Brownian noise in radiation-pressure-driven micromechanical oscillators

The authors demonstrate Brownian-noise-limited operation of an optomechanical oscillator, wherein mechanical oscillations of a silica optical microcavity are sustained by means of radiation pressure. Using phase noise measurement above threshold, it has been shown that the short-term linewidth of mechanical oscillations is fundamentally broadened, limited by thermal equipartition of energy

On special subgroups of fundamental group

Suppose $\alpha$ is a nonzero cardinal number, $\mathcal I$ is an ideal on arc connected topological space $X$, and ${\mathfrak P}_{\mathcal I}^\alpha(X)$ is the subgroup of $\pi_1(X)$ (the first fundamental group of $X$) generated by homotopy classes of $\alpha\frac{\mathcal I}{}$loops. The main aim of this text is to study ${\mathfrak P}_{\mathcal I}^\alpha(X)$s and compare them. Most interest is in $\alpha\in\{\omega,c\}$ and $\mathcal I\in\{\mathcal P_{fin}(X),\{\varnothing\}\}$, where $\mathcal P_{fin}(X)$ denotes the collection of all finite subsets of $X$. We denote ${\mathfrak P}_{\{\varnothing\}}^\alpha(X)$ with ${\mathfrak P}^\alpha(X)$. We prove the following statements: $\bullet$ for arc connected topological spaces $X$ and $Y$ if ${\mathfrak P}^\alpha(X)$ is isomorphic to ${\mathfrak P}^\alpha(Y)$ for all infinite cardinal number $\alpha$, then $\pi_1(X)$ is isomorphic to $\pi_1(Y)$; $\bullet$ there are arc connected topological spaces $X$ and $Y$ such that $\pi_1(X)$ is isomorphic to $\pi_1(Y)$ but ${\mathfrak P}^\omega(X)$ is not isomorphic to ${\mathfrak P}^\omega(Y)$; $\bullet$ for arc connected topological space $X$ we have ${\mathfrak P}^\omega(X)\subseteq{\mathfrak P}^c(X) \subseteq\pi_1(X)$; $\bullet$ for Hawaiian earring $\mathcal X$, the sets ${\mathfrak P}^\omega({\mathcal X})$, ${\mathfrak P}^c({\mathcal X})$, and $\pi_1({\mathcal X})$ are pairwise distinct. So ${\mathfrak P}^\alpha(X)$s and ${\mathfrak P}_{\mathcal I}^\alpha(X)$s will help us to classify the class of all arc connected topological spaces with isomorphic fundamental groups.Comment: 29 page

Information Sharing Along Supply Chain In Malaysian Manufacturing Companies

Perkongsian maklumat di antara rakan kongsi rantaian bekalan adalah penubuhan utama untuk mengeratkan koordinasi dan kerjasama dalam meningkatkan pengurusan pelaksanaan rantaian bekalan dan dalam menguruskan aliran maklumat bagi proses rantaian bekalan. Walaubagaimanapun, kebanyakan firma masih enggan untuk berkongsi maklumat dengan rakan kongsi rantaian bekalan. Dengan ini, kajian ini mengkaji kepentingan perkongsian maklumat dalam konteks syarikat pembuatan di Malaysia dan bagaimana perkongsian maklumat dapat meningkatkan prestasi rantaian bekalan. Kajian ini juga menyiasat hubungan antara kualiti maklumat, teknologi maklumat, keselamatan maklumat dan perkongsian maklumat terhadap rantaian bekalan. Di samping itu, ia juga mengkaji bagaimana budaya keselamatan maklumat disederhanakan oleh perhubungan antara keselamatan maklumat dan perkongsian maklumat. Selain itu, kajian ini menyiasat kesan penyerderhanaan teknologi keselamatan maklumat terhadap perhubungan diantara teknologi maklumat dan perkongsian maklumat. Tambahan pula, kajian ini mengkaji bagaimana kebocoran maklumat disederhanakan oleh perhubungan diantara perkongsian maklumat dan prestasi rantaian bekalan. Teori RBV diaplikasikan dalam model kajian bagi menyokong perhubungan diantara kualiti maklumat, teknologi maklumat, dan keselamatan maklumat sebagai sumber untuk bekalan rantaian kepada perkongsian maklumat iaitu keupayaan. Tambahan lagi, RBV menyokong perhubungan diantara perkongsian maklumat sebagai keupayaan kepada prestasi rantaian bekalan sebagai kelebihan daya saing

Mathematical Modeling of Hydraulic Fracturing In Shale Gas Reservoirs

During the past few years, hydraulic fracturing and horizontal drilling have facilitated the production of gas from shale reserves that were uneconomic to produce in the past. Each shale formation has a specific nature, therefore every basin or well may need to be treated differently. Additionally, shales have characteristics such as extremely low permeability, sensitivity to contacting fluids, and existing micro fractures which cause complications while evaluating them. There is also an absence of a clear explanation for the application of 2D models and the effect of various parameters on the fracture in shale formations. Therefore, the objective of this study is to analyze different 2D hydraulic fracture geometry models while examining these models for their application in shale gas formations and to identify a 2D model that is most suitable to be used in the hydraulic fracture treatment design of shale gas reservoirs. It is also intended to investigate the effect of fracture height, fluid loss and rock stiffness on the fracture geometry and the well. In this study the two most commonly used hydraulic fracture geometry models in the oil and gas industry, PKN and KGD, have been discussed and based on these models two mathematical computer codes were developed in order to calculate various parameters such as fracture length, average fracture width, wellbore net pressure, pumping time, and maximum fracture width at wellbore. The PKN-C model is identified as the most suitable 2D model to be used in shale gas reservoirs due to its more acceptable vertical plane strain assumption. Low permeability formations such as shale reservoirs require narrower and longer fractures for a higher productivity. Thus, using a model that would predict longer and narrower fractures, such as the PKN-C model, would be more suitable. The KGD-C model predicts a higher dimensionless fracture conductivity compared to the PKN-C model. However, the fracture geometry predicted by the PKN-C model results in higher post-fracture productivity. Additionally, it was observed that longer and narrower fractures are produced in rocks with a high Young’s modulus (such as shale). Additionally, increasing the leak off coefficient when fluid loss is small will result in slightly shorter fracture lengths, while increasing the leak off coefficients when fluid loss is high will result in significantly shorter fracture lengths

Covariant fuzzy observables and coarse-graining

A fuzzy observable is regarded as a smearing of a sharp observable, and the structure of covariant fuzzy observables is studied. It is shown that the covariant coarse-grainings of sharp observables are exactly the covariant fuzzy observables. A necessary and sufficient condition for a covariant fuzzy observable to be informationally equivalent to the corresponding sharp observable is given.Comment: 19 page

Optimal measurements in quantum mechanics

Four common optimality criteria for measurements are formulated using relations in the set of observables, and their connections are clarified. As case studies, 1-0 observables, localization observables, and photon counting observables are considered.Comment: minor correction