In this paper we introduce the concept of generalized trees and compute the HILBERT SERIES of their binomial edge ideals

in this paper, HILBERT Huang transform (HHT) for time SERIES analysis of the status of permanent GPS stations can be provided. HILBERT Huang transform and its, related spectrun is a new method for the analysis of nonlinear processes. This method represents not only a precision analysis in the time-frequency space, but also it declares the physics of the dynamic processes. This method has two speps. At the first step, the data is disintegrated into IMF elements by EMD method. At the second step HILBERT transform is applied for IMF elements and distribution of the time-frequency-HILBERT energy spectrum is then determined. In this spectrum, Location, frequency and energy defined by time events for the Hillbert transform will be reserved. So instantaneous frequency will have a major role in this method.

In this paper, an intrinsic description of the space H(D) and its topology is presented.

In this paper we obtain a characterization of finite-dimensional HILBERT C*-modules. It is known that those are the modules for which both underlying C*-algebras are finite-dimensional. We show that such modules can be described by a certain property of bounded sequences of their elements. It turns out that similar property leads to another characterization of HILBERT C*-modules over C*-algebras of compact operators.

Here, we develop the generalized frame theory. We introduce two methods for generating g-frames of a HILBERT space H. The first method uses bounded linear operators between HILBERT spaces. The second method uses bounded linear operators on `2 to generate g-frames of H. We characterize all the bounded linear mappings that transform g-frames into other g-frames. We also characterize similar and unitary equivalent g-frames in term of the range of their linear analysis operators. Finally, we generalize the fundamental frame identity to g-frames and derive some new results.

Fusion frames are an extension to frames that provide a framework for applications and providing efficient and robust information processing algorithms. In this article we study the erasure of subspaces of a fusion frame.