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result(s) for
"Tie-Hong, Zhao"
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Quadratic transformation inequalities for Gaussian hypergeometric function
In the article, we present several quadratic transformation inequalities for Gaussian hypergeometric function and find the analogs of duplication inequalities for the generalized Grötzsch ring function.
Journal Article
Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means
In the article, we present the best possible parameters α1, β1, α2, β2 ∈ ℝ and α3, β3 ∈ [1/2, 1] such that the double inequalitiesα1C(a,b)+(1−α1)A(a,b) 0 with a ≠ b, and provide new bounds for the complete elliptic integral of the second kind, where A(a, b) = (a + b)/2 is the arithmetic mean, Q(a,b)=a2+b2/2 $\\begin{array}{}\\displaystyleQ(a, b)=\\sqrt{\\left(a^{2}+b^{2}\\right)/2}\\end{array}$is the quadratic mean, C(a, b) = (a2 + b2)/(a + b) is the contra-harmonic mean, C(p; a, b) = C[pa + (1 – p)b, pb + (1 – p)a] is the one-parameter contra-harmonic mean and T3(a,b)=(2π∫0π/2a3cos2θ+b3sin2θdθ)2/3 $\\begin{array}{}T_{3}(a,b)=\\Big(\\frac{2}{\\pi}\\int\\limits_{0}^{\\pi/2}\\sqrt{a^{3}\\cos^{2}\\theta+b^{3}\\sin^{2}\\theta}\\text{d}\\theta\\Big)^{2/3}\\end{array}$is the Toader mean of order 3.
Journal Article
A sharp double inequality involving generalized complete elliptic integral of the first kind
In the article, we establish a sharp double inequality involving the ratio of generalized complete elliptic integrals of the first kind, which is the improvement and generalization of some previously known results.
Journal Article
On some refinements for inequalities involving zero-balanced hypergeometric function
In the article, we present an elegant double inequality for the ratio of the zero-balanced hypergeometric functions, which improve and refine some previously known results and also give a positive answer the question by proposed by Ismail.
Journal Article
On approximating the quasi-arithmetic mean
In this article, we prove that the double inequalities α1[7C(a,b)16+9H(a,b)16]+(1−α1)[3A(a,b)4+G(a,b)4]0\\(a, b>0\\) with a≠b\\(a b\\) if and only if α1≤3/16=0.1875\\(_1 3/16=0.1875\\), β1≥64/π2−6=0.484555…\\(_164/^2-6= 0.484555\\), α2≤3/16=0.1875\\(_23/16=0.1875\\) and β2≥(5log2−log3−2logπ)/(log7−log6)=0.503817…\\(_2(52-3-2 )/(7-6)= 0.503817\\), where E(a,b)=(2π∫0π/2acos2θ+bsin2θdθ)2\\(E(a,b)= (2ınt^/2_0a^2 +b^2\\,d )^2\\), H(a,b)=2ab/(a+b)\\(H(a,b)=2ab/(a+b)\\), G(a,b)=ab\\(G(a,b)=ab\\), A(a,b)=(a+b)/2\\(A(a,b)=(a+b)/2\\) and C(a,b)=(a2+b2)/(a+b)\\(C(a,b)=(a^2+b^2)/(a+b)\\) are the quasi-arithmetic, harmonic, geometric, arithmetic and contra-harmonic means of a and b, respectively.
Journal Article
Monotonicity properties and bounds involving the two-parameter generalized Grötzsch ring function
In the article, we present several new monotonicity properties and bounds involving the generalized Grötzsch ring functions μa,b in the theory of Ramanujan’s generalized modular equation for 0
Journal Article
A sharp lower bound for the weighted Lehmer mean involving complete p-elliptic integrals
In the article, we provide a sharp lower bound for the weighted Lehmer mean of the complete p-elliptic integrals of the first and second kinds, which is the extension of the previous results for complete p-elliptic integrals.
Journal Article
Sharp power-type Heronian and Lehmer means inequalities for the complete elliptic integrals
In the article, we prove that the inequalities Hp(K(r),ℰ(r))>π2,Lq(K(r),ℰ(r))>π2 hold for all r ∈ (0, 1) if and only if p ≥ −3/4 and q ≥ −3/4, where Hp(a, b) and Lq(a, b) are respectively the p-th power-type Heronian mean and q-th Lehmer mean of a and b, and K(r) and ℰ(r) are respectively the complete elliptic integrals of the first and second kinds.
Journal Article
Experimental and Theoretical Studies of Bidirectional Variable Curvature Friction Pendulum Bearing
In this study, to satisfy the base isolation demand of large-scale building structures under different earthquake records, a new bidirectional variable curvature friction pendulum bearing (BD-VCFPB) is proposed. The VCFPB is designed in detail based on the basic principle of a friction pendulum system. Moreover, the sliding interface function, gap between the slider and the sliding interface, and polytetrafluoroethylene (PTFE) plate stress are studied. Finally, a dynamic cyclic test is conducted to study the influence of the slider size, contact pressure on the PTFE plate, and loading frequency on the hysteretic behavior of the VCFPB. The results indicate that the hysteretic curves of the horizontal force and the displacement are regular, symmetrical, stable, and full, and clearly reflect the variable curvature convex and concave characteristics and the excellent behavior of energy dissipation of the BD-VCFPB. The sliding friction coefficient varies significantly with the contact pressure on the PTFE plate and the loading frequency; however, it has little relation with the slider size. A hysteretic model is proposed based on the results of a unidirectional test, and it is in good agreement with the hysteretic curves of the horizontal force and the displacement from a bidirectional test.
Journal Article
Optimal Bounds for Neuman-Sándor Mean in Terms of the Convex Combinations of Harmonic, Geometric, Quadratic, and Contraharmonic Means
We present the best possible lower and upper bounds for the Neuman-Sándor mean in terms of the convex combinations of either the harmonic and quadratic means or the geometric and quadratic means or the harmonic and contraharmonic means.
Journal Article