‎In this paper‎, ‎we propose a feasible interior-point method for‎ ‎convex quadratic programming over symmetric cones‎. ‎The proposed algorithm relaxes the‎ ‎accuracy requirements in the solution of the Newton equation system‎, ‎by using an inexact Newton direction‎. ‎Furthermore‎, ‎we obtain an‎ ‎acceptable level of error in the inexact algorithm on convex‎ ‎quadratic symmetric cone programmin...

For a holomorphic function $f$ on complex manifold $\mathscr {M}$ we explain in this article that the distribution associated to $\lvert f\rvert^{2\alpha } (\textrm{Log} \lvert f\rvert^2)^q f^{-N}$ by taking corresponding limit sets $\{ f\rvert \geq \varepsilon \}$ when $\varepsilon $ goes $0$, coincides for $\Re (\alpha ) non negative and $q, N \in \mathbb {N}$, with value at $\lambda = \alpha...

We show that entangled measurements provide an exponential advantage in sample complexity for Pauli channel estimation, which is both a fundamental problem and practically important subroutine benchmarking near-term quantum devices. The specific task we consider to simultaneously learn all the eigenvalues of $n$-qubit $\pm\varepsilon$ precision. give estimation protocol with ancilla succeeds hi...

The dimer Mott insulator $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}{\mathrm{Cu}}_{2}{(\mathrm{CN})}_{3}$ can be tuned into metallic and superconducting states on applying pressure of 1.5 kbar more. We have performed dielectric measurements (7.5 kHz to 5 MHz) single crystals as a function temperature (down $T=8$ K) (up $p=4.3$ kbar). In additi...

‎in this paper‎, ‎we propose a feasible interior-point method for‎ ‎convex quadratic programming over symmetric cones‎. ‎the proposed algorithm relaxes the‎ ‎accuracy requirements in the solution of the newton equation system‎, ‎by using an inexact newton direction‎. ‎furthermore‎, ‎we obtain an‎ ‎acceptable level of error in the inexact algorithm on convex‎ ‎quadratic symmetric cone programmin...

Flows within porous media play important roles in many scientific and industrial systems. However, the case wherein such flows become turbulent has not been completely understood, particularly, from a mathematical viewpoint. In this study, $k-\varepsilon$ model (the variable $k$ denotes kinetic energy per unit mass $\varepsilon$ dissipation rate for energy), which widely used usual flow clear f...

In the $\varepsilon$-Consensus-Halving problem, a fundamental problem in fair division, there are $n$ agents with valuations over interval $[0,1]$, and goal is to divide into pieces assign label "$+$" or "$-$" each piece, such that every agent values total amount of almost equally. The was recently proven by Filos-Ratsikas Goldberg [2019] be first "natural" complete for computational class PPA,...

Abstract The matrix $A:{{\mathbb{R}}}^n \to{{\mathbb{R}}}^m$ is $(\delta ,k)$-regular if for any $k$-sparse vector $x$, $$\begin{align*} & \left| \|Ax\|_2^2-\|x\|_2^2\right| \leq \delta \sqrt{k} \|x\|_2^2. \end{align*}$$We show that $A$ $1 k 1/\delta ^2$, then by multiplying the columns of independent random signs, resulting ensemble $A_\varepsilon $ acts on an arbitrary subset $T \subset{{...

A bounded subset $M$ of a Banach space $X$ is said to be $\varepsilon $-weakly precompact, for given \geq 0$, if every sequence $(x_n)_{n\in \mathbb N}$ in $M$ admits subsequence $(x_{n_k})_{k\in such that $$ \limsup