Many projectively unique polytopes

We construct an infinite family of 4-polytopes whose realization spaces have dimension smaller or equal to 96. This in particular settles a problem going back to Legendre and Steinitz: whether and how the dimension of the realization space of a polytope is determined/bounded by its f-vector. From this, we derive an infinite family of combinatorially distinct 69-dimensional polytopes whose realization is unique up to projective transformation. This answers a problem posed by Perles and Shephard in the sixties. Moreover, our methods naturally lead to several interesting classes of projectively unique polytopes, among them projectively unique polytopes inscribed to the sphere. The proofs rely on a novel construction technique for polytopes based on solving Cauchy problems for discrete conjugate nets in S^d, a new Alexandrov--van Heijenoort Theorem for manifolds with boundary and a generalization of Lawrence's extension technique for point configurations.Comment: 44 pages, 18 figures; to appear in Invent. mat

Some Notes on Madrasah Education in Bangladesh: a Historical Description

This paper tries to describe a historical development on Madrasah education system in Bangladesh. Bangladesh or formerly known as Eats Pakistan has significant contribution in spreading Islam in Asia. In education level, this major role played by thousands of Madrasah (state or private) in Bangladesh. While some people argued that the alumni of the Madrasah are inferior to the alumni of Western education institutions, the history proved that the alumni of Madrasah have substantial contribution in creating Muslim scholars not only expertise in religious teaching but also in secular sciences. This analysis also expected to be a role model in comparing Madrasah education system in Indonesia

Toleransi UmaT Beragama Di Desa Loloan, JemBrana, Bali (Ditinjau Dari Perspektif Sejarah)

This paper aims to discuss the history of religious tolerance in Jembrana, Bali, which is shaped by the culture embraced by the local community; both Hindus and Muslims. Culture itself can be a unifier of the differences that exist, including in terms of religious differences. Based on that, the reality of Jembrana society, which repersent Balinese culture with religious diversity (Hinduism as a native and Islam as migrants from Java and Makassar) could be approached through a cultural one. This study traces the historical record of religious harmony in Jembrana, ranging from the advent of Islam, the local responses to it, and the harmonious relations between Muslims and Hindus in the light of cultural frame

Hubungan Agama-Negara Pasca Reformasi

Studying relations between the Religion (Islam) and the state in Indonesia always presented special characteristics. The Islam Religion has become deeply rooted in the Indonesian Moslem's inner self. The matter is how the state puts Islam in the dynamics of her government form. Until now, we have found Islam can afford to be soul and spirit for implementing changes toward the better ones. Islam spirit has been proved in the historical path of Indonesian nation that it was able to liberate herself from colonial domination, backwardness, and underdevelopment. Thus, in the relations between Islam as a religion institution and the state (government) as a constitutional policy holder don't to suspect each other, but they must be able to result in a new cosmos that is mutually profitable.They are no longer to exploit mutually, but to create harmonization for the sustained nation

Supersolids in confined fermions on one-dimensional optical lattices

Using quantum Monte Carlo simulations, we show that density-density and pairing correlation functions of the one-dimensional attractive fermionic Hubbard model in a harmonic confinement potential are characterized by the anomalous dimension $K_\rho$ of a corresponding periodic system, and hence display quantum critical behavior. The corresponding fluctuations render the SU(2) symmetry breaking by the confining potential irrelevant, leading to structure form factors for both correlation functions that scale with the same exponent upon increasing the system size, thus giving rise to a (quasi)supersolid.Comment: 4 pages, 5 figures, published versio

Cooper pair islanding model of insulating nanohoneycomb films

We first review evidence for the Cooper pair insulator (CPI) phase in amorphous nanohoneycomb (NHC) films. We then extend our analysis of superconducting islands induced by film thickness variations in NHC films to examine the evolution of island sizes through the magnetic field-driven SIT. Finally, using the islanding picture, we present a plausible model for the appearance and behavior of the CPI phase in amorphous NHC films.Comment: 7 pages, 3 figure

Free-free and H42alpha emission from the dusty starburst within NGC 4945 as observed by ALMA

We present observations of the 85.69 GHz continuum emission and H42alpha line emission from the central 30 arcsec within NGC 4945. Both sources of emission originate from nearly identical structures that can be modelled as exponential discs with a scale length of ~2.1 arcsec (or ~40 pc). An analysis of the spectral energy distribution based on combining these data with archival data imply that 84% +/- 10% of the 85.69 GHz continuum emission originates from free-free emission. The electron temperature is 5400 +/- 600 K, which is comparable to what has been measured near the centre of the Milky Way Galaxy. The star formation rate (SFR) based on the H42alpha and 85.69 GHz free-free emission (and using a distance of 3.8 Mpc) is 4.35 +/- 0.25 M/yr. This is consistent with the SFR from the total infrared flux and with previous measurements based on recombination line emission, and it is within a factor of ~2 of SFRs derived from radio data. The Spitzer Space Telescope 24 micron data and Wide-field Infrared Survey Explorer 22 micron data yield SFRs ~10x lower than the ALMA measurements, most likely because the mid-infrared data are strongly affected by dust attenuation equivalent to A_V=150. These results indicate that SFRs based on mid-infrared emission may be highly inaccurate for dusty, compact circumnuclear starbursts.Comment: 19 pages, 9 figures, accepted for publication in MNRA