In this brief note, we prove that every space is a sequence-covering image of a topological sum of convergent sequences. As the application of this result, sequence-covering images of locally compact metric spaces (or, locally separable metric spaces, metric spaces) and sequentially-quotient images of a locally compact metric spaces (or, locally separable metric spaces, metric spaces) are equiv...

There are noncomputable c.e. sets, computable from every SJT-hard c.e. set. This yields a natural pseudo-jump operator, increasing on all sets, which cannot be inverted back to a minimal pair or even avoiding an upper cone.

Abstract. Computing the Fourier transform of a function in polar coordinates is an important building block in many scientific disciplines and numerical schemes. In this paper we present the pseudo-polar Fourier transform that samples the Fourier transform on the pseudo-polar grid, also known as the concentric squares grid. The pseudo-polar grid consists of equally spaced samples along rays, wh...

In this paper, a compact low-power (LP) low-voltage (LV) metal–oxide–semiconductor-only (MOS-only) variable gain amplifier (VGA) is introduced. This amplifier based on complementary MOS (CMOS) transistors operating in strong inversion is composed of a pseudo-exponential current-to-voltage converter, analog multiplier, and output stage. The gain of the amplifier is controlled exponentially by a ...

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact $L^{p_1}(w_1)$ $w_1\in R^d)$. Then $L^p(w)$ $p\in(1,\infty)$ $w\in A_p(\mathbb This "compact version" of Rubio de Francia's celebrated weighted extrapolation theorem follows from combination results the interpolation theory spaces one h...

In this article, we further consider the above system. In particular, we give a sufficient condition under which the above system is Kato chaotic for $eta=0$ and a necessary condition for the above system to be Kato chaotic for $eta=0$. Moreover, it is deduced that for $eta=0$, if $Theta$ is P-chaotic then so is this system, where a continuous map $Theta$ from a compact metric space $Z$ to itse...