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，∞）→［…     

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

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

An Equivalent Form of the Dedekind Axiomand Its Application(Ⅰ)——Also on theunity ofthe ContinuousInduction,theMathem aticalInduction and theTransfiniteInduction

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ［１］，ｔｈｅａｃａｄｅｍｉｃｉａｎ，ＺｈａｎｇＪｉｎｇｚｈｏｎｇｏｐｅｎｕｐｔｈｅｒｅｓｅａｒｃｈｆｉｅｌｄｏｆ“ｅｄｕｃａｔｉｏｎａｌｍａｔｈ－ｅｍａｔｉｃｓ”．Ｉｎ［１］，ｔｈｅｃｏｎｔｉｎｕｏｕｓｉｎｄｕｃｔｉｏｎｉｓｐｒｅｓｅｎｔｅｄ：ＬｅｔＰｘｂｅａｐｒｏｐｏｓｉｔｉｏｎｃｏｎｃｅｒｎｉｎｇａｒｅａｌｎｕｍｂｅｒｘ．（ｉ）Ｉｆｔｈｅｒｅｉｓｓｏｍｅｘ０ｓｕｃｈｔｈａｔＰｘｉｓｔｒｕｅｆｏｒｅｖｅｒｙｘ＜ｘ０；（ｉｉ）ＩｆＰｘｉｓｔｒｕｅｆｏｒｅｖ－…     

Characterizations of F-V-rings by Quasi-continuous Modules

ＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｓｏｆＦ－Ｖ－ｒｉｎｇｓｂｙＱｕａｓｉ－ｃｏｎｔｉｎｕｏｕｓＭｏｄｕｌｅｓＬｉｕＺｈｏｎｇｋｕｉ（刘仲奎）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｏｒｔｈｕｅｓｔＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｌａｎｃｈ...     

Interval Algorithm for a Kind of Nonsmooth Global Optimization

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆｏｌｌｏｗｉｎｇｇｌｏｂａｌｏｐｔｉｍｉｚａｔｉｏｎｐｒｏｂｌｅｍｉｓｃｏｎｓｉｄｅｒｅｄ：ｇｌｏｂａｌｍｉｎｉｍｉｚｅｆ（ｘ）,ｆ：Ｘ０Ｒｎ→Ｒ,（１）ｗｈｅｒｅＸ０ｉｓａｎｙｃｌｏｓｅｄｄｏｍａｉｎ,ｆｉｓａｃｏｎｔｉｎｕｏｕｓａｎｄｐｉｅｃｅｗｉｓｅｓｍｏｏｔｈｆｕｎｃｔｉｏｎｏｖｅｒＸ０,ａｎｄｉｔｓｒｉｇｈｔａｎｄｌｅｆｔｄｅｒｉｖａｔｉｖｅｅｘｉｓｔａｔｎｏｎ－ｄｉｆｆｉｅｒｅｎｔｉａｂｌｅｐｏｉｎｔ,ｆｉｓｃａｌｌｅｄｑｕａｓｉ－ｓｍｏｏｔ…     

An Example of Variational Equation not Containing Continuous Bifurcation

ＡｎＥｘａｍｐｌｅｏｆＶａｒｉａｔｉｏｎａｌＥｑｕａｔｉｏｎｎｏｔＣｏｎｔａｉｎｉｎｇＣｏｎｔｉｎｕｏｕｓＢｉｆｕｒｃａｔｉｏｎＨｕａｎｇＷｅｎｚａｏ（黄文灶）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉ...     

A Formula for the Number of solutions of the Congruence αx~a＋βy~b＋γz~c≡0（modp~n）

ＡＦｏｒｍｕｌａｆｏｒｔｈｅＮｕｍｂｅｒｏｆｓｏｌｕｔｉｏｎｓｏｆｔｈｅＣｏｎｇｒｕｅｎｃｅαｘ~ａ＋βｙ~ｂ＋γｚ~ｃ≡０（ｍｏｄｐ~ｎ）ＨａｎＱｉｎｇ（韩清）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＳｉｃｈｕａｎＵｎｉｖ，Ｃｈｅｎｇｄｕ，Ｓｉｃｈｕａｎ，６１６０...     

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｝；…     

L-nets and Weakly Continuous L-fuzzy Multifunctions

Ｌ－ｎｅｔｓａｎｄＷｅａｋｌｙＣｏｎｔｉｎｕｏｕｓＬ－ｆｕｚｚｙＭｕｌｔｉｆｕｎｃｔｉｏｎｓＣｈｅｎｇＪｉｓｈｕ（ＱｉｎｇｈａｉＪｕｎｉｏｒＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ，Ｘｉｎｉｎｇ８１０００７，Ｑｉｎｇｈａｉ，Ｐ．Ｒ．Ｃｈｉｎａ）Ａｂｓｔｒａｃ...     

NOTE ON THE OSCILLATION OF THE SOLUTION FOR GENERALIZED LIENARD EQUATIONS

Ｃｏｎｓｉｄｅｒｉｎｇｓｙｓｔｅｍ：ｘ＝φ（ｙ）－Ｆ（ｘ），ｙ＝－ｇ（ｘ）｛（Ｅ）ｉｎｗｈｉｃｈＦ（ｘ）＝∫ｘ０ｆ（ｔ）ｄｔ，ｆ（ｘ），ｇ（ｘ），φ（ｙ）ａｒｅｃｏｎｔｉｎｕｏｕｓ，ａｎｄｓａｔｉｓｆｙｔｈｅｃｏｎｄｉｔｉｏｎｓｗｈｉｃｈｅｎｓｕｒ...     

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…     

The Semigroup Characterizations of Positive Implicative BCK—algebras

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＢｙａＢＣＩ－ａｌｇｅｂｒａｗｅｍｅａｎａｎａｌｇｅｂｒａ（Ｘ，，０）ｏｆｔｙｐｅ（２，０）ｗｉｔｈｔｈｅｆｏｌｌｏｗｉｎｇｃｏｎｄｉ－ｔｉｏｎｓ：（１）（（ｘｙ）（ｘｚ））（ｚｙ）＝０；（２）（ｘ（ｘｙ））ｙ＝０；（３）ｘｘ＝０；（４）ｘｙ＝ｙｘ＝０ｉｍｐｌｉｅｓｘ＝ｙ．ＩｆａＢＣＩ－ａｌｇｅｂｒａ（Ｘ，，０）ｓａｔｉｓｆｉｅｓ（５）０ｘ＝０．ｔｈｅｎｉｔｉｓｃａｌｌｅｄａＢＣＫ－ａｌｇｅｂｒａ．ＩｎａＢＣＩ－ａｌｇｅｂｒａ，ｔｈｅｆ…     

Stability of a Chem ostatModelfor a Single Specieswith Delayed NutrientRecycling——Case ofWeak KernelFunction

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｏｍｍｏｎｃｈｅｍｏｓｔａｔｍｏｄｅｌｈａｓｂｅｅｎｃｏｎｓｉｄｅｒｅｄｂｙｍａｎｙｍａｔｈｅｍａｔｉａｎｓ（ｓｅｅ［１］）．Ｃｈｅｍｏｓｔａｔｍｏｄｅｌｓｉｎｃｏｒｐｏｒａｔｉｎｇｄｉｓｃｒｅｔｅｔｉｍｅｄｅｌａｙｈａｖｅｂｅｅｎｉｎｖｅｓｔｉｇａｔｅｄｉｎ［２］ａｎｄ［３］．Ｉｎ［４］ａｎｄ［５］，ｃｈｅｍｏｓｔａｔｍｏｄｅｌｓｗｉｔｈｃｏｎｔｉｎｕｏｕｓｔｉｍｅｄｅｌａｙｉｎｎｕｔｒｉｅｎｔｒｅｃｙｃｌｉｎｇｗｅｒｅｃｏｎｓｉｄ－ｅｒｅｄ．Ｉｎｔｈｉ…     

Computation of K0(RMNS_(θ,h))

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

Dynamical Behavior in Behavior in Simple and Coupled Systems of Continuous Josephson－Junctions

ＤｙｎａｍｉｃａｌＢｅｈａｖｉｏｒｉｎＢｅｈａｖｉｏｒｉｎＳｉｍｐｌｅａｎｄＣｏｕｐｌｅｄＳｙｓｔｅｍｓｏｆＣｏｎｔｉｎｕｏｕｓＪｏｓｅｐｈｓｏｎ－ＪｕｎｃｔｉｏｎｓＱｉａｎＭｉｎ（钱敏）ＺｈｏｕＳｈｅｎｇｆａｎ（周盛凡）（ＤｅｐａｒｔｍｅｎｏｆＭａ...     

Global Discontinuous Solutions to A Class of Generalizd Riemann Problems for Quasilinear Hyperbolic Systems（Ⅰ）

ＧｌｏｂａｌＤｉｓｃｏｎｔｉｎｕｏｕｓＳｏｌｕｔｉｏｎｓｔｏＡＣｌａｓｓｏｆＧｅｎｅｒａｌｉｚｄＲｉｅｍａｎｎＰｒｏｂｌｅｍｓｆｏｒＱｕａｓｉｌｉｎｅａｒＨｙｐｅｒｂｏｌｉｃＳｙｓｔｅｍｓ（Ⅰ）￥ＣｈｅｎＳｈｏｕｘｉｎ；ＷｕＲｕｉｊｉｅ（陈守信，吴瑞...     

Weighted Norm Inequalities for the Laplace Transform

ＷｅｉｇｈｔｅｄＮｏｒｍＩｎｅｑｕａｌｉｔｉｅｓｆｏｒｔｈｅＬａｐｌａｃｅＴｒａｎｓｆｏｒｍＷａｎｇＺｏｎｇｓｈｅｎ（王宗申）（ＮａｎｙａｎｇＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ，Ｎａｎｙａｎｇ，４７３０６１）５１．ＲｅｓｕｌｔｓＬｅｔＬｆ＜．，￣Ｊ０ｃ...     

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…     

On a Class of Additive Functions

ＯｎａＣｌａｓｓｏｆＡｄｄｉｔｉｖｅＦｕｎｃｔｉｏｎｓＺｈａｉｗｅｎｇｕａｎｇ（翟文广）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＳｈａｎｄｏｎｇＵｎｉｖ．，Ｊｉｎａｎ，Ｓｈｏｎｄｏｎｇ，２５０１Ｏ０）ＣｏｍｍｕｎｉｃａｔｅｄｂｙＰａｎＣｈｅｎｇｂｉａｏＲｅｃｅｉ...     

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…