arXiv subjects
Publications and source records attributed to Li Yin.
In this paper, we prove logarithmically complete monotonicity properties of certain ratios of the $k$-gamma function. As a consequence, we deduce some inequalities involving the $k$-gamma and $k$-trigamma functions.
In this paper, authors study the generalized complete $(p,q)$-elliptic integrals of the first and the second kind as an application of generalized trigonometric functions with two parameters, and establish the Turán type inequalities of these functions.
Motivated by the work of Alzer and Richards \cite{ar}, here authors study the monotonicity and convexity properties of the function $$Δ_{p,q} (r) = \frac{{E_{p,q}(r) - \left( {r'} \right)^p K_{p,q}(r) }}{r^p } - \frac{{E'_{p,q}(r) - r^p K'_{p,q}(r) }}{{\left( {r'} \right)^p }},$$ where $K_{p,q}$ and $E_{p,q}$ denote the complete $(p,q)$- elliptic integrals of the first and the second kind, respectively.
Motivated by the work of Anderson, Vamanamurthy and Vuorinen \cite{avv}, in this paper authors study the log-convexity and log-concavity of Power mean, Identric mean, weighted Power mean, Lehmer mean, Modified Alzer mean, and establish the relation of these means with each other.
We investigate the existence and multiplicity of solutions to the following $p(x)$-Laplacian problem in $\mathbb{R}^{N}$ via critical point theory \begin{equation*} \left\{ \begin{array}{l} -\bigtriangleup _{p(x)}u+V(x)\left\vert u\right\vert ^{p(x)-2}u=f(x,u),\text{ in } \mathbb{R}^{N}, \\ u\in W^{1,p(\cdot )}(\mathbb{R}^{N}). \end{array} \right. \end{equation*} We propose a new set of growth conditions which matches the variable exponent nature of the problem. Under this new set of assumptions, we manage to verify the Cerami compactness condition. Therefore, we succeed in proving the existence of multiple solutions to the above problem without the well-known Ambrosetti--Rabinowitz type growth condition. Meanwhile, we could also characterize the pointwise asymptotic behaviors of these solutions. In our main argument, the idea of localization, decomposition of the domain, regularity of weak solutions and comparison principle are crucial ingredients among others.
We investigate the following Dirichlet problem with variable exponents: \begin{equation*} \left\{ \begin{array}{l} -\bigtriangleup _{p(x)}u=λα(x)\left\vert u\right\vert ^{α(x)-2}u\left\vert v\right\vert ^{β(x)}+F_{u}(x,u,v),\text{ in }Ω, \\ -\bigtriangleup _{q(x)}v=λβ(x)\left\vert u\right\vert ^{α(x)}\left\vert v\right\vert ^{β(x)-2}v+F_{v}(x,u,v),\text{ in }Ω, \\ u=0=v,\text{ on }\partial Ω. \end{array} \right. \end{equation*} We present here, in the system setting, a new set of growth conditions under which we manage to use a novel method to verify the Cerami compactness condition. By localization argument, decomposition technique and variational methods, we are able to show the existence of multiple solutions with constant sign for the problem without the well-known Ambrosetti--Rabinowitz type growth condition. More precisely, we manage to show that the problem admits four, six and infinitely many solutions respectively.
In this paper, we provide some new generalizations of Feng Qi type integral inequalities on time scales by using elementary analytic methods.
Suppose that a sequence of treatments are assigned to influence an outcome of interest that occurs after the last treatment. Between treatments there exist time-dependent covariates that may be posttreatment variables of the earlier treatments and confounders of the subsequent treatments. In this article, we develop a parametric approach to inference of the causal effect of the treatment sequence on the outcome called the sequential causal effect. We construct a point parametrization for the conditional distribution of an outcome given all treatments and time-dependent covariates, in which the point parameters of interest are the point effects of treatments considered as single-point treatments. We (1) identify net effects of treatments by point effects of treatments, (2) express patterns of net effects of treatments by constraints on point effects of treatments, and (3) show that all sequential causal effects are determined by net effects of treatments. Accordingly we (1) estimate net effects of treatments through point effects of treatments by maximum likelihood, (2) improve the estimation by constraints on point effects of treatments and assignment conditions of treatments, and (3) use the estimates of net effects of treatments to obtain those of sequential causal effects. As a result, we obtain unbiased consistent maximum-likelihood estimates of sequential causal effects even for long treatment sequences. For illustration of our method, we study the causal effects of various sequences of recreational drugs on the CD4 count among HIV patients.
In observational studies for the interaction between exposures on dichotomous outcome of a population, one usually uses one parameter of a regression model to describe the interaction, leading to one measure of the interaction. In this article, we use the conditional risk of outcome given exposures and covariates to describe the interaction and obtain five different measures for the interaction in observational studies, i.e. difference between the marginal risk differences, ratio of the marginal risk ratios, ratio of the marginal odds ratios, ratio of the conditional risk ratios, and ratio of the conditional odds ratios. By using only one regression model for the conditional risk of outcome given exposures and covariates, we obtain the maximum-likelihood estimates of all these measures. By generating approximate distributions of the maximum-likelihood estimates of these measures, we obtain interval estimates of these measures. The method is presented by studying the interaction between a therapy and the environment on eradication of Helicobacter pylori among Vietnamese children.
In observational studies with dichotomous outcome of a population, researchers need to present the effects of exposures and interaction between the exposures jointly in order to learn the relationship between the exposure effects and the interaction. In this article we study point and interval estimation of exposure effects and the interaction based on logistic model, where the exposure effects are measured by risk differences while the interaction is measured by difference between risk differences. Using approximate normal distribution of the maximum-likelihood (ML) estimate of the model parameters, we obtain approximate non-normal distribution of the ML estimate of the exposure effects and the interaction. Using the obtained distribution, we obtain point estimate and confidence region of (exposure effect, interaction) as well as point estimate and confidence interval of the interaction when the ML estimate of an exposure effect falls into specified range. Our maximum-likelihood-based approach provides a simple but reliable method of interval estimation of exposure effects and the interaction.
In this article we estimate confidence regions of the common measures of (baseline, treatment effect) in observational studies, where the measure of baseline is baseline risk or baseline odds while the measure of treatment effect is odds ratio, risk difference, risk ratio or attributable fraction, and where confounding is controlled in estimation of both baseline and treatment effect. To avoid high complexity of the normal approximation method and the parametric or non-parametric bootstrap method, we obtain confidence regions for measures of (baseline, treatment effect) by generating approximate distributions of the ML estimates of these measures based on one logistic model.
In this paper, authors study the convexity and concavity properties of real-valued function with respect to the classical means, and prove a conjecture posed by Bruce Ebanks in \cite{e}.
In sequential causal inference, one estimates the causal net effect of treatment in treatment sequence on an outcome after last treatment in the presence of time-dependent covariates between treatments, improves the estimation by the untestable assumption of strongly ignorable treatment assignment, and obtains consistent but non-genuine likelihood-based estimate. In this article, we introduce the net effect of treatment as parameter for the conditional distribution of outcome given all treatments and time-dependent covariates and show that it is equal to the causal net effect of treatment under the assumption of strongly ignorable treatment assignment. As a result, we can estimate the net effect of treatment and evaluate its causal interpretation in two separate steps. The first step is fucus of this article while the second step can be accomplished by usual sensitivity analyses. We construct point parametrization for the conditional outcome distribution in which the parameters of interest are the point effects of single-point treatments. With point parametrization and without the untestable assumption, we estimate the net effect of treatment by maximum likelihood, improve the estimation by testable pattern of the net effect of treatment, and obtain unbiased consistent maximum-likelihood estimate for the net effect of treatment with finite-dimensional pattern.
In this paper we study the convexity and concavity properties of generalized trigonometric and hyperbolic functions in case of Logarithmic mean.
In this paper we prove the conjecture posed by Klén et al. in \cite{kvz}, and give optimal inequalities for generalized trigonometric and hyperbolic functions.
In the paper, by using Lupaş integral inequality, the authors find some new inequalities for the complete elliptic integrals of the first and second kinds. These results improve some known inequalities.
In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.