Projective symmetry group classification of Abrikosov fermion mean-field ans\"atze on the square-octagon lattice

We perform a projective symmetry group (PSG) classification of symmetric quantum spin liquids with different gauge groups on the square-octagon lattice. Employing the Abrikosov fermion representation for spin-$1/2$, we obtain $32$ $SU(2)$, $1808$ $U(1)$ and $384$ $\mathbb{Z}_{2}$ algebraic PSGs. Constraining ourselves to mean-field parton ans\"atze with short-range amplitudes, the classification reduces to a limited number, with 4 $SU(2)$, 24 $U(1)$ and 36 $\mathbb{Z}_{2}$, distinct phases. We discuss their ground state properties and spinon dispersions within a self-consistent treatment of the Heisenberg Hamiltonian with frustrating couplings.Comment: 28 pages, 8 figures, 5 table

Quantum spin liquids on the diamond lattice

We perform a projective symmetry group classification of spin $S=1/2$ symmetric quantum spin liquids with different gauge groups on the diamond lattice. Employing the Abrikosov fermion representation, we obtain $8$ $SU(2)$, $62$ $U(1)$ and $80$ $\mathbb{Z}_{2}$ algebraic PSGs. Constraining these solutions to mean-field parton Ans\"atze with short-range amplitudes, the classification reduces to only $2$ $SU(2)$, $7$ $U(1)$ and $8$ $\mathbb{Z}_{2}$ distinctly realizable phases. We obtain both the singlet and triplet fields for all Ans\"atze, discuss the spinon dispersions, and present the dynamical spin structure factors within a self-consistent treatment of the Heisenberg Hamiltonian with up to third-nearest neighbor couplings. Interestingly, we find that a zero-flux $SU(2)$ state and some descendent $U(1)$ and $\mathbb{Z}_{2}$ states host robust gapless nodal loops in their dispersion spectrum, owing their stability at the mean-field level to the projective implementation of rotoinversion and screw symmetries. A nontrivial connection is drawn between one of our $U(1)$ spinon Hamiltonians (belonging to the nonprojective class) and the Fu-Kane-Mele model for a three-dimensional topological insulator on the diamond lattice. We show that Gutzwiller projection of the 0- and $\pi$-flux $SU(2)$ spin liquids generates long-range N\'eel order.Comment: Editors' Suggestion. 36 pages, 9 figures, 9 table

Design and Development of a Solar Artifact using Structural Analysis

740-745The Flat or rooftop mountings of PV systems require large area of land for the generation of electricity. As per the present scenario, the availability of suitable land is a major problem in cities as well as in the villages in India. Keeping it in mind, a solar artifact has been designed and developed at our Institute. The necessary structural analysis and mechanical load has been done in reference with sustainable wind load of the structure. By taking Factor of safety as 15, the Von Mises Stress is found to be 307.948 MPa. A typical shadow analysis has also been carried out on the solar panels attached with the solar artifact to determine whether there is any overlap of solar panels and thereby to get maximum solar energy

Design and Development of a Solar Artifact using Structural Analysis

The Flat or rooftop mountings of PV systems require large area of land for the generation of electricity. As per the present scenario, the availability of suitable land is a major problem in cities as well as in the villages in India. Keeping it in mind, a solar artifact has been designed and developed at our Institute. The necessary structural analysis and mechanical load has been done in reference with sustainable wind load of the structure. By taking Factor of safety as 15, the Von Mises Stress is found to be 307.948 MPa. A typical shadow analysis has also been carried out on the solar panels attached with the solar artifact to determine whether there is any overlap of solar panels and thereby to get maximum solar energy

Ethnic Preparation of Haria, a Rice-Based Fermented Beverage, in the Province of Lateritic West Bengal, India

Haria is a rice-based fermented beverage that is popular among tribal and low income people in lateritic West Bengal and East-Central India. The principal ingredient of this beverage is low grade boiled rice (Oryza sativa L.), which is mixed with a traditional starter, called bakhar, and fermented within a heat-sterilized earthen pot for 3-4 days. The main aim of this study was to investigate the ethnobotanical importance and traditional process of haria preparation. The method adopted for this study was based on interactive questionnaires and laboratory experiments. It was found that the pH decreased during the course of fermentation with increased titratable acidity of 1.42%. The alcohol content was 2-3% (v/v) in the consumable beverages. This documentation will be useful for further exploitation of haria as a health drink

Differential cross section measurements for the production of a W boson in association with jets in proton–proton collisions at √s = 7 TeV

Measurements are reported of differential cross sections for the production of a W boson, which decays into a muon and a neutrino, in association with jets, as a function of several variables, including the transverse momenta (pT) and pseudorapidities of the four leading jets, the scalar sum of jet transverse momenta (HT), and the difference in azimuthal angle between the directions of each jet and the muon. The data sample of pp collisions at a centre-of-mass energy of 7 TeV was collected with the CMS detector at the LHC and corresponds to an integrated luminosity of 5.0 fb[superscript −1]. The measured cross sections are compared to predictions from Monte Carlo generators, MadGraph + pythia and sherpa, and to next-to-leading-order calculations from BlackHat + sherpa. The differential cross sections are found to be in agreement with the predictions, apart from the pT distributions of the leading jets at high pT values, the distributions of the HT at high-HT and low jet multiplicity, and the distribution of the difference in azimuthal angle between the leading jet and the muon at low values.United States. Dept. of EnergyNational Science Foundation (U.S.)Alfred P. Sloan Foundatio

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis