Boosting is one of the important ensemble classifiers emerging in the past decade. [10] provides a statistical insight: AdaBoost can be viewed as a Newton-like updates minimizing exponential criterion. This powerful insight, however, does not address (1) whether the Newton update converges (2) whether the update procedure converge to the Bayes procedure if it does converge. Under a normal-normal setting, we cast the learning problem as a Bayesian minimization problem. It is shown that the Bayes procedure can be obtained via an iterative Newton update minimizing exponential criterion. In addition, the step sizes of AdaBoost are shown to be highly effective and lead to a one-step convergence. While our results based on strong distributional assumption, they require little conditions on the complexity of base learners nor regularization on step sizes or number of boosting iterations.

This paper is devoted to approximation of integrated semigroups in space and in time variables. The presentation is given in the abstract framework of discrete approximation scheme, which includes finite element methods, finite difference schemes and projection method.

Ishikawa and Halpern’s iterations are modified to prove the strong convergence problems of such iteration processes for uniformly Lipschitzian mappings which are relatively asymptotically nonexpansive in Banach spaces, which extend the result due to Matsushita and Takahashi [J. Approx. Theory, 134 (2005), 257–266] for relatively nonexpansive mappings, and also some recent results due to Martinez-Yanez and Xu [Nonlinear Anal., 64 (2006), 2400–2411], and Kim and Xu [Nonlinear Anal., 64 (2006), 1140–1152] for nonexpansive mappings and asymptotically nonexpansive mappings, respectively, which are considered in the Hilbert space frameworks.

The family of Euler-Halley type methods is extended for sections on Riemannian manifolds. Its convergence criterion is established under the assumption that the sections’ covariant derivatives satisfy a kind of Lipschitz condition. Applications to special cases such as the classical Kantorovich’s type condition, the $\gamma$-condition, Smale’s analysis condition are provided.

The work develops the approach proposed in 1982 by the author and V.Ya. Shirman for analysis of asymptotic stability of a linear differential equation in Banach space. It is shown that the method introduced in the mentioned above work allows also to prove the nonexistence of the fastest growing solution for a wide class of linear equations.

In this paper, we prove the existence of Hayman $T$ directions of meromorphic functions. To achieve our purpose, we establish a fundamental inequality about the Ahlfors-Shimizu characteristic for an angle and explain that the inequality is best possible in terms of the existence of Julia directions and Hayman $T$ directions.

In this paper, Carlitz’s $q$-operator and the auxiliary ones are applied to prove $q$-Christoffel-Darboux formulas and some Carlitz type generating functions. In addition, the technique of exponential operator decomposition to deduce $q$-Mehler’s formulas for Rogers-Szego and Hahn polynomials are shown.

In this paper we obtain some new characterizations for Bloch spaces on the unit ball of $\mathbb{C}^n$. These characterizations are new even in the unit disk.

Every indecomposable module over a generalized uniserial ring is uniserial, hence local. This motivates one to study rings R satisfying the condition (*): R is a right artinian ring such that every finitely generated, indecomposable right R-module is local. The rings R satisfying (*) have been recently studied by Singh and Al-Bleahed (2004), they have proved some results giving the structure of local right R-modules. In this paper some more structure theorems for local right R-modules are proved. Examples given in this paper show that a rich class of rings satisfying condition (*) can be constructed. Using these results, it is proved that any ring R satisfying (*) is such that mod-R is of finite representation type. It follows from a theorem by Ringel and Tachikawa that any right R-module is a direct sum of local modules. If M is right module over a right artinian ring such that any finitely generated submodule of any homomorphic image of M is a direct sum of local modules, it is proved that it is a direct sum of local modules. This provides an alternative proof for that any right module over a right artinian ring R satisfying (*) is a direct sum of local modules.

Here we obtain a Taylor’s expansion of the function $\rho(x,r) = \frac{|B(x,r)|}{|B(x,r) \cap \Omega|}$ for $r$ small and $x \in \partial \Omega$ where the boundary of domain $\Omega$ is assumed to be analytic. The coefficients are expressed as recurrence relation and it is proved yhat the series is odd.

For Banach spaces $X$ and $Y$, $\mathcal{F}_{C,\delta}(X,Y)$ is a large and meaningful extension of the family $L(X,Y)$ of linear operators. For classical Banach sequence spaces $l^{\infty}(X)$ and $l^{p}(Y)$ ($p \geq 1$) we find a characterization of the $l^{\infty}(X) − l^{p}(Y)$ transformation of matrices of mappings in $\mathcal{F}_{C,\delta}(X,Y)$.

We study the convergence of a proximal-like minimization algorithm using Bregman functions. We extend the convergence results by Censor and Zenios (1992) and by Chen and Teboulle (1993) by showing that the convergence of the algorithm is preserved in the presence of computational errors.

The paper is devoted to developing the viscosity-type approximation algorithm of finding efficient solutions to the vector optimization problem for a mapping between finite dimensional Hilbert spaces with respect to the partial order induced by a pointed closed convex cone. We prove that under some suitable conditions either the sequence generated by our method converges to an efficient solution or its cluster points belong to the set of all efficient solutions of this problem.

In this note we give a survey on results concerning the Siegel moduli spaces with parahoric level structure and the Kottwitz-Rapoport stratification, due to many people. We also report some aspects of KR strata in higher dimensional cases, which are obtained jointly with U. Görtz.

The main purpose of the paper is to prove the existence, uniqueness and smoothness with respect to time variable of the generalized $L_p$-solution of the first initial boundary value problem for higher hyperbolic systems in cylinders with non-smooth base. We also show that the smoothness with respect to time variable of the generalized $L_p$-solution is independent of the smoothness of base of cylinders.

This paper is concerned with the identification problems of unknown parameters in viscoelastic materials with long nonlinear memory. The unknown parameters are diffusion constants and kernels in nonlinear memory terms, and the identification of such parameters is studied by means of quadratic optimal control theory due to Lions [10]. The existence of optimal parameters is proved, and the necessary condition is established for distributive and terminal values observation by using the transposition method.

A class of stochastic networks with ring structure is considered in which the flow of information depends on a Markov chain. We find sufficient conditions such that the mean square differences between the even or odd or all units in the network will eventually tend to zero. Such probabilistic synchronization then leads to pattern formation in our networks. Although we have discussed only one or two colored patterns, it is hoped that our investigations will lead to more interesting patterns in stochastic networks in the future.

In this paper we introduce the concepts of well-posedness and generalized well-posedness for a system of equilibrium problems. We derive a metric characterization of well-posedness by considering the diameter of approximating solution set and a Furi-Vignoli type characterization of generalized well-posedness by considering the Kuratowski noncompactness measure of approximating solution set. Under suitable conditions, we prove that the well-posedness of a system of equilibrium problems is equivalent to the existence and uniqueness of its solution.

In this paper, we first define a $\mathbb{T}$-cone which is a unified version of several cones, namely, contingent cone, radial cone, $C$-tangent cone, Clarke tangent cone, $S$-cone, adjacent cone, etc. Then, we define the $\mathbb{T}$-epiderivative of a set-valued map which includes the contingent epiderivative, radial epiderivative, $S$-epiderivative, adjacent epiderivative etc. as special cases. We present several properties of such an epiderivative. The generalized vector $\mathbb{T}$-variational inequality problem is also considered. We provide necessary and sufficient conditions for a solution of a set optimization problem. Several existence results for solutions of set optimization problems and a generalized vector $\mathbb{T}$-variational inequality problem are given.

In recent years, various operators of fractional calculus (that is, calculus of integrals and derivatives of arbitrary real or complex orders) have been investigated and applied in many remarkably diverse fields. The main object of this paper is to consider some miscellaneous properties and applications which are associated with several fractional differintegral operators. We first investigate, in a systematic and unified manner, various families of series identities which emerged in connection with some of these fractional differintegral formulas. By using such operators of fractional calculus, a number of integral formulas as well as fractional differintegral formulas involving inverse hyperbolic functions are also evaluate.

In this paper, we first consider a broad class of nonlinear mappings containing the classes of nonexpansive mappings, nonspreading mappings, and hybrid mappings in a Hilbert space. Then, we deal with fixed point theorems and weak convergence theorems for these nonlinear mappings in a Hilbert space.