Kyunguk Na

Toeplitz operators on harmonic Bergman spaces

We study Toeplitz operators on the harmonic Bergman spaces on bounded smooth domains. Two classes of symbols are considered; one is the class of positive symbols and the other is the class of uniformly continuous symbols. For positive symbols, boundedness, compactness, and membership in the Schatten classes are characterized. For uniformly continuous symbols, the essential spectra are described.

Positive Toeplitz Operators of Schatten–Herz Type

Motivated by a recent work of Loaiza et al. for the holomorphic case on the disk, we introduce and study the notion of Schatten-Herz type Toeplitz operators acting on the harmonic Bergman space of the ball. We obtain characterizations of positive Toeplitz operators of Schatten-Herz type in terms of averaging functions and Berezin transforms of symbol functions. Our characterization in terms of Berezin transforms settles a question posed by Loaizaet al.

Note on Characterizations of the Harmonic Bergman Space

In this paper, we solve the problem which was stated in [6].A ctually we obtain a characterization of harmonic Bergman space in terms of Lipschitz type condition with pseudo-hyperbolic metric on the unit ball in R n.

Optimum configuration of helical piles with material cost minimized by harmony search algorithm

Helical piles are a manufactured steel foundation composed of one or multiple helix plates affixed to a central shaft. A helical pile is installed by rotating the central shaft with hydraulic torque motors. There are three representative theoretical predictions for the bearing capacity of helical piles: individual bearing method, cylindrical shear method, and torque correlation method. The bearing capacity of helical piles is governed by the helical pile’s configuration, geologic conditions and penetration depth. The high variability of influence factors makes an optimum design for helical pile configuration difficult in practice. In this paper, the harmony search algorithm is adopted to minimize the material cost of helical piles by optimizing the components composing a helical pile based on the proposed bearing capacity prediction. The optimization process based on the combined prediction method with the aid of the harmony search algorithm leads to an economical design by saving about 27percent of the helical pile material cost.