In this paper, we introduce the concept of $g$-dual frames for Hilbert $C^{*}$-modules, and then the properties and stability results of $g$-dual frames  are given.  A characterization of $g$-dual frames, approximately dual frames and dual frames of a given frame is established. We also give some examples to show that the characterization of $g$-dual frames for Riesz bases in Hilbert spaces is ...

This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular, we try to extend this concept and prove some related theorems. Moreover, we focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular, we extend reproducing kernels to relative reproducing kernels an...

In this paper the use of the Hilbert-Huang Transform (HHT), for the decomposition and characterization of seismic ground response, is discussed. The HHT, integrated by the Empirical Mode Decomposition (EMD) and the Hilbert Transformation (HT), enables engineers to analyze non-stationary oscillation systems and to obtain more detailed intensity descriptions on time-varying frequency diagrams. Th...

For non-stationary signal in ultrasonic inspection, an effective denoising method based on Hilbert-Huang transform (HHT) is presented and a few key questions using the HHT method are discussed. The overall scheme of HHT includes two parts which are empirical mode decomposition (EMD) algorithm and a sum of intrinsic mode functions (IMF). Through the EMD process, individual IMF can be found. The ...

The effective noise reduction schemes in ultrasonic inspection have shown significant role for detection of flaws in materials. This paper presents the comparative result of noise reducing schemes based on Hilbert-Huang transform and Wavelet transform. The basic principle of HHT scheme includes two parts which are empirical mode decomposition (EMD) algorithm and a sum of intrinsic mode function...

G-frames are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coefficients. First, they were defined in Hilbert spaces and then generalized on C*-Hilbert modules. In this paper, we first generalize the concept of g-frames to Hilbert modules over pro-C*-algebras. Then, we introduce the g-frame operators in such spaces and show that they sha...

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...

in this work, we define a fuzzy soft set theory and its related properties. we then define fuzzy soft aggregation operator that allows constructing more efficient decision making method. finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties.