Some inequalities for the Euclidean operator radius of two operators in Hilbert C∗C^{\ast}-Modules space

The Euclidean operator radius of two bounded linear operators in the Hilbert $C^*$-module over \A is given some precise bounds. Their relationship to recent findings in the literature that offer precise upper and lower bounds on the numerical radius of linear operators is also established.Comment: 12 page

Testing collapse models with levitated nanoparticles: the detection challenge

We consider a nanoparticle levitated in a Paul trap in ultrahigh cryogenic vacuum, and look for the conditions which allow for a stringent noninterferometric test of spontaneous collapse models. In particular we compare different possible techniques to detect the particle motion. Key conditions which need to be achieved are extremely low residual pressure and the ability to detect the particle at ultralow power. We compare three different detection approaches based respectively on a optical cavity, optical tweezer and a electrical readout, and for each one we assess advantages, drawbacks and technical challenges

An estimate for the numerical radius of the Hilbert space operators and a numerical radius inequality

We provide a number of sharp inequalities involving the usual operator norms of Hilbert space operators and powers of the numerical radii. Based on the traditional convexity inequalities for nonnegative real numbers and some generalize earlier numerical radius inequalities, operator. Precisely, we prove that if \A_i,\B_i,\X_i\in\bh ($i=1,2,\cdots,n$), $m\in\N$, $p,q>1$ with $\frac{1}{p}+\frac{1}{q}=1$ and $\phi$ and $\psi$ are non-negative functions on $[0,\infty)$ which are continuous such that $\phi(t)\psi(t)=t$ for all $t \in [0,\infty)$, then \begin{equation*} w^{2r}\bra{\sum_{i=1}^{n}\X_i\A_i^m\B_i}\leq \frac{n^{2r-1}}{m}\sum_{j=1}^{m}\norm{\sum_{i=1}^{n}\frac{1}{p}S_{i,j}^{pr}+\frac{1}{q}T_{i,j}^{qr}}-r_0\inf_{\norm{x}=1}\rho(\xi), \end{equation*} where $r_0=\min\{\frac{1}{p},\frac{1}{q}\}$, S_{i,j}=\X_i\phi^2\bra{\abs{\A_i^{j*}}}\X_i^*, T_{i,j}=\bra{\A_i^{m-j}\B_i}^*\psi^2\bra{\abs{\A_i^j}}\A_i^{m-j}\B_i and \rho(x)=\frac{n^{2r-1}}{m}\sum_{j=1}^{m}\sum_{i=1}^{n}\bra{\seq{S_{i,j}^r\xi,\xi}^{\frac{p}{2}}-\seq{T_{i,j}^r\xi,\xi}^{\frac{q}{2}}}^2.Comment: No comment

Hydrophobicity properties of graphite and reduced graphene oxide of the polysulfone (PSf) mixed matrix membrane

Hydrophobicity properties of graphite and reduced graphene oxide (rGO) (from exfoliated graphite/rGO) towards PSf polymer membrane characteristic and properties at different additives weight concentrations (1, 2, 3, 4 and 5 wt. %) were investigated. Both PSF/graphite and PSf/rGO membranes were characterized in term of hydrophobicity, surface bonding, surface roughness and porosity. FTIR peaks revealed that membrane with graphite and reduced graphene oxide nearly diminished their O-H bonding which was opposite to the graphene oxide peak that shows a strong O-H bonding as increased exfoliated times. These results were in line with the contact angle results that showed strong hydrophobicity of graphite and reduced graphene oxide membranes as increased these additives concentration. The effect of strong hydrophobicity in these membranes also has resulted in smoother surface roughness compared to pristine PSf membrane. Further investigation of the performance of water flux also proved that both above membranes have strong hydrophobic effect, with the lowest pure water flux rate (L/m2h) was given by PSf/rGO 3% membrane at 19.2437 L/m2h

Study of the superconducting properties of the Bi-Ca-Sr-Cu-O system

High Temperature Superconductivity in the Bi-Ca-Sr-Cu-O System has been observed and has attracted considerable attention in 1988. The 80 K superconductivity phase has been identified to have a composition of Bi2CaSr2Cu2Ox, while the 110 K phase as reported in the literature has a possible composition of Bi2Ca2Sr2Cu3Ox. Researchers present here a study of the electrical properties of bulk samples of the slowly cooled and rapidly quenched 2:1:2:2 system. The samples used in this study were prepared from appropriate amounts of Bi2O3, CuO, SrCO3, CaCO3

Entrepreneurship through Bricolage. A Study of Displaced Entrepreneurs at Times of War and Conflict

War and conflict brings about adverse changes for those who are displaced. How do entrepreneurial individuals respond to such adversity to either set-up, or continue with their existing entrepreneurial endeavours that would improve their own livelihood or that of others who have been affected? Whilst previous studies have found local knowledge, networks and resources to be crucial in the development of ventures in the war and conflict context, alienation from mainstream society within the host location often means that to succeed, those who are displaced require alternative strategies and approaches. Through examining the entrepreneurship ventures of six internally displaced entrepreneurs in Pakistan, our study identifies that entrepreneurial individuals find different ways to adapt to the new order, with both internal and external bricolage becoming the key strategies deployed to either re-establish their previous business(es) or to develop new endeavour(s) in the host location. To compensate for lack of local knowledge, networks and resources, we found that entrepreneurs followed closely their previous paths in their bricolage attempts, relying on reconfigurations of their pre-existing competencies, as well as utilising pre-established and clandestine networks

Formal Analysis of Linear Control Systems using Theorem Proving

Control systems are an integral part of almost every engineering and physical system and thus their accurate analysis is of utmost importance. Traditionally, control systems are analyzed using paper-and-pencil proof and computer simulation methods, however, both of these methods cannot provide accurate analysis due to their inherent limitations. Model checking has been widely used to analyze control systems but the continuous nature of their environment and physical components cannot be truly captured by a state-transition system in this technique. To overcome these limitations, we propose to use higher-order-logic theorem proving for analyzing linear control systems based on a formalized theory of the Laplace transform method. For this purpose, we have formalized the foundations of linear control system analysis in higher-order logic so that a linear control system can be readily modeled and analyzed. The paper presents a new formalization of the Laplace transform and the formal verification of its properties that are frequently used in the transfer function based analysis to judge the frequency response, gain margin and phase margin, and stability of a linear control system. We also formalize the active realizations of various controllers, like Proportional-Integral-Derivative (PID), Proportional-Integral (PI), Proportional-Derivative (PD), and various active and passive compensators, like lead, lag and lag-lead. For illustration, we present a formal analysis of an unmanned free-swimming submersible vehicle using the HOL Light theorem prover.Comment: International Conference on Formal Engineering Method