begin{abstract} The relations between the spectrum of the matrix $Q+R$ and the spectra of the matrices $(gamma + delta)Q+(alpha + beta)R-QR-RQ$, $QR-RQ$, $alpha beta R-QRQ$, $alpha RQR-(QR)^{2}$, and $beta R-QR$ have been given on condition that the matrix $Q+R$ is diagonalizable, where $Q$, $R$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of ord...

A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...

Baker (2019), Barany and Kaenmaki (2019) independently showed that there exist iterated function systems without exact overlaps are super-exponentially close cylinders at all small levels. We adapt the method of obtain further examples this type. prove for any algebraic number \(\beta\ge 2\) real numbers \(s, t\) such system \(\left \{\frac{x}{\beta}, \frac{x+1}{\beta}, \frac{x+s}{\beta}, \fr...

If S 0 , 1 2 S_{0}, S_{1}, S_{2}...

We report the crystal structure of a class D beta-lactamase, the broad spectrum enzyme OXA-10 from Pseudomonas aeruginosa at 2.0 A resolution. There are significant differences between the overall fold observed in this structure and those of the evolutionarily related class A and class C beta-lactamases. Furthermore, the structure suggests the unique, cation mediated formation of a homodimer. K...

In this paper, we define a subclass of analytic functions by denote $T_{\beta}H\left( z,C_{n}^{\left( \lambda \right) }\left( t\right) $ satisfying the following subordinate condition \begin{equation*} \left( 1-\beta \frac{zf^{^{\prime }}\left( z\right) }{f\left( }\right) +\beta 1+\frac{zf^{^{\prime \prime }{f^{^{\prime \prec \frac{1}{\left( 1-2tz+z^{2}\right) ^{\lambda }}, \end{equation*} wher...