On certain equations of arbitrary length over torsion-free groups

Let $G$ be a non-trivial torsion free group and $t$ be an unknown. In this paper we consider three equations (over $G$) of arbitrary length and show that they have a solution (over $G$) provided two relations among their coefficients hold. Such equations appear for all lengths greater than or equal to eight and the results presented in this article can substantially simplify their solution.Comment: arXiv admin note: substantial text overlap with arXiv:1903.0650

21-Hy­droxy­pregna-1,4-diene-3,20-dione

The title compound, C21H28O3, is a fungal transformed metabolite of decoxycorticosterone acetate, consisting of four fused rings A, B, C and D. Ring A is nearly planar, with a maximum deviation of 0.010 (3) Å from the least-squares plane, while the trans-fused rings B and C adopt chair conformations. The five-membered ring D is in an envelope conformation. The orientation of the side chain is stabilized by an intramolecular O—H⋯O hydrogen bond. In the crystal, adjecent mol­ecules are linked by C—H⋯O hydrogen bonds into extended zigzag chains along the a axis

The Vector Direction of the Interstellar Magnetic Field Outside the Heliosphere

We propose that magnetic reconnection at the heliopause only occurs where the interstellar magnetic field points nearly anti-parallel to the heliospheric field. By using large-scale magnetohydrodynamic (MHD) simulations of the heliosphere to provide the initial conditions for kinetic simulations of heliopause (HP) reconnection we show that the energetic pickup ions downstream from the solar wind termination shock induce large diamagnetic drifts in the reconnecting plasma and stabilize non-anti-parallel reconnection. With this constraint the MHD simulations can show where HP reconnection most likely occurs. We also suggest that reconnection triggers the 2-3 kHz radio bursts that emanate from near the HP. Requiring the burst locations to coincide with the loci of anti-parallel reconnection allows us to determine, for the first time, the vector direction of the local interstellar magnetic field. We find it to be oriented towards the southern solar magnetic pole.Comment: Submitted to ApJ; incorporates minor referee-suggested revision

Cervicofacial actinomycosis with chronic parotid sialadenitis-mimicking malignant neoplasm of parotid gland: a rare case

Cervicofacial actinomycosis is an uncommon disease caused by Actinomycosis israelii. Chronic ‘sialadenitis’ of parotid gland is an insidious inflammatory disorder and may form a fibrous mass. We report a case of 55 years old female presenting with mass in right parotid region-on imaging-malignant neoplasm of parotid gland. But on histopathology-actinomycosis and chronic parotid sialadenitis.

4-Nitro­phenyl 1-naphthoate

In the title compound, C17H11NO4, the dihedral angle between the two benzene rings is 8.66 (3)°. The nitro group is twisted by 4.51 (9)° out of the plane of the aromatic ring to which it is attached. The presence of inter­molecular C—H⋯O contacts in the crystal structure leads to the formation of chains along the c axis

Penentuan Harga Jual Amplang pada Anisa Amplang di Samarinda

The purpose of this study was to determine the percentage increase in selling price per pack amplang set by Enterprises. Formulation of the problem in this study Is amplang pricing sell for Rp 10,000, - per set Ons Enterprises Anisa has a 17.5% gain. Basic theory of management accounting is used, the hypothesis in this study that the percentage increase in the selling price set by Anisa Enterprises using mark-up wisdom greater than 17.5%Based on the results of the analysis and discussion:Cost of Production amplang with regard to the cost elements of the cost of production Raw material costs, Costs Direct Labor and Factory Overhead and General & Marketing costs resulting calculation of Cost of Production per day of Rp. 1,697,358, -.Cost of Production for 1 ounce size is Rp. 1,697,358, - 220 packs divided by Rp. 7715, -Price Mark-Up in theory = Rp. 7715 + (Rp. 7,715, - x 17.5%) = Rp. 9065, - Price Mark-Up according to calculations greater than 10,000, - according to calculations by the company or by 29.6% of the cost of production.The hypothesis put forward earlier that allegedly setting the selling price set by the Business amplang Anisa already give a greater profit margin of 17.5% accepted on the grounds that the selling price set Anisa Enterprises is Rp. 10,000, - above the cost of production and the price mark-up is 29.6% of the cost of production amplang, while the results of calculations using the selling price Mark-Up 17.5% obtained Mark-Up selling price of Rp. 9065, -. This means that dikenakkan Mark-Up by Anisa Enterprises in the sale price amplangnya benefit greater than 17.5%

Federalism and the Arab League: A theoretical synergy

Abstract. The paper is a theoretical analogy of the Arab league as a regional organization. The paper also discusses the objectives, strengths and weaknesses of the league. By adopting descriptive-historical research from library instrument, findings show that, there is no doubt that the league had recorded some appreciable level of achievements since its inception and there have equally been some challenges along the line. The paper concludes that, the Arab league must find a way to reduce the perpetual tension and violence in Palestine by working towards enthroning a peaceful relationship with Israel while retaining their cultural identity. The paper also recommends that, the Arab league should strengthen their relationship with the non-Arab Nations especially in the face of globalization to reap the benefits therein involved as a league. Arab league must ensure that Arab states stop waging needless wars between and among themselves. The Syria and Yemeni crises among others is a disgrace to the Arab world.Keywords: Arab league, Theoretical, Synergy, Federalism, Integration.JEL. A10, F15