Unique local determination of convex bodies

Barker and Larman asked the following. Let $K' \subset {\Bbb{R}}^d$ be a convex body, whose interior contains a given convex body $K \subset {\Bbb{R}}^d$, and let, for all supporting hyperplanes $H$ of $K$, the $(d-1)$-volumes of the intersections $K' \cap H$ be given. Is $K'$ then uniquely determined? Yaskin and Zhang asked the analogous question when, for all supporting hyperplanes $H$ of $K$, the $d$-volumes of the "caps" cut off from $K'$ by $H$ are given. We give local positive answers to both of these questions, for small $C^2$-perturbations of $K$, provided the boundary of $K$ is $C^2_+$. In both cases, $(d-1)$-volumes or $d$-volumes can be replaced by $k$-dimensional quermassintegrals for $1 \le k \le d-1$ or for $1 \le k \le d$, respectively. Moreover, in the first case we can admit, rather than hyperplane sections, sections by $l$-dimensional affine planes, where $1 \le k \le l \le d-1$. In fact, here not all $l$-dimensional affine subspaces are needed, but only a small subset of them (actually, a $(d-1)$-manifold), for unique local determination of $K'$.Comment: 16 pdf-page

Multiparticle Quantum Superposition and Stimulated Entanglement by Parity Selective Amplification of Entangled States

A multiparticle quantum superposition state has been generated by a novel phase-selective parametric amplifier of an entangled two-photon state. This realization is expected to open a new field of investigations on the persistence of the validity of the standard quantum theory for systems of increasing complexity, in a quasi decoherence-free environment. Because of its nonlocal structure the new system is expected to play a relevant role in the modern endeavor on quantum information and in the basic physics of entanglement.Comment: 13 pages and 3 figure

Bars from the Inside Out: An HST Study of their Dusty Circumnuclear Regions

The results of bar-driven mass inflow are directly observable in high-resolution HST observations of their circumnuclear regions. These observations reveal a wealth of structures dominated by dust lanes, often with a spiral-like morphology, and recent star formation. Recent work has shown that some of these structures are correlated with the presence or absence of a bar. I extend this work with an investigation of circumnuclear morphology as a function of bar strength for a sample of 48 galaxies with both measured bar strengths and ``structure maps'' computed from HST images. The structure maps for these galaxies, which have projected spatial resolutions of 2 - 15 pc, show that the fraction of galaxies with grand-design (GD) circumnuclear dust spirals increases significantly with bar strength, while tightly wound dust spirals are only present in the most axisymmetric galaxies. GD structure is only found at the centers of galaxies classified as SB(s) or SB(rs) and not SB(r). SB(s) galaxies on average have stronger bars than SB(r) galaxies. There is also a modest increase in the fraction of loosely wound dust spirals at later morphological types, which may reflect an increase in the fraction of galaxies with circumnuclear, gaseous disks. (abridged)Comment: 10 pages, 6 figures. To appear in "Penetrating Bars through Masks of Cosmic Dust: The Hubble Tuning Fork strikes a New Note" held June 7-12th, 2004 in Pilanesberg National Park, South Africa. Version with higher resolution figures is available at http://cfa-www.harvard.edu/~pmartini/professional/publications/safrica04.pd

Structural mapping from MSS-LANDSAT imagery: A proposed methodology for international geological correlation studies

A methodology is proposed for international geological correlation studies based on LANDSAT-MSS imagery, Bullard's model of continental fit and compatible structural trends between Northeast Brazil and the West African counterpart. Six extensive lineaments in the Brazilian study area are mapped and discussed according to their regional behavior and in relation to the adjacent continental margin. Among the first conclusions, correlations were found between the Sobral Pedro II Lineament and the megafaults that surround the West African craton; and the Pernambuco Lineament with the Ngaurandere Linemanet in Cameroon. Ongoing research to complete the methodological stages includes the mapping of the West African structural framework, reconstruction of the pre-drift puzzle, and an analysis of the counterpart correlations

Pengamatan Tentang Penerapan Sistem Plat Nomor Ganjil/Genap sebagai Alternatif Pengurangan Kepadatan Kendaraan Pribadi di Jalan Raya

Kemacetan yang terjadi DKI Jakarta sudah melampaui ambang batas kewajaran sehingga menyebabkan kinerja masyarakat DKI Jakarta menjadi menurun. Pemerintah dengan berbagai cara membuat alternative kebijakan guna mengurangi kepadatan kendaraan di jalan raya. Salah satunya dengan akan diterapkannya system plat nomor ganjil/genap. Penerapan system plat nomor ganjil/genap ini masih pro dan kontra sehingga pelaksanaannya menjadi tertunda. Pengamatan penulis dilihat dari segi positif dan negative dan mendapatkan kesimpulan bahwa penerapan system plat nomor ganjil/genap ini baik diterapkan dengan syarat bahwa selain system ini dilaksanakan, adapun infrastruktur seperti jalan, transportasi umum harus dikembangkan dan dipantau mengenai kondisi kendaraan (perawatan kendaraan) serta keamanannya

Perkembangan Kota Menurut Parameter Kota (Studi Kasus: Wilayah Jakarta Pusat)

Pertumbuhan penduduk yang sangat pesat dan urbanisasi menyebabkan terjadinya kepadatan penduduk di seluruh wilayah DKI Jakarta. Penduduk selain memerlukan sandang dan pangan yang terpenting adalah papan yaitu tempat tinggal. Sedangkan lahan di DKI Jakarta khususnya Jakarta Pusat sudah semakin langka dan harganya semakin tinggi. Hal ini harus ditangani secara tepat agar wilayah Jakarta Pusat ini penataan kotanya lebih teratur sehingga terhindar dari penumpukan kependudukan disebagian daerah. Hal tersebut dapat dilihat melalui perkembangan kota yaitu denga parameter kota. Diharapkan dengan pendekatan perkembangan kota (parameter kota) dapat dihasilkan perencanaan tata kota yang lebih baik