Electromagnetic Dipole Radiation Fields, Shear-Free Congruences and Complex Center of Charge World Lines

We show that for asymptotically vanishing Maxwell fields in Minkowski space with non-vanishing total charge, one can find a unique geometric structure, a null direction field, at null infinity. From this structure a unique complex analytic world-line in complex Minkowski space that can be found and then identified as the complex center of charge. By ''sitting'' - in an imaginary sense, on this world-line both the (intrinsic) electric and magnetic dipole moments vanish. The (intrinsic) magnetic dipole moment is (in some sense) obtained from the `distance' the complex the world line is from the real space (times the charge). This point of view unifies the asymptotic treatment of the dipole moments For electromagnetic fields with vanishing magnetic dipole moments the world line is real and defines the real (ordinary center of charge). We illustrate these ideas with the Lienard-Wiechert Maxwell field. In the conclusion we discuss its generalization to general relativity where the complex center of charge world-line has its analogue in a complex center of mass allowing a definition of the spin and orbital angular momentum - the analogues of the magnetic and electric dipole moments.Comment: 17 page

Supplementary Materials for English Lesson Grade Seven in Elia Christian Middle School

This project is based on the writer's internship in Elia Christian Junior High School from April, 7 to June, 5 2015 The writer thought that it was a good thing to make supplementary materials as a final project because of some problems the writer faced earlier during the internship. There was not sufficient interesting material in the textbook and lack of students' participation in the classroom. The writer wrote some suggested supplementary materials that he thought was good according to the analysis of the textbook to supplement the material written in the KTSP curriculum textbook. By having some creative activities during the lessons, hopefully they can change the habit of their English learning, to be more actively participated in every English class

The Large Footprints of H-Space on Asymptotically Flat Space-Times

We show that certain structures defined on the complex four dimensional space known as H-Space have considerable relevance for its closely associated asymptotically flat real physical space-time. More specifically for every complex analytic curve on the H-space there is an asymptotically shear-free null geodesic congruence in the physical space-time. There are specific geometric structures that allow this world-line to be chosen in a unique canonical fashion giving it physical meaning and significance.Comment: 7 page

On the discrepancy of random low degree set systems

Motivated by the celebrated Beck-Fiala conjecture, we consider the random setting where there are $n$ elements and $m$ sets and each element lies in $t$ randomly chosen sets. In this setting, Ezra and Lovett showed an $O((t \log t)^{1/2})$ discrepancy bound in the regime when $n \leq m$ and an $O(1)$ bound when $n \gg m^t$. In this paper, we give a tight $O(\sqrt{t})$ bound for the entire range of $n$ and $m$, under a mild assumption that $t = \Omega (\log \log m)^2$. The result is based on two steps. First, applying the partial coloring method to the case when $n = m \log^{O(1)} m$ and using the properties of the random set system we show that the overall discrepancy incurred is at most $O(\sqrt{t})$. Second, we reduce the general case to that of $n \leq m \log^{O(1)}m$ using LP duality and a careful counting argument

Perjanjian Keagenan Dan Distributor Dalam Perspektif Hukum Perdata

Tujuan dilakukannya penelitian ini adalah untuk memngetahui bagaimana aspek hukum perjanjian keagenan/distributor dan bagaimana hubungan hukum antara agen dan prinsipal serta bagaimana berakhirnya hubungan keagenan. Denagn menggunakan metode penelitian yuridis normatif, maka da[par disimpulkan: 1. Perjanjian keagenan/distributor secara khusus tidak dikenal dalam KUH Perdata dan KUHD. Sehingga perjanjian itu dapat digolongkan dalam perjanjian innominaat (perjanjian tidak bernama), serta keberadaannya dimungkinkan berdasarkan asas kebebasan berkontrak yang diatur dalam Buku III Pasal 1338 ayat (1) KUH Perdata. 2. Hubungan keagenan adalah hubungan perwakil­an karena apa yang dilakukan oleh agen merupa­kan representasi dari apa yang hendak dilakukan oleh prinsipal. Karakteristik hubungan seperti itu menimbulkan konsekuensi hukum bahwa apa yang menjadi hak agen di satu sisi akan menjadi kewajiban prinsipal di sisi lain, dan apa yang menjadi kewajiban agen secara otomatis pula akan men­jadi hak prinsipal pada ujung yang lain. 3. Dalam praktik, hubungan keagenan dapat diakhiri dengan cara kesepakatan timbal Balik oleh ke­dua belah pihak, serta berakhir karena adanya sebab­s-sebab hukum, atau berakhir karena adanya pembatalan secara sepihak baik oleh prinsipal mau­pun oleh agen

Pengaruh Penerapan Cause Related Marketing Pada Program “Satu Untuk Sepuluh” Aqua Terhadap Loyalitas Merek Kelompok Konsumen Muda

Penelitian ini bertujuan untuk menguji pengaruh penerapan cause related marketing pada program “Satu Untuk Sepuluh” produk Aqua terhadap loyalitas merek produk Aqua. Penelitian bersandar kepada jurnal Douwe Van De Brink, et al (2006). Variabel penelitian ini terdiri dari empat variabel bebas yaitu kesesuaian, dan durasi, serta satu variabel terikat, yaitu loyalitas merek. Populasi yang digunakan dalam penelitian ini adalah pemuda di bawah umur 25 tahun di Jakarta. Sampel yang digunakan dalam penelitian ini adalah sebesar 100 koresponden. Data dari koresponden dikumpulkan dengan menggunakan kuesioner dan metode analisis data yang digunakan dalam tugas akhir ini adalah regresi berganda. Hasil dari penelitian ini adalah kesesuaian dan durasi secara signifikan terhadap loyalitas merek. Berdasarkan hasil penelitian tersebut Perusahaan sebaiknya mempertimbangkan untuk mengaplikasikan program cause related marketing guna meningkatkan loyalitas merek. Dengan memperpanjang durasi program, meningkatkan kesesuaian untuk mendapatkan hasil maksimal dari penerapan program tersebut

Computing toric degenerations of flag varieties

We compute toric degenerations arising from the tropicalization of the full flag varieties $\mathcal{F}\ell_4$ and $\mathcal{F}\ell_5$ embedded in a product of Grassmannians. For $\mathcal{F}\ell_4$ and $\mathcal{F}\ell_5$ we compare toric degenerations arising from string polytopes and the FFLV polytope with those obtained from the tropicalization of the flag varieties. We also present a general procedure to find toric degenerations in the cases where the initial ideal arising from a cone of the tropicalization of a variety is not prime.Comment: 35 pages, 6 figure

Analisis Strategi Perusahaan Dalam Ekspansi Pasar Luar Negeri (Studi Kasus Pada PT. Semen Indonesia (Persero) Tbk Dalam Akuisisi Thang Long Cement Company Di Vietnam)

PT. Semen Indonesia is a state owned company which is located in Gresik, East Java. The company's vision is becoming a leading International cement company in Southeast Asia, the vision becames the foundation of the company to expand overseas market in 2012 by acquiring a cement company in Vietnam. The purpose of this study is to analyze the factors that influence the decision of PT Semen Indonesia (Persero) Tbk in expanding overseas markets, and then Knowing the strategy applied by PT. Semen Indonesia (Persero) Tbk in expanding overseas markets, the last reason is to Analyze the strengths and weaknesses of the strategy at PT. Semen Indonesia (Persero) Tbk. This type of research is descriptive. The analytical method used is SWOT analysis (Strength, Weakness, Opportunities, and Threats), with EFAS, IFAS matrix, and SWOT matrix. The conclusion of this research is PT. Semen Indonesia has managed to become the first state-owned companies to expand abroad with a strong vision and desire to grow. The company also succeeded in expanding overseas markets with the right strategy. Depth analysis and always follow the market developments is required by the company to achieve the vision and mission of the company

Image Analysis for Facility Siting: a Comparison of Lowand High-altitude Image Interpretability for Land Use/land Cover Mapping

For two test sites in Pennsylvania the interpretability of commercially acquired low-altitude and existing high-altitude aerial photography are documented in terms of time, costs, and accuracy for Anderson Level II land use/land cover mapping. Information extracted from the imagery is to be used in the evaluation process for siting energy facilities. Land use/land cover maps were drawn at 1:24,000 scale using commercially flown color infrared photography obtained from the United States Geological Surveys' EROS Data Center. Detailed accuracy assessment of the maps generated by manual image analysis was accomplished employing a stratified unaligned adequate class representation. Both 'area-weighted' and 'by-class' accuracies were documented and field-verified. A discrepancy map was also drawn to illustrate differences in classifications between the two map scales. Results show that the 1:24,000 scale map set was more accurate (99% to 94% area-weighted) than the 1:62,500 scale set, especially when sampled by class (96% to 66%). The 1:24,000 scale maps were also more time-consuming and costly to produce, due mainly to higher image acquisition costs