ON THE UNIQUENESS OF LIMIT CYCLE FOR A GENERALIZED LINARD SYSTEM

１．ＲｅｃｅｎｔｌｙｔｈｅｒｅａｒｅｓｏｍｅｇｏｏｄｌｉｔｅｒａｔｕｒｅｓｃｏｎｃｅｒｎｉｎｇｔｈｅｕｎｉｑｕｅｎｅｓｏｆｌｉｍｉｔｃｙｃｌｅｓｆｏｒｇｅｎｅｒａｌｉｚｅｄＬｉéｎａｒｄｓｙｓｔｅｍｓｘ＝φ（ｙ）－Ｆ（ｘ），ｙ＝－ｇ（ｘ），（Ｆ（ｘ）...     

Computation of K0(RMNS_(θ,h))

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｕｒｐｏｓｅｏｆｔｈｉｓｐａｐｅｒｉｓｔｏｃｏｍｐｕｔｅｔｈｅＧｒｏｔｈｅｎｄｉｅｃｋｇｒｏｕｐｏｆＴ＝ＲＭＮＳ（θ，φ）．ＴｉｓｃａｌｌｅｄｔｈｅｒｉｎｇｏｆＭｏｒｉｔａＣｏｎｔｅｘｔｉｎｓｏｍｅｌｉｔｅｒａｔｕｒｅ（ｓｅｅ［１］）．Ｉｎ１９７４，ＱｕｉｌｌｅｎａｎｎｏｕｃｅｄｔｈａｔＫ０（ＲＭＯＳ）Ｋ０（Ｒ）Ｋ０（Ｓ）．ＵｐｔｏｔｈｅｐｒｅｓｅｎｔｍｏｍｅｎｔｔｈｅｒｅｓｔｉｌｌｅｘｉｓｔｓｎｏｉｎｆｏｒｍａｔｉｏｎｃｏｎｃｅｒｎｉｎｇＫ０（Ｔ）ｆ…     

Asymptotic Behavior of Nodal Solutions for Semilinear Elliptic Equationsin R~n

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙ，ｔｈｅｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｅｑｕａｔｉｏｎｓ△ｕ＋ｆ（ｕ）＝０（１．１）ｕ（ｘ）→０ａｓ｜ｘ｜→∞（１．２）ｉｎＲｎｗｅｒｅｃｏｎｓｉｄｅｒｅｄｗｉｄｅｌｙ（ｓｅｅ［１］－［７］）．Ｉｎｔｈｅｎｉｃｅｐａｐｅｒｓ［１］ａｎｄ［２］，ｉｔｗａｓｐｒｏｖｅｄｔｈａｔａｎｙｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｏｆ（１．１）ｍｕｓｔｂｅｒａｄｉａｌｉｎｃａｓｅｆ（ｕ）∈Ｃ１＋δ（δ＞０）．Ｔｈｅｒｅｆｏｒｅ，ａｎｙｐｏｓｉｔｉｖｅｓｏｌｕｔｉ…     

The Inner Radius of Univalency of the Rhom busDom ain

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＮａｒｒａｔａｔｉｏｎｏｆｔｈｅＴｈｅｏｒｅｍＩｆｆｕｎｃｔｉｏｎｆｉｓａｎａｌｙｔｉｃｉｎｄｏｍａｉｎＤａｎｄｆ′（ｚ）≠０ａｔｐｏｉｎｔｚ，ｗｅｄｅｆｉｎｅｔｈｅｓｃｈｗａｒｚｉａｎｄｅｒｉｖａｔｉｖｅｏｆｆａｓＳｆ（ｚ）＝（ｆ″（ｚ）ｆ′（ｚ））′－１２（ｆ″（ｚ）ｆ′（ｚ））２．（１．１）　　Ｆｏｒａｌｏｃａｌｌｙｕｎｉｖａｌｅｎｔｈｏｌｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎ，ｉｔｓＳｃｈｗａｒｚｉａｎｄｅｒｉｖａｔｉｖｅｉｓｃｌｅａｒ．Ａｔｐｏｌｅｓ，ｔ…     

The Structure and Stabilization Decom position of Linear Interconnected ControlSystem swith Multidelays

§１．　ＴｈｅＥｑｕｉｖａｌｅｎｃｅｏｆＬｙａｐｕｎｏｖｓＲａｎｇｅｏｆｔｈｅＩｎｔｅｒｃｏｎｎｅｃｔｅｄＳｔａｂｉｌｉｚａｔｉｏｎＮｅｗ，ｌｅｔｕｓｃｏｎｓｉｄｅｒｔｈｅｌｉｎｅａｒｃｏｎｓｔａｎｔｉｎｔｅｒｃｏｎｎｅｃｔｅｄｃｏｎｔｒｏｌｓｙｓｔｅｍｘｉ（ｔ）＝∑ｎｊ＝１ａｉｊｘｊ（ｔ）＋∑ｍｊ＝１ｂｉｊｕｊ（ｔ）＋∑Ｎ１ｒ＝１∑ｎｊ＝１ａ（ｒ）１ｉｊｅ（ｒ）１ｉｊｘｊ（ｔ）　　　　　　　　　　＋∑Ｎ２ｓ＝１∑ｎｊ＝１ａ（ｓ）２ｉｊｅ（ｓ）２ｉｊｘｊ（ｔ－ｒ（ｓ）１ｉｊ）＋∑Ｎ２ｄ＝１∑…     

Strong Convergence Rates of Double Kernel Estimates of Conditional Desity Under Stationary Sequences

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＲｅｓｕｌｔｓＬｅｔ（ｘ,ｙ）ｂｅａｒａｎｄｏｍｖｅｃｔｏｒｔａｋｉｎｇｖａｌｕｅｓｉｎＲｐ×Ｒｑ,ａｎｄａｓｓｕｍｅｔｈａｔｆ（ｙ｜ｘ）ｉｓｔｈｅｃｏｎｄｉｔｉｏｎａｌｄｅｎｓｉｔｙｆｕｎｃｔｉｏｎｏｆＹｏｎＸａｎｄＸｈａｓｄｉｓｔｒｉｂｕｔｉｏｎｆｕｎｃｔｉｏｎＦ（ｘ）ａｎｄｕｎｋｎｏｗｎｄｅｎｓｉｔｙｆｕｎｃｔｉｏｎｆ（ｕ）．Ａｓｓｕｍｅｔｈａｔ（Ｘ１,Ｙ１）,…,（Ｘｎ,Ｙｎ）ａｒｅｒａｎｄｏｍｓａｍｐｌｅｓｔａｋｉｎｇｖａｌｕｅｓｉｎ（Ｘ,Ｙ）,ａ…     

On Rational Bases of Subspaces of F((D))~n

ＯｎＲａｔｉｏｎａｌＢａｓｅｓｏｆＳｕｂｓｐａｃｅｓｏｆＦ（（Ｄ））~ｎＷａｎＺｈｅｘｉａｎ（万哲先）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ，１０００８０ａｎｄＤｅｐａｒ?..     

A Property of MRA of Multiplicity r with an Arbitrary Dilation Matrix

ＩｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔｔｈｅｍｅｔｈｏｄｔｏｃｏｎｓｔｒｕｃｔｗａｖｅｌｅｔｉｓｍｕｌｔｉｒｅｓｏｌｕｔｉｏｎａｎａｌｙｓｉｓｗｈｉｃｈｗａｓｇｉｖｅｎｆｉｒｓｔｂｙＳ．Ｍａｌｌａｔ（［１］,［２］）ｉｎ１９８９．Ｉｎ１９９４,Ｔ．Ｎ．Ｔ．ＧｏｏｄｍａｎａｎｄＳ．Ｌ．Ｌｅｅ（［３］）ｇｅｎｅｒａｌｉｚｅｄｃｏｎｃｅｐｔｏｆｍｕｌｔｉｒｅｓｏｌｕｔｉｏｎａｎａｌｙｓｉｓｔｏｔｈｅｃａｓｅｏｆｍｕｌｔｉｐｈｃｉｔｙｒ（ｒ１）ｓｕｃｈｔｈａｔｍｕｌｔｉｗａｖｅｌｅｔｓｃａｎｂｅｃｏｎｓｔ…     

REALHYPERSURFACESWITHCONSTANTPRINCIPALCURVATUREINCOMPLEXHYPERBOLICSPACES

ＡｂｓｔｒａｃｔＬｅｔＭｂｅａｒｅａｌｈｙｐｅｒｓｕｒｆａｃｅｗｉｔｈｔｈｒｅｅ．ｄｉｓｔｉｎｃｔｃｏｎｓｔａｎｔｐｒｉｎｃｉｐａｌｃｕｒ－ｖａｔｕｒｅｓｉｎｔｗｏｄｉｍｅｎｓｉｏｎａｌｃｏｍｐｌｅｘｈｙｐｅｒｂｏｌｉｃｓｐａｃｅＣＨ，ｔｈｅｎｅｉｔｈｅｒ（ａ）Ｍｈａｓｔｗｏｐｒｉｎｃｉｐａｌｃｕｒｖａｔｕｒｅｓｗｈｏｓｅｄｉｆｆｅｒｅｎｃｅｉｓｌａｒｇｅｔｈａｎｚｅｒｏａｎｄｌｅｓｓｔｈａｎｏｎｅ．（ｂ）ＴｈｅｔｈｒｅｅｐｒｉｎｃｉｐａｌｃｕｒｖａｔｕｒｅｓｏｆＭｆｏｒｍａｎｅｑｕｉｄｉｆｆｅｒｅｎｃｅｓｅｑｕｅｎｃｅｗｈｏｓｅｃｏｍｍｏｎｄｉｆｆｅｒｅｎｃｅｉｓｏｎｅ；（ｃ）Ｍｉｓｈｏｌｏｍｏｒｐｈｉｃｃｏｎｇｒｕｅｎｔｔｏａｎｏｐｅｎｐａｒｔｏｆａｔｕｂｅａｒｏｕｎｄｒｅａｌｔｗｏｄｉｍｅｎｔｉｏｎａｌｈｙｐｅｒｂｏｌｉｃｓｐａｃｅ．．Ｋｅｙｗｏｒｄｓ．Ｒｅａｌｈｙｐｅｒｓｕｒｆａｃｅｃｏｍｐｌｅｘｈｙｐｅｒｂｏｌｉｃｓｐａｃｅｔｕｂｅｌｅｑｕｉｄｉｆｆｅｒｅｎｃｅｓｅｑｕｅｎｃｅ     

Involution Fixing∪from (i=1) to r(RP(1))~m_i×(CP(1))~s_i*)

§０．ＩｎｔｒｏｄｕｃｔｉｏｎＷｅｗｒｉｔｅＦＰ（ｎ）ｆｏｒＣＰ（ｎ）（ｎ－ｄｉｍｅｎｓｉｏｎａｌｃｏｍｐｌｅｘｐｒｏｊｅｃｔｉｖｅｓｐａｃｅ）ｏｒＨＰ（ｎ）（ｎ－ｄｉ－ｍｅｎｓｉｏｎａｌｑｕａｔｅｒｎｉｏｎｉｃｐｒｏｊｅｃｔｉｖｅｓｐａｃｅ）．Ｍｎ...     

On the Existence of Positive Solution for n OrderSingular Boundary Value Problems

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｘｉｓｔｅｎｃｅｆｏｒｔｈｅｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓｈａｖｅｂｅｅｎｗｉｄｅｌｙｓｔｕｄｉｅｄｒｅｃｅｎｔｌｙ．Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｗｉｌｌｄｉｓｃｕｓｓｔｈｅＢＶＰｏｆｔｈｅｆｏｌｌｏｗｉｎｇｃｏｎｄｉｔｉｏｎｓ：ｕ（ｎ）＋ａ（ｔ）ｆ（ｕ）＝０，０＜ｔ＜１，ｕ（ｋ）（０）＝０，０ｋｎ－２（１．１）ｕ（１）＝０，　ｗｈｅｒｅ（ｈ１）ａ：（０，１）→（０，∞）ｉｓａｃｏｎｔｉｎｕｏｕｓｆｕｎｃｔｉｏｎ．（ｈ２）ｆ：［０，∞）→［…     

THE PERIODIC SOLUTIONS OF CERTAIN EQUATIONS WITH PERIODIC COEFFICIENTS

１ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅｃｏｎｓｉｄｅｒｔｈｅｆｏｌｏｗｉｎｇｅｑｕａｔｉｏｎｓｗｉｔｈｐｅｒｉｏｄｉｃｃｏｅｆｉｃｉｅｎｔｓｘ＝Ａ（ｔ）ｘ２＋Ｂ（ｔ）ｘ＋Ｃ（ｔ），（１．１）ｘ＝－Ａ（ｔ）ｘ２＋Ｂ（ｔ）ｘ＋Ｃ（ｔ），（１...     

The Migration Equation of the Moisture in Soil with Nonlinear Initial Boundary Value Problem

Ｔｈｅｅｑｕａｔｉｏｎｕｘｔｘ＋η（ｘ,ｔ）ｕｘｘ＝Ｆ（ｘ,ｔ,ｕ,ｕｘ,ｕｘｘ）（１）ｉｓａｐｐｌｉｅｄｔｏｍａｎｙａｓｐｅｃｔｓ,ｓｕｃｈａｓｔｈｅｍｉｇｒａｔｉｏｎｏｆｍｏｉｓｔｕｒｅｉｎｓｏｉｌ,ｓｏａｋｉｎｇｔｈｅｏｒｙｉｎｍｕｌｔｉ－ｈｏｌｅｍｅｄｉａ,ｅｔｃ．,ｗｈｏｓｅｐｒｏｂｌｅｍｓｏｆｄｅｔｅｒｍｉｎａｔｅｓｏｌｕｔｉｏｎｓａｒｅｄｉｓｃｕｓｓｅｄｉｎｒｅｆ．［１－３］,ｉｎｗｈｉｃｈ,ｉｔｓｃｈａｒａｃｔｅｒｉｓｔｉｃｏｒｉｎｉｔｉａｌｖａｌｕｅｐｒｏｂｌｅｍｓａｒｅｓｔｕ…     

Correlation Wavelet and its Applications

§１．　ＤａｕｂｅｃｈｉｅｓＷａｖｅｌｅｔｓａｎｄＣｏｒｒｅｌａｔｉｏｎＷａｖｅｌｅｔｓＡｓｗｅｋｎｏｗ,Ｄａｕｂｅｃｈｉｅｓｓｃａｌｉｎｇｆｕｎｃｔｉｏｎφ（ｘ）ａｎｄｗａｖｅｌｅｔｆｕｎｃｔｉｏｎψ（ｘ）ｈａｖｅｔｈｅｆｏｌ－ｌｏｗｉｎｇｐｒｏｐｅｒｔｉｅｓ：１．φ（ｘ）ｉｓａｇｅｎｅｒａｔｉｎｇｅｌｅｍｅｎｔｆｏｒａｍｕｌｔｉｒｅｓｏｌｕｔｉｏｎａｎａｌｙｓｉｓ（ＭＲＡ）,ｓｕｐｐφ（ｘ）＝［０,２Ｎ－１］,ｏｒｔｈｏｇｏｎａｌｗｉｔｈｉｎｔｅｇｅｒｔｒａｎｓｌａｔｉｏｎｓ．Ｇｅｎｅｒａｌ…