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This paper discusses the estimation of average treatment effects in observational causal inferences. By employing a working propensity score and two working regression models for treatment and control groups, Robins et al. (1994, 1995) introduced the augmented inverse probability weighting (AIPW) method for estimation of average treatment effects, which extends the inverse probability weighting (IPW) method of Horvitz and Thompson (1952); the AIPW estimators are locally efficient and doubly robust. In this paper, we study a hybrid of the empirical likelihood method and the method of moments by employing three estimating functions, which can generate estimators for average treatment effects that are locally efficient and doubly robust. The proposed estimators of average treatment effects are efficient for the given choice of three estimating functions when the working propensity score is correctly specified, and thus are more efficient than the AIPW estimators. In addition, we consider a regression method for estimation of the average treatment effects when working regression models for both the treatment and control groups are correctly specified; the asymptotic variance of the resulting estimator is no greater than the semiparametric variance bound characterized by the theory of Robins et al. (1994, 1995). Finally, we present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the family of quotients of internally quasicontinuous functions. Moreover, we study cardinal invariants related to quotients in the case of internally quasicontinuous functions and the complement of this family. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of decomposability in the space of Henstock-Kurzweil-Pettis integrable (for short HKP-integrable) functions. We show representations theorems for decomposable sets of HKP-integrable or Henstock integrable functions, in terms of the family of selections of suitable multifunctions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of analytic functions associated with Mittag-Leffler fuction in the open unit disk. Several properties of functions belonging to this class are derived. [ABSTRACT FROM AUTHOR]

In this paper, we study differential equations arising from the generating functions of generalized degenerate tangent polynomials. We give explicit identities for the generalized degenerate tangent polynomials arising from differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the family of quotients of internally quasicontinuous functions. Moreover, we study cardinal invariants related to quotients in the case of internally quasicontinuous functions and the complement of this family. [ABSTRACT FROM AUTHOR]

Let L be a degree-2L-function associated to a Maass cusp form. We explore an algorithm that evaluates t values of L on the critical line in time O(t1+𝜖). We use this algorithm to rigorously compute an abundance of consecutive zeros and investigate their distribution. [ABSTRACT FROM AUTHOR]

A function $f:X\rightarrow X$ determines a topology $P(f)$ on $X$ by taking the closed sets to be those sets $A\subseteq X$ with $f(A)\subseteq A$. The topological space $(X,P(f))$ is called a functionally Alexandroff space. We completely characterise the homogeneous functionally Alexandroff spaces. [ABSTRACT FROM AUTHOR]

We consider the localization problem for control robust invariant compact sets of a continuous dynamical system with perturbation and control. The solution method generalizes the functional localization method, which was earlier used in localization problems for continuous autonomous and nonautonomous systems as well as in discrete systems. The properties of the corresponding localizing sets are described. [ABSTRACT FROM AUTHOR]

We study the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley g-function and -function on the generalized Morrey spaces for , where Φ is a growth function on satisfying the doubling condition. The boundedness of commutators generated by functions and intrinsic square functions is also obtained. [ABSTRACT FROM AUTHOR]

In [`Robin function and conformal welding - A new proof of the existence', submitted] a new proof of the existence of the Robin function is given using conformal welding. This proof is essentially based on the simply connected case and a conformal mapping which maps the domain onto a complement of a disk and a system of radial spires. The aim of this note is to show that this proof also has a wider meaning, namely that this mapping is the unique solution of extremal problems, which minimizes the length or the diameter of a subset of the boundary curve. As a consequence we obtain sharp inequalities for the Robin capacity and the logarithmic capacity. [ABSTRACT FROM AUTHOR]