Toward the Universal Rigidity of General Frameworks

Let (G,P) be a bar framework of n vertices in general position in R^d, d <= n-1, where G is a (d+1)-lateration graph. In this paper, we present a constructive proof that (G,P) admits a positive semi-definite stress matrix with rank n-d-1. We also prove a similar result for a sensor network where the graph consists of m(>= d+1) anchors.Comment: v2, a revised version of an earlier submission (v1

STRATEGI PENGEMBANGAN KOMPETENSI PENYULUH DI KECAMATAN BANDA BARO KABUPATEN ACEH UTARA

The implementation of agricultural extension activities in Banda Baro Subdistrict aims to increase the amount of agricultural production of farmers, add insight or skills of farmers in farming activities and in adding infrastructure for farmer groups, in addition to other general services needed by farmers in order to increase the empowerment of farmers, so that extension workers as field implementers must have good competence so that extension is carried out effectively. In their duties, agricultural instructors in Banda Baro District are not free from perceived obstacles such as the difficulty of holding direct meetings with farmers, the limited number of instructors, the difficulty of accessing transportation to locations and the difficulty of communication networks. The research aims to formulate a strategy for developing the competency of agricultural instructors in Banda Baro District, North Aceh Regency. Data analysis using SWOT Analysis. The research results show that in the SWOT position matrix. The strategy for increasing instructor competency shows that the position matrix is in quadrant I supporting the SO (Growth oriented strategy) strategy, meaning that the competency of agricultural instructors has a very favorable situation. The instructor's competency has strengths and opportunities so that he can take advantage of these opportunities by growing existing strengths

A new model of a tidally disrupted star

A new semi-analytical model of a star evolving in a tidal field is proposed. The model is a generalization of the so-called 'affine' stellar model. In our model the star is composed of elliptical shells with different parameters and different orientations, depending on time and on the radial Lagrangian coordinate of the shell. The evolution equations of this model are derived from the virial relations under certain assumptions, and the integrals of motion are identified. It is shown that the evolution equations can be deduced from a variational principle. The evolution equations are solved numerically and compared quantitatively with the results of 3D numerical computations of the tidal interaction of a star with a supermassive black hole. The comparison shows very good agreement between the main ``integral'' characteristics describing the tidal interaction event in our model and in the 3D computations. Our model is effectively a one-dimensional Lagrangian model from the point of view of numerical computations, and therefore it can be evolved numerically $10^{2}-10^{3}$ times faster than the 3D approach allows. This makes our model well suited for intensive calculations covering the whole parameter space of the problem.Comment: This version is accepted for publication in ApJ. Stylistic and grammatical changes, new Appendix adde

Robust Location-Aided Beam Alignment in Millimeter Wave Massive MIMO

Location-aided beam alignment has been proposed recently as a potential approach for fast link establishment in millimeter wave (mmWave) massive MIMO (mMIMO) communications. However, due to mobility and other imperfections in the estimation process, the spatial information obtained at the base station (BS) and the user (UE) is likely to be noisy, degrading beam alignment performance. In this paper, we introduce a robust beam alignment framework in order to exhibit resilience with respect to this problem. We first recast beam alignment as a decentralized coordination problem where BS and UE seek coordination on the basis of correlated yet individual position information. We formulate the optimum beam alignment solution as the solution of a Bayesian team decision problem. We then propose a suite of algorithms to approach optimality with reduced complexity. The effectiveness of the robust beam alignment procedure, compared with classical designs, is then verified on simulation settings with varying location information accuracies.Comment: 24 pages, 7 figures. The short version of this paper has been accepted to IEEE Globecom 201