Two Optimal Inequalities Related to the Sándor-Yang Type Mean and One-parameter Mean

In this paper, we establish two optimal the double inequalities for Sandor- Yang type mean and one-parameter mean.

An Optimal Double Inequality among the One-Parameter, Arithmetic and Geometric Means

In the present paper, we answer the question: for 0a what are the greatest value p(a) and the least value q(a) such that the double inequality Jp(a,b)aA(a,b)+ (1-a)G(a,b)Jq(a,b) holds for all a,b>0 with a is not equal to?b ?

An Optimal Inequality for One-Parameter Mean

In the present paper, we answer the question: for 0 what are the greatest value p(a) and the least value q(a) such that the inequality. For more information about abstract,please download the PDF file.

APPLICATION OF ONE-PARAMETER GROUPS OF TRANSFORMATION IN MECHANICS

In this paper,including some partial differential equations with a number of independent variables, which can he reduced by the infinitesimal form of the group, we obtain the theory of similarity transformation and its application of the second order nonlinear partial differential equations which have two independent variables and two dependent variables in mechanics.

ONE-PARAMETER FINITE DIFFERENCE METHODS AND THEIR ACCELERATED SCHEMES FOR SPACE-FRACTIONAL SINE-GORDON EQUATIONS WITH DISTRIBUTED DELAY

This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed delay.For 1D problems,we construct a kind of oneparameter finite difference(OPFD)method.It is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and space.In implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD method.For 2D problems,we develop another kind of OPFD method.For such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG scheme.In particular,we prove that ADI scheme can arrive at second-order accuracy in time and space.With some numerical experiments,the computational effectiveness and accuracy of the methods are further verified.Moreover,for the suggested methods,a numerical comparison in computational efficiency is presented.

Maximum Likelihood Estimator of the Parameter for a Continuous One-Parameter Exponential Family Under the Optimal Ranked Set Sampling

This paper studies a maximum likelihood estimator(MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling(RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed(iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice,are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.

Best Constants for Moser-Trudinger Inequalities,Fundamental Solutions and One-Parameter Representation Formulas on Groups of Heisenberg Type

We derive the explicit fundamental solutions for a class of degenerate(or singular)one- parameter subelliptic differential operators on groups of Heisenberg(H)type.This extends the result of Kaplan for the sub-Laplacian on H-type groups,which in turn generalizes Folland's result on the Heisenberg group.As an application,we obtain a one-parameter representation formula for Sobolev functions of compact support on H-type groups.By choosing the parameter equal to the homogeneous dimension Q and using the Mose-Trudinger inequality for the convolutional type operator on stratified groups obtained in[18].we get the following theorem which gives the best constant for the Moser- Trudiuger inequality for Sobolev functions on H-type groups. Let G be any group of Heisenberg type whose Lie algebra is generated by m left invariant vector fields and with a q-dimensional center.Let Q=m+2q.Q'=Q-1/Q and Then. with A_Q as the sharp constant,where ▽G denotes the subelliptic gradient on G. This continues the research originated in our earlier study of the best constants in Moser-Trudinger inequalities and fundamental solutions for one-parameter subelliptic operators on the Heisenberg group [18].

Efficiency and superefficiency in one-parameter two-sided truncated distribution families

whereθis an unknown parameter, φ(θ) is a continuous differentiable function such that θ【φ(θ), s(θ)=dφ(θ)/dθ】0, θ∈R, and f(x;θ) is a positive continuous density func-tion on [θ,φ(θ)]. The one-parameter two-sided truncated distribution families (1)

Favored one proton radioactivity within a one-parameter model

In the present work,a phenomenological one-parameter model(OPM)based on the WentzelKramers-Brillouin(WKB)theory is applied to study the favored one proton radioactivity(the orbital angular momentum l taken away by the emitted proton is equal to zero)half-lives.The calculated results can reproduce the experimental data well within a factor of~3.In addition,we extend the OPM to predict the half-lives of possible favored one proton radioactivity nuclei whose decay is energetically allowed or observed but not quantified in NUBASE2020.For comparison,a universal decay law of one proton radioactivity(UDLP)is also used.It is obviously found that our predicted results are close to the ones using UDLP.The predictions are helpful for searching for the new nuclides with favored one proton radioactivity.

SPECTRA OF COMPOSITION GROUPS ON THE WEIGHTED DIRICHLET SPACE OF THE UPPER HALF-PLANE

We prove that the group of weighted composition operators induced by continuous automorphism groups of the upper half plane U is strongly continuous on the weighted Dirichlet space of U,Dα(U).Further,we investigate when they are isometries on Dα(U).In each case,we determine the semigroup properties while in the case that the induced composition group is an isometry,we apply similarity theory to determine the spectral properties of the group.

Techniques for searching first integrals by Lie group and application to gyroscope system

In the paper, the methods of finding first integrals of an autonomous system using one-parameter Lie groups are discussed. A class of nontrivial one-parameter Lie groups admitted by the classical gyroscope system is found, and based on the properties of first integral determined by the one-parameter Lie group, the fourth first integral of the gyroscope system in Euler case, Lagrange case and Kovalevskaya case can be obtained in a uniform idea. An error on the fourth first integral in general Kovalevskaya case (A=B=2C,zG=0), which appeared in literature is found and corrected.

Effect of Temperature on the Dynamic Recrystallization of AZ31 Alloy with Pulse Current

The tensile tests of AZ31 magnesium alloy were carried out under room temperature, 100, 150 and 200 ℃ with andwithout pulse current. The effect of temperature on dynamic recrystallization （DRX） of AZ31 alloy was studied at differentconditions. One-parameter approach was used to analyze the critical conditions of DRX, the critical stress was obtainedunder different temperatures, and the related results were validated by metallography observation. The results showed thatDRX of AZ31 alloy occurred at 200 ℃ without pulse current. When pulse current with 150 Hz/50 V parameter wasapplied at room temperature, DRX occurred, while DRX was not completed until temperature over 150 ~C. With theanalysis result of critical conditions of DRX based on one-parameter approach, the relationship between critical stress andpeak stress obtained in this present study is σc = （0.746-0.773）σp.