We propose a convex optimization formulation with the Ky Fan 2-k-norm and `1-norm to find k largest approximately rank-one submatrix blocks of a given nonnegative matrix that has low-rank block diagonal structure with noise. We analyze low-rank and sparsity structures of the optimal solutions using properties of these two matrix norms. We show that, under certain hypotheses, with high probabili...

Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $Ainmathbb{C}^{ntimes n}$‎ ‎and $Dinmathbb{C}^{mtimes m}$ and let the matrix $left(begin{array}{cc}‎ A & B ‎ C & D‎ end{array} right)$ be a normal matrix and‎ assume that $lambda$ is a given complex number‎ ‎that is not eigenvalue of matrix $A$‎. ‎We present a method to calculate the distance norm (with respect to 2-norm) from $D$‎ to ...

In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.

We propose here a new idea for quantum teleportation of superposed coherent state which circumvents the problem performing non-unitary $$Z_c=|\alpha \rangle \langle \alpha |-|-\alpha -\alpha |$$ operation on qubit. The receiver only requires to perform either no unitary or $$\pi $$ phase shift in order recreate information state. use entangled resource $$\sim |\alpha ,\frac{\alpha }{\sqrt{2}}\r...

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.

This paper studies certain inverse problems in the optimal frequency-domain synthesis of robust controllers, in both the 2-norm and the infinity-norm. These inverse problems identify the class of controllers which are optimal for some choice of weights. Their implications for loopshaping are discussed. Keywords—Inverse optimality, loopshaping, H2 control, H∞ control. c.t/ g− + K.s/ u.t/ G0.s/ g...