we introduce the notions of t-dual rickart and strongly t-dual rickart modules. we provide several characterizations and investigate properties of each of these concepts. it is shown that every free (resp. finitely generated free) $r$-module is t-dual rickart if and only if $overline{z}^2(r)$ is a  direct summand of $r$ and end$(overline{z}^2(r))$ is a semisimple (resp. regular) ring. it is sho...

Consider a continuous function g ∈ L2(R) that is supported on [−1, 1] and generates a Gabor frame with translation parameter 1 and modulation parameter 0 < b < 2N 2N+1 for some N ∈ N. Under an extra condition on the zeroset of the window g we show that there exists a continuous dual window supported on [−N, N]. We also show that this result is optimal: indeed, if b > 2N 2N+1 then a dual window ...

We show that the Bronnikov theorem on nonexistence of regular electrically charged black holes can be circumvented. In the frame of nonlinear electrodynamics, we present the exact regular black hole solutions of a hybrid type. They are electrically charged, but contain a ‘dual’ core confining a polarization of magnetic charges. The considered example is based on a modification of the AyónBeato ...

In this paper, a review of Phase Locked Loop (PLL) algorithms and symmetrical component extraction methods intended for grid-connected power electronic converters are presented. Proposed classification is based on voltage representation in three coordinates: natural (abc), stationary (αβ) and rotating coordinates (dq). The three selected algorithms are described in details: Dual Second Order Ge...

We show that the Bronnikov theorem on the nonexistence of regular electrically charged black holes can be circumvented. In the frame of nonlinear electrodynamics, we present the exact regular black hole solutions of a hybrid type. They are electrically charged, but contain a ‘dual’ core confining a polarization of magnetic charges. The considered example is based on a modification of the AyónBe...

In this paper, we present simulation results for the performance gain of smart dual antennas at handsets for the forward link in the cdma2000 system. The system was modeled with the SPW of Cadence. Three types of the channel model, two levels of diversity combining, and three diversity combining schemes were investigated. Our simulation results show that the average performance gain (reduction ...

Frames have applications in numerous fields of mathematics and engineering. The fundamental property of frames which makes them so useful is their overcompleteness. In most applications, it is this overcompleteness that is exploited to yield a decomposition that is more stable, more robust, or more compact than is possible using nonredundant systems. This work presents a quantitative framework ...

Generalized fusion frame and some of their properties in tensor product Hilbert spaces are described. Also, the canonical dual g-fusion is considered. Finally, operator for a pair Bessel sequences presented.

The theory of frames is fundamental to timefrequency (TF or time-scale signal expansions like Gabor ysis of frames via two “TF frame representations” called the Weyl symbol and Wigner distribution of a frame. The T F analysis shows how a frame’s properties depend on the signal’s T F location and on certain frame parameters. 1 I N T R O D U C T I O N Linear time-frequency (TF) or time-scale sign...