We prove that the Gini mean values S（a,b; x,y） are Schur harmonic convex with respect to （x,y）∈（0,∞）×（0,∞） if and only if （a, b） ∈{（a, b）：a≥0,a ≥ b,a＋b＋1≥0}∪{（a,b）：b≥0,b≥a,a＋b＋1≥0} ...We prove that the Gini mean values S（a,b; x,y） are Schur harmonic convex with respect to （x,y）∈（0,∞）×（0,∞） if and only if （a, b） ∈{（a, b）：a≥0,a ≥ b,a＋b＋1≥0}∪{（a,b）：b≥0,b≥a,a＋b＋1≥0} and Schur harmonic concave with respect to （x,y） ∈ （0,∞）×（0,∞） if and only if （a,b）∈{（a,b）：a≤0,b≤0,a｜b｜1≤0}.展开更多
In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.
In this paper, we have suggested a new technique to transform multi-objective linear programming problem (MOLPP) to the single objective linear programming problem by using Harmonic mean for values of function and an ...In this paper, we have suggested a new technique to transform multi-objective linear programming problem (MOLPP) to the single objective linear programming problem by using Harmonic mean for values of function and an algorithm is suggested for its solution, the computer application of algorithm has been demonstrated by solving some numerical examples. We have used some other techniques, such as (sen, arithmetic mean, median) to solve the same problems, the results in Table 3 indicate that the new technique in general is promising.展开更多
Two kinds of parameter estimation methods (I) and (II) of combining forecasting based on harmontic mean are proposed and compared through a lot of simulation forecasting examples. A very helpful conclusion is obtained...Two kinds of parameter estimation methods (I) and (II) of combining forecasting based on harmontic mean are proposed and compared through a lot of simulation forecasting examples. A very helpful conclusion is obtained, which can lay solid foundations for correct application of the above methods.展开更多
Closed form expressions for the PDF and MGF of the harmonic mean of two independent exponential variates are cited and derived, and then applied to study the performance of cellular multi-node and dual-hop cooperative...Closed form expressions for the PDF and MGF of the harmonic mean of two independent exponential variates are cited and derived, and then applied to study the performance of cellular multi-node and dual-hop cooperative communication systems with non-regenerative relays over flat Rayleigh fading channels. We derive the probability density function (PDF) and asymptotic symbol error rate (SER) expression with MRC scheme. Then we use Matlab to simulate the performance.展开更多
In this paper, we first introduce the concept ＂harmonically convex functions＂ in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Final...In this paper, we first introduce the concept ＂harmonically convex functions＂ in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Finally, some applications to special mean are shown.展开更多
Since the dead zone phenomenon occurs in electro-hydraulic servo system, the output of the system corresponding to a sinusoidal input contains higher harmonic besides the fundamental input, which causes harmonic disto...Since the dead zone phenomenon occurs in electro-hydraulic servo system, the output of the system corresponding to a sinusoidal input contains higher harmonic besides the fundamental input, which causes harmonic distortion of the output signal. The method for harmonic cancellation based on adaptive filter is proposed. The task is accomplished by generating reference signals with frequency that should be eliminated from the output. The reference inputs are weighted by the adaptive filter in such a way that it closely matches the harmonic. The output of the adaptive filter is a harmonic replica and is injected to the fundamental signal such that the output harmonic is cancelled leaving the desired signal alone, and the total harmonic distortion （THD） is greatly reduced. The weights of filter are adjusted on-line according to the control error by using least-mean-square （LMS） algorithm. Simulation results performed with a hydraulic system demonstrate the efficiency and validity of the proposed adaptive feed-forward compensator （AFC） control scheme展开更多
This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+(（n-2）/2)u =(（n-2）/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is...This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+(（n-2）/2)u =(（n-2）/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is a function on S;and ε is a small positive parameter. We construct solutions of the subcritical equation(P;) which blow up at one critical point of K. We give also a sufficient condition on the function K to ensure the nonexistence of solutions for(P;) which blow up at one point. Finally, we prove a nonexistence result of single peaked solutions for the supercritical equation(P;).展开更多
We prove a Harnack inequality for positive harmonic functions on graphs whichis similar to a classical result of Yau on Riemannian manifolds. Also, we prove a mean valueinequality of nonnegative subharmonic functions ...We prove a Harnack inequality for positive harmonic functions on graphs whichis similar to a classical result of Yau on Riemannian manifolds. Also, we prove a mean valueinequality of nonnegative subharmonic functions on graphs.展开更多
In this paper we will extend the well-known chain of inequalities involving the Pythagorean means, namely the harmonic, geometric, and arithmetic means to the more refined chain of inequalities by including the logari...In this paper we will extend the well-known chain of inequalities involving the Pythagorean means, namely the harmonic, geometric, and arithmetic means to the more refined chain of inequalities by including the logarithmic and identric means using nothing more than basic calculus. Of course, these results are all well-known and several proofs of them and their generalizations have been given. See [1-6] for more information. Our goal here is to present a unified approach and give the proofs as corollaries of one basic theorem.展开更多
The purpose of this paper is to provide a direct proof on the fact that the geometric-harmonic mean of any two positive numbers can be calculated by a first complete elliptical integral, and then to give new character...The purpose of this paper is to provide a direct proof on the fact that the geometric-harmonic mean of any two positive numbers can be calculated by a first complete elliptical integral, and then to give new characterizations of some mean-values.展开更多
基金Supported by the NSFC (11071069)the NSF of Zhejiang Province (D7080080 and Y7080185)the Innovation Team Foundation of the Department of Education of Zhejiang Province (T200924)
文摘We prove that the Gini mean values S（a,b; x,y） are Schur harmonic convex with respect to （x,y）∈（0,∞）×（0,∞） if and only if （a, b） ∈{（a, b）：a≥0,a ≥ b,a＋b＋1≥0}∪{（a,b）：b≥0,b≥a,a＋b＋1≥0} and Schur harmonic concave with respect to （x,y） ∈ （0,∞）×（0,∞） if and only if （a,b）∈{（a,b）：a≤0,b≤0,a｜b｜1≤0}.
基金Supported by National Natural Science Foundation of China(Grant Nos.11801006 and 12071489).
文摘In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.
文摘In this paper, we have suggested a new technique to transform multi-objective linear programming problem (MOLPP) to the single objective linear programming problem by using Harmonic mean for values of function and an algorithm is suggested for its solution, the computer application of algorithm has been demonstrated by solving some numerical examples. We have used some other techniques, such as (sen, arithmetic mean, median) to solve the same problems, the results in Table 3 indicate that the new technique in general is promising.
文摘Two kinds of parameter estimation methods (I) and (II) of combining forecasting based on harmontic mean are proposed and compared through a lot of simulation forecasting examples. A very helpful conclusion is obtained, which can lay solid foundations for correct application of the above methods.
文摘Closed form expressions for the PDF and MGF of the harmonic mean of two independent exponential variates are cited and derived, and then applied to study the performance of cellular multi-node and dual-hop cooperative communication systems with non-regenerative relays over flat Rayleigh fading channels. We derive the probability density function (PDF) and asymptotic symbol error rate (SER) expression with MRC scheme. Then we use Matlab to simulate the performance.
基金The Doctoral Programs Foundation(20113401110009)of Education Ministry of ChinaNatural Science Research Project(2012kj11)of Hefei Normal University+1 种基金Universities Natural Science Foundation(KJ2013A220)of Anhui ProvinceResearch Project of Graduates Innovation Fund(2014yjs02)
文摘In this paper, we first introduce the concept ＂harmonically convex functions＂ in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Finally, some applications to special mean are shown.
文摘Since the dead zone phenomenon occurs in electro-hydraulic servo system, the output of the system corresponding to a sinusoidal input contains higher harmonic besides the fundamental input, which causes harmonic distortion of the output signal. The method for harmonic cancellation based on adaptive filter is proposed. The task is accomplished by generating reference signals with frequency that should be eliminated from the output. The reference inputs are weighted by the adaptive filter in such a way that it closely matches the harmonic. The output of the adaptive filter is a harmonic replica and is injected to the fundamental signal such that the output harmonic is cancelled leaving the desired signal alone, and the total harmonic distortion （THD） is greatly reduced. The weights of filter are adjusted on-line according to the control error by using least-mean-square （LMS） algorithm. Simulation results performed with a hydraulic system demonstrate the efficiency and validity of the proposed adaptive feed-forward compensator （AFC） control scheme
基金the Deanship of Scientific Research at Taibah University on material and moral support in the financing of this research project
文摘This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+(（n-2）/2)u =(（n-2）/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is a function on S;and ε is a small positive parameter. We construct solutions of the subcritical equation(P;) which blow up at one critical point of K. We give also a sufficient condition on the function K to ensure the nonexistence of solutions for(P;) which blow up at one point. Finally, we prove a nonexistence result of single peaked solutions for the supercritical equation(P;).
基金supported by the National Science Foundation of China(11671401)
文摘We prove a Harnack inequality for positive harmonic functions on graphs whichis similar to a classical result of Yau on Riemannian manifolds. Also, we prove a mean valueinequality of nonnegative subharmonic functions on graphs.
文摘In this paper we will extend the well-known chain of inequalities involving the Pythagorean means, namely the harmonic, geometric, and arithmetic means to the more refined chain of inequalities by including the logarithmic and identric means using nothing more than basic calculus. Of course, these results are all well-known and several proofs of them and their generalizations have been given. See [1-6] for more information. Our goal here is to present a unified approach and give the proofs as corollaries of one basic theorem.
文摘The purpose of this paper is to provide a direct proof on the fact that the geometric-harmonic mean of any two positive numbers can be calculated by a first complete elliptical integral, and then to give new characterizations of some mean-values.
