Geometry of warped product semi-slant submanifolds of Kenmotsu manifolds

In this paper, we study semi-slant submanifolds and their warped products in Kenmotsu manifolds. The existence of such warped products in Kenmotsu manifolds is shown by an example and a characterization. A sharp relation is obtained as a lower bound of the squared norm of second fundamental form in terms of the warping function and the slant angle. The equality case is also considered in this paper. Finally, we provide some applications of our derived results.Comment: 1

Conceptualising progression in the pedagogy of play and sustained shared thinking in early childhood education : a Vygotskian perspective

This paper is concerned specifically with the pedagogies applied in supporting learning through children‟s play, and it is framed outside mainstream discourses on the nature of play. The development of the paper also represents one stage in a continuing effort to develop a better understanding of sustained shared thinking in early childhood education. The paper also focuses on the educational potential of shared playful activities. However, given the overwhelming consensus regarding the importance of play in early childhood development, even a diehard educational pragmatist must begin by addressing subjects that are most commonly considered by psychologists. The paper begins with an account of „sustained shared thinking‟, a pedagogical concept that was first identified in a mixed method, but essentially educational effectiveness study. Then a consideration of the nature and processes of „learning‟ and „development‟ is offered. It is argued that popular accounts of a fundamental difference in the perspectives of Piaget and Vygotsky have distracted educational attention from the most important legacy that they have left to early childhood education; the notion of „emergent development‟. Pedagogic progression in the early years is then identified as an educational response to, and an engagement with, the most commonly observed, evidence based developmental trajectories of young children as they learn through play

Flows between Dualities for 3d Chern-Simons Theories

We study Seiberg-like dualities for 3d N=2 theories with flavors in fundamental and adjoint representations. The recent results of Intriligator and Seiberg provide a derivation of an Aharony duality from a Giveon-Kutasov duality. We extend their result to the case of more general theories involving various masses for fundamental quarks and adjoint fields. By fine tuning the vev of a scalar field and using various identifications between gauge groups and their singlet duals, we derive several examples of Aharony dualities. For theories with an adjoint field, we discuss the connection between the Aharony dualities proposed by Kim and Park for theories with multiple Coulomb branches and Giveon-Kutasov-Niarchos dualities.Comment: 21 page

Discovery of a Meteor of Interstellar Origin

The first interstellar object, `Oumuamua, was discovered in the Solar System by Pan-STARRS in 2017, allowing for a calibration of the abundance of interstellar objects of its size $\sim 100\;$ m. One would expect a much higher abundance of smaller interstellar objects, with some of them colliding with Earth frequently enough to be noticeable. Based on the CNEOS catalog of bolide events, we identify the $\sim 0.45$m meteor detected at 2014-01-08 17:05:34 UTC as originating from an unbound hyperbolic orbit with 99.999\% confidence. We infer that the meteor had an asymptotic speed of $v_{\infty} \sim 42.1 \pm 5.5\; \mathrm{km \; s^{-1}}$ outside of the solar system. Its origin is approximately towards R.A. $49.4 \pm 4.1^{\circ}$ and declination $11.2 \pm 1.8^{\circ}$, implying that its initial velocity vector was $58\pm6\; \mathrm{km\;s^{-1}}$ away from the velocity of the Local Standard of Rest (LSR). Its high LSR speed implies a possible origin from the deep interior of a planetary system or a star in the thick disk of the Milky Way galaxy. The local number density of its population is $10^{6{^{+0.75}_{-1.5}}} \; \mathrm{AU^{-3}}$ or $9 \times 10^{21{^{+0.75}_{-1.5}}} \; \mathrm{pc^{-3}}$ (necessitating 0.2 - 20 Earth masses of material to be ejected per local star). This discovery enables a new method for studying the composition of interstellar objects, based on spectroscopy of their gaseous debris as they burn up in the Earth's atmosphere.Comment: 4 pages, 2 figures; submitted to ApJL; uncertainties update

Identifikasi Kesulitan Siswa dalam Memahami Konsep Operasi Hitung Pecahan di SMP Negeri 1 Sawang (Integrasi dengan Dasar-dasar Pendidikan Mipa)

Penelitian ini bertujuan untuk mengetahui kesulitan yang dialami siswa dalam memahami konsep operasi hitung pecahan di SMP 1 Sawang. Metode penelitian yang digunakan adalah penelitian deskriptif dengan menggunakan pendekatan kualitatif. Penelitian dilakukan di kelas VII1 SMP Negeri 1 Sawang semester ganjil tahun ajaran 2013/2014. Data yang diperoleh dalam penelitian ini adalah nilai tes dan wawancara. Tes essay untuk menganalisis jawaban siswa tentang kesulitan yang dihadapi. Wawancara digunakan untuk mengetahui penyebab kesulitan yang dialami siswa. Analisis data dihitung dengan menggunakan rumus persentase. Siswa yang mengalami kesulitan dilandasi dengan mendapat skor < 65% dari skor maksimum soal. Hasil penelitian menunjukkan bahwa masih banyak siswa yang mengalami kesulitan dalam dalam memahami konsep porasi hitung pecahan, yaitu dari 13 orang siswa yang diteliti memilki kesulitan menggunakan konsep 19,61% dan kesulitan menggunakan prinsip 20,85%. Pada umumnya siswa mengalami kesulitan menggunakan prinsip karena kurangnya pemahaman konsep dasar. Kesulitan yang paling banyak dialami oleh siswa adalah menyamakan dua penyebut yang berbeda serta menyelesaikannya, dan menyelesaikan soal dalam bentuk gambar