Showing papers in "College Mathematics in 2008"
Journal Article•
TL;DR: In this paper, a base Hilbert-type integral inequality with the homogeneous kernel of-1-degree and the best constant factor is given by using the way of weight function, and the equivalent form and the extended integral inequalities with multi-parameters are considered.
Abstract: By using the way of weight function,a base Hilbert-type integral inequality with the homogeneous kernel of-1-degree and the best constant factor is given.The equivalent form and the extended integral inequalities with multi-parameters are considered.
13 citations
Journal Article•
TL;DR: In this paper, the influence of s-semipermutable subgroups on the structure of finite groups is investigated, where a subgroup H of a finite group G is considered to be permutable if it is permutable with every Sylow p-subgroup of G with (p,|H|) = 1.
Abstract: A subgroup H of a finite group G is called s-semipermutable in G if it is permutable with every Sylow p-subgroup of G with(p,|H|)=1. In this paper, the influence of s-semipermutable subgroups on the structure of finite groups is investigated.
12 citations
Journal Article•
TL;DR: According to desired utility function theory, the paper Application of Desired Utility Function Theory (DUF) to Library Administration as mentioned in this paper was the first paper to apply DUF to library administration.
Abstract: According to desired utility function theory,the paper Application of Desired utility function theory to Library Administration.
3 citations
Journal Article•
TL;DR: A graph G is called integral if its spectrum consists entirely of integers Cocktail party graphs CP(n)=K2n-nK2 and complete bipartite graphs Ka,a all are integral graphs.
Abstract: Let G be a simple graph and let ■ denote its complementA graph G is called integral if its spectrum consists entirely of integers Cocktail party graphs CP(n)=K2n-nK2 and complete bipartite graphs Ka,a all are integral graphs[1] This paper determines all the integral graphs of ■
2 citations
Journal Article•
TL;DR: Pulse vaccination in the SIR epidemic model with vertical transmission is studied in this article, where the global stability of an infection-free periodic solution and Basic reproductive number are proved by numerical simulations.
Abstract: Pulse Vaccination in the SIR epidemic model with vertical transmission is studied in this paper.For Proportional Vaccination model it is proved the global stability of an infection-free periodic solution and Basic reproductive number.Our theoretical results are confirmed by numerical simulations.
2 citations
Journal Article•
TL;DR: In this article, a significant refinement of Hardy-Hilbert's integral inequality can be built by introducing exponential integral with parameter t and by using Bernoulli's inequality as well as improved H ǫlder's inequality.
Abstract: It is shown that a significant refinement of Hardy-Hilbert's integral inequality can be built by introducing exponential integral with parameter t and by using Bernoulli's inequality as well as improved Hlder's inequalityIn particular,for case p=2,a sharp result of the classical Hilbert inequality is obtained
2 citations
Journal Article•
TL;DR: In this article, the authors discuss the parameter estimation of uniform distribution in a circle and obtain the estimator and confidence interval of the radius of a circle based on the order statistic.
Abstract: We discuss the parameter estimation of uniform distribution in a circle.Based on the order statistic,we obtain the estimator and confidence interval of the radius.
2 citations
Journal Article•
TL;DR: A practical numeric method to extract all real roots of polynomial equation on the basis of Bisection Method and the bound of the root of poynomial equation and Sturm theorem is presented.
Abstract: On the basis of Bisection Method and the bound of the root of polynomial equation and Sturm theorem,the paper present a practical numeric method to extract all real roots of polynomial equation.
2 citations
Journal Article•
TL;DR: The authors derived the estimation of parameters of three-parameter Weibull distribution based on grouped data and showed the feasibility of this method by Monte-Carlo simulation, and showed that this method can be used to estimate the parameters of the Weibell distribution.
Abstract: We derive the estimation of parameters of three-parameter Weibull distribution based on grouped dataThereafter we show the feasibility of this method by Monte-Carlo simulation
1 citations
Journal Article•
TL;DR: In this paper, the existence and nonexistence theorems on positive solutions for singular BVP of fourth order differential systems were established by using the fixed point theorem of cone expansion and cone compression and upper and lower solution.
Abstract: The existence and nonexistence theorems on positive solutions are established for singular BVP of fourth order differential system by using the fixed point theorem of cone expansion and cone compression and upper and lower solution.
1 citations
Journal Article•
TL;DR: Wang et al. as discussed by the authors set up a unascertained comprehensive evaluation model on index distinguish weight, and applied the model further to evaluate the water pollution of Fuyang River comprehensively.
Abstract: According to the analysis of the contribution that the index supplied for distinguish sort of the samples,distinguishing weight of the index was defined.This paper sets up a unascertained comprehensive evaluation model on index distinguish weight,we applied the model further to evaluate the water pollution of Fuyang River comprehensively.
Journal Article•
TL;DR: In this article, a comparison of research of mathematics education in University in China and United States and point out the shortcoming on mathematics education education in university is presented, and they prove that mathematics education is core of higher education.
Abstract: We prove that mathematics education in unversity is core of higher education.Mathematics education is quality education essentially.Because mathematics has applied natural sciences and social sciences.Mathematics is base of professional knowledge of science department and engineering course in university.Probe into importance on studying mathematics education in unversity.Comparisons of Research of Mathematics Education in University in China and United States and point our shortcoming on mathematics education in university.Put forward our task and aim on mathematics education in university.
Journal Article•
TL;DR: In this article, the sufficient and necessary conditions of the heterogeneous linear equation phenomenon were discussed, and it was proved that two linear equation groups have a not zero public solution, and provided a general form of the non-zero public solution.
Abstract: This paper has anlyzed the sufficient and necessary conditions of the phenomenon—two homogeneous linear equation groups have a not zero public solution,and provided a general form of the not zero public solution This paper also discussed one sufficient and necessary condition of the same one solution which two linear equation groups have,the number of linear irrelevant solutions and the expression formula of general solution to heterogeneous linear equationsConsequently,it can be proved that there exists the sufficient and necessary condtions of the phenomenon—heterogeneous linear equation groups have a solution
Journal Article•
TL;DR: In this paper, a new subclass Bp,λ,α(A,B,C,D) of analytic functions to p-valent is introduced, and the sobrdination relation, inclusion rclations, distortion theorems and the inequality properties are discussed by using differential subordination method.
Abstract: A new subclass Bp,λ,α(A,B,C,D) of analytic functions to p-valent is introduced. The sobrdination relation, inclusion rclations, distortion theorems and the inequality properties are discussed by using differential subordination method. The results obtained generalize the related works of some authors.
Journal Article•
TL;DR: It is the trend for part of the teaching content of higher education being talked in the lessons of middle school,we have to make impersonal estimation of the influence to the advance mathematics; and the innovation for advanced mathematics should be based on the principle of innovation of teaching material; focus on student and discovery and probing into the truth as discussed by the authors.
Abstract: It is the trend for part of the teaching content of higher education being talked in the lessons of middle school,we have to make impersonal estimation of the influence to the advance mathematics;and the innovation for advanced mathematics should be based on the principle of innovation of teaching material;focus on student and discovery and probing into the truth.
Journal Article•
TL;DR: A general decomposition law for this system is established on condition that the server idle time and repair time is defined as generalized vacation.
Abstract: An M/G/1 retrial queue with second optional service and starting failures is considered.We assume that customers arrive to the system according to a Poisson process with rate λ.Assuming that only the customer at the head of the orbit has priority access to the server,and the retrial time is an arbitrary distribution.All demand the first "essential" service,whereas only some of them demand the second "optional" service.The necessary and sufficient condition for the system stability is derived through embedded Markov chain.The steady-state distributions of the number of customers in the system and orbit are obtained along with method of supplementary variables.We also derived the probability that the server is in idle when retrial,the probability that there is no one in orbit and other performance measures.A general decomposition law for this system is established on condition that the server idle time and repair time is defined as generalized vacation.
Journal Article•
TL;DR: In this paper, a method for calculating the illuminance produced by a line source and reflected by a parabola is developed, and the optimal design of a headlight is well solved and the correct relation between the power and the line length is presented.
Abstract: A method for calculating the illuminance produced by a line source and reflected by a parabola is developed in this paperAs a simplified example,the problme A in CUMCM 2002,the optimal design of a line source headlight,is well solved and the correct relation between the power and the line length is presented
Journal Article•
TL;DR: This paper determines a constant M0 and proves that the big M method is convergent to an optimal solution of the primal problem when MM0.
Abstract: In the simplex method of linear programming,there is a big M method(the penalty factor method) for finding an initial feasible basis.The current textbooks of operations research only explain that the big M method is efficient when M is large enough,and never give precise evaluation to the parameter M.This paper determines a constant M0 and proves that the big M method is convergent to an optimal solution of the primal problem when MM0.